From 490fdaaefb7f465badc10b38c531979d063d6c64 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Mon, 14 Sep 2020 10:52:04 +0200 Subject: [PATCH] updating lectures --- doc/pub/Introduction/ipynb/Introduction.ipynb | 20 +- doc/src/LectureNotes/DataFiles/EoS.csv | 90 + .../LectureNotes/DataFiles/MassEval2016.dat | 3475 +++++++++ .../Results/FigureFiles/EoSfitting.png | Bin 0 -> 17591 bytes .../Results/FigureFiles/Masses2016.png | Bin 0 -> 16191 bytes .../Results/FigureFiles/Masses2016OLS.png | Bin 0 -> 12846 bytes .../Results/FigureFiles/Masses2016Trees.png | Bin 0 -> 21299 bytes .../_build/.doctrees/gettingstarted.doctree | Bin 0 -> 561553 bytes .../_build/.doctrees/introduction.doctree | Bin 0 -> 84894 bytes .../_build/.doctrees/notebooks.doctree | Bin 162646 -> 162632 bytes .../_build/.doctrees/regression.doctree | Bin 0 -> 894322 bytes .../jupyter_execute/gettingstarted.ipynb | 3297 +++++++++ .../_build/jupyter_execute/gettingstarted.py | 1320 ++++ 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create mode 100644 doc/src/LectureNotes/_build/jupyter_execute/regression_140_0.png create mode 100644 doc/src/LectureNotes/_build/jupyter_execute/regression_278_2.png create mode 100644 doc/src/LectureNotes/_build/jupyter_execute/regression_300_1.png create mode 100644 doc/src/LectureNotes/_build/jupyter_execute/regression_70_0.png create mode 100644 doc/src/LectureNotes/_build/latex/reports/gettingstarted.log create mode 100644 doc/src/LectureNotes/_build/latex/reports/regression.log create mode 100644 doc/src/LectureNotes/introduction.md create mode 100644 doc/src/NeuralNet/ode.py~ create mode 100644 doc/src/Regression/Bootstrap.py diff --git a/doc/pub/Introduction/ipynb/Introduction.ipynb b/doc/pub/Introduction/ipynb/Introduction.ipynb index cae0616f4..56c63bf60 100644 --- a/doc/pub/Introduction/ipynb/Introduction.ipynb +++ b/doc/pub/Introduction/ipynb/Introduction.ipynb @@ -346,7 +346,25 @@ ] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.3" + } + }, "nbformat": 4, "nbformat_minor": 2 } diff --git a/doc/src/LectureNotes/DataFiles/EoS.csv b/doc/src/LectureNotes/DataFiles/EoS.csv new file mode 100644 index 000000000..a958ae7b5 --- /dev/null +++ b/doc/src/LectureNotes/DataFiles/EoS.csv @@ -0,0 +1,90 @@ + 3.3773726001100143E-005, 3.1715032621225665E-002 + 2.7018980800880114E-004, 0.25379346864959029 + 9.1189060202970370E-004, 0.85691856357595775 + 2.1615184640704091E-003, 2.0322700794292126 + 4.2217157501375172E-003, 3.9716946611295496 + 7.2951248162376296E-003, 6.8678138410008760 + 1.1584388018377344E-002, 10.913973030767592 + 1.7292147712563273E-002, 16.304871533080519 + 2.4621046254802003E-002, 23.235226466525493 + 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1307.72443529019392 + 1.16191997402906422, 1384.74890303708753 + 1.21535997283458719, 1466.00110871243692 + 1.27071997159719463, 1551.73305231624181 + 1.32847997030615828, 1642.68741833061654 + 1.38895996895432461, 1739.56266307697001 + 1.45263996753096580, 1843.32947103741640 + 1.52031996601820008, 1955.19398301547858 + 1.59295996439456933, 2077.14256797538474 + 1.67167996263504026, 2211.44382304206692 + 1.75855996069312082, 2361.74471430468566 + 1.85647995850443825, 2533.64534865592441 + 1.96959995597600934, 2734.93465827410455 + 2.10543995293974895, 2980.03336671234320 diff --git a/doc/src/LectureNotes/DataFiles/MassEval2016.dat b/doc/src/LectureNotes/DataFiles/MassEval2016.dat new file mode 100644 index 000000000..4b479be45 --- /dev/null +++ b/doc/src/LectureNotes/DataFiles/MassEval2016.dat @@ -0,0 +1,3475 @@ +1 a0boogfu A T O M I C M A S S A D J U S T M E N T +0 DATE 1 Mar 2017 TIME 17:26 +0 ********************* A= 0 TO 295 + * file : mass16.txt * + ********************* + + This is one file out of a series of 3 files published in: + "The Ame2016 atomic mass evaluation (I)" by W.J.Huang, G.Audi, M.Wang, F.G.Kondev, S.Naimi and X.Xu + Chinese Physics C41 030002, March 2017. + "The Ame2016 atomic mass evaluation (II)" by M.Wang, G.Audi, F.G.Kondev, W.J.Huang, S.Naimi and X.Xu + Chinese Physics C41 030003, March 2017. + for files : mass16.txt : atomic masses + rct1-16.txt : react and sep energies, part 1 + rct2-16.txt : react and sep energies, part 2 + A fourth file is the "Rounded" version of the atomic mass table (the first file) + mass16round.txt : atomic masses "Rounded" version + + All files are 3436 lines long with 124 character per line. + Headers are 39 lines long. + Values in files 1, 2 and 3 are unrounded copy of the published ones + Values in file 4 are exact copy of the published ones + + col 1 : Fortran character control: 1 = page feed 0 = line feed + format : a1,i3,i5,i5,i5,1x,a3,a4,1x,f13.5,f11.5,f11.3,f9.3,1x,a2,f11.3,f9.3,1x,i3,1x,f12.5,f11.5 + cc NZ N Z A el o mass unc binding unc B beta unc atomic_mass unc + Warnings : this format is identical to the ones used in Ame2003 and Ame2012 + in particular "Mass Excess" and "Atomic Mass" values are given now, when necessary, + with 5 digits after decimal point. + decimal point is replaced by # for (non-experimental) estimated values. + * in place of value : not calculable + +....+....1....+....2....+....3....+....4....+....5....+....6....+....7....+....8....+....9....+...10....+...11....+...12.... + + + MASS LIST + for analysis + +1N-Z N Z A EL O MASS EXCESS BINDING ENERGY/A BETA-DECAY ENERGY ATOMIC MASS + (keV) (keV) (keV) (micro-u) +0 1 1 0 1 n 8071.31713 0.00046 0.0 0.0 B- 782.347 0.000 1 008664.91582 0.00049 + -1 0 1 1 H 7288.97061 0.00009 0.0 0.0 B- * 1 007825.03224 0.00009 +0 0 1 1 2 H 13135.72176 0.00011 1112.283 0.000 B- * 2 014101.77811 0.00012 +0 1 2 1 3 H 14949.80993 0.00022 2827.265 0.000 B- 18.592 0.000 3 016049.28199 0.00023 + -1 1 2 3 He 14931.21793 0.00021 2572.680 0.000 B- -13736# 2000# 3 016029.32265 0.00022 + -3 0 3 3 Li -pp 28667# 2000# -2267# 667# B- * 3 030775# 2147# +0 2 3 1 4 H -n 24621.127 100.000 1720.449 25.000 B- 22196.211 100.000 4 026431.868 107.354 + 0 2 2 4 He 2424.91561 0.00006 7073.915 0.000 B- -22898.273 212.132 4 002603.25413 0.00006 + -2 1 3 4 Li -p 25323.189 212.132 1153.760 53.033 B- * 4 027185.562 227.733 +0 3 4 1 5 H -nn 32892.444 89.443 1336.359 17.889 B- 21661.211 91.652 5 035311.493 96.020 + 1 3 2 5 He -n 11231.233 20.000 5512.132 4.000 B- -447.654 53.852 5 012057.224 21.470 + -1 2 3 5 Li -p 11678.886 50.000 5266.132 10.000 B- -25460# 2003# 5 012537.800 53.677 + -3 1 4 5 Be x 37139# 2003# 18# 401# B- * 5 039870# 2150# +0 4 5 1 6 H -3n 41875.721 254.127 961.639 42.354 B- 24283.626 254.127 6 044955.437 272.816 + 2 4 2 6 He 17592.095 0.053 4878.519 0.009 B- 3505.216 0.053 6 018885.891 0.057 + 0 3 3 6 Li 14086.87895 0.00144 5332.331 0.000 B- -4288.154 5.448 6 015122.88742 0.00155 + -2 2 4 6 Be - 18375.033 5.448 4487.247 0.908 B- -28945# 2003# 6 019726.409 5.848 + -4 1 5 6 B x 47320# 2003# -467# 334# B- * 6 050800# 2150# +0 5 6 1 7 H -nn 49135# 1004# 940# 143# B- 23062# 1004# 7 052749# 1078# + 3 5 2 7 He -n 26073.126 7.559 4123.057 1.080 B- 11166.021 7.559 7 027990.654 8.115 + 1 4 3 7 Li 14907.10529 0.00423 5606.439 0.001 B- -861.893 0.071 7 016003.43666 0.00454 + -1 3 4 7 Be 15768.999 0.071 5371.548 0.010 B- -11907.551 25.150 7 016928.717 0.076 + -3 2 5 7 B p4n 27676.550 25.150 3558.705 3.593 B- * 7 029712.000 27.000 +0 4 6 2 8 He 31609.681 0.089 3924.520 0.011 B- 10663.878 0.100 8 033934.390 0.095 + 2 5 3 8 Li 20945.804 0.047 5159.712 0.006 B- 16004.133 0.059 8 022486.246 0.050 + 0 4 4 8 Be -a 4941.671 0.035 7062.435 0.004 B- -17979.896 1.000 8 005305.102 0.037 + -2 3 5 8 B 22921.567 1.000 4717.155 0.125 B- -12142.701 18.270 8 024607.316 1.073 + -4 2 6 8 C 35064.268 18.243 3101.524 2.280 B- * 8 037643.042 19.584 +0 5 7 2 9 He 40935.826 46.816 3349.037 5.202 B- 15980.924 46.817 9 043946.419 50.259 + 3 6 3 9 Li -3n 24954.902 0.186 5037.768 0.021 B- 13606.449 0.201 9 026790.191 0.200 + 1 5 4 9 Be 11348.453 0.077 6462.668 0.009 B- -1068.035 0.899 9 012183.066 0.082 + -1 4 5 9 B - 12416.488 0.903 6257.070 0.100 B- -16494.484 2.319 9 013329.649 0.969 + -3 3 6 9 C -pp 28910.972 2.137 4337.423 0.237 B- * 9 031037.207 2.293 +0 6 8 2 10 He -nn 49197.143 92.848 2995.134 9.285 B- 16144.519 93.715 10 052815.308 99.676 + 4 7 3 10 Li -n 33052.624 12.721 4531.351 1.272 B- 20445.136 12.722 10 035483.453 13.656 + 2 6 4 10 Be 12607.488 0.081 6497.630 0.008 B- 556.878 0.082 10 013534.695 0.086 + 0 5 5 10 B 12050.609 0.015 6475.083 0.002 B- -3648.062 0.069 10 012936.862 0.016 + -2 4 6 10 C 15698.672 0.070 6032.042 0.007 B- -23101.355 400.000 10 016853.218 0.075 + -4 3 7 10 N -- 38800.026 400.000 3643.672 40.000 B- * 10 041653.543 429.417 +0 5 8 3 11 Li x 40728.254 0.615 4155.381 0.056 B- 20551.087 0.659 11 043723.581 0.660 + 3 7 4 11 Be 20177.167 0.238 5952.540 0.022 B- 11509.460 0.238 11 021661.081 0.255 + 1 6 5 11 B 8667.707 0.012 6927.732 0.001 B- -1981.689 0.061 11 009305.166 0.013 + -1 5 6 11 C 10649.396 0.060 6676.456 0.005 B- -13654.163 46.154 11 011432.597 0.064 + -3 4 7 11 N -p 24303.559 46.154 5364.046 4.196 B- * 11 026090.945 49.548 +0 6 9 3 12 Li -n 49009.571 30.006 3791.600 2.501 B- 23931.812 30.067 12 052613.941 32.213 + 4 8 4 12 Be 25077.760 1.909 5720.722 0.159 B- 11708.363 2.321 12 026922.083 2.048 + 2 7 5 12 B 13369.397 1.321 6631.223 0.110 B- 13369.397 1.321 12 014352.638 1.418 + 0 6 6 12 C 0.0 0.0 7680.144 0.000 B- -17338.068 1.000 12 000000.0 0.0 + -2 5 7 12 N 17338.068 1.000 6170.109 0.083 B- -14576.544 24.021 12 018613.182 1.073 + -4 4 8 12 O -pp 31914.613 24.000 4890.202 2.000 B- * 12 034261.747 25.765 +0 7 10 3 13 Li -nn 56980.888 70.003 3507.630 5.385 B- 23321.812 70.739 13 061171.503 75.150 + 5 9 4 13 Be -n 33659.077 10.180 5241.435 0.783 B- 17097.130 10.230 13 036134.507 10.929 + 3 8 5 13 B -nn 16561.947 1.000 6496.419 0.077 B- 13436.938 1.000 13 017779.981 1.073 + 1 7 6 13 C 3125.00888 0.00021 7469.849 0.000 B- -2220.472 0.270 13 003354.83521 0.00023 + -1 6 7 13 N 5345.481 0.270 7238.863 0.021 B- -17769.951 9.530 13 005738.609 0.289 + -3 5 8 13 O +3n 23115.432 9.526 5811.763 0.733 B- * 13 024815.437 10.226 +0 6 10 4 14 Be x 39954.498 132.245 4993.897 9.446 B- 16290.813 133.936 14 042892.920 141.970 + 4 9 5 14 B 23663.685 21.213 6101.644 1.515 B- 20643.792 21.213 14 025404.012 22.773 + 2 8 6 14 C 3019.89278 0.00376 7520.319 0.000 B- 156.476 0.004 14 003241.98843 0.00403 + 0 7 7 14 N 2863.41672 0.00019 7475.614 0.000 B- -5144.364 0.025 14 003074.00446 0.00021 + -2 6 8 14 O 8007.781 0.025 7052.278 0.002 B- -23956.622 41.119 14 008596.706 0.027 + -4 5 9 14 F -p 31964.402 41.119 5285.208 2.937 B- * 14 034315.199 44.142 +0 7 11 4 15 Be -n 49825.815 165.797 4540.970 11.053 B- 20867.573 167.126 15 053490.215 177.990 + 5 10 5 15 B 28958.242 21.032 5879.985 1.402 B- 19085.098 21.047 15 031087.953 22.578 + 3 9 6 15 C -n 9873.144 0.800 7100.169 0.053 B- 9771.705 0.800 15 010599.256 0.858 + 1 8 7 15 N 101.43871 0.00060 7699.460 0.000 B- -2754.166 0.491 15 000108.89894 0.00065 + -1 7 8 15 O 2855.605 0.491 7463.692 0.033 B- -13711.146 14.009 15 003065.618 0.526 + -3 6 9 15 F -p 16566.751 14.000 6497.459 0.933 B- -23648.622 68.138 15 017785.139 15.029 + -5 5 10 15 Ne -pp 40215.373 66.684 4868.728 4.446 B- * 15 043172.980 71.588 +0 8 12 4 16 Be -nn 57447.132 165.797 4285.285 10.362 B- 20334.623 167.608 16 061672.036 177.990 + 6 11 5 16 B 37112.510 24.569 5507.302 1.536 B- 23418.378 24.828 16 039841.920 26.375 + 4 10 6 16 C -nn 13694.132 3.578 6922.054 0.224 B- 8010.225 4.254 16 014701.256 3.840 + 2 9 7 16 N -n 5683.907 2.301 7373.796 0.144 B- 10420.908 2.301 16 006101.925 2.470 + 0 8 8 16 O -4737.00135 0.00016 7976.206 0.000 B- -15417.254 8.321 15 994914.61960 0.00017 + -2 7 9 16 F - 10680.253 8.321 6963.731 0.520 B- -13306.523 22.106 16 011465.723 8.932 + -4 6 10 16 Ne -- 23986.776 20.480 6083.177 1.280 B- * 16 025750.864 21.986 +0 7 12 5 17 B x 43716.317 204.104 5269.667 12.006 B- 22684.419 204.841 17 046931.399 219.114 + 5 11 6 17 C 2p-n 21031.898 17.365 6558.024 1.021 B- 13161.820 22.946 17 022578.672 18.641 + 3 10 7 17 N +p 7870.079 15.000 7286.229 0.882 B- 8678.842 15.000 17 008448.877 16.103 + 1 9 8 17 O -808.76348 0.00066 7750.728 0.000 B- -2760.465 0.248 16 999131.75664 0.00070 + -1 8 9 17 F 1951.702 0.248 7542.328 0.015 B- -14548.746 0.432 17 002095.238 0.266 + -3 7 10 17 Ne 16500.447 0.354 6640.499 0.021 B- -18672.766 1001.356 17 017713.959 0.380 + -5 6 11 17 Na x 35173.214 1001.356 5496.080 58.903 B- * 17 037760.000 1075.000 +0 8 13 5 18 B -n 51792.634 204.165 4976.630 11.342 B- 26873.370 206.357 18 055601.682 219.180 + 6 12 6 18 C ++ 24919.264 30.000 6426.131 1.667 B- 11806.096 35.282 18 026751.932 32.206 + 4 11 7 18 N + 13113.168 18.570 7038.562 1.032 B- 13895.984 18.570 18 014077.565 19.935 + 2 10 8 18 O -782.81560 0.00071 7767.097 0.000 B- -1655.929 0.463 17 999159.61284 0.00076 + 0 9 9 18 F 873.113 0.463 7631.638 0.026 B- -4444.501 0.589 18 000937.325 0.497 + -2 8 10 18 Ne 5317.614 0.363 7341.257 0.020 B- -19720.374 93.882 18 005708.693 0.390 + -4 7 11 18 Na 25037.988 93.881 6202.217 5.216 B- * 18 026879.386 100.785 +0 9 14 5 19 B x 59770.244 525.363 4719.634 27.651 B- 27356.492 534.496 19 064166.000 564.000 + 7 13 6 19 C -n 32413.752 98.389 6118.273 5.178 B- 16557.471 99.748 19 034797.596 105.625 + 5 12 7 19 N p-2n 15856.282 16.404 6948.543 0.863 B- 12523.424 16.614 19 017022.419 17.610 + 3 11 8 19 O -n 3332.858 2.637 7566.495 0.139 B- 4820.302 2.637 19 003577.970 2.830 + 1 10 9 19 F -1487.44420 0.00086 7779.018 0.000 B- -3239.494 0.160 18 998403.16288 0.00093 + -1 9 10 19 Ne +3n 1752.050 0.160 7567.343 0.008 B- -11177.340 10.536 19 001880.903 0.171 + -3 8 11 19 Na 12929.390 10.535 6937.885 0.554 B- -18898.998 51.099 19 013880.272 11.309 + -5 7 12 19 Mg -pp 31828.389 50.001 5902.025 2.632 B- * 19 034169.182 53.678 +0 10 15 5 20 B x 68450# 800# 4453# 40# B- 30946# 833# 20 073484# 859# + 8 14 6 20 C x 37503.563 230.625 5961.435 11.531 B- 15737.067 243.746 20 040261.732 247.585 + 6 13 7 20 N x 21766.496 78.894 6709.171 3.945 B- 17970.324 78.899 20 023367.295 84.696 + 4 12 8 20 O -nn 3796.172 0.885 7568.570 0.044 B- 3813.635 0.885 20 004075.358 0.950 + 2 11 9 20 F -n -17.463 0.030 7720.134 0.002 B- 7024.467 0.030 19 999981.252 0.031 + 0 10 10 20 Ne -7041.93055 0.00157 8032.240 0.000 B- -13892.535 1.114 19 992440.17619 0.00168 + -2 9 11 20 Na 6850.604 1.114 7298.496 0.056 B- -10627.088 2.171 20 007354.426 1.195 + -4 8 12 20 Mg +t 17477.692 1.863 6728.025 0.093 B- * 20 018763.075 2.000 +0 11 16 5 21 B x 77330# 900# 4203# 43# B- 31687# 1079# 21 083017# 966# + 9 15 6 21 C x 45643# 596# 5674# 28# B- 20411# 611# 21 049000# 640# + 7 14 7 21 N x 25231.913 134.048 6609.015 6.383 B- 17169.878 134.584 21 027087.573 143.906 + 5 13 8 21 O -3n 8062.035 12.000 7389.374 0.571 B- 8109.640 12.134 21 008654.950 12.882 + 3 12 9 21 F -nn -47.605 1.800 7738.293 0.086 B- 5684.171 1.800 20 999948.894 1.932 + 1 11 10 21 Ne -5731.776 0.038 7971.713 0.002 B- -3547.145 0.090 20 993846.685 0.041 + -1 10 11 21 Na -2184.631 0.098 7765.547 0.005 B- -13088.480 0.761 20 997654.702 0.105 + -3 9 12 21 Mg x 10903.850 0.755 7105.031 0.036 B- -16086# 596# 21 011705.764 0.810 + -5 8 13 21 Al x 26990# 596# 6302# 28# B- * 21 028975# 640# +0 10 16 6 22 C -nn 53611.197 231.490 5421.077 10.522 B- 21846.396 311.063 22 057553.990 248.515 + 8 15 7 22 N x 31764.801 207.779 6378.534 9.445 B- 22481.768 215.435 22 034100.918 223.060 + 6 14 8 22 O -4n 9283.033 56.921 7364.871 2.587 B- 6489.660 58.256 22 009965.746 61.107 + 4 13 9 22 F + 2793.373 12.399 7624.295 0.564 B- 10818.092 12.399 22 002998.809 13.310 + 2 12 10 22 Ne -8024.719 0.018 8080.465 0.001 B- -2843.207 0.171 21 991385.109 0.018 + 0 11 11 22 Na -5181.511 0.171 7915.667 0.008 B- -4781.578 0.321 21 994437.418 0.183 + -2 10 12 22 Mg -399.933 0.313 7662.761 0.014 B- -18601# 401# 21 999570.654 0.335 + -4 9 13 22 Al x 18201# 401# 6782# 18# B- -15137# 643# 22 019540# 430# + -6 8 14 22 Si x 33338# 503# 6058# 23# B- * 22 035790# 540# +0 11 17 6 23 C x 64171# 997# 5077# 43# B- 27450# 1082# 23 068890# 1070# + 9 16 7 23 N x 36720.425 420.570 6236.671 18.286 B- 22099.056 437.827 23 039421.000 451.500 + 7 15 8 23 O x 14621.369 121.712 7163.485 5.292 B- 11336.106 126.190 23 015696.686 130.663 + 5 14 9 23 F 3285.263 33.320 7622.344 1.449 B- 8439.312 33.321 23 003526.874 35.770 + 3 13 10 23 Ne -n -5154.049 0.104 7955.256 0.005 B- 4375.804 0.104 22 994466.900 0.112 + 1 12 11 23 Na -9529.85248 0.00181 8111.493 0.000 B- -4056.340 0.158 22 989769.28199 0.00194 + -1 11 12 23 Mg - -5473.513 0.158 7901.115 0.007 B- -12221.583 0.379 22 994123.941 0.170 + -3 10 13 23 Al -- 6748.070 0.345 7335.727 0.015 B- -16949# 503# 23 007244.351 0.370 + -5 9 14 23 Si x 23697# 503# 6565# 22# B- * 23 025440# 540# +0 10 17 7 24 N x 46938# 401# 5887# 17# B- 28438# 433# 24 050390# 430# + 8 16 8 24 O x 18500.402 164.874 7039.685 6.870 B- 10955.887 191.633 24 019861.000 177.000 + 6 15 9 24 F x 7544.515 97.670 7463.582 4.070 B- 13496.161 97.672 24 008099.370 104.853 + 4 14 10 24 Ne -nn -5951.646 0.513 7993.325 0.021 B- 2466.255 0.513 23 993610.645 0.550 + 2 13 11 24 Na -n -8417.901 0.017 8063.488 0.001 B- 5515.669 0.021 23 990963.011 0.017 + 0 12 12 24 Mg -13933.569 0.013 8260.709 0.001 B- -13884.704 0.233 23 985041.697 0.014 + -2 11 13 24 Al ep -48.865 0.233 7649.582 0.010 B- -10794.060 19.473 23 999947.541 0.250 + -4 10 14 24 Si -- 10745.195 19.472 7167.232 0.811 B- -22574# 503# 24 011535.441 20.904 + -6 9 15 24 P x 33320# 503# 6194# 21# B- * 24 035770# 540# +0 11 18 7 25 N x 55983# 503# 5613# 20# B- 28654# 529# 25 060100# 540# + 9 17 8 25 O -n 27329.027 165.084 6727.805 6.603 B- 15994.862 191.191 25 029338.919 177.225 + 7 16 9 25 F x 11334.166 96.442 7336.306 3.858 B- 13369.667 100.721 25 012167.727 103.535 + 5 15 10 25 Ne -2035.502 29.045 7839.799 1.162 B- 7322.312 29.070 24 997814.799 31.181 + 3 14 11 25 Na -nn -9357.813 1.200 8101.397 0.048 B- 3834.969 1.201 24 989953.973 1.288 + 1 13 12 25 Mg -13192.783 0.047 8223.502 0.002 B- -4276.808 0.045 24 985836.964 0.050 + -1 12 13 25 Al -8915.975 0.065 8021.136 0.003 B- -12743.299 10.000 24 990428.306 0.069 + -3 11 14 25 Si +3n 3827.324 10.000 7480.110 0.400 B- -15911# 401# 25 004108.801 10.735 + -5 10 15 25 P x 19738# 401# 6812# 16# B- * 25 021190# 430# +0 10 18 8 26 O -nn 34661.037 164.950 6497.478 6.344 B- 16012.161 198.932 26 037210.155 177.081 + 8 17 9 26 F x 18648.875 111.199 7083.240 4.277 B- 18167.762 112.716 26 020020.392 119.377 + 6 16 10 26 Ne x 481.114 18.429 7751.910 0.709 B- 7341.893 18.758 26 000516.496 19.784 + 4 15 11 26 Na x -6860.780 3.502 8004.201 0.135 B- 9353.763 3.502 25 992634.649 3.759 + 2 14 12 26 Mg -16214.542 0.030 8333.870 0.001 B- -4004.391 0.063 25 982592.971 0.032 + 0 13 13 26 Al -12210.151 0.067 8149.765 0.003 B- -5069.136 0.085 25 986891.863 0.071 + -2 12 14 26 Si - -7141.015 0.108 7924.708 0.004 B- -18114# 196# 25 992333.804 0.115 + -4 11 15 26 P x 10973# 196# 7198# 8# B- -16106# 627# 26 011780# 210# + -6 10 16 26 S x 27079# 596# 6548# 23# B- * 26 029070# 640# +0 11 19 8 27 O x 44670# 500# 6185# 19# B- 19220# 634# 27 047955# 537# + 9 18 9 27 F x 25450.279 389.830 6867.932 14.438 B- 18399.370 400.258 27 027322.000 418.500 + 7 17 10 27 Ne x 7050.909 90.770 7520.414 3.362 B- 12568.699 90.847 27 007569.462 97.445 + 5 16 11 27 Na ++ -5517.790 3.726 7956.946 0.138 B- 9068.821 3.727 26 994076.408 4.000 + 3 15 12 27 Mg -n -14586.611 0.050 8263.852 0.002 B- 2610.251 0.069 26 984340.628 0.053 + 1 14 13 27 Al -17196.861 0.047 8331.553 0.002 B- -4812.359 0.096 26 981538.408 0.050 + -1 13 14 27 Si - -12384.503 0.107 8124.341 0.004 B- -11662.044 26.340 26 986704.688 0.115 + -3 12 15 27 P p4n -722.458 26.340 7663.438 0.976 B- -17750# 400# 26 999224.409 28.277 + -5 11 16 27 S - 17028# 401# 6977# 15# B- * 27 018280# 430# +0 12 20 8 28 O x 52080# 699# 5988# 25# B- 18338# 802# 28 055910# 750# + 10 19 9 28 F -n 33741.596 393.024 6614.792 14.037 B- 22441.859 412.748 28 036223.095 421.928 + 8 18 10 28 Ne x 11299.737 126.068 7388.346 4.502 B- 12288.052 126.483 28 012130.767 135.339 + 6 17 11 28 Na x -988.315 10.246 7799.264 0.366 B- 14030.529 10.440 27 998939.000 11.000 + 4 16 12 28 Mg + -15018.845 2.001 8272.413 0.071 B- 1831.800 2.000 27 983876.606 2.148 + 2 15 13 28 Al -n -16850.645 0.077 8309.894 0.003 B- 4642.150 0.077 27 981910.087 0.083 + 0 14 14 28 Si -21492.79430 0.00049 8447.744 0.000 B- -14345.055 1.152 27 976926.53499 0.00052 + -2 13 15 28 P -7147.740 1.152 7907.479 0.041 B- -11220.945 160.004 27 992326.585 1.236 + -4 12 16 28 S -- 4073.206 160.000 7478.790 5.714 B- -23443# 617# 28 004372.766 171.767 + -6 11 17 28 Cl x 27516# 596# 6614# 21# B- * 28 029540# 640# +0 11 20 9 29 F x 40150.186 525.363 6444.031 18.116 B- 21750.385 546.221 29 043103.000 564.000 + 9 19 10 29 Ne x 18399.801 149.505 7167.067 5.155 B- 15719.807 149.685 29 019753.000 160.500 + 7 18 11 29 Na 2679.994 7.337 7682.151 0.253 B- 13282.824 13.557 29 002877.092 7.876 + 5 17 12 29 Mg x -10602.829 11.400 8113.202 0.393 B- 7604.931 11.405 28 988617.393 12.238 + 3 16 13 29 Al x -18207.760 0.345 8348.464 0.012 B- 3687.318 0.345 28 980453.164 0.370 + 1 15 14 29 Si -21895.07838 0.00056 8448.635 0.000 B- -4942.230 0.359 28 976494.66525 0.00060 + -1 14 15 29 P -16952.848 0.359 8251.236 0.012 B- -13796.432 50.001 28 981800.368 0.385 + -3 13 16 29 S +3n -3156.416 50.000 7748.520 1.724 B- -16318.592 195.192 28 996611.448 53.677 + -5 12 17 29 Cl -p 13162.176 188.680 7158.832 6.506 B- * 29 014130.178 202.555 +0 12 21 9 30 F x 48112# 596# 6233# 20# B- 24832# 648# 30 051650# 640# + 10 20 10 30 Ne 23280.117 253.250 7034.531 8.442 B- 14805.448 253.295 30 024992.235 271.875 + 8 19 11 30 Na 8474.670 4.727 7501.968 0.158 B- 17358.490 5.850 30 009097.932 5.074 + 6 18 12 30 Mg x -8883.820 3.447 8054.506 0.115 B- 6981.024 4.496 29 990462.826 3.700 + 4 17 13 30 Al x -15864.844 2.888 8261.128 0.096 B- 8568.116 2.888 29 982968.388 3.100 + 2 16 14 30 Si -n -24432.960 0.022 8520.654 0.001 B- -4232.106 0.061 29 973770.136 0.023 + 0 15 15 30 P - -20200.854 0.065 8353.506 0.002 B- -6141.601 0.196 29 978313.489 0.069 + -2 14 16 30 S - -14059.253 0.206 8122.707 0.007 B- -18502# 196# 29 984906.769 0.221 + -4 13 17 30 Cl x 4443# 196# 7480# 7# B- -16488# 284# 30 004770# 210# + -6 12 18 30 Ar -pp 20931.147 206.155 6904.204 6.872 B- * 30 022470.511 221.316 +0 13 22 9 31 F -nn 56143# 546# 6033# 18# B- 24961# 608# 31 060272# 587# + 11 21 10 31 Ne 31181.591 266.195 6813.090 8.587 B- 18935.559 266.562 31 033474.816 285.772 + 9 20 11 31 Na x 12246.031 13.972 7398.677 0.451 B- 15368.182 14.307 31 013146.656 15.000 + 7 19 12 31 Mg x -3122.151 3.074 7869.188 0.099 B- 11828.555 3.801 30 996648.232 3.300 + 5 18 13 31 Al x -14950.706 2.236 8225.517 0.072 B- 7998.330 2.236 30 983949.756 2.400 + 3 17 14 31 Si -n -22949.036 0.043 8458.291 0.001 B- 1491.505 0.043 30 975363.194 0.046 + 1 16 15 31 P -24440.54095 0.00067 8481.167 0.000 B- -5398.016 0.229 30 973761.99863 0.00072 + -1 15 16 31 S -19042.525 0.229 8281.800 0.007 B- -12007.974 3.454 30 979557.007 0.246 + -3 14 17 31 Cl -- -7034.551 3.447 7869.209 0.111 B- -18360# 200# 30 992448.098 3.700 + -5 13 18 31 Ar - 11325# 200# 7252# 6# B- * 31 012158# 215# +0 12 22 10 32 Ne x 36999# 503# 6671# 16# B- 18359# 504# 32 039720# 540# + 10 21 11 32 Na x 18640.151 37.260 7219.881 1.164 B- 19469.051 37.402 32 020011.026 40.000 + 8 20 12 32 Mg x -828.900 3.260 7803.840 0.102 B- 10270.467 7.879 31 999110.139 3.500 + 6 19 13 32 Al x -11099.367 7.173 8100.344 0.224 B- 12978.319 7.179 31 988084.339 7.700 + 4 18 14 32 Si x -24077.686 0.298 8481.468 0.009 B- 227.188 0.301 31 974151.539 0.320 + 2 17 15 32 P -n -24304.874 0.040 8464.120 0.001 B- 1710.660 0.040 31 973907.643 0.042 + 0 16 16 32 S -26015.53355 0.00132 8493.129 0.000 B- -12680.860 0.562 31 972071.17443 0.00141 + -2 15 17 32 Cl -13334.674 0.562 8072.404 0.018 B- -11134.323 1.857 31 985684.637 0.603 + -4 14 18 32 Ar x -2200.351 1.770 7700.008 0.055 B- -23299# 401# 31 997637.826 1.900 + -6 13 19 32 K x 21098# 401# 6947# 13# B- * 32 022650# 430# +0 13 23 10 33 Ne x 45997# 596# 6440# 18# B- 22217# 747# 33 049380# 640# + 11 22 11 33 Na x 23780.110 449.912 7089.926 13.634 B- 18817.813 449.921 33 025529.000 483.000 + 9 21 12 33 Mg x 4962.297 2.888 7636.455 0.088 B- 13459.677 7.559 33 005327.245 3.100 + 7 20 13 33 Al x -8497.380 6.986 8020.616 0.212 B- 12016.945 7.021 32 990877.687 7.500 + 5 19 14 33 Si x -20514.325 0.699 8361.059 0.021 B- 5823.021 1.295 32 977976.964 0.750 + 3 18 15 33 P + -26337.346 1.090 8513.806 0.033 B- 248.508 1.090 32 971725.694 1.170 + 1 17 16 33 S -26585.85434 0.00135 8497.630 0.000 B- -5582.517 0.391 32 971458.90985 0.00145 + -1 16 17 33 Cl -21003.337 0.391 8304.755 0.012 B- -11619.044 0.560 32 977451.989 0.419 + -3 15 18 33 Ar x -9384.292 0.401 7928.955 0.012 B- -16426# 196# 32 989925.547 0.430 + -5 14 19 33 K x 7042# 196# 7407# 6# B- * 33 007560# 210# +0 14 24 10 34 Ne -nn 52842# 513# 6287# 15# B- 21161# 789# 34 056728# 551# + 12 23 11 34 Na x 31680.111 599.416 6886.437 17.630 B- 23356.764 600.112 34 034010.000 643.500 + 10 22 12 34 Mg x 8323.348 28.876 7550.390 0.849 B- 11323.637 29.039 34 008935.481 31.000 + 8 21 13 34 Al x -3000.289 3.074 7860.428 0.090 B- 16956.563 14.448 33 996779.057 3.300 + 6 20 14 34 Si +pp -19956.852 14.118 8336.141 0.415 B- 4591.847 14.141 33 978575.437 15.155 + 4 19 15 34 P x -24548.698 0.810 8448.185 0.024 B- 5382.987 0.812 33 973645.887 0.870 + 2 18 16 34 S -29931.685 0.045 8583.498 0.001 B- -5491.603 0.038 33 967867.012 0.047 + 0 17 17 34 Cl -24440.082 0.049 8398.970 0.001 B- -6061.792 0.063 33 973762.491 0.052 + -2 16 18 34 Ar -18378.290 0.078 8197.672 0.002 B- -17158# 196# 33 980270.093 0.083 + -4 15 19 34 K x -1220# 196# 7670# 6# B- -15072# 357# 33 998690# 210# + -6 14 20 34 Ca x 13851# 298# 7204# 9# B- * 34 014870# 320# +0 13 24 11 35 Na -n 38231# 670# 6733# 19# B- 22592# 723# 35 041043# 720# + 11 23 12 35 Mg x 15639.784 269.668 7356.233 7.705 B- 15863.512 269.768 35 016790.000 289.500 + 9 22 13 35 Al x -223.728 7.359 7787.124 0.210 B- 14167.729 36.605 34 999759.817 7.900 + 7 21 14 35 Si 2p-n -14391.457 35.857 8169.563 1.024 B- 10466.342 35.905 34 984550.134 38.494 + 5 20 15 35 P +p -24857.799 1.866 8446.249 0.053 B- 3988.407 1.867 34 973314.053 2.003 + 3 19 16 35 S -28846.206 0.040 8537.850 0.001 B- 167.322 0.026 34 969032.322 0.043 + 1 18 17 35 Cl -29013.528 0.035 8520.278 0.001 B- -5966.243 0.679 34 968852.694 0.038 + -1 17 18 35 Ar - -23047.284 0.680 8327.461 0.019 B- -11874.394 0.852 34 975257.721 0.730 + -3 16 19 35 K 4n -11172.891 0.512 7965.840 0.015 B- -15961# 196# 34 988005.407 0.550 + -5 15 20 35 Ca x 4788# 196# 7487# 6# B- * 35 005140# 210# +0 14 25 11 36 Na -n 46303# 678# 6546# 19# B- 25923# 967# 36 049708# 728# + 12 24 12 36 Mg x 20380.157 690.237 7244.419 19.173 B- 14429.774 706.243 36 021879.000 741.000 + 10 23 13 36 Al x 5950.384 149.505 7623.515 4.153 B- 18386.508 165.851 36 006388.000 160.500 + 8 22 14 36 Si x -12436.124 71.797 8112.519 1.994 B- 7814.911 72.985 35 986649.271 77.077 + 6 21 15 36 P + -20251.034 13.114 8307.868 0.364 B- 10413.096 13.112 35 978259.619 14.078 + 4 20 16 36 S -30664.131 0.188 8575.389 0.005 B- -1142.126 0.189 35 967080.699 0.201 + 2 19 17 36 Cl -29522.005 0.036 8521.931 0.001 B- 709.535 0.045 35 968306.822 0.038 + 0 18 18 36 Ar -30231.540 0.027 8519.909 0.001 B- -12814.475 0.342 35 967545.105 0.028 + -2 17 19 36 K -17417.065 0.341 8142.219 0.009 B- -10965.916 40.001 35 981302.010 0.366 + -4 16 20 36 Ca 4n -6451.149 40.000 7815.879 1.111 B- -21802# 301# 35 993074.406 42.941 + -6 15 21 36 Sc x 15351# 298# 7189# 8# B- * 36 016480# 320# +0 15 26 11 37 Na -nn 53534# 687# 6392# 19# B- 25323# 980# 37 057471# 737# + 13 25 12 37 Mg -n 28211.474 698.947 7055.111 18.890 B- 18401.911 721.814 37 030286.265 750.350 + 11 24 13 37 Al x 9809.563 180.244 7531.315 4.871 B- 16381.075 213.168 37 010531.000 193.500 + 9 23 14 37 Si x -6571.511 113.809 7952.903 3.076 B- 12424.486 119.969 36 992945.191 122.179 + 7 22 15 37 P p-2n -18995.998 37.948 8267.555 1.026 B- 7900.419 37.947 36 979606.956 40.738 + 5 21 16 37 S -n -26896.417 0.198 8459.935 0.005 B- 4865.121 0.196 36 971125.507 0.212 + 3 20 17 37 Cl -31761.538 0.052 8570.281 0.001 B- -813.873 0.200 36 965902.584 0.055 + 1 19 18 37 Ar - -30947.664 0.207 8527.139 0.006 B- -6147.465 0.227 36 966776.314 0.221 + -1 18 19 37 K -p -24800.199 0.094 8339.847 0.003 B- -11664.133 0.641 36 973375.889 0.100 + -3 17 20 37 Ca x -13136.066 0.634 8003.456 0.017 B- -16656# 300# 36 985897.852 0.680 + -5 16 21 37 Sc x 3520# 300# 7532# 8# B- * 37 003779# 322# +0 14 26 12 38 Mg x 34074# 503# 6928# 13# B- 17864# 627# 38 036580# 540# + 12 25 13 38 Al x 16209.859 374.461 7377.097 9.854 B- 20380.157 388.847 38 017402.000 402.000 + 10 24 14 38 Si x -4170.299 104.793 7892.829 2.758 B- 10451.265 127.474 37 995523.000 112.500 + 8 23 15 38 P x -14621.563 72.581 8147.274 1.910 B- 12239.640 72.934 37 984303.105 77.918 + 6 22 16 38 S + -26861.203 7.172 8448.782 0.189 B- 2936.900 7.171 37 971163.310 7.699 + 4 21 17 38 Cl -n -29798.103 0.098 8505.481 0.003 B- 4916.718 0.218 37 968010.418 0.105 + 2 20 18 38 Ar -34714.821 0.195 8614.280 0.005 B- -5914.066 0.045 37 962732.104 0.209 + 0 19 19 38 K -28800.755 0.195 8438.058 0.005 B- -6742.256 0.063 37 969081.116 0.209 + -2 18 20 38 Ca -22058.499 0.194 8240.043 0.005 B- -17809# 200# 37 976319.226 0.208 + -4 17 21 38 Sc x -4249# 200# 7751# 5# B- -15119# 361# 37 995438# 215# + -6 16 22 38 Ti x 10870# 300# 7332# 8# B- * 38 011669# 322# +0 15 27 12 39 Mg -n 42275# 513# 6747# 13# B- 21625# 650# 39 045384# 551# + 13 26 13 39 Al x 20650# 400# 7281# 10# B- 18330# 422# 39 022169# 429# + 11 25 14 39 Si x 2320.352 135.532 7730.979 3.475 B- 15094.986 176.232 39 002491.000 145.500 + 9 24 15 39 P x -12774.634 112.645 8097.969 2.888 B- 10388.033 123.243 38 986285.865 120.929 + 7 23 16 39 S 2p-n -23162.667 50.000 8344.269 1.282 B- 6637.538 50.030 38 975133.852 53.677 + 5 22 17 39 Cl -nn -29800.205 1.732 8494.402 0.044 B- 3441.985 5.292 38 968008.162 1.859 + 3 21 18 39 Ar + -33242.190 5.000 8562.598 0.128 B- 565.000 5.000 38 964313.039 5.367 + 1 20 19 39 K -33807.19010 0.00458 8557.025 0.000 B- -6524.488 0.596 38 963706.48661 0.00492 + -1 19 20 39 Ca -27282.702 0.596 8369.670 0.015 B- -13109.993 24.007 38 970710.813 0.640 + -3 18 21 39 Sc 2n-p -14172.709 24.000 8013.456 0.615 B- -16373# 202# 38 984784.970 25.765 + -5 17 22 39 Ti x 2200# 200# 7574# 5# B- * 39 002362# 215# +0 16 28 12 40 Mg x 48350# 500# 6628# 13# B- 20760# 640# 40 051906# 537# + 14 27 13 40 Al x 27590# 400# 7127# 10# B- 22160# 528# 40 029619# 429# + 12 26 14 40 Si x 5429.679 345.119 7661.754 8.628 B- 13544.049 377.749 40 005829.000 370.500 + 10 25 15 40 P x -8114.370 153.582 7980.796 3.840 B- 14723.476 153.633 39 991288.865 164.876 + 8 24 16 40 S -22837.846 3.982 8329.325 0.100 B- 4719.967 32.312 39 975482.562 4.274 + 6 23 17 40 Cl + -27557.813 32.066 8427.765 0.802 B- 7482.082 32.066 39 970415.469 34.423 + 4 22 18 40 Ar -35039.89464 0.00224 8595.259 0.000 B- -1504.403 0.056 39 962383.12378 0.00240 + 2 21 19 40 K -33535.492 0.056 8538.090 0.001 B- 1310.893 0.060 39 963998.166 0.060 + 0 20 20 40 Ca -34846.384 0.021 8551.303 0.001 B- -14323.050 2.828 39 962590.865 0.022 + -2 19 21 40 Sc - -20523.335 2.828 8173.669 0.071 B- -11672.950 160.025 39 977967.292 3.036 + -4 18 22 40 Ti -- -8850.384 160.000 7862.286 4.000 B- -21020# 340# 39 990498.721 171.767 + -6 17 23 40 V x 12170# 300# 7317# 7# B- * 40 013065# 322# +0 15 28 13 41 Al x 33420# 500# 7008# 12# B- 21300# 747# 41 035878# 537# + 13 27 14 41 Si x 12119.668 554.705 7508.573 13.529 B- 17099.435 567.571 41 013011.000 595.500 + 11 26 15 41 P x -4979.767 120.163 7906.551 2.931 B- 14028.810 120.233 40 994654.000 129.000 + 9 25 16 41 S x -19008.577 4.099 8229.635 0.100 B- 8298.611 68.846 40 979593.451 4.400 + 7 24 17 41 Cl x -27307.189 68.723 8412.959 1.676 B- 5760.317 68.724 40 970684.525 73.777 + 5 23 18 41 Ar -n -33067.505 0.347 8534.372 0.008 B- 2492.038 0.347 40 964500.571 0.372 + 3 22 19 41 K -35559.54331 0.00380 8576.072 0.000 B- -421.653 0.138 40 961825.25796 0.00408 + 1 21 20 41 Ca -35137.890 0.138 8546.706 0.003 B- -6495.478 0.158 40 962277.921 0.147 + -1 20 21 41 Sc -28642.412 0.083 8369.198 0.002 B- -12944.875 27.945 40 969251.104 0.088 + -3 19 22 41 Ti x -15697.537 27.945 8034.388 0.682 B- -16018# 202# 40 983148.000 30.000 + -5 18 23 41 V x 320# 200# 7625# 5# B- * 41 000344# 215# +0 16 29 13 42 Al x 40100# 600# 6874# 14# B- 23630# 781# 42 043049# 644# + 14 28 14 42 Si x 16470# 500# 7418# 12# B- 15460# 591# 42 017681# 537# + 12 27 15 42 P x 1009.740 314.379 7767.866 7.485 B- 18647.485 314.392 42 001084.000 337.500 + 10 26 16 42 S x -17637.746 2.794 8193.227 0.067 B- 7194.021 59.681 41 981065.100 3.000 + 8 25 17 42 Cl x -24831.767 59.616 8345.886 1.419 B- 9590.908 59.895 41 973342.000 64.000 + 6 24 18 42 Ar x -34422.675 5.775 8555.613 0.138 B- 599.351 5.776 41 963045.736 6.200 + 4 23 19 42 K -n -35022.026 0.106 8551.256 0.003 B- 3525.219 0.183 41 962402.306 0.113 + 2 22 20 42 Ca -38547.245 0.149 8616.563 0.004 B- -6426.092 0.097 41 958617.828 0.159 + 0 21 21 42 Sc -32121.153 0.169 8444.933 0.004 B- -7016.479 0.224 41 965516.522 0.181 + -2 20 22 42 Ti -25104.674 0.277 8259.247 0.007 B- -17485# 196# 41 973049.022 0.297 + -4 19 23 42 V x -7620# 196# 7824# 5# B- -14350# 445# 41 991820# 210# + -6 18 24 42 Cr x 6730# 400# 7464# 10# B- * 42 007225# 429# +0 17 30 13 43 Al x 47020# 800# 6741# 19# B- 23919# 998# 43 050478# 859# + 15 29 14 43 Si x 23101# 596# 7279# 14# B- 18421# 814# 43 024800# 640# + 13 28 15 43 P x 4679.826 554.705 7689.572 12.900 B- 16875.285 554.727 43 005024.000 595.500 + 11 27 16 43 S x -12195.459 4.970 8063.827 0.116 B- 11964.049 62.058 42 986907.635 5.335 + 9 26 17 43 Cl x -24159.508 61.858 8323.866 1.439 B- 7850.300 62.086 42 974063.700 66.407 + 7 25 18 43 Ar x -32009.808 5.310 8488.237 0.123 B- 4565.581 5.325 42 965636.055 5.700 + 5 24 19 43 K -4n -36575.389 0.410 8576.220 0.010 B- 1833.434 0.469 42 960734.703 0.440 + 3 23 20 43 Ca -38408.822 0.228 8600.663 0.005 B- -2220.720 1.865 42 958766.430 0.244 + 1 22 21 43 Sc -p -36188.102 1.863 8530.825 0.043 B- -6867.020 7.481 42 961150.472 1.999 + -1 21 22 43 Ti -n2p -29321.082 7.245 8352.932 0.168 B- -11404.726 43.457 42 968522.521 7.777 + -3 20 23 43 V x -17916.356 42.849 8069.512 0.996 B- -15946# 402# 42 980766.000 46.000 + -5 19 24 43 Cr x -1970# 400# 7680# 9# B- * 42 997885# 429# +0 16 30 14 44 Si x 28513# 596# 7174# 14# B- 18063# 778# 44 030610# 640# + 14 29 15 44 P x 10450# 500# 7567# 11# B- 19655# 500# 44 011219# 537# + 12 28 16 44 S x -9204.233 5.216 7996.015 0.119 B- 11180.290 136.421 43 990118.848 5.600 + 10 27 17 44 Cl x -20384.523 136.321 8232.332 3.098 B- 12288.731 136.330 43 978116.312 146.346 + 8 26 18 44 Ar x -32673.255 1.584 8493.840 0.036 B- 3108.237 1.638 43 964923.816 1.700 + 6 25 19 44 K x -35781.492 0.419 8546.701 0.010 B- 5687.183 0.530 43 961586.986 0.450 + 4 24 20 44 Ca -41468.675 0.325 8658.175 0.007 B- -3652.690 1.757 43 955481.543 0.348 + 2 23 21 44 Sc -p -37815.985 1.756 8557.379 0.040 B- -267.416 1.890 43 959402.867 1.884 + 0 22 22 44 Ti -a -37548.569 0.700 8533.520 0.016 B- -13432.189 181.643 43 959689.951 0.751 + -2 21 23 44 V x -24116.380 181.641 8210.463 4.128 B- -10756# 351# 43 974110.000 195.000 + -4 20 24 44 Cr x -13360# 300# 7948# 7# B- -20390# 583# 43 985657# 322# + -6 19 25 44 Mn x 7030# 500# 7467# 11# B- * 44 007547# 537# +0 17 31 14 45 Si x 37490# 700# 6995# 16# B- 21890# 860# 45 040247# 751# + 15 30 15 45 P x 15600# 500# 7464# 11# B- 19589# 1150# 45 016747# 537# + 13 29 16 45 S x -3989.589 1035.356 7881.807 23.008 B- 14272.954 1044.271 44 995717.000 1111.500 + 11 28 17 45 Cl x -18262.543 136.163 8181.598 3.026 B- 11508.254 136.164 44 980394.353 146.177 + 9 27 18 45 Ar x -29770.796 0.512 8419.952 0.011 B- 6844.841 0.731 44 968039.733 0.550 + 7 26 19 45 K x -36615.638 0.522 8554.674 0.012 B- 4196.536 0.637 44 960691.493 0.560 + 5 25 20 45 Ca -40812.174 0.366 8630.545 0.008 B- 259.722 0.747 44 956186.326 0.392 + 3 24 21 45 Sc -41071.896 0.675 8618.931 0.015 B- -2062.056 0.509 44 955907.503 0.724 + 1 23 22 45 Ti -39009.840 0.845 8555.722 0.019 B- -7123.824 0.214 44 958121.211 0.907 + -1 22 23 45 V -31886.016 0.872 8380.029 0.019 B- -12371.217 35.408 44 965768.951 0.935 + -3 21 24 45 Cr x -19514.799 35.397 8087.728 0.787 B- -14265# 401# 44 979050.000 38.000 + -5 20 25 45 Mn x -5250# 400# 7753# 9# B- -19012# 565# 44 994364# 429# + -7 19 26 45 Fe -pp 13762# 400# 7313# 9# B- * 45 014774# 429# +0 16 31 15 46 P x 22970# 700# 7317# 15# B- 22630# 860# 46 024659# 751# + 14 30 16 46 S x 340# 500# 7792# 11# B- 14199# 542# 46 000365# 537# + 12 29 17 46 Cl x -13859.398 208.661 8083.480 4.536 B- 15913.528 208.664 45 985121.323 224.006 + 10 28 18 46 Ar x -29772.926 1.118 8412.419 0.024 B- 5640.997 1.333 45 968037.446 1.200 + 8 27 19 46 K x -35413.924 0.727 8518.042 0.016 B- 7725.438 2.350 45 961981.586 0.780 + 6 26 20 46 Ca -43139.361 2.235 8668.979 0.049 B- -1378.143 2.333 45 953687.988 2.399 + 4 25 21 46 Sc -n -41761.219 0.683 8622.012 0.015 B- 2366.581 0.667 45 955167.485 0.732 + 2 24 22 46 Ti -44127.799 0.165 8656.451 0.004 B- -7052.449 0.093 45 952626.856 0.176 + 0 23 23 46 V -37075.351 0.202 8486.130 0.004 B- -7603.784 11.455 45 960197.971 0.216 + -2 22 24 46 Cr -29471.567 11.453 8303.823 0.249 B- -16902# 400# 45 968360.970 12.295 + -4 21 25 46 Mn x -12570# 400# 7919# 9# B- -13480# 640# 45 986506# 429# + -6 20 26 46 Fe x 910# 500# 7609# 11# B- * 46 000977# 537# +0 17 32 15 47 P x 29710# 800# 7190# 17# B- 22340# 944# 47 031895# 859# + 15 31 16 47 S x 7370# 500# 7648# 11# B- 17150# 640# 47 007912# 537# + 13 30 17 47 Cl x -9780# 400# 7996# 9# B- 15587# 400# 46 989501# 429# + 11 29 18 47 Ar x -25366.338 1.118 8311.404 0.024 B- 10345.638 1.789 46 972768.114 1.200 + 9 28 19 47 K x -35711.976 1.397 8514.879 0.030 B- 6632.442 2.625 46 961661.614 1.500 + 7 27 20 47 Ca -42344.418 2.222 8639.349 0.047 B- 1992.177 1.185 46 954541.394 2.385 + 5 26 21 47 Sc -44336.595 1.933 8665.090 0.041 B- 600.769 1.929 46 952402.704 2.074 + 3 25 22 47 Ti -44937.364 0.115 8661.227 0.002 B- -2930.746 0.138 46 951757.752 0.123 + 1 24 23 47 V -42006.618 0.169 8582.225 0.004 B- -7444.040 6.032 46 954904.038 0.181 + -1 23 24 47 Cr -34562.578 6.030 8407.195 0.128 B- -11996.204 32.240 46 962895.544 6.473 + -3 22 25 47 Mn x -22566.374 31.671 8135.311 0.674 B- -15697# 501# 46 975774.000 34.000 + -5 21 26 47 Fe x -6870# 500# 7785# 11# B- -17240# 781# 46 992625# 537# + -7 20 27 47 Co x 10370# 600# 7401# 13# B- * 47 011133# 644# +0 16 32 16 48 S x 12761# 596# 7545# 12# B- 17042# 778# 48 013700# 640# + 14 31 17 48 Cl x -4280# 500# 7883# 10# B- 18001# 587# 47 995405# 537# + 12 30 18 48 Ar x -22281.337 307.393 8242.132 6.404 B- 10003.140 307.394 47 976080.000 330.000 + 10 29 19 48 K x -32284.477 0.773 8434.232 0.016 B- 11940.153 0.779 47 965341.186 0.830 + 8 28 20 48 Ca -44224.629 0.096 8666.686 0.002 B- 279.213 4.950 47 952522.904 0.103 + 6 27 21 48 Sc -44503.842 4.951 8656.204 0.103 B- 3988.866 4.950 47 952223.157 5.314 + 4 26 22 48 Ti -48492.709 0.109 8723.006 0.002 B- -4015.015 0.969 47 947940.932 0.117 + 2 25 23 48 V -44477.694 0.975 8623.061 0.020 B- -1655.673 7.388 47 952251.229 1.046 + 0 24 24 48 Cr +nn -42822.020 7.324 8572.269 0.153 B- -13525.682 10.087 47 954028.667 7.862 + -2 23 25 48 Mn -29296.338 6.939 8274.185 0.145 B- -11296# 400# 47 968549.085 7.449 + -4 22 26 48 Fe x -18000# 400# 8023# 8# B- -19500# 640# 47 980676# 429# + -6 21 27 48 Co x 1500# 500# 7600# 10# B- -15293# 708# 48 001610# 537# + -8 20 28 48 Ni -pp 16793# 502# 7265# 10# B- * 48 018028# 538# +0 17 33 16 49 S -n 21093# 667# 7385# 14# B- 20153# 897# 49 022644# 716# + 15 32 17 49 Cl x 940# 600# 7781# 12# B- 18130# 721# 49 001009# 644# + 13 31 18 49 Ar x -17190# 400# 8135# 8# B- 12422# 400# 48 981546# 429# + 11 30 19 49 K x -29611.490 0.801 8372.274 0.016 B- 11688.275 0.826 48 968210.755 0.860 + 9 29 20 49 Ca -n -41299.765 0.201 8594.844 0.004 B- 5261.500 2.702 48 955662.875 0.216 + 7 28 21 49 Sc -46561.265 2.698 8686.256 0.055 B- 2002.522 2.697 48 950014.423 2.896 + 5 27 22 49 Ti -48563.787 0.114 8711.157 0.002 B- -601.856 0.820 48 947864.627 0.122 + 3 26 23 49 V - -47961.931 0.828 8682.908 0.017 B- -2628.871 2.391 48 948510.746 0.889 + 1 25 24 49 Cr -45333.060 2.243 8613.291 0.046 B- -7712.426 0.233 48 951332.955 2.407 + -1 24 25 49 Mn -37620.634 2.255 8439.929 0.046 B- -12869.907 24.324 48 959612.585 2.420 + -3 23 26 49 Fe x -24750.727 24.219 8161.311 0.494 B- -14870# 501# 48 973429.000 26.000 + -5 22 27 49 Co x -9880# 500# 7842# 10# B- -18080# 781# 48 989393# 537# + -7 21 28 49 Ni x 8200# 600# 7457# 12# B- * 49 008803# 644# +0 16 33 17 50 Cl x 7740# 600# 7651# 12# B- 21069# 781# 50 008309# 644# + 14 32 18 50 Ar x -13330# 500# 8056# 10# B- 12398# 500# 49 985690# 537# + 12 31 19 50 K x -25727.848 7.731 8288.582 0.155 B- 13861.376 7.892 49 972380.017 8.300 + 10 30 20 50 Ca x -39589.224 1.584 8550.163 0.032 B- 4958.158 15.084 49 957499.217 1.700 + 8 29 21 50 Sc -pn -44547.382 15.000 8633.679 0.300 B- 6884.278 15.000 49 952176.415 16.103 + 6 28 22 50 Ti -51431.660 0.121 8755.718 0.002 B- -2207.647 0.426 49 944785.839 0.129 + 4 27 23 50 V +n -49224.013 0.409 8695.918 0.008 B- 1038.059 0.299 49 947155.845 0.438 + 2 26 24 50 Cr -50262.072 0.437 8701.032 0.009 B- -7634.477 0.067 49 946041.443 0.468 + 0 25 25 50 Mn -42627.595 0.442 8532.696 0.009 B- -8151.139 8.395 49 954237.391 0.474 + -2 24 26 50 Fe x -34476.456 8.383 8354.026 0.168 B- -16846# 400# 49 962988.000 9.000 + -4 23 27 50 Co x -17630# 400# 8001# 8# B- -13510# 640# 49 981073# 429# + -6 22 28 50 Ni x -4120# 500# 7716# 10# B- * 49 995577# 537# +0 17 34 17 51 Cl x 14290# 700# 7530# 14# B- 20980# 922# 51 015341# 751# + 15 33 18 51 Ar x -6690# 600# 7926# 12# B- 15826# 600# 50 992818# 644# + 13 32 19 51 K x -22516.196 13.047 8221.349 0.256 B- 13816.107 13.057 50 975827.867 14.006 + 11 31 20 51 Ca x -36332.304 0.522 8476.913 0.010 B- 6896.381 20.007 50 960995.665 0.560 + 9 30 21 51 Sc -p2n -43228.684 20.000 8596.796 0.392 B- 6504.153 20.006 50 953592.095 21.471 + 7 29 22 51 Ti -n -49732.837 0.505 8708.988 0.010 B- 2471.005 0.644 50 946609.600 0.541 + 5 28 23 51 V -52203.842 0.401 8742.099 0.008 B- -752.447 0.213 50 943956.867 0.430 + 3 27 24 51 Cr -51451.395 0.400 8712.005 0.008 B- -3207.518 0.346 50 944764.652 0.429 + 1 26 25 51 Mn -48243.877 0.502 8633.772 0.010 B- -8041.321 8.977 50 948208.065 0.539 + -1 25 26 51 Fe -40202.555 8.964 8460.759 0.176 B- -12860.412 49.260 50 956840.779 9.623 + -3 24 27 51 Co x -27342.143 48.438 8193.254 0.950 B- -15442# 503# 50 970647.000 52.000 + -5 23 28 51 Ni x -11900# 500# 7875# 10# B- * 50 987225# 537# +0 16 34 18 52 Ar x -1280# 600# 7825# 12# B- 15858# 601# 51 998626# 644# + 14 33 19 52 K x -17137.627 33.534 8115.029 0.645 B- 17128.639 33.540 51 981602.000 36.000 + 12 32 20 52 Ca x -34266.266 0.671 8429.381 0.013 B- 6177.013 81.855 51 963213.648 0.720 + 10 31 21 52 Sc x -40443.279 81.852 8533.125 1.574 B- 9026.541 82.157 51 956582.351 87.871 + 8 30 22 52 Ti -nn -49469.820 7.072 8691.667 0.136 B- 1973.948 7.085 51 946891.960 7.592 + 6 29 23 52 V -n -51443.769 0.420 8714.582 0.008 B- 3975.473 0.531 51 944772.839 0.450 + 4 28 24 52 Cr -55419.242 0.340 8775.989 0.007 B- -4711.958 1.851 51 940504.992 0.364 + 2 27 25 52 Mn -50707.284 1.845 8670.329 0.035 B- -2376.920 5.017 51 945563.488 1.980 + 0 26 26 52 Fe -48330.363 5.117 8609.574 0.098 B- -13969.413 9.822 51 948115.217 5.493 + -2 25 27 52 Co x -34360.951 8.383 8325.886 0.161 B- -12031# 400# 51 963112.000 9.000 + -4 24 28 52 Ni x -22330# 400# 8079# 8# B- -20049# 721# 51 976028# 429# + -6 23 29 52 Cu x -2280# 600# 7679# 12# B- * 51 997552# 644# +0 17 35 18 53 Ar x 6791# 699# 7677# 13# B- 19086# 708# 53 007290# 750# + 15 34 19 53 K x -12295.721 111.779 8022.848 2.109 B- 17091.983 120.047 52 986800.000 120.000 + 13 33 20 53 Ca x -29387.704 43.780 8330.577 0.826 B- 9519.104 103.774 52 968451.000 47.000 + 11 32 21 53 Sc x -38906.808 94.087 8495.421 1.775 B- 7924.253 137.339 52 958231.821 101.006 + 9 31 22 53 Ti + -46831.061 100.049 8630.174 1.888 B- 5020.000 100.000 52 949724.785 107.406 + 7 30 23 53 V +p -51851.061 3.120 8710.130 0.059 B- 3435.938 3.102 52 944335.593 3.349 + 5 29 24 53 Cr -55286.999 0.348 8760.198 0.007 B- -596.884 0.356 52 940646.961 0.373 + 3 28 25 53 Mn -54690.116 0.450 8734.175 0.009 B- -3742.586 1.686 52 941287.742 0.483 + 1 27 26 53 Fe -50947.530 1.656 8648.799 0.031 B- -8288.101 0.443 52 945305.574 1.777 + -1 26 27 53 Co -42659.428 1.713 8477.658 0.032 B- -13028.604 25.209 52 954203.217 1.839 + -3 25 28 53 Ni x -29630.824 25.150 8217.074 0.475 B- -16361# 501# 52 968190.000 27.000 + -5 24 29 53 Cu x -13270# 500# 7894# 9# B- * 52 985754# 537# +0 16 35 19 54 K x -5002# 596# 7889# 11# B- 20158# 598# 53 994630# 640# + 14 34 20 54 Ca x -25160.585 48.438 8247.496 0.897 B- 8730.315 277.066 53 972989.000 52.000 + 12 33 21 54 Sc x -33890.900 272.800 8394.681 5.052 B- 11731.081 284.990 53 963616.620 292.862 + 10 32 22 54 Ti x -45621.981 82.461 8597.435 1.527 B- 4271.192 83.815 53 951022.786 88.526 + 8 31 23 54 V + -49893.173 15.004 8662.043 0.278 B- 7041.592 15.000 53 946437.472 16.107 + 6 30 24 54 Cr -56934.765 0.353 8777.955 0.007 B- -1377.136 1.008 53 938878.012 0.378 + 4 29 25 54 Mn -p -55557.629 1.059 8737.965 0.020 B- 696.872 1.076 53 940356.429 1.136 + 2 28 26 54 Fe -56254.500 0.372 8736.382 0.007 B- -8244.547 0.089 53 939608.306 0.399 + 0 27 27 54 Co -48009.953 0.383 8569.217 0.007 B- -8731.646 4.673 53 948459.192 0.411 + -2 26 28 54 Ni x -39278.308 4.657 8393.032 0.086 B- -17868# 400# 53 957833.000 5.000 + -4 25 29 54 Cu x -21410# 400# 8048# 7# B- -15139# 565# 53 977015# 429# + -6 24 30 54 Zn -pp -6272# 400# 7753# 7# B- * 53 993267# 430# +0 17 36 19 55 K x 708# 699# 7788# 13# B- 19058# 760# 55 000760# 750# + 15 35 20 55 Ca x -18350# 300# 8120# 5# B- 11809# 544# 54 980300# 322# + 13 34 21 55 Sc x -30159.352 454.342 8320.955 8.261 B- 11508.735 482.226 54 967622.601 487.756 + 11 33 22 55 Ti -41668.088 161.602 8515.980 2.938 B- 7476.498 157.206 54 955267.465 173.486 + 9 32 23 55 V -49144.586 95.104 8637.692 1.729 B- 5965.125 95.103 54 947241.114 102.098 + 7 31 24 55 Cr -55109.710 0.399 8731.924 0.007 B- 2602.703 0.368 54 940837.289 0.428 + 5 30 25 55 Mn -57712.413 0.303 8765.022 0.006 B- -231.114 0.179 54 938043.172 0.325 + 3 29 26 55 Fe -57481.300 0.342 8746.595 0.006 B- -3451.417 0.324 54 938291.283 0.367 + 1 28 27 55 Co -54029.883 0.428 8669.618 0.008 B- -8694.034 0.578 54 941996.531 0.459 + -1 27 28 55 Ni - -45335.849 0.719 8497.320 0.013 B- -13700.449 155.561 54 951329.961 0.771 + -3 26 29 55 Cu x -31635.399 155.559 8233.996 2.828 B- -17065# 429# 54 966038.000 167.000 + -5 25 30 55 Zn x -14570# 400# 7909# 7# B- * 54 984358# 429# +0 18 37 19 56 K x 7927# 801# 7664# 14# B- 21825# 895# 56 008510# 860# + 16 36 20 56 Ca x -13898# 400# 8040# 7# B- 10954# 710# 55 985080# 429# + 14 35 21 56 Sc x -24852.260 586.841 8221.728 10.479 B- 14467.788 599.236 55 973320.000 630.000 + 12 34 22 56 Ti -39320.048 121.247 8466.110 2.165 B- 6834.833 194.550 55 957788.190 130.164 + 10 33 23 56 V -46154.881 176.898 8574.191 3.159 B- 9130.120 176.899 55 950450.694 189.907 + 8 32 24 56 Cr ++ -55285.001 0.603 8723.258 0.011 B- 1626.538 0.561 55 940649.107 0.647 + 6 31 25 56 Mn -n -56911.538 0.331 8738.333 0.006 B- 3695.544 0.207 55 938902.947 0.355 + 4 30 26 56 Fe -60607.082 0.302 8790.354 0.005 B- -4566.680 0.411 55 934935.617 0.324 + 2 29 27 56 Co -56040.402 0.493 8694.836 0.009 B- -2132.863 0.374 55 939838.150 0.529 + 0 28 28 56 Ni -53907.539 0.422 8642.779 0.008 B- -15264.511 14.910 55 942127.872 0.452 + -2 27 29 56 Cu x -38643.029 14.904 8356.227 0.266 B- -13253# 400# 55 958515.000 16.000 + -4 26 30 56 Zn x -25390# 400# 8106# 7# B- -22000# 640# 55 972743# 429# + -6 25 31 56 Ga x -3390# 500# 7699# 9# B- * 55 996361# 537# +0 17 37 20 57 Ca x -6874# 400# 7917# 7# B- 14121# 1364# 56 992620# 429# + 15 36 21 57 Sc x -20995.875 1304.092 8151.433 22.879 B- 12919.758 1329.062 56 977460.000 1400.000 + 13 35 22 57 Ti x -33915.633 256.417 8364.370 4.499 B- 10497.818 268.750 56 963590.068 275.274 + 11 34 23 57 V x -44413.450 80.479 8534.817 1.412 B- 8111.252 80.486 56 952320.197 86.397 + 9 33 24 57 Cr x -52524.702 1.068 8663.394 0.019 B- 4961.548 1.846 56 943612.409 1.146 + 7 32 25 57 Mn -57486.251 1.505 8736.713 0.026 B- 2695.589 1.526 56 938285.968 1.615 + 5 31 26 57 Fe -60181.839 0.304 8770.279 0.005 B- -836.276 0.451 56 935392.134 0.326 + 3 30 27 57 Co -59345.564 0.533 8741.882 0.009 B- -3261.731 0.642 56 936289.913 0.572 + 1 29 28 57 Ni -56083.833 0.582 8670.933 0.010 B- -8774.947 0.439 56 939791.525 0.624 + -1 28 29 57 Cu -47308.886 0.519 8503.262 0.009 B- -14759# 200# 56 949211.819 0.557 + -3 27 30 57 Zn x -32550# 200# 8231# 4# B- -17540# 447# 56 965056# 215# + -5 26 31 57 Ga x -15010# 400# 7909# 7# B- * 56 983886# 429# +0 18 38 20 58 Ca x -1919# 500# 7835# 9# B- 12957# 640# 57 997940# 537# + 16 37 21 58 Sc x -14876# 400# 8045# 7# B- 16234# 447# 57 984030# 429# + 14 36 22 58 Ti x -31110# 200# 8311# 3# B- 9292# 219# 57 966602# 215# + 12 35 23 58 V x -40401.753 89.374 8457.658 1.541 B- 11590.049 89.386 57 956626.932 95.947 + 10 34 24 58 Cr x -51991.801 1.490 8643.998 0.026 B- 3835.759 3.085 57 944184.502 1.600 + 8 33 25 58 Mn x -55827.560 2.701 8696.643 0.047 B- 6327.553 2.723 57 940066.646 2.900 + 6 32 26 58 Fe -62155.113 0.343 8792.250 0.006 B- -2307.955 1.139 57 933273.738 0.368 + 4 31 27 58 Co -59847.158 1.160 8738.969 0.020 B- 381.586 1.107 57 935751.429 1.245 + 2 30 28 58 Ni -60228.744 0.373 8732.059 0.006 B- -8561.019 0.443 57 935341.780 0.400 + 0 29 29 58 Cu -51667.725 0.578 8570.967 0.010 B- -9368.981 50.002 57 944532.413 0.621 + -2 28 30 58 Zn -- -42298.744 50.001 8395.944 0.862 B- -18759# 304# 57 954590.428 53.678 + -4 27 31 58 Ga x -23540# 300# 8059# 5# B- -16459# 583# 57 974729# 322# + -6 26 32 58 Ge x -7080# 500# 7762# 9# B- * 57 992399# 537# +0 17 38 21 59 Sc x -10302# 400# 7967# 7# B- 15208# 447# 58 988940# 429# + 15 37 22 59 Ti x -25510# 200# 8212# 3# B- 12322# 258# 58 972614# 215# + 13 36 23 59 V x -37832.015 161.874 8407.555 2.744 B- 10253.745 270.218 58 959385.659 173.778 + 11 35 24 59 Cr x -48085.760 216.367 8568.087 3.667 B- 7439.560 216.380 58 948377.810 232.279 + 9 34 25 59 Mn x -55525.320 2.329 8680.921 0.039 B- 5139.485 2.356 58 940391.113 2.500 + 7 33 26 59 Fe -60664.805 0.355 8754.771 0.006 B- 1564.903 0.369 58 934873.649 0.380 + 5 32 27 59 Co -62229.709 0.418 8768.035 0.007 B- -1073.002 0.194 58 933193.656 0.448 + 3 31 28 59 Ni -61156.707 0.374 8736.588 0.006 B- -4798.380 0.397 58 934345.571 0.402 + 1 30 29 59 Cu -56358.327 0.544 8642.000 0.009 B- -9142.775 0.602 58 939496.844 0.584 + -1 29 30 59 Zn -47215.551 0.771 8473.777 0.013 B- -13455# 170# 58 949312.017 0.827 + -3 28 31 59 Ga x -33760# 170# 8232# 3# B- -17890# 434# 58 963757# 183# + -5 27 32 59 Ge x -15870# 400# 7916# 7# B- * 58 982963# 429# +0 18 39 21 60 Sc x -4052# 500# 7865# 8# B- 18278# 583# 59 995650# 537# + 16 38 22 60 Ti x -22330# 300# 8157# 5# B- 10912# 372# 59 976028# 322# + 14 37 23 60 V x -33241.956 220.159 8325.450 3.669 B- 13427.621 293.169 59 964313.290 236.350 + 12 36 24 60 Cr x -46669.576 193.593 8536.205 3.227 B- 6298.361 193.607 59 949898.146 207.830 + 10 35 25 60 Mn x -52967.938 2.329 8628.138 0.039 B- 8445.079 4.128 59 943136.576 2.500 + 8 34 26 60 Fe -nn -61413.017 3.409 8755.851 0.057 B- 237.293 3.411 59 934070.411 3.659 + 6 33 27 60 Co -n -61650.309 0.424 8746.766 0.007 B- 2822.809 0.212 59 933815.667 0.455 + 4 32 28 60 Ni -64473.118 0.376 8780.774 0.006 B- -6127.982 1.573 59 930785.256 0.403 + 2 31 29 60 Cu - -58345.137 1.618 8665.602 0.027 B- -4170.797 1.629 59 937363.916 1.736 + 0 30 30 60 Zn -54174.340 0.564 8583.050 0.009 B- -14584# 200# 59 941841.450 0.605 + -2 29 31 60 Ga x -39590# 200# 8327# 3# B- -12501# 361# 59 957498# 215# + -4 28 32 60 Ge x -27090# 300# 8106# 5# B- -21620# 500# 59 970918# 322# + -6 27 33 60 As x -5470# 400# 7732# 7# B- * 59 994128# 429# +0 19 40 21 61 Sc x 931# 600# 7787# 10# B- 17281# 721# 61 001000# 644# + 17 39 22 61 Ti x -16350# 400# 8057# 7# B- 14157# 979# 60 982448# 429# + 15 38 23 61 V x -30506.429 894.234 8276.439 14.660 B- 11968.800 899.958 60 967250.000 960.000 + 13 37 24 61 Cr x -42475.229 101.341 8459.824 1.661 B- 9266.893 101.367 60 954400.963 108.793 + 11 36 25 61 Mn x -51742.122 2.329 8598.915 0.038 B- 7178.372 3.497 60 944452.544 2.500 + 9 35 26 61 Fe x -58920.494 2.608 8703.768 0.043 B- 3977.572 2.742 60 936746.244 2.800 + 7 34 27 61 Co p2n -62898.066 0.846 8756.148 0.014 B- 1323.839 0.790 60 932476.145 0.908 + 5 33 28 61 Ni -64221.905 0.378 8765.025 0.006 B- -2237.845 0.966 60 931054.945 0.405 + 3 32 29 61 Cu p2n -61984.059 0.953 8715.514 0.016 B- -5635.156 15.903 60 933457.371 1.023 + 1 31 30 61 Zn -56348.903 15.899 8610.309 0.261 B- -9214.245 37.679 60 939506.960 17.068 + -1 30 31 61 Ga -47134.659 37.994 8446.431 0.623 B- -13775# 302# 60 949398.859 40.787 + -3 29 32 61 Ge x -33360# 300# 8208# 5# B- -16459# 424# 60 964187# 322# + -5 28 33 61 As x -16900# 300# 7925# 5# B- * 60 981857# 322# +0 18 40 22 62 Ti x -12500# 400# 7995# 6# B- 12977# 499# 61 986581# 429# + 16 39 23 62 V x -25476# 298# 8192# 5# B- 15419# 333# 61 972650# 320# + 14 38 24 62 Cr x -40894.961 148.099 8428.069 2.389 B- 7628.996 148.244 61 956097.451 158.991 + 12 37 25 62 Mn IT -48523.957 6.542 8538.499 0.106 B- 10354.091 7.114 61 947907.386 7.023 + 10 36 26 62 Fe x -58878.048 2.794 8692.882 0.045 B- 2546.235 18.784 61 936791.812 3.000 + 8 35 27 62 Co + -61424.282 18.575 8721.332 0.300 B- 5322.040 18.570 61 934058.317 19.940 + 6 34 28 62 Ni -66746.323 0.439 8794.553 0.007 B- -3958.896 0.475 61 928344.871 0.470 + 4 33 29 62 Cu - -62787.426 0.647 8718.081 0.010 B- -1619.455 0.651 61 932594.921 0.694 + 2 32 30 62 Zn -61167.972 0.625 8679.343 0.010 B- -9181.066 0.376 61 934333.477 0.670 + 0 31 31 62 Ga -51986.906 0.647 8518.642 0.010 B- -10247# 140# 61 944189.757 0.694 + -2 30 32 62 Ge x -41740# 140# 8341# 2# B- -17420# 331# 61 955190# 150# + -4 29 33 62 As x -24320# 300# 8047# 5# B- * 61 973891# 322# +0 19 41 22 63 Ti x -5750# 500# 7889# 8# B- 16140# 640# 62 993827# 537# + 17 40 23 63 V x -21890# 400# 8133# 6# B- 14117# 537# 62 976500# 429# + 15 39 24 63 Cr x -36007.474 358.073 8344.828 5.684 B- 10879.579 358.092 62 961344.384 384.407 + 13 38 25 63 Mn x -46887.053 3.726 8505.101 0.059 B- 8748.568 5.692 62 949664.675 4.000 + 11 37 26 63 Fe -55635.621 4.302 8631.549 0.068 B- 6215.819 19.067 62 940272.700 4.618 + 9 36 27 63 Co -61851.440 18.575 8717.795 0.295 B- 3661.335 18.570 62 933599.744 19.941 + 7 35 28 63 Ni -65512.775 0.440 8763.493 0.007 B- 66.977 0.015 62 929669.139 0.472 + 5 34 29 63 Cu -65579.752 0.440 8752.138 0.007 B- -3366.355 1.546 62 929597.236 0.472 + 3 33 30 63 Zn -62213.397 1.561 8686.285 0.025 B- -5666.304 2.034 62 933211.167 1.676 + 1 32 31 63 Ga x -56547.093 1.304 8583.926 0.021 B- -9625.877 37.283 62 939294.195 1.400 + -1 31 32 63 Ge x -46921.216 37.260 8418.716 0.591 B- -13421# 204# 62 949628.000 40.000 + -3 30 33 63 As x -33500# 200# 8193# 3# B- * 62 964036# 215# +0 20 42 22 64 Ti x -1025# 600# 7818# 9# B- 15295# 721# 63 998900# 644# + 18 41 23 64 V x -16320# 400# 8045# 6# B- 17160# 594# 63 982480# 429# + 16 40 24 64 Cr x -33479.757 439.665 8301.058 6.870 B- 9509.277 439.679 63 964058.000 472.000 + 14 39 25 64 Mn x -42989.035 3.540 8437.417 0.055 B- 11980.510 6.140 63 953849.370 3.800 + 12 38 26 64 Fe x -54969.544 5.017 8612.388 0.078 B- 4822.785 20.625 63 940987.763 5.386 + 10 37 27 64 Co + -59792.329 20.006 8675.520 0.313 B- 7306.592 20.000 63 935810.291 21.476 + 8 36 28 64 Ni -67098.921 0.475 8777.461 0.007 B- -1674.376 0.225 63 927966.341 0.510 + 6 35 29 64 Cu -65424.545 0.448 8739.075 0.007 B- 579.469 0.650 63 929763.857 0.481 + 4 34 30 64 Zn -66004.014 0.647 8735.905 0.010 B- -7171.194 1.483 63 929141.772 0.694 + 2 33 31 64 Ga -58832.821 1.429 8611.631 0.022 B- -4517.325 3.991 63 936840.365 1.533 + 0 32 32 64 Ge x -54315.496 3.726 8528.823 0.058 B- -14783# 203# 63 941689.913 4.000 + -2 31 33 64 As -p -39532# 203# 8286# 3# B- -12832# 543# 63 957560# 218# + -4 30 34 64 Se x -26700# 503# 8073# 8# B- * 63 971336# 540# +0 19 42 23 65 V x -11780# 500# 7976# 8# B- 16440# 583# 64 987354# 537# + 17 41 24 65 Cr x -28220# 300# 8217# 5# B- 12748# 300# 64 969705# 322# + 15 40 25 65 Mn x -40967.339 3.726 8400.681 0.057 B- 10250.557 6.326 64 956019.750 4.000 + 13 39 26 65 Fe x -51217.895 5.112 8546.346 0.079 B- 7967.303 5.520 64 945015.324 5.487 + 11 38 27 65 Co x -59185.198 2.083 8656.884 0.032 B- 5940.487 2.141 64 936462.073 2.235 + 9 37 28 65 Ni -n -65125.685 0.495 8736.240 0.008 B- 2137.975 0.706 64 930084.697 0.531 + 7 36 29 65 Cu -67263.660 0.650 8757.096 0.010 B- -1351.640 0.360 64 927789.487 0.697 + 5 35 30 65 Zn -65912.019 0.650 8724.265 0.010 B- -3254.513 0.662 64 929240.532 0.697 + 3 34 31 65 Ga -62657.507 0.815 8662.160 0.013 B- -6179.291 2.313 64 932734.395 0.874 + 1 33 32 65 Ge -56478.216 2.165 8555.058 0.033 B- -9541.165 84.794 64 939368.137 2.323 + -1 32 33 65 As x -46937.051 84.766 8396.234 1.304 B- -13917# 312# 64 949611.000 91.000 + -3 31 34 65 Se x -33020# 300# 8170# 5# B- * 64 964552# 322# +0 20 43 23 66 V x -5610# 500# 7884# 8# B- 19110# 640# 65 993977# 537# + 18 42 24 66 Cr x -24720# 400# 8161# 6# B- 12030# 400# 65 973462# 429# + 16 41 25 66 Mn x -36750.387 11.178 8331.798 0.169 B- 13317.452 11.906 65 960546.834 12.000 + 14 40 26 66 Fe x -50067.839 4.099 8521.724 0.062 B- 6340.694 14.561 65 946249.960 4.400 + 12 39 27 66 Co x -56408.533 13.972 8605.941 0.212 B- 9597.752 14.042 65 939442.945 15.000 + 10 38 28 66 Ni x -66006.285 1.397 8739.508 0.021 B- 251.987 1.543 65 929139.334 1.500 + 8 37 29 66 Cu -66258.272 0.655 8731.472 0.010 B- 2640.888 0.931 65 928868.814 0.703 + 6 36 30 66 Zn -68899.160 0.749 8759.632 0.011 B- -5175.500 0.800 65 926033.704 0.804 + 4 35 31 66 Ga - -63723.660 1.096 8669.361 0.017 B- -2116.628 2.639 65 931589.832 1.176 + 2 34 32 66 Ge x -61607.032 2.401 8625.437 0.036 B- -9581.955 6.168 65 933862.126 2.577 + 0 33 33 66 As x -52025.077 5.682 8468.403 0.086 B- -10365# 200# 65 944148.779 6.100 + -2 32 34 66 Se x -41660# 200# 8300# 3# B- * 65 955276# 215# +0 21 44 23 67 V x -650# 600# 7812# 9# B- 18030# 721# 66 999302# 644# + 19 43 24 67 Cr x -18680# 400# 8070# 6# B- 14780# 500# 66 979946# 429# + 17 42 25 67 Mn x -33460# 300# 8279# 4# B- 12150# 404# 66 964079# 322# + 15 41 26 67 Fe x -45610.155 270.285 8448.469 4.034 B- 9711.620 270.362 66 951035.482 290.163 + 13 40 27 67 Co x -55321.775 6.443 8581.741 0.096 B- 8420.905 7.061 66 940609.628 6.917 + 11 39 28 67 Ni x -63742.680 2.888 8695.750 0.043 B- 3576.832 3.023 66 931569.414 3.100 + 9 38 29 67 Cu -67319.513 0.894 8737.458 0.013 B- 560.800 0.830 66 927729.526 0.959 + 7 37 30 67 Zn -67880.313 0.760 8734.152 0.011 B- -1001.265 1.122 66 927127.482 0.815 + 5 36 31 67 Ga -66879.048 1.181 8707.531 0.018 B- -4220.819 4.799 66 928202.384 1.268 + 3 35 32 67 Ge -n2p -62658.230 4.661 8632.857 0.070 B- -6071.005 4.682 66 932733.620 5.003 + 1 34 33 67 As -56587.225 0.443 8530.568 0.007 B- -10006.936 67.069 66 939251.111 0.475 + -1 33 34 67 Se x -46580.289 67.068 8369.534 1.001 B- -13790# 405# 66 949994.000 72.000 + -3 32 35 67 Br x -32790# 400# 8152# 6# B- * 66 964798# 429# +0 20 44 24 68 Cr x -14800# 500# 8013# 7# B- 13580# 640# 67 984112# 537# + 18 43 25 68 Mn x -28380# 400# 8201# 6# B- 15107# 541# 67 969533# 429# + 16 42 26 68 Fe x -43486.914 365.259 8411.698 5.371 B- 8443.751 411.489 67 953314.875 392.121 + 14 41 27 68 Co x -51930.665 189.497 8524.366 2.787 B- 11533.150 189.520 67 944250.135 203.433 + 12 40 28 68 Ni x -63463.814 2.981 8682.466 0.044 B- 2103.220 3.375 67 931868.789 3.200 + 10 39 29 68 Cu x -65567.035 1.584 8701.890 0.023 B- 4440.057 1.767 67 929610.889 1.700 + 8 38 30 68 Zn -70007.092 0.784 8755.680 0.012 B- -2921.100 1.200 67 924844.291 0.841 + 6 37 31 68 Ga - -67085.992 1.433 8701.218 0.021 B- -107.203 2.361 67 927980.221 1.538 + 4 36 32 68 Ge x -66978.789 1.876 8688.136 0.028 B- -8084.270 2.632 67 928095.308 2.014 + 2 35 33 68 As -58894.519 1.846 8557.745 0.027 B- -4705.078 1.911 67 936774.130 1.981 + 0 34 34 68 Se x -54189.441 0.496 8477.047 0.007 B- -15398# 259# 67 941825.239 0.532 + -2 33 35 68 Br -p -38791# 259# 8239# 4# B- * 67 958356# 278# +0 21 45 24 69 Cr x -8580# 500# 7924# 7# B- 16190# 640# 68 990789# 537# + 19 44 25 69 Mn x -24770# 400# 8147# 6# B- 14259# 565# 68 973408# 429# + 17 43 26 69 Fe x -39030# 400# 8342# 6# B- 11250# 424# 68 958100# 429# + 15 42 27 69 Co x -50279.157 140.506 8493.865 2.036 B- 9699.492 140.556 68 946023.102 150.839 + 13 41 28 69 Ni x -59978.648 3.726 8623.099 0.054 B- 5757.564 3.979 68 935610.268 4.000 + 11 40 29 69 Cu x -65736.213 1.397 8695.204 0.020 B- 2681.632 1.610 68 929429.268 1.500 + 9 39 30 69 Zn -n -68417.845 0.800 8722.729 0.012 B- 909.964 1.426 68 926550.418 0.858 + 7 38 31 69 Ga -69327.809 1.197 8724.579 0.017 B- -2227.146 0.550 68 925573.531 1.285 + 5 37 32 69 Ge -67100.663 1.318 8680.963 0.019 B- -3988.492 31.982 68 927964.471 1.414 + 3 36 33 69 As -63112.171 31.999 8611.821 0.464 B- -6677.465 32.021 68 932246.294 34.352 + 1 35 34 69 Se -56434.706 1.490 8503.707 0.022 B- -10175.236 42.029 68 939414.847 1.599 + -1 34 35 69 Br -p -46259.470 42.003 8344.902 0.609 B- -13825# 403# 68 950338.413 45.092 + -3 33 36 69 Kr x -32435# 401# 8133# 6# B- * 68 965180# 430# +0 22 46 24 70 Cr x -4480# 600# 7867# 9# B- 15020# 781# 69 995191# 644# + 20 45 25 70 Mn x -19500# 500# 8070# 7# B- 17010# 640# 69 979066# 537# + 18 44 26 70 Fe x -36510# 400# 8302# 6# B- 10120# 500# 69 960805# 429# + 16 43 27 70 Co x -46630# 300# 8436# 4# B- 12584# 300# 69 949941# 322# + 14 42 28 70 Ni x -59213.860 2.144 8604.291 0.031 B- 3762.513 2.401 69 936431.303 2.301 + 12 41 29 70 Cu x -62976.373 1.082 8646.865 0.015 B- 6588.362 2.202 69 932392.079 1.161 + 10 40 30 70 Zn -69564.735 1.918 8729.808 0.027 B- -654.595 1.574 69 925319.181 2.058 + 8 39 31 70 Ga -68910.140 1.201 8709.280 0.017 B- 1651.736 1.462 69 926021.917 1.289 + 6 38 32 70 Ge -70561.876 0.838 8721.700 0.012 B- -6220.000 50.000 69 924248.706 0.900 + 4 37 33 70 As - -64341.876 50.007 8621.666 0.714 B- -2411.985 50.032 69 930926.151 53.684 + 2 36 34 70 Se x -61929.891 1.584 8576.033 0.023 B- -10504.272 14.988 69 933515.523 1.700 + 0 35 35 70 Br x -51425.619 14.904 8414.796 0.213 B- -10325# 201# 69 944792.323 16.000 + -2 34 36 70 Kr x -41100# 200# 8256# 3# B- * 69 955877# 215# +0 21 46 25 71 Mn x -15570# 500# 8015# 7# B- 15860# 640# 70 983285# 537# + 19 45 26 71 Fe x -31430# 400# 8227# 6# B- 12940# 613# 70 966259# 429# + 17 44 27 71 Co x -44369.926 465.030 8398.734 6.550 B- 11036.302 465.035 70 952366.923 499.230 + 15 43 28 71 Ni x -55406.228 2.237 8543.156 0.032 B- 7304.899 2.688 70 940518.964 2.401 + 13 42 29 71 Cu x -62711.127 1.490 8635.022 0.021 B- 4617.651 3.044 70 932676.832 1.600 + 11 41 30 71 Zn -67328.777 2.654 8689.041 0.037 B- 2810.358 2.775 70 927719.580 2.849 + 9 40 31 71 Ga -70139.135 0.812 8717.604 0.011 B- -232.638 0.223 70 924702.536 0.871 + 7 39 32 71 Ge -69906.497 0.834 8703.309 0.012 B- -2013.400 4.082 70 924952.284 0.894 + 5 38 33 71 As - -67893.097 4.167 8663.932 0.059 B- -4746.590 5.017 70 927113.758 4.473 + 3 37 34 71 Se x -63146.507 2.794 8586.060 0.039 B- -6644.089 6.082 70 932209.432 3.000 + 1 36 35 71 Br -56502.418 5.402 8481.462 0.076 B- -10175.212 128.845 70 939342.156 5.799 + -1 35 36 71 Kr -46327.205 128.769 8327.130 1.814 B- -14267# 420# 70 950265.696 138.238 + -3 34 37 71 Rb x -32060# 400# 8115# 6# B- * 70 965582# 429# +0 22 47 25 72 Mn x -9900# 600# 7937# 8# B- 18530# 781# 71 989372# 644# + 20 46 26 72 Fe x -28430# 500# 8184# 7# B- 11769# 640# 71 969479# 537# + 18 45 27 72 Co x -40200# 400# 8336# 6# B- 14027# 400# 71 956844# 429# + 16 44 28 72 Ni x -54226.060 2.237 8520.211 0.031 B- 5556.938 2.637 71 941785.926 2.401 + 14 43 29 72 Cu x -59782.999 1.397 8586.525 0.019 B- 8362.487 2.558 71 935820.307 1.500 + 12 42 30 72 Zn x -68145.486 2.142 8691.805 0.030 B- 442.807 2.294 71 926842.807 2.300 + 10 41 31 72 Ga -68588.293 0.819 8687.089 0.011 B- 3997.607 0.822 71 926367.434 0.878 + 8 40 32 72 Ge -72585.900 0.076 8731.745 0.001 B- -4356.102 4.082 71 922075.826 0.081 + 6 39 33 72 As - -68229.798 4.083 8660.378 0.057 B- -361.618 4.528 71 926752.295 4.383 + 4 38 34 72 Se x -67868.180 1.956 8644.489 0.027 B- -8806.437 2.208 71 927140.507 2.100 + 2 37 35 72 Br x -59061.743 1.025 8511.312 0.014 B- -5121.168 8.076 71 936594.607 1.100 + 0 36 36 72 Kr x -53940.575 8.011 8429.319 0.111 B- -15611# 500# 71 942092.407 8.600 + -2 35 37 72 Rb x -38330# 500# 8202# 7# B- * 71 958851# 537# +0 21 47 26 73 Fe x -22900# 500# 8106# 7# B- 14518# 640# 72 975416# 537# + 19 46 27 73 Co x -37418# 400# 8295# 5# B- 12690# 400# 72 959830# 429# + 17 45 28 73 Ni x -50108.152 2.423 8457.652 0.033 B- 8879.285 3.104 72 946206.683 2.601 + 15 44 29 73 Cu -58987.437 1.942 8568.569 0.027 B- 6605.966 2.691 72 936674.378 2.084 + 13 43 30 73 Zn x -65593.402 1.863 8648.345 0.026 B- 4105.932 2.506 72 929582.582 2.000 + 11 42 31 73 Ga x -69699.335 1.677 8693.873 0.023 B- 1598.188 1.678 72 925174.682 1.800 + 9 41 32 73 Ge -71297.523 0.057 8705.049 0.001 B- -344.776 3.853 72 923458.956 0.061 + 7 40 33 73 As -70952.747 3.853 8689.609 0.053 B- -2725.360 7.399 72 923829.089 4.136 + 5 39 34 73 Se -68227.387 7.424 8641.558 0.102 B- -4579.912 10.388 72 926754.883 7.969 + 3 38 35 73 Br x -63647.475 7.266 8568.103 0.100 B- -7095.725 9.801 72 931671.621 7.800 + 1 37 36 73 Kr x -56551.751 6.578 8460.184 0.090 B- -10470# 200# 72 939289.195 7.061 + -1 36 37 73 Rb -p -46082# 200# 8306# 3# B- -14131# 448# 72 950529# 215# + -3 35 38 73 Sr x -31950# 401# 8102# 5# B- * 72 965700# 430# +0 22 48 26 74 Fe x -19590# 600# 8061# 8# B- 13230# 781# 73 978969# 644# + 20 47 27 74 Co x -32820# 500# 8229# 7# B- 15636# 537# 73 964766# 537# + 18 46 28 74 Ni x -48456# 196# 8430# 3# B- 7550# 196# 73 947980# 210# + 16 45 29 74 Cu x -56006.205 6.148 8521.562 0.083 B- 9750.507 6.642 73 939874.862 6.600 + 14 44 30 74 Zn x -65756.712 2.515 8642.754 0.034 B- 2292.905 3.910 73 929407.262 2.700 + 12 43 31 74 Ga x -68049.617 2.994 8663.167 0.040 B- 5372.824 2.994 73 926945.726 3.214 + 10 42 32 74 Ge -73422.442 0.013 8725.200 0.000 B- -2562.387 1.693 73 921177.762 0.013 + 8 41 33 74 As -70860.054 1.693 8680.001 0.023 B- 1353.147 1.693 73 923928.598 1.817 + 6 40 34 74 Se -72213.201 0.015 8687.715 0.000 B- -6925.049 5.835 73 922475.935 0.015 + 4 39 35 74 Br -65288.153 5.835 8583.561 0.079 B- -2956.317 6.173 73 929910.281 6.264 + 2 38 36 74 Kr -62331.836 2.013 8533.038 0.027 B- -10415.827 3.424 73 933084.017 2.161 + 0 37 37 74 Rb -51916.009 3.027 8381.712 0.041 B- -11089# 100# 73 944265.868 3.249 + -2 36 38 74 Sr x -40827# 100# 8221# 1# B- * 73 956170# 107# +0 23 49 26 75 Fe x -13640# 600# 7982# 8# B- 16010# 781# 74 985357# 644# + 21 48 27 75 Co x -29649# 500# 8185# 7# B- 14380# 583# 74 968170# 537# + 19 47 28 75 Ni x -44030# 300# 8366# 4# B- 10441# 300# 74 952732# 322# + 17 46 29 75 Cu x -54471.341 2.330 8495.094 0.031 B- 8087.567 3.042 74 941522.606 2.501 + 15 45 30 75 Zn x -62558.908 1.956 8592.497 0.026 B- 5905.672 3.113 74 932840.246 2.100 + 13 44 31 75 Ga x -68464.580 2.422 8660.808 0.032 B- 3392.384 2.422 74 926500.246 2.600 + 11 43 32 75 Ge -n -71856.965 0.052 8695.609 0.001 B- 1177.231 0.885 74 922858.371 0.055 + 9 42 33 75 As -73034.195 0.884 8700.874 0.012 B- -864.714 0.882 74 921594.562 0.948 + 7 41 34 75 Se -72169.481 0.073 8678.913 0.001 B- -3062.472 4.285 74 922522.871 0.078 + 5 40 35 75 Br x -69107.009 4.285 8627.649 0.057 B- -4783.385 9.167 74 925810.570 4.600 + 3 39 36 75 Kr x -64323.624 8.104 8553.439 0.108 B- -7104.929 8.189 74 930945.746 8.700 + 1 38 37 75 Rb x -57218.694 1.180 8448.275 0.016 B- -10600.000 220.000 74 938573.201 1.266 + -1 37 38 75 Sr - -46618.694 220.003 8296.511 2.933 B- -14799# 372# 74 949952.770 236.183 + -3 36 39 75 Y x -31820# 300# 8089# 4# B- * 74 965840# 322# +0 22 49 27 76 Co x -24510# 600# 8116# 8# B- 17120# 721# 75 973687# 644# + 20 48 28 76 Ni x -41630# 400# 8331# 5# B- 9346# 400# 75 955308# 429# + 18 47 29 76 Cu x -50975.985 6.707 8443.527 0.088 B- 11327.031 6.863 75 945275.025 7.200 + 16 46 30 76 Zn -62303.016 1.456 8582.273 0.019 B- 3993.624 2.438 75 933114.957 1.562 + 14 45 31 76 Ga x -66296.640 1.956 8624.526 0.026 B- 6916.249 1.956 75 928827.625 2.100 + 12 44 32 76 Ge -73212.889 0.018 8705.236 0.000 B- -921.512 0.886 75 921402.726 0.019 + 10 43 33 76 As -n -72291.377 0.886 8682.816 0.012 B- 2960.573 0.886 75 922392.010 0.951 + 8 42 34 76 Se -75251.950 0.016 8711.477 0.000 B- -4962.881 9.322 75 919213.704 0.017 + 6 41 35 76 Br - -70289.068 9.322 8635.882 0.123 B- -1275.355 10.149 75 924541.577 10.007 + 4 40 36 76 Kr -69013.714 4.013 8608.807 0.053 B- -8534.633 4.121 75 925910.726 4.308 + 2 39 37 76 Rb x -60479.081 0.938 8486.215 0.012 B- -6231.442 34.478 75 935073.032 1.006 + 0 38 38 76 Sr x -54247.639 34.465 8393.929 0.453 B- -15768# 302# 75 941762.761 37.000 + -2 37 39 76 Y x -38480# 300# 8176# 4# B- * 75 958690# 322# +0 23 50 27 77 Co x -21015# 600# 8070# 8# B- 15785# 781# 76 977440# 644# + 21 49 28 77 Ni x -36800# 500# 8265# 6# B- 11824# 522# 76 960494# 537# + 19 48 29 77 Cu x -48624# 149# 8408# 2# B- 10165# 149# 76 947800# 160# + 17 47 30 77 Zn -58789.195 1.973 8530.003 0.026 B- 7203.149 3.124 76 936887.199 2.117 + 15 46 31 77 Ga x -65992.344 2.422 8613.390 0.031 B- 5220.518 2.422 76 929154.300 2.600 + 13 45 32 77 Ge -n -71212.862 0.053 8671.028 0.001 B- 2703.456 1.694 76 923549.844 0.056 + 11 44 33 77 As -73916.318 1.693 8695.978 0.022 B- 683.170 1.693 76 920647.564 1.817 + 9 43 34 77 Se -74599.488 0.062 8694.690 0.001 B- -1364.680 2.810 76 919914.150 0.067 + 7 42 35 77 Br - -73234.809 2.811 8666.806 0.037 B- -3065.366 3.424 76 921379.194 3.017 + 5 41 36 77 Kr x -70169.443 1.956 8616.836 0.025 B- -5338.951 2.351 76 924670.000 2.100 + 3 40 37 77 Rb x -64830.492 1.304 8537.339 0.017 B- -7027.055 8.024 76 930401.600 1.400 + 1 39 38 77 Sr x -57803.436 7.918 8435.918 0.103 B- -11365# 203# 76 937945.455 8.500 + -1 38 39 77 Y -p -46439# 203# 8278# 3# B- -14399# 448# 76 950146# 218# + -3 37 40 77 Zr x -32040# 400# 8081# 5# B- * 76 965604# 429# +0 22 50 28 78 Ni x -33890# 600# 8225# 8# B- 10608# 783# 77 963618# 644# + 20 49 29 78 Cu x -44497.469 503.007 8350.925 6.449 B- 12985.766 503.011 77 952230.000 540.000 + 18 48 30 78 Zn -57483.235 1.944 8507.379 0.025 B- 6222.716 2.719 77 938289.205 2.086 + 16 47 31 78 Ga -63705.950 1.903 8577.127 0.024 B- 8156.099 4.015 77 931608.845 2.043 + 14 46 32 78 Ge -nn -71862.050 3.536 8671.663 0.045 B- 954.890 10.400 77 922852.912 3.795 + 12 45 33 78 As +pn -72816.940 9.781 8673.875 0.125 B- 4209.004 9.782 77 921827.795 10.500 + 10 44 34 78 Se -77025.944 0.179 8717.806 0.002 B- -3573.784 3.575 77 917309.243 0.191 + 8 43 35 78 Br - -73452.160 3.580 8661.959 0.046 B- 726.116 3.584 77 921145.859 3.842 + 6 42 36 78 Kr -74178.275 0.307 8661.238 0.004 B- -7242.857 3.252 77 920366.341 0.329 + 4 41 37 78 Rb x -66935.419 3.237 8558.350 0.042 B- -3761.477 8.125 77 928141.868 3.475 + 2 40 38 78 Sr x -63173.941 7.452 8500.096 0.096 B- -11001# 298# 77 932179.980 8.000 + 0 39 39 78 Y x -52173# 298# 8349# 4# B- -11323# 499# 77 943990# 320# + -2 38 40 78 Zr x -40850# 400# 8194# 5# B- * 77 956146# 429# +0 23 51 28 79 Ni x -27570# 600# 8143# 8# B- 14170# 671# 78 970402# 644# + 21 50 29 79 Cu x -41740# 300# 8312# 4# B- 11692# 300# 78 955190# 322# + 19 49 30 79 Zn -53432.295 2.225 8450.582 0.028 B- 9115.384 2.901 78 942638.068 2.388 + 17 48 31 79 Ga -62547.679 1.868 8556.063 0.024 B- 6978.913 37.147 78 932852.301 2.005 + 15 47 32 79 Ge -69526.592 37.181 8634.501 0.471 B- 4109.457 37.456 78 925360.129 39.915 + 13 46 33 79 As -73636.049 5.328 8676.616 0.067 B- 2281.410 5.331 78 920948.445 5.719 + 11 45 34 79 Se -n -75917.459 0.223 8695.592 0.003 B- 150.576 1.038 78 918499.251 0.238 + 9 44 35 79 Br +n -76068.035 1.021 8687.594 0.013 B- -1625.778 3.333 78 918337.601 1.095 + 7 43 36 79 Kr - -74442.257 3.486 8657.112 0.044 B- -3639.271 4.092 78 920082.945 3.742 + 5 42 37 79 Rb x -70802.985 2.142 8601.142 0.027 B- -5326.096 8.653 78 923989.864 2.300 + 3 41 38 79 Sr x -65476.889 8.383 8523.820 0.106 B- -7659.056 79.620 78 929707.664 9.000 + 1 40 39 79 Y x -57817.833 79.177 8416.967 1.002 B- -11048# 310# 78 937930.000 85.000 + -1 39 40 79 Zr x -46770# 300# 8267# 4# B- -15120# 583# 78 949790# 322# + -3 38 41 79 Nb x -31650# 500# 8066# 6# B- * 78 966022# 537# +0 24 52 28 80 Ni x -22630# 700# 8080# 9# B- 13570# 806# 79 975706# 751# + 22 51 29 80 Cu x -36200# 400# 8240# 5# B- 15449# 400# 79 961138# 429# + 20 50 30 80 Zn -51648.612 2.585 8423.545 0.032 B- 7575.055 3.877 79 944552.930 2.774 + 18 49 31 80 Ga x -59223.667 2.891 8508.454 0.036 B- 10311.639 3.541 79 936420.774 3.103 + 16 48 32 80 Ge x -69535.306 2.054 8627.570 0.026 B- 2679.187 3.915 79 925350.774 2.205 + 14 47 33 80 As x -72214.493 3.333 8651.280 0.042 B- 5544.964 3.445 79 922474.548 3.577 + 12 46 34 80 Se -77759.457 0.963 8710.813 0.012 B- -1870.464 0.310 79 916521.785 1.034 + 10 45 35 80 Br - -75888.993 1.012 8677.653 0.013 B- 2004.353 1.154 79 918529.810 1.086 + 8 44 36 80 Kr -77893.346 0.691 8692.928 0.009 B- -5717.879 1.987 79 916378.048 0.742 + 6 43 37 80 Rb x -72175.467 1.863 8611.675 0.023 B- -1864.009 3.933 79 922516.444 2.000 + 4 42 38 80 Sr x -70311.459 3.464 8578.596 0.043 B- -9163.307 7.139 79 924517.540 3.718 + 2 41 39 80 Y x -61148.152 6.242 8454.275 0.078 B- -6788# 300# 79 934354.755 6.701 + 0 40 40 80 Zr x -54360# 300# 8360# 4# B- -15940# 500# 79 941642# 322# + -2 39 41 80 Nb x -38420# 400# 8151# 5# B- * 79 958754# 429# +0 23 52 29 81 Cu x -31420# 500# 8179# 6# B- 14779# 500# 80 966269# 537# + 21 51 30 81 Zn x -46199.663 5.030 8351.925 0.062 B- 11428.292 5.996 80 950402.619 5.400 + 19 50 31 81 Ga x -57627.954 3.264 8483.357 0.040 B- 8663.733 3.851 80 938133.842 3.503 + 17 49 32 81 Ge x -66291.687 2.055 8580.658 0.025 B- 6241.617 3.344 80 928832.942 2.205 + 15 48 33 81 As -72533.304 2.644 8648.056 0.033 B- 3855.684 2.812 80 922132.290 2.838 + 13 47 34 81 Se -76388.988 0.992 8685.999 0.012 B- 1588.046 1.389 80 917993.044 1.065 + 11 46 35 81 Br -77977.034 0.978 8695.946 0.012 B- -280.853 0.471 80 916288.206 1.049 + 9 45 36 81 Kr -77696.181 1.074 8682.820 0.013 B- -2239.511 5.019 80 916589.714 1.152 + 7 44 37 81 Rb -75456.670 4.904 8645.513 0.061 B- -3928.545 5.817 80 918993.927 5.264 + 5 43 38 81 Sr x -71528.125 3.128 8587.354 0.039 B- -5815.214 6.245 80 923211.394 3.358 + 3 42 39 81 Y x -65712.912 5.405 8505.902 0.067 B- -8252.773 94.236 80 929454.283 5.802 + 1 41 40 81 Zr x -57460.139 94.081 8394.358 1.161 B- -11100# 411# 80 938314.000 101.000 + -1 40 41 81 Nb x -46360# 400# 8248# 5# B- -14610# 640# 80 950230# 429# + -3 39 42 81 Mo x -31750# 500# 8058# 6# B- * 80 965915# 537# +0 24 53 29 82 Cu x -25320# 600# 8103# 7# B- 16994# 600# 81 972818# 644# + 22 52 30 82 Zn x -42313.954 3.074 8301.117 0.037 B- 10616.764 3.916 81 954574.099 3.300 + 20 51 31 82 Ga x -52930.719 2.426 8421.049 0.030 B- 12484.348 3.296 81 943176.533 2.604 + 18 50 32 82 Ge x -65415.067 2.241 8563.756 0.027 B- 4690.352 4.345 81 929774.033 2.405 + 16 49 33 82 As x -70105.419 3.729 8611.414 0.045 B- 7488.463 3.758 81 924738.733 4.003 + 14 48 34 82 Se -77593.882 0.467 8693.196 0.006 B- -95.221 1.077 81 916699.537 0.500 + 12 47 35 82 Br -77498.661 0.971 8682.494 0.012 B- 3093.124 0.971 81 916801.760 1.042 + 10 46 36 82 Kr -80591.78515 0.00549 8710.675 0.000 B- -4403.982 3.009 81 913481.15520 0.00589 + 8 45 37 82 Rb IT -76187.803 3.009 8647.427 0.037 B- -177.751 6.705 81 918209.024 3.230 + 6 44 38 82 Sr -76010.053 5.992 8635.718 0.073 B- -7945.961 8.132 81 918399.847 6.432 + 4 43 39 82 Y x -68064.091 5.499 8529.275 0.067 B- -4432.804 12.457 81 926930.188 5.902 + 2 42 40 82 Zr x -63631.287 11.178 8465.676 0.136 B- -11541# 300# 81 931689.000 12.000 + 0 41 41 82 Nb x -52090# 300# 8315# 4# B- -11720# 500# 81 944079# 322# + -2 40 42 82 Mo x -40370# 400# 8163# 5# B- * 81 956661# 429# +0 23 53 30 83 Zn x -36290# 300# 8226# 4# B- 12967# 300# 82 961041# 322# + 21 52 31 83 Ga x -49257.122 2.613 8372.575 0.031 B- 11719.312 3.559 82 947120.301 2.804 + 19 51 32 83 Ge x -60976.435 2.427 8504.345 0.029 B- 8692.888 3.698 82 934539.101 2.605 + 17 50 33 83 As x -69669.323 2.799 8599.653 0.034 B- 5671.207 4.129 82 925206.901 3.004 + 15 49 34 83 Se -n -75340.530 3.036 8658.555 0.037 B- 3673.179 4.839 82 919118.609 3.259 + 13 48 35 83 Br -79013.709 3.795 8693.384 0.046 B- 976.924 3.795 82 915175.289 4.073 + 11 47 36 83 Kr -79990.633 0.009 8695.729 0.000 B- -920.004 2.329 82 914126.518 0.009 + 9 46 37 83 Rb -79070.630 2.329 8675.218 0.028 B- -2273.024 6.424 82 915114.182 2.500 + 7 45 38 83 Sr -76797.606 6.834 8638.407 0.082 B- -4591.941 19.844 82 917554.374 7.336 + 5 44 39 83 Y x -72205.665 18.631 8573.656 0.224 B- -6294.012 19.707 82 922484.025 20.000 + 3 43 40 83 Zr x -65911.654 6.430 8488.399 0.077 B- -8355.571 151.039 82 929240.925 6.902 + 1 42 41 83 Nb x -57556.083 150.902 8378.304 1.818 B- -11216# 428# 82 938211.000 162.000 + -1 41 42 83 Mo x -46340# 401# 8234# 5# B- -15020# 641# 82 950252# 430# + -3 40 43 83 Tc x -31320# 500# 8043# 6# B- * 82 966377# 537# +0 24 54 30 84 Zn x -31930# 400# 8172# 5# B- 12158# 447# 83 965722# 429# + 22 53 31 84 Ga x -44088# 200# 8307# 2# B- 14061# 200# 83 952670# 215# + 20 52 32 84 Ge x -58148.428 3.171 8465.524 0.038 B- 7705.132 4.479 83 937575.091 3.403 + 18 51 33 84 As x -65853.560 3.171 8547.938 0.038 B- 10094.161 3.722 83 929303.291 3.403 + 16 50 34 84 Se -75947.721 1.961 8658.793 0.023 B- 1835.363 25.765 83 918466.762 2.105 + 14 49 35 84 Br -77783.084 25.730 8671.329 0.306 B- 4656.251 25.730 83 916496.419 27.622 + 12 48 36 84 Kr -82439.33510 0.00379 8717.446 0.000 B- -2680.371 2.194 83 911497.72863 0.00407 + 10 47 37 84 Rb -79758.964 2.194 8676.224 0.026 B- 890.606 2.336 83 914375.225 2.355 + 8 46 38 84 Sr -80649.570 1.243 8677.512 0.015 B- -6755.139 4.411 83 913419.120 1.334 + 6 45 39 84 Y -73894.431 4.299 8587.780 0.051 B- -2472.745 6.977 83 920671.061 4.615 + 4 44 40 84 Zr x -71421.686 5.499 8549.029 0.065 B- -10202.968 14.153 83 923325.662 5.903 + 2 43 41 84 Nb x -61218.717 13.041 8418.252 0.155 B- -7049# 298# 83 934279.000 14.000 + 0 42 42 84 Mo x -54170# 298# 8325# 4# B- -16470# 499# 83 941846# 320# + -2 41 43 84 Tc x -37700# 400# 8120# 5# B- * 83 959527# 429# +0 25 55 30 85 Zn x -25230# 500# 8092# 6# B- 14619# 582# 84 972914# 537# + 23 54 31 85 Ga x -39849# 298# 8255# 4# B- 13274# 298# 84 957220# 320# + 21 53 32 85 Ge x -53123.420 3.729 8401.768 0.044 B- 10065.724 4.830 84 942969.659 4.003 + 19 52 33 85 As x -63189.144 3.078 8510.984 0.036 B- 9224.492 4.031 84 932163.659 3.304 + 17 51 34 85 Se +3p -72413.636 2.613 8610.304 0.031 B- 6161.833 4.031 84 922260.759 2.804 + 15 50 35 85 Br +n2p -78575.469 3.078 8673.592 0.036 B- 2904.861 3.671 84 915645.759 3.304 + 13 49 36 85 Kr + -81480.331 2.000 8698.562 0.024 B- 687.000 2.000 84 912527.262 2.147 + 11 48 37 85 Rb -82167.33050 0.00498 8697.441 0.000 B- -1064.051 2.813 84 911789.73760 0.00534 + 9 47 38 85 Sr -81103.280 2.813 8675.718 0.033 B- -3261.157 19.173 84 912932.043 3.020 + 7 46 39 85 Y x -77842.123 18.965 8628.148 0.223 B- -4666.934 20.026 84 916433.039 20.360 + 5 45 40 85 Zr x -73175.189 6.430 8564.039 0.076 B- -6895.514 7.625 84 921443.198 6.902 + 3 44 41 85 Nb x -66279.676 4.099 8473.711 0.048 B- -8769.923 16.357 84 928845.837 4.400 + 1 43 42 85 Mo x -57509.753 15.835 8361.331 0.186 B- -11660# 400# 84 938260.737 17.000 + -1 42 43 85 Tc x -45850# 400# 8215# 5# B- -14900# 640# 84 950778# 429# + -3 41 44 85 Ru x -30950# 500# 8030# 6# B- * 84 966774# 537# +0 24 55 31 86 Ga x -34080# 400# 8186# 5# B- 15320# 593# 85 963414# 429# + 22 54 32 86 Ge x -49399.922 437.802 8354.629 5.091 B- 9562.221 437.816 85 946967.000 470.000 + 20 53 33 86 As x -58962.142 3.450 8456.721 0.040 B- 11541.024 4.267 85 936701.533 3.703 + 18 52 34 86 Se x -70503.167 2.520 8581.822 0.029 B- 5129.085 3.972 85 924311.733 2.705 + 16 51 35 86 Br +pp -75632.252 3.078 8632.365 0.036 B- 7633.414 3.078 85 918805.433 3.304 + 14 50 36 86 Kr -83265.66564 0.00369 8712.029 0.000 B- -518.672 0.200 85 910610.62627 0.00396 + 12 49 37 86 Rb -n -82746.993 0.200 8696.901 0.002 B- 1776.096 0.200 85 911167.443 0.214 + 10 48 38 86 Sr -84523.08935 0.00522 8708.456 0.000 B- -5240.000 14.142 85 909260.72631 0.00561 + 8 47 39 86 Y - -79283.089 14.142 8638.428 0.164 B- -1314.075 14.585 85 914886.098 15.182 + 6 46 40 86 Zr -77969.014 3.566 8614.051 0.041 B- -8834.960 6.552 85 916296.815 3.827 + 4 45 41 86 Nb x -69134.054 5.499 8502.222 0.064 B- -5023.810 6.642 85 925781.535 5.903 + 2 44 42 86 Mo x -64110.245 3.726 8434.709 0.043 B- -12540# 300# 85 931174.817 4.000 + 0 43 43 86 Tc x -51570# 300# 8280# 3# B- -11800# 500# 85 944637# 322# + -2 42 44 86 Ru x -39770# 400# 8133# 5# B- * 85 957305# 429# +0 25 56 31 87 Ga x -29250# 500# 8129# 6# B- 14828# 583# 86 968599# 537# + 23 55 32 87 Ge x -44078# 300# 8290# 3# B- 11540# 300# 86 952680# 322# + 21 54 33 87 As x -55617.907 2.985 8413.851 0.034 B- 10808.218 3.726 86 940291.718 3.204 + 19 53 34 87 Se x -66426.125 2.241 8529.091 0.026 B- 7465.552 3.877 86 928688.618 2.405 + 17 52 35 87 Br 2p-n -73891.676 3.171 8605.910 0.036 B- 6817.845 3.181 86 920674.018 3.404 + 15 51 36 87 Kr -n -80709.522 0.246 8675.283 0.003 B- 3888.269 0.246 86 913354.759 0.264 + 13 50 37 87 Rb -84597.791 0.006 8710.983 0.000 B- 282.275 0.006 86 909180.531 0.006 + 11 49 38 87 Sr -84880.06595 0.00510 8705.236 0.000 B- -1861.690 1.128 86 908877.49615 0.00548 + 9 48 39 87 Y - -83018.376 1.128 8674.844 0.013 B- -3671.239 4.296 86 910876.102 1.210 + 7 47 40 87 Zr -79347.137 4.146 8623.654 0.048 B- -5472.651 7.963 86 914817.339 4.450 + 5 46 41 87 Nb x -73874.486 6.802 8551.757 0.078 B- -6989.678 7.378 86 920692.472 7.302 + 3 45 42 87 Mo -66884.808 2.857 8462.424 0.033 B- -9194.764 5.073 86 928196.201 3.067 + 1 44 43 87 Tc x -57690.044 4.192 8347.744 0.048 B- -12170# 400# 86 938067.187 4.500 + -1 43 44 87 Ru x -45520# 400# 8199# 5# B- * 86 951132# 429# +0 24 56 32 88 Ge x -40138# 400# 8243# 5# B- 10582# 445# 87 956910# 429# + 22 55 33 88 As x -50720# 196# 8354# 2# B- 13164# 196# 87 945550# 210# + 20 54 34 88 Se x -63884.195 3.357 8495.004 0.038 B- 6831.763 4.613 87 931417.491 3.604 + 18 53 35 88 Br ++ -70715.959 3.171 8563.747 0.036 B- 8975.327 4.106 87 924083.291 3.404 + 16 52 36 88 Kr x -79691.286 2.608 8656.849 0.030 B- 2917.709 2.613 87 914447.881 2.800 + 14 51 37 88 Rb -82608.995 0.159 8681.115 0.002 B- 5312.623 0.159 87 911315.591 0.171 + 12 50 38 88 Sr -87921.61793 0.00558 8732.595 0.000 B- -3622.600 1.500 87 905612.25561 0.00599 + 10 49 39 88 Y - -84299.018 1.500 8682.539 0.017 B- -670.147 5.608 87 909501.276 1.610 + 8 48 40 88 Zr -83628.871 5.403 8666.033 0.061 B- -7455.284 58.886 87 910220.709 5.800 + 6 47 41 88 Nb -76173.586 58.810 8572.424 0.668 B- -3487.042 58.933 87 918224.287 63.134 + 4 46 42 88 Mo x -72686.544 3.819 8523.908 0.043 B- -11005.229 149.088 87 921967.781 4.100 + 2 45 43 88 Tc x -61681.315 149.039 8389.958 1.694 B- -7342# 335# 87 933782.381 160.000 + 0 44 44 88 Ru x -54340# 300# 8298# 3# B- -17479# 500# 87 941664# 322# + -2 43 45 88 Rh x -36860# 400# 8090# 5# B- * 87 960429# 429# +0 25 57 32 89 Ge x -33729# 400# 8169# 4# B- 13069# 499# 88 963790# 429# + 23 56 33 89 As x -46798# 298# 8307# 3# B- 12194# 298# 88 949760# 320# + 21 55 34 89 Se x -58992.391 3.729 8435.279 0.042 B- 9281.872 4.951 88 936669.059 4.003 + 19 54 35 89 Br x -68274.263 3.264 8530.779 0.037 B- 8261.522 3.904 88 926704.559 3.504 + 17 53 36 89 Kr x -76535.785 2.142 8614.815 0.024 B- 5176.604 5.834 88 917835.450 2.300 + 15 52 37 89 Rb -81712.388 5.427 8664.189 0.061 B- 4496.628 5.427 88 912278.137 5.825 + 13 51 38 89 Sr -86209.017 0.092 8705.922 0.001 B- 1499.336 1.615 88 907450.808 0.098 + 11 50 39 89 Y -87708.352 1.612 8713.978 0.018 B- -2832.792 2.776 88 905841.205 1.730 + 9 49 40 89 Zr -84875.561 3.083 8673.359 0.035 B- -4250.351 23.743 88 908882.332 3.310 + 7 48 41 89 Nb -80625.209 23.631 8616.812 0.266 B- -5610.275 23.953 88 913445.272 25.369 + 5 47 42 89 Mo x -75014.935 3.912 8544.984 0.044 B- -7620.087 5.467 88 919468.150 4.200 + 3 46 43 89 Tc x -67394.848 3.819 8450.575 0.043 B- -9135# 298# 88 927648.650 4.100 + 1 45 44 89 Ru x -58260# 298# 8339# 3# B- -12400# 468# 88 937455# 320# + -1 44 45 89 Rh -p -45861# 361# 8191# 4# B- * 88 950767# 387# +0 26 58 32 90 Ge x -29221# 500# 8118# 6# B- 12109# 640# 89 968630# 537# + 24 57 33 90 As x -41330# 400# 8244# 4# B- 14470# 518# 89 955630# 429# + 22 56 34 90 Se x -55800.217 329.749 8395.766 3.664 B- 8200.081 329.766 89 940096.000 354.000 + 20 55 35 90 Br x -64000.298 3.357 8478.186 0.037 B- 10958.952 3.840 89 931292.850 3.604 + 18 54 36 90 Kr x -74959.250 1.863 8591.259 0.021 B- 4405.154 6.746 89 919527.930 2.000 + 16 53 37 90 Rb -79364.404 6.484 8631.512 0.072 B- 6583.723 6.544 89 914798.803 6.960 + 14 52 38 90 Sr -85948.127 2.124 8695.972 0.024 B- 545.934 1.406 89 907730.885 2.280 + 12 51 39 90 Y -86494.062 1.611 8693.345 0.018 B- 2278.474 1.609 89 907144.800 1.729 + 10 50 40 90 Zr -88772.535 0.118 8709.969 0.001 B- -6111.016 3.316 89 904698.758 0.126 + 8 49 41 90 Nb -82661.519 3.317 8633.376 0.037 B- -2489.016 3.316 89 911259.204 3.561 + 6 48 42 90 Mo -80172.503 3.463 8597.028 0.038 B- -9447.816 3.611 89 913931.272 3.717 + 4 47 43 90 Tc x -70724.687 1.025 8483.359 0.011 B- -5840.895 3.869 89 924073.921 1.100 + 2 46 44 90 Ru -64883.792 3.730 8409.768 0.041 B- -13184# 300# 89 930344.379 4.004 + 0 45 45 90 Rh x -51700# 300# 8255# 3# B- -11990# 500# 89 944498# 322# + -2 44 46 90 Pd x -39710# 400# 8113# 4# B- * 89 957370# 429# +0 25 58 33 91 As x -36896# 400# 8193# 4# B- 13684# 589# 90 960390# 429# + 23 57 34 91 Se x -50580.124 433.145 8334.837 4.760 B- 10527.169 433.159 90 945700.000 465.000 + 21 56 35 91 Br -n2p -61107.294 3.544 8441.923 0.039 B- 9866.671 4.190 90 934398.618 3.804 + 19 55 36 91 Kr x -70973.965 2.236 8541.751 0.025 B- 6771.072 8.115 90 923806.310 2.400 + 17 54 37 91 Rb -77745.037 7.801 8607.561 0.086 B- 5906.890 8.873 90 916537.265 8.375 + 15 53 38 91 Sr -83651.927 5.453 8663.875 0.060 B- 2699.369 5.247 90 910195.958 5.853 + 13 52 39 91 Y -86351.295 1.843 8684.941 0.020 B- 1544.271 1.840 90 907298.066 1.978 + 11 51 40 91 Zr -87895.566 0.105 8693.314 0.001 B- -1257.565 2.924 90 905640.223 0.112 + 9 50 41 91 Nb -86638.001 2.926 8670.897 0.032 B- -4429.180 6.744 90 906990.274 3.141 + 7 49 42 91 Mo -82208.821 6.238 8613.628 0.069 B- -6222.175 6.671 90 911745.195 6.696 + 5 48 43 91 Tc -75986.646 2.363 8536.655 0.026 B- -7746.824 3.242 90 918424.975 2.536 + 3 47 44 91 Ru -68239.823 2.221 8442.928 0.024 B- -9670# 298# 90 926741.532 2.384 + 1 46 45 91 Rh x -58570# 298# 8328# 3# B- -12639# 499# 90 937123# 320# + -1 45 46 91 Pd x -45930# 401# 8181# 4# B- * 90 950692# 430# +0 26 59 33 92 As x -30981# 500# 8127# 5# B- 15742# 640# 91 966740# 537# + 24 58 34 92 Se x -46724# 400# 8290# 4# B- 9509# 400# 91 949840# 429# + 22 57 35 92 Br x -56232.805 6.709 8384.911 0.073 B- 12536.514 7.232 91 939631.597 7.202 + 20 56 36 92 Kr x -68769.320 2.701 8512.674 0.029 B- 6003.118 6.692 91 926173.094 2.900 + 18 55 37 92 Rb -74772.438 6.123 8569.422 0.067 B- 8094.923 6.419 91 919728.481 6.573 + 16 54 38 92 Sr -82867.361 3.423 8648.906 0.037 B- 1949.132 9.384 91 911038.224 3.675 + 14 53 39 92 Y -84816.492 9.127 8661.589 0.099 B- 3642.535 9.127 91 908945.745 9.798 + 12 52 40 92 Zr -88459.028 0.102 8692.678 0.001 B- -2005.736 1.782 91 905035.322 0.109 + 10 51 41 92 Nb -86453.292 1.785 8662.372 0.019 B- 355.284 1.791 91 907188.568 1.915 + 8 50 42 92 Mo -86808.576 0.157 8657.730 0.002 B- -7882.884 3.106 91 906807.155 0.168 + 6 49 43 92 Tc -78925.693 3.102 8563.543 0.034 B- -4624.492 4.125 91 915269.779 3.330 + 4 48 44 92 Ru -74301.201 2.718 8504.773 0.030 B- -11302.114 5.153 91 920234.375 2.917 + 2 47 45 92 Rh x -62999.087 4.378 8373.420 0.048 B- -8419# 300# 91 932367.694 4.700 + 0 46 46 92 Pd x -54580# 300# 8273# 3# B- -17450# 583# 91 941406# 322# + -2 45 47 92 Ag x -37130# 500# 8075# 5# B- * 91 960139# 537# +0 25 59 34 93 Se x -40716# 400# 8223# 4# B- 12175# 588# 92 956290# 429# + 23 58 35 93 Br x -52890.230 430.816 8345.598 4.632 B- 11245.765 430.823 92 943220.000 462.500 + 21 57 36 93 Kr x -64135.994 2.515 8458.108 0.027 B- 8483.907 8.224 92 931147.174 2.700 + 19 56 37 93 Rb -72619.901 7.830 8540.920 0.084 B- 7465.938 8.876 92 922039.325 8.406 + 17 55 38 93 Sr -80085.838 7.554 8612.787 0.081 B- 4141.319 11.697 92 914024.311 8.109 + 15 54 39 93 Y -84227.157 10.488 8648.905 0.113 B- 2894.875 10.483 92 909578.422 11.259 + 13 53 40 93 Zr -87122.032 0.457 8671.620 0.005 B- 90.806 1.484 92 906470.646 0.490 + 11 52 41 93 Nb -87212.838 1.491 8664.184 0.016 B- -405.769 1.501 92 906373.161 1.600 + 9 51 42 93 Mo -n -86807.069 0.181 8651.409 0.002 B- -3200.963 1.004 92 906808.773 0.193 + 7 50 43 93 Tc -p -83606.106 1.012 8608.577 0.011 B- -6389.393 2.299 92 910245.149 1.086 + 5 49 44 93 Ru -77216.713 2.065 8531.462 0.022 B- -8204.913 3.343 92 917104.444 2.216 + 3 48 45 93 Rh -69011.800 2.629 8434.825 0.028 B- -10011# 301# 92 925912.781 2.821 + 1 47 46 93 Pd +p -59001# 300# 8319# 3# B- -12734# 501# 92 936660# 323# + -1 46 47 93 Ag x -46267# 401# 8173# 4# B- * 92 950330# 430# +0 26 60 34 94 Se x -36803# 500# 8180# 5# B- 10597# 583# 93 960490# 537# + 24 59 35 94 Br x -47400# 300# 8284# 3# B- 13948# 300# 93 949114# 322# + 22 58 36 94 Kr x -61347.772 12.109 8424.331 0.129 B- 7215.013 12.278 93 934140.454 13.000 + 20 57 37 94 Rb -68562.785 2.029 8492.764 0.022 B- 10282.926 2.623 93 926394.818 2.177 + 18 56 38 94 Sr -78845.711 1.663 8593.834 0.018 B- 3505.752 6.422 93 915355.643 1.785 + 16 55 39 94 Y -82351.463 6.380 8622.806 0.068 B- 4917.859 6.380 93 911592.063 6.849 + 14 54 40 94 Zr -87269.322 0.164 8666.801 0.002 B- -900.260 1.500 93 906312.524 0.175 + 12 53 41 94 Nb -86369.062 1.491 8648.901 0.016 B- 2045.002 1.494 93 907278.992 1.601 + 10 52 42 94 Mo -88414.065 0.141 8662.333 0.002 B- -4255.748 4.069 93 905083.592 0.151 + 8 51 43 94 Tc - -84158.317 4.071 8608.736 0.043 B- -1574.726 5.143 93 909652.325 4.370 + 6 50 44 94 Ru -82583.591 3.143 8583.661 0.033 B- -9675.978 4.615 93 911342.863 3.374 + 4 49 45 94 Rh -72907.613 3.379 8472.402 0.036 B- -6805.345 5.459 93 921730.453 3.627 + 2 48 46 94 Pd x -66102.268 4.287 8391.682 0.046 B- -13693# 400# 93 929036.292 4.602 + 0 47 47 94 Ag x -52410# 400# 8238# 4# B- -12270# 640# 93 943736# 429# + -2 46 48 94 Cd x -40140# 500# 8099# 5# B- * 93 956908# 537# +0 27 61 34 95 Se x -30460# 500# 8112# 5# B- 13311# 582# 94 967300# 537# + 25 60 35 95 Br x -43771# 298# 8244# 3# B- 12388# 299# 94 953010# 320# + 23 59 36 95 Kr x -56158.913 18.630 8365.995 0.196 B- 9732.580 27.513 94 939710.923 20.000 + 21 58 37 95 Rb -65891.493 20.245 8460.208 0.213 B- 9228.058 20.204 94 929262.568 21.734 + 19 57 38 95 Sr -75119.551 5.812 8549.111 0.061 B- 6089.296 7.240 94 919355.840 6.239 + 17 56 39 95 Y -81208.848 6.779 8604.973 0.071 B- 4451.092 6.772 94 912818.711 7.277 + 15 55 40 95 Zr -85659.940 0.869 8643.592 0.009 B- 1126.318 0.985 94 908040.267 0.933 + 13 54 41 95 Nb -86786.258 0.508 8647.212 0.005 B- 925.601 0.494 94 906831.115 0.545 + 11 53 42 95 Mo -87711.858 0.123 8648.720 0.001 B- -1690.518 5.078 94 905837.442 0.132 + 9 52 43 95 Tc -86021.341 5.080 8622.690 0.053 B- -2563.596 10.531 94 907652.287 5.453 + 7 51 44 95 Ru -83457.745 9.502 8587.470 0.100 B- -5117.138 10.266 94 910404.420 10.200 + 5 50 45 95 Rh -78340.606 3.886 8525.370 0.041 B- -8374.706 4.928 94 915897.895 4.171 + 3 49 46 95 Pd x -69965.900 3.031 8428.980 0.032 B- -10369# 298# 94 924888.512 3.253 + 1 48 47 95 Ag x -59597# 298# 8312# 3# B- -12966# 499# 94 936020# 320# + -1 47 48 95 Cd x -46631# 401# 8167# 4# B- * 94 949940# 430# +0 26 61 35 96 Br x -38163# 298# 8184# 3# B- 14916# 299# 95 959030# 320# + 24 60 36 96 Kr x -53079.678 20.493 8330.851 0.213 B- 8274.671 20.765 95 943016.618 22.000 + 22 59 37 96 Rb -61354.349 3.353 8408.896 0.035 B- 11569.808 9.115 95 934133.393 3.599 + 20 58 38 96 Sr -72924.157 8.475 8521.265 0.088 B- 5411.738 9.726 95 921712.692 9.098 + 18 57 39 96 Y -78335.895 6.088 8569.488 0.063 B- 7102.951 6.087 95 915902.953 6.535 + 16 56 40 96 Zr -85438.846 0.114 8635.327 0.001 B- 163.971 0.100 95 908277.621 0.122 + 14 55 41 96 Nb -85602.816 0.147 8628.886 0.002 B- 3192.059 0.107 95 908101.591 0.157 + 12 54 42 96 Mo -88794.876 0.120 8653.987 0.001 B- -2973.242 5.145 95 904674.774 0.128 + 10 53 43 96 Tc - -85821.634 5.146 8614.866 0.054 B- 258.738 5.146 95 907866.681 5.524 + 8 52 44 96 Ru -86080.372 0.170 8609.412 0.002 B- -6392.654 10.000 95 907588.914 0.182 + 6 51 45 96 Rh - -79687.718 10.001 8534.673 0.104 B- -3504.312 10.844 95 914451.710 10.737 + 4 50 46 96 Pd x -76183.406 4.194 8490.020 0.044 B- -11671.771 90.181 95 918213.744 4.502 + 2 49 47 96 Ag ep -64511.636 90.084 8360.290 0.938 B- -8939# 411# 95 930743.906 96.708 + 0 48 48 96 Cd x -55573# 401# 8259# 4# B- -17683# 641# 95 940340# 430# + -2 47 49 96 In x -37890# 500# 8067# 5# B- * 95 959323# 537# +0 27 62 35 97 Br x -34055# 401# 8140# 4# B- 13368# 421# 96 963440# 430# + 25 61 36 97 Kr x -47423.492 130.409 8269.864 1.344 B- 11095.645 130.423 96 949088.784 140.000 + 23 60 37 97 Rb -58519.137 1.912 8376.186 0.020 B- 10062.317 3.888 96 937177.118 2.052 + 21 59 38 97 Sr -68581.454 3.385 8471.856 0.035 B- 7539.969 7.521 96 926374.776 3.633 + 19 58 39 97 Y + -76121.424 6.719 8541.522 0.069 B- 6821.237 6.707 96 918280.286 7.213 + 17 57 40 97 Zr -82942.661 0.414 8603.779 0.004 B- 2663.115 4.248 96 910957.386 0.444 + 15 56 41 97 Nb -85605.776 4.249 8623.168 0.044 B- 1938.915 4.248 96 908098.414 4.561 + 13 55 42 97 Mo -87544.691 0.165 8635.092 0.002 B- -320.266 4.117 96 906016.903 0.176 + 11 54 43 97 Tc -87224.424 4.118 8623.725 0.042 B- -1103.873 4.956 96 906360.723 4.420 + 9 53 44 97 Ru -n -86120.552 2.763 8604.279 0.028 B- -3523.000 35.355 96 907545.779 2.965 + 7 52 45 97 Rh - -82597.552 35.463 8559.894 0.366 B- -4791.709 35.792 96 911327.876 38.071 + 5 51 46 97 Pd x -77805.843 4.844 8502.430 0.050 B- -6980.000 110.000 96 916471.987 5.200 + 3 50 47 97 Ag - -70825.843 110.107 8422.405 1.135 B- -10372# 318# 96 923965.326 118.204 + 1 49 48 97 Cd x -60454# 298# 8307# 3# B- -13264# 499# 96 935100# 320# + -1 48 49 97 In x -47189# 401# 8163# 4# B- * 96 949340# 430# +0 28 63 35 98 Br x -28250# 400# 8080# 4# B- 16061# 499# 97 969672# 429# + 26 62 36 98 Kr x -44311# 298# 8236# 3# B- 10058# 299# 97 952430# 320# + 24 61 37 98 Rb -54369.146 16.083 8330.729 0.164 B- 12053.958 16.403 97 941632.317 17.265 + 22 60 38 98 Sr -66423.104 3.226 8445.745 0.033 B- 5871.673 8.558 97 928691.860 3.463 + 20 59 39 98 Y p-2n -72294.777 7.929 8497.677 0.081 B- 8991.932 11.576 97 922388.360 8.511 + 18 58 40 98 Zr -81286.709 8.451 8581.448 0.086 B- 2237.890 9.819 97 912735.124 9.072 + 16 57 41 98 Nb -pn -83524.598 5.001 8596.301 0.051 B- 4591.373 5.003 97 910332.650 5.369 + 14 56 42 98 Mo -88115.972 0.174 8635.168 0.002 B- -1683.766 3.377 97 905403.608 0.186 + 12 55 43 98 Tc -86432.205 3.380 8610.004 0.034 B- 1792.653 7.157 97 907211.205 3.628 + 10 54 44 98 Ru -88224.858 6.463 8620.313 0.066 B- -5049.653 10.000 97 905286.713 6.937 + 8 53 45 98 Rh - -83175.205 11.906 8560.803 0.121 B- -1854.229 12.816 97 910707.740 12.782 + 6 52 46 98 Pd -81320.975 4.742 8533.899 0.048 B- -8254.560 33.098 97 912698.337 5.090 + 4 51 47 98 Ag -73066.415 32.907 8441.686 0.336 B- -5430.000 40.000 97 921559.972 35.327 + 2 50 48 98 Cd - -67636.415 51.797 8378.295 0.529 B- -13740# 303# 97 927389.317 55.605 + 0 49 49 98 In x -53896# 298# 8230# 3# B- * 97 942140# 320# +0 27 63 36 99 Kr x -38759# 401# 8178# 4# B- 12362# 401# 98 958390# 430# + 25 62 37 99 Rb x -51121.143 4.031 8295.300 0.041 B- 11400.258 6.223 98 945119.192 4.327 + 23 61 38 99 Sr -62521.401 4.741 8402.552 0.048 B- 8128.424 8.138 98 932880.511 5.089 + 21 60 39 99 Y x -70649.825 6.627 8476.755 0.067 B- 6970.792 12.409 98 924154.288 7.114 + 19 59 40 99 Zr -77620.617 10.502 8539.264 0.106 B- 4714.724 15.950 98 916670.835 11.274 + 17 58 41 99 Nb +p -82335.341 12.004 8578.985 0.121 B- 3634.758 12.006 98 911609.371 12.886 + 15 57 42 99 Mo -85970.098 0.229 8607.797 0.002 B- 1357.764 0.890 98 907707.298 0.245 + 13 56 43 99 Tc -87327.862 0.908 8613.610 0.009 B- 297.519 0.946 98 906249.678 0.974 + 11 55 44 99 Ru -87625.381 0.344 8608.712 0.003 B- -2044.081 6.690 98 905930.278 0.369 + 9 54 45 99 Rh -85581.300 6.697 8580.163 0.068 B- -3398.649 8.008 98 908124.690 7.189 + 7 53 46 99 Pd -82182.651 4.981 8537.930 0.050 B- -5470.178 8.004 98 911773.290 5.347 + 5 52 47 99 Ag x -76712.473 6.265 8474.774 0.063 B- -6781.350 6.462 98 917645.768 6.725 + 3 51 48 99 Cd x -69931.123 1.584 8398.373 0.016 B- -8555# 298# 98 924925.847 1.700 + 1 50 49 99 In x -61376# 298# 8304# 3# B- -13432# 585# 98 934110# 320# + -1 49 50 99 Sn x -47944# 503# 8160# 5# B- * 98 948530# 540# +0 28 64 36 100 Kr x -35052# 401# 8140# 4# B- 11195# 401# 99 962370# 430# + 26 63 37 100 Rb x -46247.064 19.561 8244.320 0.196 B- 13573.838 20.831 99 950351.731 21.000 + 24 62 38 100 Sr -59820.903 7.160 8372.234 0.072 B- 7506.493 13.273 99 935779.615 7.686 + 22 61 39 100 Y x -67327.396 11.186 8439.476 0.112 B- 9050.041 13.830 99 927721.063 12.008 + 20 60 40 100 Zr -76377.437 8.149 8522.153 0.081 B- 3419.963 11.398 99 918005.444 8.748 + 18 59 41 100 Nb IT -79797.399 7.986 8548.529 0.080 B- 6395.626 7.992 99 914333.963 8.573 + 16 58 42 100 Mo -86193.025 0.302 8604.662 0.003 B- -172.080 1.371 99 907467.976 0.323 + 14 57 43 100 Tc -n -86020.945 1.351 8595.118 0.014 B- 3206.444 1.376 99 907652.711 1.450 + 12 56 44 100 Ru -89227.389 0.343 8619.359 0.003 B- -3636.262 18.123 99 904210.452 0.368 + 10 55 45 100 Rh -85591.126 18.125 8575.172 0.181 B- -378.348 25.289 99 908114.141 19.458 + 8 54 46 100 Pd -85212.778 17.638 8563.566 0.176 B- -7074.819 18.333 99 908520.315 18.935 + 6 53 47 100 Ag x -78137.959 5.000 8484.994 0.050 B- -3943.363 5.273 99 916115.445 5.367 + 4 52 48 100 Cd -74194.596 1.677 8437.737 0.017 B- -9881.624 182.517 99 920348.820 1.799 + 2 51 49 100 In -64312.972 182.519 8331.097 1.825 B- -7030.000 240.000 99 930957.180 195.942 + 0 50 50 100 Sn - -57282.972 301.518 8252.974 3.015 B- * 99 938504.196 323.693 +0 29 65 36 101 Kr x -29128# 503# 8081# 5# B- 13717# 541# 100 968730# 540# + 27 64 37 101 Rb + -42845# 200# 8209# 2# B- 12480# 200# 100 954004# 215# + 25 63 38 101 Sr x -55324.907 8.480 8324.740 0.084 B- 9736.095 11.055 100 940606.266 9.103 + 23 62 39 101 Y x -65061.002 7.092 8413.391 0.070 B- 8104.955 10.933 100 930154.138 7.614 + 21 61 40 101 Zr -73165.957 8.339 8485.892 0.083 B- 5725.534 9.143 100 921453.110 8.951 + 19 60 41 101 Nb x -78891.491 3.749 8534.835 0.037 B- 4628.458 3.738 100 915306.496 4.024 + 17 59 42 101 Mo -n -83519.949 0.309 8572.915 0.003 B- 2824.645 24.002 100 910337.641 0.331 + 15 58 43 101 Tc + -86344.594 24.004 8593.136 0.238 B- 1613.520 24.000 100 907305.260 25.768 + 13 57 44 101 Ru -87958.114 0.415 8601.365 0.004 B- -545.697 5.852 100 905573.075 0.445 + 11 56 45 101 Rh -87412.416 5.841 8588.216 0.058 B- -1980.284 3.903 100 906158.905 6.270 + 9 55 46 101 Pd -85432.132 4.588 8560.864 0.045 B- -4097.759 6.668 100 908284.828 4.925 + 7 54 47 101 Ag x -81334.374 4.838 8512.546 0.048 B- -5497.918 5.063 100 912683.953 5.193 + 5 53 48 101 Cd x -75836.456 1.490 8450.365 0.015 B- -7223# 196# 100 918586.211 1.600 + 3 52 49 101 In x -68614# 196# 8371# 2# B- -8308# 358# 100 926340# 210# + 1 51 50 101 Sn ep -60305.626 300.005 8281.102 2.970 B- * 100 935259.244 322.068 +0 28 65 37 102 Rb x -37707# 298# 8157# 3# B- 14452# 306# 101 959520# 320# + 26 64 38 102 Sr x -52159.304 67.068 8291.220 0.658 B- 9013.873 67.191 101 944004.680 72.000 + 24 63 39 102 Y x -61173.177 4.077 8371.922 0.040 B- 10414.530 9.669 101 934327.889 4.377 + 22 62 40 102 Zr -71587.707 8.767 8466.355 0.086 B- 4716.837 9.053 101 923147.431 9.412 + 20 61 41 102 Nb -76304.544 2.545 8504.928 0.025 B- 7261.517 8.675 101 918083.697 2.732 + 18 60 42 102 Mo -83566.061 8.312 8568.450 0.081 B- 1006.817 12.373 101 910288.138 8.923 + 16 59 43 102 Tc -84572.878 9.166 8570.650 0.090 B- 4533.558 9.165 101 909207.275 9.840 + 14 58 44 102 Ru -89106.437 0.418 8607.427 0.004 B- -2323.119 6.396 101 904340.300 0.448 + 12 57 45 102 Rh - -86783.318 6.410 8576.981 0.063 B- 1119.853 6.406 101 906834.270 6.881 + 10 56 46 102 Pd -87903.171 0.554 8580.290 0.005 B- -5656.480 8.190 101 905632.058 0.594 + 8 55 47 102 Ag + -82246.691 8.171 8517.164 0.080 B- -2587.000 8.000 101 911704.540 8.771 + 6 54 48 102 Cd -79659.691 1.662 8484.131 0.016 B- -8964.807 4.865 101 914481.799 1.784 + 4 53 49 102 In -70694.884 4.573 8388.571 0.045 B- -5760.000 100.000 101 924105.916 4.909 + 2 52 50 102 Sn - -64934.884 100.105 8324.430 0.981 B- * 101 930289.530 107.466 +0 29 66 37 103 Rb x -33608# 401# 8117# 4# B- 13814# 446# 102 963920# 430# + 27 65 38 103 Sr x -47422# 196# 8243# 2# B- 11035# 196# 102 949090# 210# + 25 64 39 103 Y x -58457.575 11.204 8342.638 0.109 B- 9357.759 14.518 102 937243.208 12.028 + 23 63 40 103 Zr x -67815.334 9.232 8425.895 0.090 B- 7213.337 10.036 102 927197.240 9.911 + 21 62 41 103 Nb x -75028.671 3.935 8488.331 0.038 B- 5931.999 10.036 102 919453.403 4.224 + 19 61 42 103 Mo x -80960.670 9.232 8538.328 0.090 B- 3643.197 13.471 102 913085.140 9.911 + 17 60 43 103 Tc +p -84603.867 9.810 8566.103 0.095 B- 2663.304 9.808 102 909174.008 10.531 + 15 59 44 103 Ru -87267.171 0.443 8584.365 0.004 B- 764.538 2.260 102 906314.833 0.475 + 13 58 45 103 Rh -88031.708 2.301 8584.192 0.022 B- -574.519 2.420 102 905494.068 2.470 + 11 57 46 103 Pd -n -87457.189 0.950 8571.019 0.009 B- -2654.498 4.207 102 906110.840 1.019 + 9 56 47 103 Ag x -84802.692 4.099 8537.651 0.040 B- -4151.075 4.481 102 908960.560 4.400 + 7 55 48 103 Cd -80651.616 1.811 8489.754 0.018 B- -6019.026 9.754 102 913416.923 1.943 + 5 54 49 103 In -74632.591 9.625 8423.721 0.093 B- -7660.000 70.000 102 919878.613 10.332 + 3 53 50 103 Sn - -66972.591 70.659 8341.757 0.686 B- -10794# 306# 102 928101.962 75.855 + 1 52 51 103 Sb x -56178# 298# 8229# 3# B- * 102 939690# 320# +0 28 66 38 104 Sr x -44106# 298# 8210# 3# B- 9958# 499# 103 952650# 320# + 26 65 39 104 Y x -54064# 401# 8298# 4# B- 11660# 401# 103 941960# 430# + 24 64 40 104 Zr x -65724.060 9.325 8402.377 0.090 B- 6094.952 9.699 103 929442.315 10.011 + 22 63 41 104 Nb x -71819.012 2.737 8453.459 0.026 B- 8530.957 9.311 103 922899.115 2.938 + 20 62 42 104 Mo -80349.968 8.921 8527.965 0.086 B- 2153.476 24.167 103 913740.756 9.576 + 18 61 43 104 Tc -82503.444 24.888 8541.149 0.239 B- 5592.266 24.939 103 911428.905 26.718 + 16 60 44 104 Ru -88095.710 2.498 8587.399 0.024 B- -1136.362 3.364 103 905425.360 2.681 + 14 59 45 104 Rh -n -86959.348 2.303 8568.949 0.022 B- 2435.758 2.660 103 906645.295 2.472 + 12 58 46 104 Pd +n -89395.105 1.336 8584.848 0.013 B- -4278.654 4.000 103 904030.401 1.434 + 10 57 47 104 Ag - -85116.452 4.217 8536.184 0.041 B- -1148.072 4.537 103 908623.725 4.527 + 8 56 48 104 Cd -83968.380 1.673 8517.622 0.016 B- -7785.716 6.013 103 909856.230 1.795 + 6 55 49 104 In x -76182.665 5.775 8435.237 0.056 B- -4555.617 8.146 103 918214.540 6.200 + 4 54 50 104 Sn -71627.047 5.745 8383.911 0.055 B- -12453.427 122.579 103 923105.197 6.167 + 2 53 51 104 Sb -p -59173.620 122.444 8256.644 1.177 B- * 103 936474.502 131.449 +0 29 67 38 105 Sr x -38610# 503# 8156# 5# B- 12660# 1428# 104 958550# 540# + 27 66 39 105 Y x -51270.361 1336.694 8269.020 12.730 B- 10194.373 1336.749 104 944959.000 1435.000 + 25 65 40 105 Zr x -61464.734 12.118 8358.659 0.115 B- 8450.817 12.770 104 934014.890 13.008 + 23 64 41 105 Nb x -69915.551 4.028 8431.692 0.038 B- 7421.590 9.920 104 924942.564 4.324 + 21 63 42 105 Mo -77337.141 9.065 8494.923 0.086 B- 4952.947 35.031 104 916975.159 9.731 + 19 62 43 105 Tc -82290.088 35.264 8534.643 0.336 B- 3644.402 35.280 104 911657.952 37.857 + 17 61 44 105 Ru -85934.490 2.499 8561.900 0.024 B- 1916.752 2.851 104 907745.525 2.682 + 15 60 45 105 Rh -87851.243 2.502 8572.704 0.024 B- 566.646 2.346 104 905687.806 2.685 + 13 59 46 105 Pd -88417.888 1.138 8570.650 0.011 B- -1347.052 4.670 104 905079.487 1.222 + 11 58 47 105 Ag -87070.836 4.544 8550.370 0.043 B- -2736.997 4.362 104 906525.607 4.877 + 9 57 48 105 Cd -84333.839 1.392 8516.852 0.013 B- -4693.267 10.341 104 909463.895 1.494 + 7 56 49 105 In x -79640.572 10.246 8464.704 0.098 B- -6302.580 10.989 104 914502.324 11.000 + 5 55 50 105 Sn -73337.992 3.971 8397.228 0.038 B- -9322.510 22.185 104 921268.423 4.263 + 3 54 51 105 Sb +a -64015.482 21.827 8300.992 0.208 B- -11203.972 300.813 104 931276.549 23.431 + 1 53 52 105 Te -a -52811.510 300.020 8186.836 2.857 B- * 104 943304.508 322.084 +0 30 68 38 106 Sr x -34790# 600# 8119# 6# B- 11263# 783# 105 962651# 644# + 28 67 39 106 Y x -46053# 503# 8218# 5# B- 12497# 664# 105 950560# 540# + 26 66 40 106 Zr x -58549.987 433.145 8328.450 4.086 B- 7653.370 433.164 105 937144.000 465.000 + 24 65 41 106 Nb x -66203.357 4.122 8393.271 0.039 B- 9931.170 10.026 105 928927.768 4.424 + 22 64 42 106 Mo x -76134.528 9.140 8479.581 0.086 B- 3641.695 15.284 105 918266.218 9.812 + 20 63 43 106 Tc + -79776.223 12.250 8506.556 0.116 B- 6547.000 11.000 105 914356.697 13.150 + 18 62 44 106 Ru -86323.223 5.391 8560.940 0.051 B- 39.404 0.212 105 907328.203 5.787 + 16 61 45 106 Rh -86362.627 5.390 8553.931 0.051 B- 3544.901 5.335 105 907285.901 5.785 + 14 60 46 106 Pd -89907.527 1.106 8579.992 0.010 B- -2965.145 2.817 105 903480.293 1.186 + 12 59 47 106 Ag -86942.383 3.016 8544.639 0.028 B- 189.755 2.819 105 906663.507 3.237 + 10 58 48 106 Cd -87132.138 1.104 8539.048 0.010 B- -6524.004 12.176 105 906459.797 1.184 + 8 57 49 106 In - -80608.134 12.226 8470.120 0.115 B- -3254.447 13.244 105 913463.603 13.125 + 6 56 50 106 Sn -77353.687 5.091 8432.038 0.048 B- -10880.396 9.025 105 916957.396 5.465 + 4 55 51 106 Sb x -66473.292 7.452 8322.012 0.070 B- -8253.544 100.816 105 928637.982 8.000 + 2 54 52 106 Te -a -58219.748 100.541 8236.767 0.948 B- * 105 937498.526 107.934 +0 31 69 38 107 Sr x -28900# 700# 8064# 7# B- 13465# 862# 106 968975# 751# + 29 68 39 107 Y x -42364# 503# 8182# 5# B- 12015# 1230# 106 954520# 540# + 27 67 40 107 Zr x -54379.688 1122.450 8287.073 10.490 B- 9344.122 1122.479 106 941621.000 1205.000 + 25 66 41 107 Nb x -63723.810 8.023 8367.089 0.075 B- 8827.750 12.232 106 931589.672 8.612 + 23 65 42 107 Mo x -72551.560 9.233 8442.280 0.086 B- 6198.355 12.667 106 922112.692 9.912 + 21 64 43 107 Tc x -78749.914 8.673 8492.897 0.081 B- 5112.598 11.724 106 915458.485 9.310 + 19 63 44 107 Ru -nn -83862.512 8.673 8533.366 0.081 B- 3001.191 14.847 106 909969.885 9.310 + 17 62 45 107 Rh +p -86863.703 12.051 8554.103 0.113 B- 1508.936 12.111 106 906747.974 12.937 + 15 61 46 107 Pd -88372.639 1.201 8560.894 0.011 B- 34.031 2.318 106 905128.064 1.289 + 13 60 47 107 Ag -88406.670 2.382 8553.900 0.022 B- -1416.409 2.567 106 905091.531 2.557 + 11 59 48 107 Cd -86990.261 1.665 8533.351 0.016 B- -3426.000 11.000 106 906612.108 1.787 + 9 58 49 107 In - -83564.261 11.125 8494.021 0.104 B- -5052.033 12.327 106 910290.071 11.943 + 7 57 50 107 Sn x -78512.228 5.310 8439.494 0.050 B- -7858.989 6.738 106 915713.651 5.700 + 5 56 51 107 Sb -70653.239 4.148 8358.734 0.039 B- -10113.913 70.952 106 924150.624 4.452 + 3 55 52 107 Te -a -60539.326 70.830 8256.899 0.662 B- -11110# 308# 106 935008.356 76.039 + 1 54 53 107 I x -49430# 300# 8146# 3# B- * 106 946935# 322# +0 30 69 39 108 Y x -37297# 596# 8134# 6# B- 14056# 718# 107 959960# 640# + 28 68 40 108 Zr x -51353# 401# 8257# 4# B- 8193# 401# 107 944870# 430# + 26 67 41 108 Nb x -59545.765 8.237 8325.665 0.076 B- 11210.177 12.373 107 936074.988 8.842 + 24 66 42 108 Mo x -70755.942 9.233 8422.219 0.085 B- 5166.835 12.734 107 924040.367 9.912 + 22 65 43 108 Tc x -75922.778 8.769 8462.816 0.081 B- 7738.573 11.790 107 918493.541 9.413 + 20 64 44 108 Ru -3n -83661.350 8.680 8527.225 0.080 B- 1370.370 16.469 107 910185.841 9.318 + 18 63 45 108 Rh x -85031.721 13.996 8532.670 0.130 B- 4492.486 14.039 107 908714.688 15.024 + 16 62 46 108 Pd -89524.206 1.108 8567.023 0.010 B- -1917.444 2.633 107 903891.805 1.189 + 14 61 47 108 Ag -n -87606.763 2.388 8542.025 0.022 B- 1645.651 2.639 107 905950.266 2.563 + 12 60 48 108 Cd -89252.414 1.123 8550.019 0.010 B- -5132.595 8.584 107 904183.587 1.205 + 10 59 49 108 In -84119.819 8.641 8495.251 0.080 B- -2049.881 9.836 107 909693.655 9.276 + 8 58 50 108 Sn -82069.938 5.382 8469.027 0.050 B- -9624.607 7.692 107 911894.292 5.778 + 6 57 51 108 Sb x -72445.331 5.496 8372.666 0.051 B- -6663.664 7.712 107 922226.734 5.900 + 4 56 52 108 Te -65781.667 5.411 8303.721 0.050 B- -13132.062 132.370 107 929380.471 5.808 + 2 55 53 108 I -a -52649.605 132.260 8174.884 1.225 B- * 107 943478.321 141.986 +0 31 70 39 109 Y x -33200# 700# 8096# 6# B- 12992# 862# 108 964358# 751# + 29 69 40 109 Zr x -46193# 503# 8208# 5# B- 10497# 566# 108 950410# 540# + 27 68 41 109 Nb x -56689.794 258.490 8297.130 2.371 B- 9976.202 258.732 108 939141.000 277.500 + 25 67 42 109 Mo x -66665.996 11.188 8381.477 0.103 B- 7616.780 14.787 108 928431.106 12.010 + 23 66 43 109 Tc x -74282.775 9.669 8444.178 0.089 B- 6455.626 12.657 108 920254.156 10.380 + 21 65 44 109 Ru -4n -80738.401 8.954 8496.227 0.082 B- 4261.054 9.822 108 913323.756 9.612 + 19 64 45 109 Rh -84999.455 4.039 8528.142 0.037 B- 2607.021 4.187 108 908749.326 4.336 + 17 63 46 109 Pd -87606.476 1.114 8544.882 0.010 B- 1112.950 1.402 108 905950.574 1.195 + 15 62 47 109 Ag -88719.426 1.287 8547.915 0.012 B- -215.105 1.780 108 904755.773 1.381 + 13 61 48 109 Cd -88504.321 1.536 8538.764 0.014 B- -2014.809 4.066 108 904986.698 1.649 + 11 60 49 109 In -86489.511 3.969 8513.102 0.036 B- -3859.327 8.887 108 907149.685 4.261 + 9 59 50 109 Sn -82630.184 7.949 8470.518 0.073 B- -6379.206 8.807 108 911292.843 8.533 + 7 58 51 109 Sb -76250.977 5.265 8404.815 0.048 B- -8535.587 6.850 108 918141.204 5.652 + 5 57 52 109 Te -67715.390 4.382 8319.330 0.040 B- -10042.894 8.030 108 927304.534 4.704 + 3 56 53 109 I -p -57672.496 6.729 8220.016 0.062 B- -11502.948 300.183 108 938086.025 7.223 + 1 55 54 109 Xe -a -46169.548 300.108 8107.306 2.753 B- * 108 950434.948 322.178 +0 30 70 40 110 Zr x -42886# 596# 8177# 5# B- 9424# 1029# 109 953960# 640# + 28 69 41 110 Nb x -52309.909 838.345 8255.260 7.621 B- 12232.677 838.694 109 943843.000 900.000 + 26 68 42 110 Mo x -64542.585 24.223 8359.354 0.220 B- 6491.925 26.018 109 930710.680 26.004 + 24 67 43 110 Tc x -71034.510 9.497 8411.259 0.086 B- 9038.066 12.509 109 923741.312 10.195 + 22 66 44 110 Ru -80072.576 8.924 8486.311 0.081 B- 2756.110 19.404 109 914038.548 9.580 + 20 65 45 110 Rh -82828.686 17.805 8504.254 0.162 B- 5502.218 17.797 109 911079.742 19.114 + 18 64 46 110 Pd -88330.905 0.612 8547.162 0.006 B- -873.603 1.378 109 905172.868 0.657 + 16 63 47 110 Ag -87457.302 1.286 8532.108 0.012 B- 2890.667 1.277 109 906110.719 1.380 + 14 62 48 110 Cd -90347.969 0.380 8551.275 0.003 B- -3878.000 11.547 109 903007.460 0.407 + 12 61 49 110 In - -86469.969 11.553 8508.908 0.105 B- -627.985 17.980 109 907170.665 12.402 + 10 60 50 110 Sn x -85841.983 13.777 8496.087 0.125 B- -8392.250 15.012 109 907844.835 14.790 + 8 59 51 110 Sb x -77449.734 5.962 8412.681 0.054 B- -5219.923 8.875 109 916854.286 6.400 + 6 58 52 110 Te -72229.811 6.575 8358.115 0.060 B- -11765.635 50.978 109 922458.104 7.058 + 4 57 53 110 I -a -60464.176 50.552 8244.043 0.460 B- -8541.551 112.934 109 935089.033 54.270 + 2 56 54 110 Xe -a -51922.625 100.988 8159.280 0.918 B- * 109 944258.765 108.415 +0 31 71 40 111 Zr x -37560# 700# 8128# 6# B- 11316# 760# 110 959678# 751# + 29 70 41 111 Nb x -48875# 298# 8223# 3# B- 11064# 298# 110 947530# 320# + 27 69 42 111 Mo + -59939.761 12.578 8315.292 0.113 B- 9084.861 6.800 110 935652.016 13.502 + 25 68 43 111 Tc x -69024.622 10.581 8390.089 0.095 B- 7760.649 13.848 110 925899.016 11.359 + 23 67 44 111 Ru x -76785.271 9.682 8452.957 0.087 B- 5519.181 11.860 110 917567.616 10.394 + 21 66 45 111 Rh -82304.452 6.850 8495.631 0.062 B- 3681.435 6.887 110 911642.531 7.354 + 19 65 46 111 Pd -n -85985.888 0.731 8521.749 0.007 B- 2229.560 1.572 110 907690.347 0.785 + 17 64 47 111 Ag + -88215.447 1.459 8534.787 0.013 B- 1036.800 1.414 110 905296.816 1.565 + 15 63 48 111 Cd -89252.247 0.357 8537.079 0.003 B- -860.204 3.417 110 904183.766 0.383 + 13 62 49 111 In -88392.043 3.424 8522.282 0.031 B- -2453.456 6.337 110 905107.233 3.675 + 11 61 50 111 Sn +n -85938.587 5.336 8493.130 0.048 B- -5101.851 10.334 110 907741.126 5.728 + 9 60 51 111 Sb x -80836.736 8.849 8440.120 0.080 B- -7249.259 10.937 110 913218.189 9.500 + 7 59 52 111 Te x -73587.477 6.427 8367.763 0.058 B- -8633.692 7.994 110 921000.589 6.900 + 5 58 53 111 I -64953.785 4.754 8282.934 0.043 B- -10558.252 86.830 110 930269.239 5.103 + 3 57 54 111 Xe -a -54395.534 86.700 8180.766 0.781 B- -11575# 214# 110 941603.989 93.076 + 1 56 55 111 Cs x -42821# 196# 8069# 2# B- * 110 954030# 210# +0 32 72 40 112 Zr x -33810# 700# 8094# 6# B- 10463# 760# 111 963703# 751# + 30 71 41 112 Nb x -44274# 298# 8180# 3# B- 13190# 357# 111 952470# 320# + 28 70 42 112 Mo x -57464# 196# 8291# 2# B- 7795# 196# 111 938310# 210# + 26 69 43 112 Tc x -65258.938 5.515 8353.621 0.049 B- 10371.881 11.060 111 929941.644 5.920 + 24 68 44 112 Ru x -75630.818 9.599 8439.242 0.086 B- 4100.685 45.118 111 918806.972 10.305 + 22 67 45 112 Rh -79731.503 44.085 8468.870 0.394 B- 6590.059 43.927 111 914404.705 47.327 + 20 66 46 112 Pd -86321.562 6.544 8520.724 0.058 B- 262.156 6.978 111 907329.986 7.025 + 18 65 47 112 Ag x -86583.718 2.422 8516.080 0.022 B- 3991.141 2.435 111 907048.550 2.600 + 16 64 48 112 Cd -90574.859 0.250 8544.730 0.002 B- -2584.728 4.243 111 902763.883 0.268 + 14 63 49 112 In -87990.131 4.251 8514.667 0.038 B- 664.925 4.243 111 905538.704 4.563 + 12 62 50 112 Sn -88655.056 0.294 8513.618 0.003 B- -7056.091 17.832 111 904824.877 0.315 + 10 61 51 112 Sb x -81598.965 17.829 8443.632 0.159 B- -4031.457 19.702 111 912399.903 19.140 + 8 60 52 112 Te x -77567.508 8.383 8400.652 0.075 B- -10504.178 13.239 111 916727.850 9.000 + 6 59 53 112 I x -67063.330 10.246 8299.879 0.091 B- -7036.991 13.175 111 928004.550 11.000 + 4 58 54 112 Xe -a -60026.338 8.283 8230.064 0.074 B- -13736.062 87.190 111 935559.071 8.891 + 2 57 55 112 Cs -p -46290.277 86.796 8100.435 0.775 B- * 111 950305.341 93.178 +0 31 72 41 113 Nb x -40511# 401# 8146# 4# B- 11979# 500# 112 956510# 430# + 29 71 42 113 Mo x -52490# 300# 8245# 3# B- 10322# 300# 112 943650# 322# + 27 70 43 113 Tc x -62811.541 3.353 8329.464 0.030 B- 9056.578 37.028 112 932569.033 3.600 + 25 69 44 113 Ru -71868.119 36.875 8402.688 0.326 B- 6899.417 37.558 112 922846.396 39.587 + 23 68 45 113 Rh x -78767.536 7.130 8456.821 0.063 B- 4823.555 9.881 112 915439.567 7.653 + 21 67 46 113 Pd x -83591.092 6.945 8492.584 0.061 B- 3435.731 18.033 112 910261.267 7.455 + 19 66 47 113 Ag + -87026.822 16.643 8516.065 0.147 B- 2016.462 16.641 112 906572.858 17.866 + 17 65 48 113 Cd -89043.284 0.244 8526.987 0.002 B- 323.833 0.265 112 904408.097 0.262 + 15 64 49 113 In -89367.117 0.188 8522.929 0.002 B- -1038.985 1.573 112 904060.448 0.202 + 13 63 50 113 Sn -88328.132 1.575 8506.811 0.014 B- -3911.164 17.121 112 905175.845 1.690 + 11 62 51 113 Sb - -84416.968 17.193 8465.275 0.152 B- -6069.939 32.810 112 909374.652 18.457 + 9 61 52 113 Te x -78347.029 27.945 8404.636 0.247 B- -7227.522 29.070 112 915891.000 30.000 + 7 60 53 113 I x -71119.507 8.011 8333.752 0.071 B- -8915.889 10.533 112 923650.064 8.600 + 5 59 54 113 Xe -62203.618 6.840 8247.927 0.061 B- -10439.088 10.970 112 933221.666 7.342 + 3 58 55 113 Cs -p -51764.530 8.577 8148.622 0.076 B- -11980# 298# 112 944428.488 9.207 + 1 57 56 113 Ba x -39784# 298# 8036# 3# B- * 112 957290# 320# +0 32 73 41 114 Nb x -35387# 503# 8100# 4# B- 14420# 585# 113 962010# 540# + 30 72 42 114 Mo x -49807# 298# 8220# 3# B- 8793# 526# 113 946530# 320# + 28 71 43 114 Tc x -58600.288 433.145 8290.259 3.800 B- 11621.524 433.159 113 937090.000 465.000 + 26 70 44 114 Ru x -70221.811 3.550 8385.340 0.031 B- 5488.813 71.643 113 924613.780 3.811 + 24 69 45 114 Rh -75710.625 71.561 8426.624 0.628 B- 7780.319 71.891 113 918721.296 76.824 + 22 68 46 114 Pd x -83490.943 6.945 8488.010 0.061 B- 1439.856 8.311 113 910368.780 7.456 + 20 67 47 114 Ag x -84930.800 4.564 8493.778 0.040 B- 5084.133 4.573 113 908823.031 4.900 + 18 66 48 114 Cd -90014.932 0.276 8531.513 0.002 B- -1445.132 0.382 113 903364.990 0.296 + 16 65 49 114 In -88569.801 0.301 8511.973 0.003 B- 1989.923 0.302 113 904916.402 0.323 + 14 64 50 114 Sn -90559.723 0.029 8522.566 0.000 B- -6063.149 21.838 113 902780.132 0.031 + 12 63 51 114 Sb -84496.574 21.838 8462.518 0.192 B- -2608.005 35.466 113 909289.191 23.444 + 10 62 52 114 Te x -81888.569 27.945 8432.778 0.245 B- -9092# 152# 113 912089.000 30.000 + 8 61 53 114 I x -72796# 149# 8346# 1# B- -5710# 149# 113 921850# 160# + 6 60 54 114 Xe x -67085.890 11.178 8289.205 0.098 B- -12403.629 71.976 113 927980.331 12.000 + 4 59 55 114 Cs -a -54682.261 71.102 8173.538 0.624 B- -8776.835 124.892 113 941296.175 76.331 + 2 58 56 114 Ba -a -45905.426 102.676 8089.686 0.901 B- * 113 950718.495 110.227 +0 33 74 41 115 Nb x -31354# 503# 8065# 4# B- 13395# 643# 114 966340# 540# + 31 73 42 115 Mo x -44749# 401# 8175# 3# B- 11571# 885# 114 951960# 430# + 29 72 43 115 Tc x -56319.990 789.441 8268.527 6.865 B- 9869.744 794.386 114 939538.000 847.500 + 27 71 44 115 Ru x -66189.734 88.496 8347.547 0.770 B- 8040.097 88.790 114 928942.393 95.004 + 25 70 45 115 Rh x -74229.831 7.316 8410.658 0.064 B- 6196.554 15.350 114 920310.993 7.854 + 23 69 46 115 Pd -80426.386 13.546 8457.738 0.118 B- 4556.268 21.649 114 913658.718 14.541 + 21 68 47 115 Ag -84982.654 18.268 8490.555 0.159 B- 3101.825 18.274 114 908767.363 19.611 + 19 67 48 115 Cd -88084.479 0.651 8510.724 0.006 B- 1451.867 0.651 114 905437.417 0.699 + 17 66 49 115 In -89536.346 0.012 8516.546 0.000 B- 497.489 0.010 114 903878.773 0.012 + 15 65 50 115 Sn -90033.835 0.015 8514.069 0.000 B- -3030.432 16.025 114 903344.697 0.016 + 13 64 51 115 Sb x -87003.403 16.025 8480.915 0.139 B- -4940.644 32.214 114 906598.000 17.203 + 11 63 52 115 Te x -82062.759 27.945 8431.150 0.243 B- -5724.962 40.184 114 911902.000 30.000 + 9 62 53 115 I x -76337.797 28.876 8374.564 0.251 B- -7681.049 31.313 114 918048.000 31.000 + 7 61 54 115 Xe x -68656.748 12.109 8300.970 0.105 B- -8957# 103# 114 926293.945 13.000 + 5 60 55 115 Cs x -59699# 102# 8216# 1# B- -10680# 225# 114 935910# 110# + 3 59 56 115 Ba x -49020# 200# 8117# 2# B- * 114 947375# 215# +0 32 74 42 116 Mo x -41500# 500# 8146# 4# B- 9956# 582# 115 955448# 537# + 30 73 43 116 Tc x -51456# 298# 8225# 3# B- 12613# 298# 115 944760# 320# + 28 72 44 116 Ru x -64068.909 3.726 8326.883 0.032 B- 6667.213 73.926 115 931219.193 4.000 + 26 71 45 116 Rh -70736.122 73.832 8377.615 0.636 B- 9095.512 74.169 115 924061.645 79.261 + 24 70 46 116 Pd x -79831.635 7.132 8449.280 0.061 B- 2711.019 7.842 115 914297.210 7.656 + 22 69 47 116 Ag x -82542.653 3.260 8465.907 0.028 B- 6169.827 3.264 115 911386.812 3.500 + 20 68 48 116 Cd -88712.480 0.160 8512.350 0.001 B- -462.731 0.272 115 904763.230 0.172 + 18 67 49 116 In -n -88249.749 0.220 8501.617 0.002 B- 3276.221 0.240 115 905259.992 0.236 + 16 66 50 116 Sn -91525.970 0.096 8523.116 0.001 B- -4703.820 5.160 115 901742.824 0.103 + 14 65 51 116 Sb -86822.150 5.160 8475.821 0.044 B- -1553.189 28.417 115 906792.583 5.539 + 12 64 52 116 Te x -85268.961 27.945 8455.687 0.241 B- -7776.725 100.553 115 908460.000 30.000 + 10 63 53 116 I + -77492.236 96.592 8381.902 0.833 B- -4445.512 95.707 115 916808.658 103.695 + 8 62 54 116 Xe x -73046.724 13.041 8336.834 0.112 B- -11004# 101# 115 921581.112 14.000 + 6 61 55 116 Cs ea -62043# 100# 8235# 1# B- -7463# 224# 115 933395# 108# + 4 60 56 116 Ba x -54580# 200# 8164# 2# B- -13935# 371# 115 941406# 215# + 2 59 57 116 La -a -40645# 312# 8037# 3# B- * 115 956365# 335# +0 33 75 42 117 Mo x -36170# 500# 8100# 4# B- 12212# 641# 116 961170# 537# + 31 74 43 117 Tc x -48382# 401# 8197# 3# B- 11108# 590# 116 948060# 430# + 29 73 44 117 Ru x -59489.865 433.145 8285.562 3.702 B- 9407.508 433.236 116 936135.000 465.000 + 27 72 45 117 Rh x -68897.373 8.892 8359.281 0.076 B- 7527.104 11.411 116 926035.623 9.546 + 25 71 46 117 Pd -76424.477 7.252 8416.929 0.062 B- 5757.537 14.766 116 917954.944 7.785 + 23 70 47 117 Ag -82182.014 13.572 8459.452 0.116 B- 4236.375 13.610 116 911773.974 14.570 + 21 69 48 117 Cd -n -86418.389 1.013 8488.973 0.009 B- 2524.653 4.983 116 907226.038 1.087 + 19 68 49 117 In -88943.042 4.881 8503.865 0.042 B- 1454.709 4.857 116 904515.712 5.239 + 17 67 50 117 Sn -90397.751 0.483 8509.611 0.004 B- -1758.212 8.445 116 902954.017 0.518 + 15 66 51 117 Sb -88639.539 8.437 8487.897 0.072 B- -3544.128 13.079 116 904841.535 9.057 + 13 65 52 117 Te -85095.411 13.456 8450.919 0.115 B- -4659.334 28.673 116 908646.313 14.446 + 11 64 53 117 I -80436.077 26.196 8404.409 0.224 B- -6250.740 28.177 116 913648.314 28.123 + 9 63 54 117 Xe x -74185.337 10.378 8344.297 0.089 B- -7692.245 63.267 116 920358.760 11.141 + 7 62 55 117 Cs x -66493.092 62.410 8271.864 0.533 B- -9035.338 258.002 116 928616.726 67.000 + 5 61 56 117 Ba ep -57457.753 250.340 8187.953 2.140 B- -10987# 321# 116 938316.561 268.750 + 3 60 57 117 La -p -46471# 200# 8087# 2# B- * 116 950111# 215# +0 34 76 42 118 Mo x -32630# 500# 8069# 4# B- 11159# 641# 117 964970# 537# + 32 75 43 118 Tc x -43790# 401# 8157# 3# B- 13470# 448# 117 952990# 430# + 30 74 44 118 Ru x -57260# 200# 8265# 2# B- 7628# 202# 117 938529# 215# + 28 73 45 118 Rh x -64887.460 24.235 8322.858 0.205 B- 10501.286 24.342 117 930340.443 26.017 + 26 72 46 118 Pd -75388.746 2.491 8405.222 0.021 B- 4165.046 3.539 117 919066.847 2.673 + 24 71 47 118 Ag x -79553.792 2.515 8433.889 0.021 B- 7147.849 20.158 117 914595.487 2.700 + 22 70 48 118 Cd -nn -86701.641 20.001 8487.834 0.169 B- 526.570 21.450 117 906921.955 21.471 + 20 69 49 118 In -87228.211 7.752 8485.667 0.066 B- 4424.643 7.740 117 906356.659 8.322 + 18 68 50 118 Sn -91652.853 0.499 8516.533 0.004 B- -3656.640 2.975 117 901606.609 0.536 + 16 67 51 118 Sb - -87996.213 3.016 8478.915 0.026 B- -299.630 18.726 117 905532.174 3.238 + 14 66 52 118 Te +nn -87696.584 18.481 8469.746 0.157 B- -6725.536 27.056 117 905853.839 19.840 + 12 65 53 118 I x -80971.048 19.760 8406.120 0.167 B- -2891.991 22.320 117 913074.000 21.213 + 10 64 54 118 Xe x -78079.057 10.378 8374.981 0.088 B- -9669.689 16.442 117 916178.680 11.141 + 8 63 55 118 Cs IT -68409.367 12.753 8286.404 0.108 B- -6055# 196# 117 926559.519 13.690 + 6 62 56 118 Ba x -62354# 196# 8228# 2# B- -12794# 358# 117 933060# 210# + 4 61 57 118 La x -49560# 300# 8113# 3# B- * 117 946795# 322# +0 33 76 43 119 Tc x -40371# 503# 8128# 4# B- 12193# 585# 118 956660# 540# + 31 75 44 119 Ru x -52564# 298# 8224# 3# B- 10259# 298# 118 943570# 320# + 29 74 45 119 Rh x -62822.794 9.315 8303.394 0.078 B- 8585.108 12.440 118 932556.952 10.000 + 27 73 46 119 Pd x -71407.902 8.245 8368.964 0.069 B- 7237.863 16.855 118 923340.459 8.851 + 25 72 47 119 Ag -78645.765 14.703 8423.212 0.124 B- 5331.303 35.926 118 915570.293 15.783 + 23 71 48 119 Cd -83977.068 37.695 8461.438 0.317 B- 3722.212 38.088 118 909846.903 40.467 + 21 70 49 119 In -87699.281 7.307 8486.143 0.061 B- 2365.742 7.336 118 905850.944 7.844 + 19 69 50 119 Sn -90065.022 0.725 8499.449 0.006 B- -590.843 7.689 118 903311.216 0.778 + 17 68 51 119 Sb -89474.180 7.701 8487.910 0.065 B- -2293.000 2.000 118 903945.512 8.267 + 15 67 52 119 Te - -87181.180 7.957 8462.066 0.067 B- -3415.650 29.055 118 906407.148 8.541 + 13 66 53 119 I x -83765.530 27.945 8426.789 0.235 B- -4971.117 29.810 118 910074.000 30.000 + 11 65 54 119 Xe x -78794.413 10.378 8378.441 0.087 B- -6489.361 17.379 118 915410.713 11.141 + 9 64 55 119 Cs IT -72305.051 13.940 8317.334 0.117 B- -7714.965 200.754 118 922377.330 14.965 + 7 63 56 119 Ba ep -64590.086 200.269 8245.928 1.683 B- -9801# 361# 118 930659.686 214.997 + 5 62 57 119 La x -54790# 300# 8157# 3# B- -10849# 583# 118 941181# 322# + 3 61 58 119 Ce x -43940# 500# 8059# 4# B- * 118 952828# 537# +0 34 77 43 120 Tc x -35518# 503# 8087# 4# B- 14494# 643# 119 961870# 540# + 32 76 44 120 Ru x -50012# 401# 8201# 3# B- 8803# 446# 119 946310# 430# + 30 75 45 120 Rh x -58815# 196# 8268# 2# B- 11466# 196# 119 936860# 210# + 28 74 46 120 Pd -70280.050 2.291 8357.085 0.019 B- 5371.451 5.024 119 924551.258 2.459 + 26 73 47 120 Ag x -75651.502 4.471 8395.327 0.037 B- 8305.853 5.820 119 918784.767 4.800 + 24 72 48 120 Cd x -83957.354 3.726 8458.023 0.031 B- 1771.015 40.183 119 909868.067 4.000 + 22 71 49 120 In + -85728.369 40.010 8466.262 0.333 B- 5370.000 40.000 119 907966.805 42.952 + 20 70 50 120 Sn -91098.369 0.896 8504.492 0.007 B- -2680.608 7.140 119 902201.873 0.962 + 18 69 51 120 Sb - -88417.761 7.196 8475.635 0.060 B- 950.226 7.811 119 905079.624 7.725 + 16 68 52 120 Te -89367.987 3.085 8477.034 0.026 B- -5615.000 15.000 119 904059.514 3.311 + 14 67 53 120 I - -83752.987 15.314 8423.722 0.128 B- -1580.563 19.343 119 910087.465 16.440 + 12 66 54 120 Xe x -82172.423 11.817 8404.031 0.098 B- -8283.785 15.461 119 911784.270 12.686 + 10 65 55 120 Cs IT -73888.639 9.970 8328.480 0.083 B- -5000.000 300.000 119 920677.279 10.702 + 8 64 56 120 Ba - -68888.639 300.166 8280.294 2.501 B- -11319# 424# 119 926045.000 322.241 + 6 63 57 120 La x -57570# 300# 8179# 2# B- -7970# 583# 119 938196# 322# + 4 62 58 120 Ce x -49600# 500# 8107# 4# B- * 119 946752# 537# +0 35 78 43 121 Tc x -31780# 500# 8056# 4# B- 13267# 641# 120 965883# 537# + 33 77 44 121 Ru x -45047# 401# 8159# 3# B- 11203# 738# 120 951640# 430# + 31 76 45 121 Rh x -56250.128 619.444 8245.239 5.119 B- 9932.201 619.453 120 939613.000 665.000 + 29 75 46 121 Pd x -66182.329 3.353 8320.858 0.028 B- 8220.492 12.565 120 928950.343 3.600 + 27 74 47 121 Ag x -74402.821 12.109 8382.330 0.100 B- 6671.005 12.264 120 920125.282 13.000 + 25 73 48 121 Cd x -81073.826 1.942 8430.996 0.016 B- 4762.148 27.483 120 912963.663 2.085 + 23 72 49 121 In +p -85835.974 27.414 8463.887 0.227 B- 3361.291 27.408 120 907851.286 29.430 + 21 71 50 121 Sn -89197.265 0.955 8485.201 0.008 B- 403.057 2.690 120 904242.792 1.025 + 19 70 51 121 Sb -89600.321 2.582 8482.066 0.021 B- -1054.819 25.767 120 903810.093 2.771 + 17 69 52 121 Te -88545.502 25.850 8466.883 0.214 B- -2294.053 26.047 120 904942.488 27.751 + 15 68 53 121 I -86251.449 5.356 8441.458 0.044 B- -3770.463 11.558 120 907405.255 5.749 + 13 67 54 121 Xe -82480.986 10.243 8403.832 0.085 B- -5378.654 13.979 120 911453.014 10.995 + 11 66 55 121 Cs -77102.331 14.290 8352.914 0.118 B- -6357.495 141.176 120 917227.238 15.340 + 9 65 56 121 Ba - -70744.837 141.898 8293.907 1.173 B- -8555# 332# 120 924052.289 152.333 + 7 64 57 121 La x -62190# 300# 8217# 2# B- -9500# 500# 120 933236# 322# + 5 63 58 121 Ce x -52690# 401# 8132# 3# B- -11268# 641# 120 943435# 430# + 3 62 59 121 Pr -p -41422# 500# 8032# 4# B- * 120 955532# 537# +0 34 78 44 122 Ru x -42150# 500# 8135# 4# B- 9930# 583# 121 954750# 537# + 32 77 45 122 Rh x -52080# 300# 8210# 2# B- 12536# 301# 121 944090# 322# + 30 76 46 122 Pd x -64616.161 19.561 8305.975 0.160 B- 6489.948 42.909 121 930631.694 21.000 + 28 75 47 122 Ag x -71106.108 38.191 8352.758 0.313 B- 9506.265 38.260 121 923664.448 41.000 + 26 74 48 122 Cd -80612.374 2.299 8424.266 0.019 B- 2960.368 50.110 121 913459.052 2.468 + 24 73 49 122 In + -83572.741 50.057 8442.118 0.410 B- 6368.592 50.000 121 910280.966 53.738 + 22 72 50 122 Sn -89941.333 2.395 8487.907 0.020 B- -1605.963 3.384 121 903444.001 2.570 + 20 71 51 122 Sb -88335.370 2.578 8468.331 0.021 B- 1979.089 2.127 121 905168.074 2.768 + 18 70 52 122 Te -90314.460 1.507 8478.140 0.012 B- -4234.000 5.000 121 903043.434 1.617 + 16 69 53 122 I - -86080.460 5.222 8437.023 0.043 B- -725.483 12.277 121 907588.820 5.606 + 14 68 54 122 Xe x -85354.977 11.111 8424.664 0.091 B- -7210.218 35.472 121 908367.658 11.928 + 12 67 55 122 Cs -78144.759 33.687 8359.151 0.276 B- -3535.815 43.769 121 916108.145 36.164 + 10 66 56 122 Ba x -74608.944 27.945 8323.756 0.229 B- -10066# 299# 121 919904.000 30.000 + 8 65 57 122 La x -64543# 298# 8235# 2# B- -6669# 499# 121 930710# 320# + 6 64 58 122 Ce x -57874# 401# 8174# 3# B- -13094# 641# 121 937870# 430# + 4 63 59 122 Pr x -44780# 500# 8060# 4# B- * 121 951927# 537# +0 35 79 44 123 Ru x -37080# 500# 8093# 4# B- 12280# 640# 122 960193# 537# + 33 78 45 123 Rh x -49360# 400# 8186# 3# B- 11070# 885# 122 947010# 429# + 31 77 46 123 Pd x -60429.742 789.441 8270.031 6.418 B- 9118.336 790.039 122 935126.000 847.500 + 29 76 47 123 Ag x -69548.078 30.739 8337.803 0.250 B- 7866.103 30.857 122 925337.062 33.000 + 27 75 48 123 Cd -77414.181 2.696 8395.395 0.022 B- 6016.172 19.893 122 916892.453 2.894 + 25 74 49 123 In -83430.353 19.827 8437.946 0.161 B- 4385.828 19.839 122 910433.826 21.285 + 23 73 50 123 Sn -87816.181 2.416 8467.243 0.020 B- 1407.888 2.662 122 905725.446 2.594 + 21 72 51 123 Sb -89224.069 1.506 8472.328 0.012 B- -51.913 0.066 122 904214.016 1.616 + 19 71 52 123 Te -89172.156 1.505 8465.546 0.012 B- -1228.429 3.445 122 904269.747 1.615 + 17 70 53 123 I -87943.727 3.740 8449.198 0.030 B- -2695.027 9.690 122 905588.520 4.014 + 15 69 54 123 Xe -85248.701 9.537 8420.927 0.078 B- -4205.055 15.414 122 908481.750 10.238 + 13 68 55 123 Cs x -81043.646 12.109 8380.379 0.098 B- -5388.693 17.125 122 912996.062 13.000 + 11 67 56 123 Ba x -75654.953 12.109 8330.208 0.098 B- -7004# 196# 122 918781.062 13.000 + 9 66 57 123 La x -68651# 196# 8267# 2# B- -8365# 357# 122 926300# 210# + 7 65 58 123 Ce x -60286# 298# 8193# 2# B- -10056# 499# 122 935280# 320# + 5 64 59 123 Pr x -50230# 400# 8104# 3# B- * 122 946076# 429# +0 36 80 44 124 Ru x -33960# 600# 8068# 5# B- 10929# 721# 123 963542# 644# + 34 79 45 124 Rh x -44890# 400# 8149# 3# B- 13500# 499# 123 951809# 429# + 32 78 46 124 Pd x -58390# 298# 8252# 2# B- 7810# 390# 123 937316# 320# + 30 77 47 124 Ag x -66200.134 251.503 8308.655 2.028 B- 10501.538 251.521 123 928931.229 270.000 + 28 76 48 124 Cd -76701.672 2.995 8387.035 0.024 B- 4168.529 30.539 123 917657.363 3.215 + 26 75 49 124 In -80870.201 30.572 8414.343 0.247 B- 7363.992 30.576 123 913182.263 32.820 + 24 74 50 124 Sn -88234.193 1.014 8467.421 0.008 B- -613.944 1.513 123 905276.692 1.088 + 22 73 51 124 Sb -n -87620.248 1.507 8456.160 0.012 B- 2905.073 0.132 123 905935.789 1.618 + 20 72 52 124 Te -90525.321 1.502 8473.279 0.012 B- -3159.587 1.859 123 902817.064 1.612 + 18 71 53 124 I - -87365.734 2.390 8441.489 0.019 B- 295.686 2.846 123 906209.021 2.566 + 16 70 54 124 Xe -87661.421 1.793 8437.565 0.014 B- -5930.086 8.495 123 905891.588 1.924 + 14 69 55 124 Cs x -81731.334 8.304 8383.432 0.067 B- -2641.559 15.004 123 912257.798 8.914 + 12 68 56 124 Ba x -79089.775 12.497 8355.820 0.101 B- -8831.165 58.030 123 915093.629 13.416 + 10 67 57 124 La x -70258.610 56.669 8278.292 0.457 B- -5343# 303# 123 924574.275 60.836 + 8 66 58 124 Ce x -64916# 298# 8229# 2# B- -11765# 499# 123 930310# 320# + 6 65 59 124 Pr x -53151# 401# 8128# 3# B- -8626# 643# 123 942940# 430# + 4 64 60 124 Nd x -44525# 503# 8052# 4# B- * 123 952200# 540# +0 35 80 45 125 Rh x -42000# 500# 8126# 4# B- 12120# 640# 124 954911# 537# + 33 79 46 125 Pd x -54120# 400# 8216# 3# B- 10400# 589# 124 941900# 429# + 31 78 47 125 Ag x -64519.932 433.145 8293.314 3.465 B- 8828.163 433.154 124 930735.000 465.000 + 29 77 48 125 Cd -73348.095 2.885 8357.681 0.023 B- 7128.710 27.119 124 921257.577 3.097 + 27 76 49 125 In -80476.805 27.023 8408.452 0.216 B- 5419.571 27.011 124 913604.591 29.010 + 25 75 50 125 Sn -85896.376 1.033 8445.550 0.008 B- 2359.899 2.610 124 907786.442 1.109 + 23 74 51 125 Sb + -88256.274 2.599 8458.170 0.021 B- 766.700 2.121 124 905252.987 2.790 + 21 73 52 125 Te -89022.974 1.502 8458.045 0.012 B- -185.770 0.060 124 904429.900 1.612 + 19 72 53 125 I - -88837.204 1.504 8450.300 0.012 B- -1643.824 2.192 124 904629.333 1.614 + 17 71 54 125 Xe -87193.381 1.836 8430.890 0.015 B- -3105.430 7.831 124 906394.050 1.971 + 15 70 55 125 Cs -84087.950 7.744 8399.788 0.062 B- -4418.985 13.446 124 909727.867 8.313 + 13 69 56 125 Ba -79668.965 10.992 8358.178 0.088 B- -5909.481 27.631 124 914471.843 11.800 + 11 68 57 125 La -73759.484 25.997 8304.643 0.208 B- -7102# 197# 124 920815.932 27.909 + 9 67 58 125 Ce x -66658# 196# 8242# 2# B- -8718# 358# 124 928440# 210# + 7 66 59 125 Pr x -57940# 300# 8166# 2# B- -10341# 500# 124 937799# 322# + 5 65 60 125 Nd x -47599# 401# 8077# 3# B- * 124 948900# 430# +0 36 81 45 126 Rh x -37300# 500# 8088# 4# B- 14560# 640# 125 959957# 537# + 34 80 46 126 Pd x -51860# 400# 8197# 3# B- 8820# 447# 125 944326# 429# + 32 79 47 126 Ag x -60680# 200# 8261# 2# B- 11576# 200# 125 934857# 215# + 30 78 48 126 Cd -72256.802 2.476 8346.747 0.020 B- 5516.106 26.908 125 922429.127 2.658 + 28 77 49 126 In -77772.908 26.921 8384.317 0.214 B- 8242.332 27.078 125 916507.344 28.901 + 26 76 50 126 Sn -86015.240 10.447 8443.523 0.083 B- 378.000 30.000 125 907658.836 11.215 + 24 75 51 126 Sb - -86393.240 31.767 8440.314 0.252 B- 3672.108 31.787 125 907253.036 34.103 + 22 74 52 126 Te -90065.348 1.504 8463.248 0.012 B- -2154.031 3.677 125 903310.866 1.614 + 20 73 53 126 I -87911.318 3.809 8439.944 0.030 B- 1235.644 5.173 125 905623.313 4.089 + 18 72 54 126 Xe -89146.962 3.500 8443.541 0.028 B- -4796.133 10.671 125 904296.794 3.757 + 16 71 55 126 Cs -84350.829 10.401 8399.268 0.083 B- -1680.927 16.259 125 909445.655 11.166 + 14 70 56 126 Ba x -82669.902 12.497 8379.718 0.099 B- -7696.435 91.366 125 911250.204 13.416 + 12 69 57 126 La x -74973.468 90.508 8312.426 0.718 B- -4152.910 94.723 125 919512.667 97.163 + 10 68 58 126 Ce x -70820.558 27.945 8273.257 0.222 B- -10497# 198# 125 923971.000 30.000 + 8 67 59 126 Pr x -60324# 196# 8184# 2# B- -7331# 357# 125 935240# 210# + 6 66 60 126 Nd x -52993# 298# 8119# 2# B- -13643# 582# 125 943110# 320# + 4 65 61 126 Pm x -39350# 500# 8005# 4# B- * 125 957756# 537# +0 37 82 45 127 Rh x -34030# 600# 8062# 5# B- 13150# 781# 126 963467# 644# + 35 81 46 127 Pd x -47180# 500# 8159# 4# B- 11260# 539# 126 949350# 537# + 33 80 47 127 Ag x -58440# 200# 8242# 2# B- 10307# 201# 126 937262# 215# + 31 79 48 127 Cd x -68747.402 12.109 8316.945 0.095 B- 8148.782 24.378 126 926196.624 13.000 + 29 78 49 127 In -76896.184 21.157 8374.949 0.167 B- 6574.619 19.098 126 917448.546 22.713 + 27 77 50 127 Sn -83470.803 10.057 8420.557 0.079 B- 3228.674 10.875 126 910390.401 10.796 + 25 76 51 127 Sb -86699.477 5.126 8439.820 0.040 B- 1582.201 4.913 126 906924.277 5.502 + 23 75 52 127 Te -88281.678 1.514 8446.118 0.012 B- 702.231 3.575 126 905225.714 1.625 + 21 74 53 127 I -88983.909 3.647 8445.487 0.029 B- -662.349 2.044 126 904471.838 3.915 + 19 73 54 127 Xe -88321.560 4.110 8434.111 0.032 B- -2081.406 6.421 126 905182.899 4.412 + 17 72 55 127 Cs -86240.154 5.578 8411.562 0.044 B- -3422.210 12.653 126 907417.381 5.988 + 15 71 56 127 Ba -82817.944 11.357 8378.455 0.089 B- -4921.836 27.740 126 911091.275 12.192 + 13 70 57 127 La -77896.108 26.000 8333.540 0.205 B- -5916.772 38.857 126 916375.084 27.912 + 11 69 58 127 Ce x -71979.336 28.876 8280.791 0.227 B- -7436# 198# 126 922727.000 31.000 + 9 68 59 127 Pr x -64543# 196# 8216# 2# B- -9008# 357# 126 930710# 210# + 7 67 60 127 Nd x -55536# 298# 8139# 2# B- -10749# 499# 126 940380# 320# + 5 66 61 127 Pm x -44786# 401# 8048# 3# B- * 126 951920# 430# +0 36 82 46 128 Pd x -44490# 500# 8138# 4# B- 10130# 583# 127 952238# 537# + 34 81 47 128 Ag x -54620# 300# 8211# 2# B- 12622# 300# 127 941363# 322# + 32 80 48 128 Cd -67241.890 7.244 8303.264 0.057 B- 6904.051 153.554 127 927812.857 7.776 + 30 79 49 128 In -74145.941 153.479 8351.090 1.199 B- 9216.067 153.027 127 920401.053 164.766 + 28 78 50 128 Sn -83362.008 17.660 8416.979 0.138 B- 1268.278 13.796 127 910507.197 18.958 + 26 77 51 128 Sb IT -84630.286 19.119 8420.775 0.149 B- 4363.429 19.117 127 909145.645 20.525 + 24 76 52 128 Te -88993.716 0.866 8448.752 0.007 B- -1254.992 3.714 127 904461.311 0.929 + 22 75 53 128 I -87738.724 3.647 8432.836 0.028 B- 2121.575 3.748 127 905808.600 3.915 + 20 74 54 128 Xe -89860.298 1.061 8443.298 0.008 B- -3928.717 5.380 127 903530.996 1.138 + 18 73 55 128 Cs -85931.581 5.443 8406.493 0.043 B- -553.084 7.525 127 907748.648 5.843 + 16 72 56 128 Ba -85378.497 5.195 8396.060 0.041 B- -6753.066 54.695 127 908342.408 5.577 + 14 71 57 128 La x -78625.431 54.448 8337.190 0.425 B- -3091.513 61.200 127 915592.123 58.452 + 12 70 58 128 Ce x -75533.917 27.945 8306.925 0.218 B- -9203.161 40.859 127 918911.000 30.000 + 10 69 59 128 Pr x -66330.757 29.808 8228.913 0.233 B- -6017# 198# 127 928791.000 32.000 + 8 68 60 128 Nd x -60314# 196# 8176# 2# B- -12529# 357# 127 935250# 210# + 6 67 61 128 Pm x -47786# 298# 8072# 2# B- -9116# 582# 127 948700# 320# + 4 66 62 128 Sm x -38670# 500# 7994# 4# B- * 127 958486# 537# +0 37 83 46 129 Pd x -37610# 600# 8084# 5# B- 14370# 721# 128 959624# 644# + 35 82 47 129 Ag x -51980# 400# 8189# 3# B- 11078# 400# 128 944197# 429# + 33 81 48 129 Cd x -63058.046 16.767 8269.034 0.130 B- 9779.674 16.982 128 932304.399 18.000 + 31 80 49 129 In -72837.720 2.693 8338.780 0.021 B- 7753.183 17.302 128 921805.486 2.891 + 29 79 50 129 Sn -80590.903 17.277 8392.818 0.134 B- 4038.404 27.372 128 913482.102 18.547 + 27 78 51 129 Sb + -84629.307 21.231 8418.058 0.165 B- 2375.500 21.213 128 909146.696 22.792 + 25 77 52 129 Te -87004.807 0.869 8430.409 0.007 B- 1502.318 3.142 128 906596.492 0.933 + 23 76 53 129 I -88507.125 3.168 8435.990 0.025 B- 188.934 3.168 128 904983.687 3.401 + 21 75 54 129 Xe -88696.05896 0.00537 8431.390 0.000 B- -1196.813 4.555 128 904780.85892 0.00576 + 19 74 55 129 Cs -87499.246 4.555 8416.047 0.035 B- -2436.048 10.623 128 906065.690 4.889 + 17 73 56 129 Ba -85063.198 10.577 8391.098 0.082 B- -3738.625 21.639 128 908680.896 11.354 + 15 72 57 129 La -81324.573 21.351 8356.052 0.166 B- -5037.077 35.168 128 912694.475 22.920 + 13 71 58 129 Ce x -76287.496 27.945 8310.940 0.217 B- -6513.938 40.859 128 918102.000 30.000 + 11 70 59 129 Pr x -69773.558 29.808 8254.380 0.231 B- -7459# 204# 128 925095.000 32.000 + 9 69 60 129 Nd ep -62315# 202# 8190# 2# B- -9434# 360# 128 933102# 217# + 7 68 61 129 Pm x -52881# 298# 8111# 2# B- -10881# 582# 128 943230# 320# + 5 67 62 129 Sm x -42000# 500# 8021# 4# B- * 128 954911# 537# +0 36 83 47 130 Ag -nn -45697# 500# 8140# 4# B- 15420# 500# 129 950942# 537# + 34 82 48 130 Cd x -61117.589 22.356 8252.586 0.172 B- 8765.617 44.128 129 934387.566 24.000 + 32 81 49 130 In + -69883.206 38.046 8313.996 0.293 B- 10249.000 38.000 129 924977.288 40.844 + 30 80 50 130 Sn -80132.206 1.873 8386.816 0.014 B- 2153.470 14.113 129 913974.533 2.010 + 28 79 51 130 Sb -82285.676 14.212 8397.363 0.109 B- 5067.273 14.212 129 911662.688 15.257 + 26 78 52 130 Te -87352.949 0.011 8430.324 0.000 B- -416.811 3.168 129 906222.747 0.012 + 24 77 53 130 I -n -86936.138 3.168 8421.100 0.024 B- 2944.325 3.168 129 906670.211 3.401 + 22 76 54 130 Xe -89880.463 0.009 8437.731 0.000 B- -2980.720 8.357 129 903509.349 0.010 + 20 75 55 130 Cs -86899.743 8.357 8408.784 0.064 B- 361.801 8.738 129 906709.283 8.971 + 18 74 56 130 Ba -87261.544 2.553 8405.549 0.020 B- -5634.178 26.071 129 906320.874 2.741 + 16 73 57 130 La x -81627.366 25.946 8356.191 0.200 B- -2204.461 38.133 129 912369.413 27.854 + 14 72 58 130 Ce x -79422.905 27.945 8333.216 0.215 B- -8247.448 70.085 129 914736.000 30.000 + 12 71 59 130 Pr x -71175.457 64.273 8263.756 0.494 B- -4579.225 70.085 129 923590.000 69.000 + 10 70 60 130 Nd x -66596.232 27.945 8222.513 0.215 B- -11200# 198# 129 928506.000 30.000 + 8 69 61 130 Pm x -55396# 196# 8130# 2# B- -7890# 446# 129 940530# 210# + 6 68 62 130 Sm x -47506# 401# 8064# 3# B- -13823# 641# 129 949000# 430# + 4 67 63 130 Eu -p -33683# 500# 7951# 4# B- * 129 963840# 537# +0 37 84 47 131 Ag x -40380# 500# 8099# 4# B- 14839# 511# 130 956650# 537# + 35 83 48 131 Cd x -55218.965 102.464 8206.175 0.782 B- 12806.066 102.500 130 940720.000 110.000 + 33 82 49 131 In x -68025.030 2.701 8297.959 0.021 B- 9239.541 4.518 130 926972.122 2.900 + 31 81 50 131 Sn -77264.571 3.621 8362.517 0.028 B- 4716.830 3.962 130 917053.066 3.887 + 29 80 51 131 Sb -81981.401 2.084 8392.552 0.016 B- 3229.611 2.085 130 911989.341 2.236 + 27 79 52 131 Te -n -85211.012 0.061 8411.233 0.001 B- 2231.699 0.608 130 908522.211 0.065 + 25 78 53 131 I + -87442.710 0.605 8422.297 0.005 B- 970.848 0.605 130 906126.384 0.649 + 23 77 54 131 Xe -88413.558 0.009 8423.736 0.000 B- -354.772 4.974 130 905084.136 0.009 + 21 76 55 131 Cs -88058.786 4.974 8415.056 0.038 B- -1375.055 5.279 130 905464.999 5.340 + 19 75 56 131 Ba -86683.731 2.569 8398.587 0.020 B- -2914.475 28.063 130 906941.181 2.757 + 17 74 57 131 La x -83769.256 27.945 8370.367 0.213 B- -4060.816 43.092 130 910070.000 30.000 + 15 73 58 131 Ce -79708.440 32.802 8333.396 0.250 B- -5407.784 55.446 130 914429.465 35.214 + 13 72 59 131 Pr -74300.656 46.995 8286.143 0.359 B- -6532.623 53.081 130 920234.960 50.451 + 11 71 60 131 Nd -67768.033 27.517 8230.304 0.210 B- -8108# 202# 130 927248.020 29.541 + 9 70 61 131 Pm x -59660# 200# 8162# 2# B- -9527# 448# 130 935952# 215# + 7 69 62 131 Sm x -50133# 401# 8084# 3# B- -10863# 566# 130 946180# 430# + 5 68 63 131 Eu -p -39270# 401# 7995# 3# B- * 130 957842# 430# +0 38 85 47 132 Ag x -33790# 500# 8049# 4# B- 16473# 537# 131 963725# 537# + 36 84 48 132 Cd x -50263# 196# 8168# 1# B- 12148# 205# 131 946040# 210# + 34 83 49 132 In + -62411.542 60.033 8253.715 0.455 B- 14135.000 60.000 131 932998.449 64.447 + 32 82 50 132 Sn -76546.542 1.976 8354.872 0.015 B- 3088.729 3.161 131 917823.902 2.121 + 30 81 51 132 Sb -79635.271 2.467 8372.344 0.019 B- 5552.915 4.271 131 914508.015 2.648 + 28 80 52 132 Te -85188.186 3.486 8408.485 0.026 B- 515.304 3.483 131 908546.716 3.742 + 26 79 53 132 I -85703.490 4.065 8406.462 0.031 B- 3575.472 4.065 131 907993.514 4.364 + 24 78 54 132 Xe -89278.96179 0.00515 8427.622 0.000 B- -2126.280 1.036 131 904155.08697 0.00553 + 22 77 55 132 Cs -87152.681 1.036 8405.587 0.008 B- 1282.336 1.478 131 906437.743 1.112 + 20 76 56 132 Ba -88435.017 1.054 8409.375 0.008 B- -4711.367 36.354 131 905061.098 1.131 + 18 75 57 132 La -83723.650 36.359 8367.756 0.275 B- -1252.754 41.718 131 910118.959 39.032 + 16 74 58 132 Ce -82470.896 20.442 8352.338 0.155 B- -7243.440 35.380 131 911463.846 21.945 + 14 73 59 132 Pr x -75227.456 28.876 8291.537 0.219 B- -3801.648 37.679 131 919240.000 31.000 + 12 72 60 132 Nd x -71425.807 24.205 8256.810 0.183 B- -9798# 151# 131 923321.237 25.985 + 10 71 61 132 Pm x -61628# 149# 8177# 1# B- -6548# 333# 131 933840# 160# + 8 70 62 132 Sm x -55079# 298# 8121# 2# B- -12879# 499# 131 940870# 320# + 6 69 63 132 Eu x -42200# 400# 8018# 3# B- * 131 954696# 429# +0 37 85 48 133 Cd x -43920# 298# 8119# 2# B- 13544# 357# 132 952850# 320# + 35 84 49 133 In x -57464# 196# 8215# 1# B- 13410# 196# 132 938310# 210# + 33 83 50 133 Sn -70873.880 1.904 8310.088 0.014 B- 8049.623 3.662 132 923913.756 2.044 + 31 82 51 133 Sb -78923.503 3.128 8364.729 0.024 B- 4013.619 3.518 132 915272.130 3.357 + 29 81 52 133 Te -82937.122 2.066 8389.025 0.016 B- 2921.139 6.751 132 910963.332 2.218 + 27 80 53 133 I ++ -85858.260 6.427 8405.106 0.048 B- 1785.311 6.861 132 907827.361 6.900 + 25 79 54 133 Xe + -87643.571 2.400 8412.647 0.018 B- 427.360 2.400 132 905910.750 2.576 + 23 78 55 133 Cs -88070.931 0.008 8409.978 0.000 B- -517.319 0.992 132 905451.961 0.008 + 21 77 56 133 Ba -87553.613 0.992 8400.206 0.007 B- -2059.230 27.962 132 906007.325 1.065 + 19 76 57 133 La x -85494.383 27.945 8378.841 0.210 B- -3076.168 32.379 132 908218.000 30.000 + 17 75 58 133 Ce x -82418.214 16.354 8349.829 0.123 B- -4480.634 20.583 132 911520.402 17.557 + 15 74 59 133 Pr x -77937.581 12.497 8310.258 0.094 B- -5605.208 48.222 132 916330.561 13.416 + 13 73 60 133 Nd x -72332.372 46.575 8262.231 0.350 B- -6924.726 68.552 132 922348.000 50.000 + 11 72 61 133 Pm x -65407.646 50.301 8204.283 0.378 B- -8177# 302# 132 929782.000 54.000 + 9 71 62 133 Sm x -57231# 298# 8137# 2# B- -9995# 422# 132 938560# 320# + 7 70 63 133 Eu x -47236# 298# 8056# 2# B- -11376# 582# 132 949290# 320# + 5 69 64 133 Gd x -35860# 500# 7964# 4# B- * 132 961503# 537# +0 38 86 48 134 Cd x -38920# 400# 8082# 3# B- 12741# 499# 133 958218# 429# + 36 85 49 134 In x -51661# 298# 8171# 2# B- 14773# 298# 133 944540# 320# + 34 84 50 134 Sn x -66433.748 3.167 8275.171 0.024 B- 7586.794 3.597 133 928680.433 3.400 + 32 83 51 134 Sb x -74020.542 1.705 8325.950 0.013 B- 8513.200 3.233 133 920535.675 1.830 + 30 82 52 134 Te -82533.741 2.746 8383.643 0.020 B- 1509.687 4.933 133 911396.379 2.948 + 28 81 53 134 I -84043.429 4.857 8389.071 0.036 B- 4082.393 4.857 133 909775.663 5.213 + 26 80 54 134 Xe -88125.822 0.009 8413.699 0.000 B- -1234.667 0.018 133 905393.033 0.010 + 24 79 55 134 Cs -86891.154 0.016 8398.646 0.000 B- 2058.699 0.304 133 906718.503 0.017 + 22 78 56 134 Ba -88949.853 0.304 8408.171 0.002 B- -3731.204 19.932 133 904508.399 0.326 + 20 77 57 134 La x -85218.650 19.930 8374.488 0.149 B- -385.760 28.510 133 908514.011 21.395 + 18 76 58 134 Ce x -84832.889 20.387 8365.771 0.152 B- -6304.898 28.781 133 908928.142 21.886 + 16 75 59 134 Pr x -78527.991 20.316 8312.881 0.152 B- -2881.559 23.503 133 915696.729 21.810 + 14 74 60 134 Nd x -75646.432 11.817 8285.538 0.088 B- -8907.681 58.949 133 918790.210 12.686 + 12 73 61 134 Pm x -66738.751 57.753 8213.225 0.431 B- -5363# 204# 133 928353.000 62.000 + 10 72 62 134 Sm x -61376# 196# 8167# 1# B- -11448# 357# 133 934110# 210# + 8 71 63 134 Eu x -49928# 298# 8076# 2# B- -8626# 499# 133 946400# 320# + 6 70 64 134 Gd x -41302# 401# 8006# 3# B- * 133 955660# 430# +0 37 86 49 135 In x -46528# 401# 8132# 3# B- 14104# 401# 134 950050# 430# + 35 85 50 135 Sn x -60632.244 3.074 8230.687 0.023 B- 9058.079 4.052 134 934908.605 3.300 + 33 84 51 135 Sb -69690.323 2.640 8291.989 0.020 B- 8038.457 3.152 134 925184.357 2.834 + 31 83 52 135 Te -77728.780 1.722 8345.738 0.013 B- 6050.366 2.686 134 916554.718 1.848 + 29 82 53 135 I -83779.145 2.061 8384.760 0.015 B- 2634.005 3.868 134 910059.382 2.212 + 27 81 54 135 Xe -86413.151 3.720 8398.476 0.028 B- 1168.492 3.675 134 907231.661 3.993 + 25 80 55 135 Cs -87581.643 0.992 8401.336 0.007 B- 268.855 1.038 134 905977.234 1.064 + 23 79 56 135 Ba -87850.498 0.306 8397.533 0.002 B- -1207.181 9.430 134 905688.606 0.328 + 21 78 57 135 La -86643.317 9.434 8382.795 0.070 B- -2027.146 4.610 134 906984.568 10.127 + 19 77 58 135 Ce -84616.171 10.267 8361.984 0.076 B- -3680.310 15.655 134 909160.799 11.022 + 17 76 59 135 Pr x -80935.861 11.817 8328.928 0.088 B- -4722.252 22.484 134 913111.774 12.686 + 15 75 60 135 Nd x -76213.609 19.128 8288.153 0.142 B- -6161.534 77.838 134 918181.320 20.534 + 13 74 61 135 Pm x -70052.075 75.451 8236.717 0.559 B- -7194.860 172.054 134 924796.000 81.000 + 11 73 62 135 Sm x -62857.215 154.628 8177.626 1.145 B- -8709# 249# 134 932520.000 166.000 + 9 72 63 135 Eu x -54148# 196# 8107# 1# B- -9757# 445# 134 941870# 210# + 7 71 64 135 Gd x -44390# 400# 8029# 3# B- -11565# 566# 134 952345# 429# + 5 70 65 135 Tb -p -32825# 401# 7938# 3# B- * 134 964760# 430# +0 38 87 49 136 In x -40510# 400# 8087# 3# B- 15389# 499# 135 956511# 429# + 36 86 50 136 Sn x -55899# 298# 8195# 2# B- 8608# 298# 135 939990# 320# + 34 85 51 136 Sb -64506.880 5.830 8252.252 0.043 B- 9918.389 6.260 135 930749.011 6.258 + 32 84 52 136 Te -74425.269 2.281 8319.429 0.017 B- 5119.945 14.188 135 920101.182 2.448 + 30 83 53 136 I -79545.214 14.188 8351.323 0.104 B- 6883.945 14.188 135 914604.695 15.231 + 28 82 54 136 Xe -86429.159 0.007 8396.188 0.000 B- -90.462 1.882 135 907214.476 0.007 + 26 81 55 136 Cs + -86338.697 1.882 8389.770 0.014 B- 2548.224 1.857 135 907311.590 2.020 + 24 80 56 136 Ba -88886.921 0.306 8402.755 0.002 B- -2849.443 53.172 135 904575.959 0.328 + 22 79 57 136 La x -86037.479 53.171 8376.050 0.391 B- 470.893 53.173 135 907634.962 57.081 + 20 78 58 136 Ce -86508.372 0.408 8373.760 0.003 B- -5168.017 11.457 135 907129.438 0.438 + 18 77 59 136 Pr -81340.355 11.455 8330.008 0.084 B- -2141.068 16.458 135 912677.532 12.297 + 16 76 60 136 Nd x -79199.287 11.817 8308.512 0.087 B- -8029.371 70.076 135 914976.064 12.686 + 14 75 61 136 Pm x -71169.915 69.073 8243.720 0.508 B- -4359.026 70.194 135 923595.949 74.152 + 12 74 62 136 Sm x -66810.890 12.497 8205.916 0.092 B- -10567# 196# 135 928275.555 13.416 + 10 73 63 136 Eu x -56244# 196# 8122# 1# B- -7154# 357# 135 939620# 210# + 8 72 64 136 Gd x -49090# 298# 8064# 2# B- -12960# 582# 135 947300# 320# + 6 71 65 136 Tb x -36130# 500# 7963# 4# B- * 135 961213# 537# +0 39 88 49 137 In x -35040# 500# 8047# 4# B- 14748# 641# 136 962383# 537# + 37 87 50 137 Sn x -49788# 401# 8149# 3# B- 10272# 404# 136 946550# 430# + 35 86 51 137 Sb x -60060.384 52.164 8218.476 0.381 B- 9243.369 52.206 136 935522.522 56.000 + 33 85 52 137 Te -69303.753 2.100 8280.235 0.015 B- 7052.506 8.643 136 925599.357 2.254 + 31 84 53 137 I p-2n -76356.258 8.383 8326.002 0.061 B- 6027.145 8.384 136 918028.180 9.000 + 29 83 54 137 Xe -n -82383.404 0.103 8364.286 0.001 B- 4162.203 0.373 136 911557.773 0.111 + 27 82 55 137 Cs + -86545.606 0.358 8388.956 0.003 B- 1175.629 0.172 136 907089.464 0.384 + 25 81 56 137 Ba -87721.235 0.314 8391.827 0.002 B- -580.547 1.632 136 905827.375 0.337 + 23 80 57 137 La + -87140.688 1.659 8381.879 0.012 B- -1222.100 1.600 136 906450.618 1.780 + 21 79 58 137 Ce -85918.588 0.437 8367.248 0.003 B- -2716.895 8.133 136 907762.596 0.469 + 19 78 59 137 Pr -83201.693 8.137 8341.706 0.059 B- -3617.126 14.282 136 910679.304 8.735 + 17 77 60 137 Nd -79584.567 11.737 8309.593 0.086 B- -5511.719 17.545 136 914562.448 12.600 + 15 76 61 137 Pm x -74072.848 13.041 8263.651 0.095 B- -6046.323 44.355 136 920479.522 14.000 + 13 75 62 137 Sm -68026.525 42.395 8213.806 0.309 B- -7880.630 42.620 136 926970.517 45.512 + 11 74 63 137 Eu x -60145.895 4.378 8150.573 0.032 B- -8932# 298# 136 935430.722 4.700 + 9 73 64 137 Gd x -51214# 298# 8080# 2# B- -10246# 499# 136 945020# 320# + 7 72 65 137 Tb x -40967# 401# 7999# 3# B- 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141 La -82931.636 4.219 8343.217 0.030 B- 2501.280 3.928 140 910969.222 4.528 + 25 83 58 141 Ce -85432.916 1.597 8355.408 0.011 B- 582.728 1.202 140 908283.987 1.714 + 23 82 59 141 Pr -86015.644 1.665 8353.992 0.012 B- -1823.014 2.809 140 907658.403 1.787 + 21 81 60 141 Nd - -84192.630 3.265 8335.515 0.023 B- -3669.709 14.349 140 909615.488 3.505 + 19 80 61 141 Pm x -80522.921 13.972 8303.940 0.099 B- -4589.012 16.375 140 913555.084 15.000 + 17 79 62 141 Sm -75933.909 8.539 8265.845 0.061 B- -6008.280 14.285 140 918481.591 9.167 + 15 78 63 141 Eu -69925.629 12.639 8217.684 0.090 B- -6701.405 23.456 140 924931.745 13.568 + 13 77 64 141 Gd x -63224.224 19.760 8164.608 0.140 B- -8683.387 107.098 140 932126.000 21.213 + 11 76 65 141 Tb x -54540.837 105.259 8097.475 0.747 B- -9158# 316# 140 941448.000 113.000 + 9 75 66 141 Dy x -45382# 298# 8027# 2# B- -11018# 499# 140 951280# 320# + 7 74 67 141 Ho -p -34364# 401# 7943# 3# B- * 140 963108# 430# +0 38 90 52 142 Te x -46370# 503# 8111# 4# B- 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963578.673 10.491 + 16 93 77 170 Ir -a -23360# 89# 7854# 1# B- -7060# 89# 169 974922# 95# + 14 92 78 170 Pt -16299.193 18.247 7808.236 0.107 B- -12547# 197# 169 982502.095 19.588 + 12 91 79 170 Au -p -3752# 196# 7730# 1# B- * 169 995972# 211# +0 41 106 65 171 Tb x -44032# 503# 8031# 3# B- 6157# 585# 170 952730# 540# + 39 105 66 171 Dy x -50189# 298# 8063# 2# B- 4330# 670# 170 946120# 320# + 37 104 67 171 Ho + -54518.956 600.002 8083.608 3.509 B- 3200.000 600.000 170 941471.490 644.128 + 35 103 68 171 Er -57718.956 1.557 8097.746 0.009 B- 1491.342 1.256 170 938036.148 1.670 + 33 102 69 171 Tm -59210.298 0.972 8101.893 0.006 B- 96.512 0.972 170 936435.126 1.043 + 31 101 70 171 Yb -59306.810 0.013 8097.882 0.000 B- -1478.414 1.862 170 936331.517 0.014 + 29 100 71 171 Lu -57828.395 1.862 8084.661 0.011 B- -2397.050 28.936 170 937918.660 1.998 + 27 99 72 171 Hf x -55431.345 28.876 8066.068 0.169 B- -3711.072 40.184 170 940492.000 31.000 + 25 98 73 171 Ta x -51720.273 27.945 8039.791 0.163 B- -4634.183 39.520 170 944476.000 30.000 + 23 97 74 171 W x -47086.090 27.945 8008.115 0.163 B- -5835.810 39.520 170 949451.000 30.000 + 21 96 75 171 Re x -41250.280 27.945 7969.412 0.163 B- -6948.339 33.145 170 955716.000 30.000 + 19 95 76 171 Os -34301.942 17.823 7924.204 0.104 B- -7889.916 42.395 170 963175.348 19.133 + 17 94 77 171 Ir -a -26412.025 38.466 7873.489 0.225 B- -8942.323 82.291 170 971645.522 41.295 + 15 93 78 171 Pt -a -17469.702 72.747 7816.619 0.425 B- -9907.407 75.639 170 981245.502 78.097 + 13 92 79 171 Au -p -7562.295 20.713 7754.106 0.121 B- -11043# 303# 170 991881.542 22.236 + 11 91 80 171 Hg -a 3480# 303# 7685# 2# B- * 171 003736# 325# +0 42 107 65 172 Tb x -39850# 503# 8007# 3# B- 8159# 585# 171 957219# 540# + 40 106 66 172 Dy x -48009# 298# 8050# 2# B- 3474# 357# 171 948460# 320# + 38 105 67 172 Ho x -51484# 196# 8066# 1# B- 5000# 196# 171 944730# 210# + 36 104 68 172 Er -56483.612 4.008 8090.410 0.023 B- 890.767 4.543 171 939362.344 4.302 + 34 103 69 172 Tm -57374.379 5.503 8091.041 0.032 B- 1881.067 5.503 171 938406.067 5.907 + 32 102 70 172 Yb -59255.446 0.014 8097.429 0.000 B- -2519.466 2.336 171 936386.658 0.014 + 30 101 71 172 Lu -56735.980 2.336 8078.232 0.014 B- -333.754 24.540 171 939091.417 2.507 + 28 100 72 172 Hf x -56402.226 24.428 8071.743 0.142 B- -5072.248 37.117 171 939449.716 26.224 + 26 99 73 172 Ta x -51329.977 27.945 8037.705 0.162 B- -2232.791 39.520 171 944895.000 30.000 + 24 98 74 172 W x -49097.186 27.945 8020.175 0.162 B- -7560.080 47.974 171 947292.000 30.000 + 22 97 75 172 Re -41537.106 38.995 7971.672 0.227 B- -4293.264 41.036 171 955408.079 41.862 + 20 96 76 172 Os -37243.842 12.782 7942.163 0.074 B- -9864.473 34.832 171 960017.088 13.721 + 18 95 77 172 Ir -a -27379.369 32.402 7880.263 0.188 B- -6272.449 34.023 171 970607.036 34.785 + 16 94 78 172 Pt -21106.920 10.377 7839.247 0.060 B- -11788.914 57.108 171 977340.788 11.139 + 14 93 79 172 Au -a -9318.006 56.158 7766.158 0.326 B- -8259.262 140.853 171 989996.708 60.287 + 12 92 80 172 Hg -a -1058.744 150.079 7713.591 0.873 B- * 171 998863.391 161.116 +0 41 107 66 173 Dy x -43939# 401# 8027# 2# B- 5412# 499# 172 952830# 430# + 39 106 67 173 Ho x -49351# 298# 8054# 2# B- 4304# 357# 172 947020# 320# + 37 105 68 173 Er x -53654# 196# 8074# 1# B- 2602# 196# 172 942400# 210# + 35 104 69 173 Tm p2n -56256.059 4.400 8084.463 0.025 B- 1295.166 4.400 172 939606.632 4.723 + 33 103 70 173 Yb -57551.225 0.011 8087.427 0.000 B- -670.310 1.567 172 938216.215 0.012 + 31 102 71 173 Lu -56880.916 1.567 8079.030 0.009 B- -1469.132 27.989 172 938935.822 1.682 + 29 101 72 173 Hf x -55411.784 27.945 8066.016 0.162 B- -3015.246 39.520 172 940513.000 30.000 + 27 100 73 173 Ta x -52396.538 27.945 8044.064 0.162 B- -3669.155 39.520 172 943750.000 30.000 + 25 99 74 173 W x -48727.383 27.945 8018.333 0.162 B- -5173.518 39.520 172 947689.000 30.000 + 23 98 75 173 Re x -43553.865 27.945 7983.906 0.162 B- -6115.608 31.697 172 953243.000 30.000 + 21 97 76 173 Os -37438.257 14.959 7944.033 0.086 B- -7169.822 18.583 172 959808.375 16.059 + 19 96 77 173 Ir -30268.435 11.026 7898.067 0.064 B- -8325.524 57.052 172 967505.496 11.837 + 17 95 78 173 Pt -a -21942.911 55.977 7845.420 0.324 B- -9110.471 60.421 172 976443.315 60.093 + 15 94 79 173 Au +a -12832.440 22.784 7788.237 0.132 B- -10123# 197# 172 986223.808 24.459 + 13 93 80 173 Hg -a -2710# 196# 7725# 1# B- * 172 997091# 210# +0 42 108 66 174 Dy x -41370# 503# 8012# 3# B- 4319# 585# 173 955587# 540# + 40 107 67 174 Ho x -45690# 298# 8033# 2# B- 6260# 422# 173 950950# 320# + 38 106 68 174 Er x -51949# 298# 8064# 2# B- 1915# 301# 173 944230# 320# + 36 105 69 174 Tm + -53864.512 44.721 8070.642 0.257 B- 3080.000 44.721 173 942174.064 48.010 + 34 104 70 174 Yb -56944.512 0.011 8083.847 0.000 B- -1374.317 1.567 173 938867.548 0.011 + 32 103 71 174 Lu -55570.195 1.567 8071.453 0.009 B- 274.286 2.169 173 940342.938 1.682 + 30 102 72 174 Hf -55844.481 2.259 8068.533 0.013 B- -4103.715 28.036 173 940048.480 2.424 + 28 101 73 174 Ta x -51740.766 27.945 8040.452 0.161 B- -1513.678 39.520 173 944454.000 30.000 + 26 100 74 174 W x -50227.088 27.945 8027.256 0.161 B- -6553.992 39.520 173 946079.000 30.000 + 24 99 75 174 Re x -43673.096 27.945 7985.094 0.161 B- -3677.681 29.767 173 953115.000 30.000 + 22 98 76 174 Os -39995.416 10.254 7959.461 0.059 B- -9131.924 26.395 173 957063.152 11.008 + 20 97 77 174 Ir -30863.492 24.322 7902.483 0.140 B- -5545.329 26.433 173 966866.676 26.111 + 18 96 78 174 Pt -a -25318.163 10.351 7866.117 0.059 B- -11083# 89# 173 972819.832 11.112 + 16 95 79 174 Au -a -14235# 89# 7798# 1# B- -7594# 89# 173 984718# 95# + 14 94 80 174 Hg -a -6641.009 19.211 7749.784 0.110 B- * 173 992870.583 20.624 +0 41 108 67 175 Ho x -43203# 401# 8019# 2# B- 5449# 566# 174 953620# 430# + 39 107 68 175 Er x -48652# 401# 8045# 2# B- 3659# 404# 174 947770# 430# + 37 106 69 175 Tm + -52310.549 50.000 8061.766 0.286 B- 2385.000 50.000 174 943842.313 53.677 + 35 105 70 175 Yb -54695.549 0.071 8070.925 0.000 B- 470.033 1.206 174 941281.910 0.076 + 33 104 71 175 Lu -55165.582 1.207 8069.140 0.007 B- -683.920 1.952 174 940777.308 1.295 + 31 103 72 175 Hf -54481.662 2.282 8060.761 0.013 B- -2073.015 28.038 174 941511.527 2.449 + 29 102 73 175 Ta x -52408.647 27.945 8044.445 0.160 B- -2775.852 39.520 174 943737.000 30.000 + 27 101 74 175 W x -49632.795 27.945 8024.112 0.160 B- -4344.488 39.520 174 946717.000 30.000 + 25 100 75 175 Re x -45288.307 27.945 7994.816 0.160 B- -5182.931 30.324 174 951381.000 30.000 + 23 99 76 175 Os -40105.376 11.775 7960.729 0.067 B- -6710.870 17.089 174 956945.105 12.640 + 21 98 77 175 Ir -33394.506 12.384 7917.910 0.071 B- -7681.040 22.001 174 964149.521 13.295 + 19 97 78 175 Pt -25713.466 18.185 7869.548 0.104 B- -8309.511 42.705 174 972395.457 19.522 + 17 96 79 175 Au -a -17403.955 38.640 7817.595 0.221 B- -9431.379 82.504 174 981316.085 41.481 + 15 95 80 175 Hg -a -7972.576 72.896 7759.231 0.417 B- * 174 991441.086 78.257 +0 42 109 67 176 Ho x -39290# 503# 7997# 3# B- 7340# 643# 175 957820# 540# + 40 108 68 176 Er x -46631# 401# 8034# 2# B- 2741# 413# 175 949940# 430# + 38 107 69 176 Tm + -49371.314 100.000 8045.121 0.568 B- 4120.000 100.000 175 946997.711 107.354 + 36 106 70 176 Yb -53491.314 0.015 8064.085 0.000 B- -109.078 1.212 175 942574.708 0.015 + 34 105 71 176 Lu -53382.236 1.212 8059.020 0.007 B- 1194.085 0.874 175 942691.809 1.301 + 32 104 72 176 Hf -54576.321 1.481 8061.359 0.008 B- -3210.948 30.775 175 941409.905 1.590 + 30 103 73 176 Ta x -51365.374 30.739 8038.670 0.175 B- -723.771 41.543 175 944857.000 33.000 + 28 102 74 176 W x -50641.603 27.945 8030.112 0.159 B- -5578.718 39.520 175 945634.000 30.000 + 26 101 75 176 Re x -45062.885 27.945 7993.970 0.159 B- -2964.945 39.520 175 951623.000 30.000 + 24 100 76 176 Os x -42097.940 27.945 7972.679 0.159 B- -8219.614 32.580 175 954806.000 30.000 + 22 99 77 176 Ir -33878.326 16.750 7921.531 0.095 B- -4944.459 21.035 175 963630.119 17.981 + 20 98 78 176 Pt -28933.867 12.724 7888.992 0.072 B- -10412.904 35.541 175 968938.214 13.660 + 18 97 79 176 Au -a -18520.963 33.185 7825.383 0.189 B- -6736.013 34.998 175 980116.927 35.625 + 16 96 80 176 Hg -11784.950 11.119 7782.665 0.063 B- -12366.544 75.904 175 987348.335 11.937 + 14 95 81 176 Tl -p 581.594 75.086 7707.955 0.427 B- * 176 000624.367 80.607 +0 41 109 68 177 Er x -42858# 503# 8013# 3# B- 4611# 585# 176 953990# 540# + 39 108 69 177 Tm x -47469# 298# 8035# 2# B- 3517# 298# 176 949040# 320# + 37 107 70 177 Yb -n -50986.397 0.220 8049.973 0.001 B- 1397.409 1.240 176 945263.848 0.236 + 35 106 71 177 Lu -52383.806 1.220 8053.448 0.007 B- 496.810 0.791 176 943763.668 1.310 + 33 105 72 177 Hf -52880.616 1.408 8051.835 0.008 B- -1166.000 3.000 176 943230.320 1.511 + 31 104 73 177 Ta - -51714.616 3.314 8040.827 0.019 B- -2012.890 28.141 176 944482.073 3.557 + 29 103 74 177 W x -49701.726 27.945 8025.035 0.158 B- -3432.555 39.520 176 946643.000 30.000 + 27 102 75 177 Re x -46269.170 27.945 8001.222 0.158 B- -4312.708 31.535 176 950328.000 30.000 + 25 101 76 177 Os +a -41956.462 14.613 7972.436 0.083 B- -5909.041 24.576 176 954957.882 15.687 + 23 100 77 177 Ir x -36047.421 19.760 7934.632 0.112 B- -6676.976 24.801 176 961301.500 21.213 + 21 99 78 177 Pt -29370.444 14.988 7892.489 0.085 B- -7825.341 18.297 176 968469.529 16.090 + 19 98 79 177 Au -21545.103 10.496 7843.858 0.059 B- -8762.561 75.786 176 976870.379 11.268 + 17 97 80 177 Hg -a -12782.542 75.056 7789.932 0.424 B- -9442.016 78.098 176 986277.376 80.575 + 15 96 81 177 Tl IT -3340.526 21.629 7732.167 0.122 B- * 176 996413.797 23.219 +0 42 110 68 178 Er x -40260# 596# 7999# 3# B- 3855# 718# 177 956779# 640# + 40 109 69 178 Tm x -44116# 401# 8016# 2# B- 5580# 401# 177 952640# 430# + 38 108 70 178 Yb -nn -49695.475 10.000 8042.841 0.056 B- 642.309 10.250 177 946649.710 10.735 + 36 107 71 178 Lu -50337.784 2.251 8042.054 0.013 B- 2097.451 2.057 177 945960.162 2.416 + 34 106 72 178 Hf -52435.236 1.412 8049.442 0.008 B- -1837# 52# 177 943708.456 1.516 + 32 105 73 178 Ta IT -50598# 52# 8035# 0# B- -191# 50# 177 945681# 56# + 30 104 74 178 W - -50406.936 15.199 8029.257 0.085 B- -4753.483 31.810 177 945885.925 16.316 + 28 103 75 178 Re x -45653.453 27.945 7998.157 0.157 B- -2109.183 31.093 177 950989.000 30.000 + 26 102 76 178 Os -43544.270 13.632 7981.912 0.077 B- -7292.386 24.006 177 953253.300 14.634 + 24 101 77 178 Ir x -36251.884 19.760 7936.549 0.111 B- -4254.365 22.207 177 961082.000 21.213 + 22 100 78 178 Pt -31997.519 10.133 7908.252 0.057 B- -9693.776 14.297 177 965649.248 10.878 + 20 99 79 178 Au -22303.743 10.086 7849.398 0.057 B- -5987.841 14.755 177 976055.945 10.827 + 18 98 80 178 Hg -a -16315.901 10.770 7811.363 0.061 B- -11526# 90# 177 982484.158 11.562 + 16 97 81 178 Tl -a -4790# 89# 7742# 1# B- -8365# 91# 177 994857# 96# + 14 96 82 178 Pb -a 3574.294 23.963 7690.830 0.135 B- * 178 003837.163 25.724 +0 41 110 69 179 Tm x -41601# 503# 8002# 3# B- 4937# 540# 178 955340# 540# + 39 109 70 179 Yb x -46537# 196# 8025# 1# B- 2521# 196# 178 950040# 210# + 37 108 71 179 Lu -49058.918 5.150 8035.073 0.029 B- 1403.989 5.067 178 947333.082 5.528 + 35 107 72 179 Hf -50462.907 1.413 8038.546 0.008 B- -105.584 0.409 178 945825.838 1.517 + 33 106 73 179 Ta -50357.323 1.463 8033.585 0.008 B- -1062.195 14.520 178 945939.187 1.571 + 31 105 74 179 W -49295.127 14.573 8023.281 0.081 B- -2710.847 26.802 178 947079.501 15.644 + 29 104 75 179 Re -46584.280 24.639 8003.766 0.138 B- -3564.785 29.656 178 949989.715 26.450 + 27 103 76 179 Os -43019.495 16.504 7979.480 0.092 B- -4937.781 19.180 178 953816.669 17.718 + 25 102 77 179 Ir -38081.714 9.771 7947.524 0.055 B- -5813.569 12.613 178 959117.596 10.489 + 23 101 78 179 Pt -32268.145 7.977 7910.675 0.045 B- -7279.578 14.157 178 965358.719 8.563 + 21 100 79 179 Au -24988.567 11.696 7865.637 0.065 B- -8060.433 29.669 178 973173.668 12.555 + 19 99 80 179 Hg -16928.134 27.267 7816.236 0.152 B- -8659.639 47.417 178 981826.899 29.272 + 17 98 81 179 Tl -a -8268.495 38.793 7763.487 0.217 B- -10319.134 84.963 178 991123.405 41.646 + 15 97 82 179 Pb -a 2050.639 75.590 7701.468 0.422 B- * 179 002201.452 81.149 +0 42 111 69 180 Tm x -37920# 503# 7982# 3# B- 6680# 585# 179 959291# 540# + 40 110 70 180 Yb x -44600# 298# 8015# 2# B- 2076# 306# 179 952120# 320# + 38 109 71 180 Lu + -46676.348 70.725 8022.038 0.393 B- 3103.000 70.711 179 949890.876 75.926 + 36 108 72 180 Hf -49779.348 1.419 8034.930 0.008 B- -846.471 2.269 179 946559.669 1.522 + 34 107 73 180 Ta +n -48932.877 1.939 8025.881 0.011 B- 703.238 2.281 179 947468.392 2.081 + 32 106 74 180 W -49636.115 1.436 8025.442 0.008 B- -3798.757 21.440 179 946713.435 1.542 + 30 105 75 180 Re x -45837.359 21.392 7999.991 0.119 B- -1479.549 26.950 179 950791.568 22.965 + 28 104 76 180 Os -44357.810 16.391 7987.425 0.091 B- -6380.284 27.200 179 952379.930 17.596 + 26 103 77 180 Ir x -37977.526 21.706 7947.633 0.121 B- -3541.649 24.323 179 959229.446 23.302 + 24 102 78 180 Pt +a -34435.877 10.974 7923.611 0.061 B- -8810.368 11.973 179 963031.563 11.781 + 22 101 79 180 Au -25625.509 4.786 7870.318 0.027 B- -5375.062 13.524 179 972489.883 5.137 + 20 100 80 180 Hg -20250.447 12.649 7836.110 0.070 B- -10863.800 61.329 179 978260.249 13.579 + 18 99 81 180 Tl -a -9386.647 60.010 7771.409 0.333 B- -7445.267 61.277 179 989923.019 64.423 + 16 98 82 180 Pb -a -1941.380 12.396 7725.700 0.069 B- * 179 997915.842 13.307 +0 43 112 69 181 Tm x -35170# 596# 7967# 3# B- 5918# 667# 180 962243# 640# + 41 111 70 181 Yb x -41088# 298# 7996# 2# B- 3709# 324# 180 955890# 320# + 39 110 71 181 Lu x -44797.410 125.752 8011.929 0.695 B- 2605.421 125.760 180 951908.000 135.000 + 37 109 72 181 Hf -n -47402.831 1.420 8022.002 0.008 B- 1035.480 1.834 180 949110.965 1.524 + 35 108 73 181 Ta -48438.311 1.403 8023.400 0.008 B- -204.493 1.854 180 947999.331 1.506 + 33 107 74 181 W -n -48233.818 1.445 8017.948 0.008 B- -1716.427 12.629 180 948218.863 1.551 + 31 106 75 181 Re 4n -46517.391 12.549 8004.143 0.069 B- -2967.428 28.275 180 950061.523 13.471 + 29 105 76 181 Os -43549.963 25.338 7983.426 0.140 B- -4086.935 25.876 180 953247.188 27.201 + 27 104 77 181 Ir +a -39463.028 5.245 7956.523 0.029 B- -5081.517 14.660 180 957634.694 5.631 + 25 103 78 181 Pt -34381.511 13.689 7924.126 0.076 B- -6510.375 24.216 180 963089.927 14.695 + 23 102 79 181 Au -a -27871.136 19.976 7883.835 0.110 B- -7210.000 25.212 180 970079.103 21.445 + 21 101 80 181 Hg -20661.136 15.382 7839.679 0.085 B- -7862.401 17.876 180 977819.357 16.513 + 19 100 81 181 Tl -12798.735 9.108 7791.918 0.050 B- -9681.385 75.959 180 986259.992 9.778 + 17 99 82 181 Pb -a -3117.350 75.411 7734.107 0.417 B- * 180 996653.386 80.957 +0 42 112 70 182 Yb x -38820# 401# 7984# 2# B- 3060# 446# 181 958325# 430# + 40 111 71 182 Lu x -41880# 196# 7996# 1# B- 4170# 196# 181 955040# 210# + 38 110 72 182 Hf -nn -46049.508 6.165 8014.837 0.034 B- 380.425 6.274 181 950563.816 6.618 + 36 109 73 182 Ta -46429.934 1.405 8012.628 0.008 B- 1816.126 1.399 181 950155.413 1.508 + 34 108 74 182 W -48246.060 0.738 8018.308 0.004 B- -2800.000 101.980 181 948205.721 0.791 + 32 107 75 182 Re IT -45446.060 101.983 7998.625 0.560 B- -836.955 104.276 181 951211.645 109.483 + 30 106 76 182 Os -44609.104 21.745 7989.728 0.119 B- -5557.426 30.207 181 952110.153 23.344 + 28 105 77 182 Ir -39051.679 20.967 7954.894 0.115 B- -2883.230 24.720 181 958076.296 22.509 + 26 104 78 182 Pt -36168.449 13.095 7934.754 0.072 B- -7867.680 24.123 181 961171.571 14.057 + 24 103 79 182 Au -a -28300.768 20.260 7887.226 0.111 B- -4723.846 22.501 181 969617.874 21.749 + 22 102 80 182 Hg -23576.922 9.790 7856.972 0.054 B- -10248.994 15.363 181 974689.132 10.510 + 20 101 81 182 Tl -a -13327.927 11.839 7796.360 0.065 B- -6502.815 16.927 181 985691.880 12.709 + 18 100 82 182 Pb -a -6825.112 12.098 7756.332 0.066 B- * 181 992672.940 12.987 +0 43 113 70 183 Yb x -35100# 401# 7964# 2# B- 4616# 408# 182 962319# 430# + 41 112 71 183 Lu x -39716.110 80.108 7984.812 0.438 B- 3566.687 85.553 182 957363.000 86.000 + 39 111 72 183 Hf + -43282.796 30.034 8000.027 0.164 B- 2010.000 30.000 182 953534.004 32.242 + 37 110 73 183 Ta -n -45292.796 1.419 8006.735 0.008 B- 1072.783 1.413 182 951376.180 1.523 + 35 109 74 183 W -46365.580 0.737 8008.322 0.004 B- -556.000 8.000 182 950224.500 0.790 + 33 108 75 183 Re - -45809.580 8.034 8001.009 0.044 B- -2145.537 50.405 182 950821.390 8.624 + 31 107 76 183 Os -43664.043 49.760 7985.010 0.272 B- -3460.732 52.733 182 953124.719 53.420 + 29 106 77 183 Ir -40203.311 24.398 7961.823 0.133 B- -4430.824 28.923 182 956839.968 26.191 + 27 105 78 183 Pt -35772.487 15.533 7933.336 0.085 B- -5581.004 18.168 182 961596.653 16.675 + 25 104 79 183 Au -30191.483 9.423 7898.564 0.051 B- -6386.809 11.789 182 967588.108 10.116 + 23 103 80 183 Hg -23804.674 7.084 7859.388 0.039 B- -7217.417 11.716 182 974444.629 7.604 + 21 102 81 183 Tl -16587.257 9.331 7815.673 0.051 B- -9012.038 29.657 182 982192.846 10.017 + 19 101 82 183 Pb -a -7575.218 28.151 7762.152 0.154 B- * 182 991867.668 30.221 +0 44 114 70 184 Yb x -32540# 503# 7951# 3# B- 3872# 585# 183 965067# 540# + 42 113 71 184 Lu x -36412# 298# 7967# 2# B- 5087# 301# 183 960910# 320# + 40 112 72 184 Hf + -41499.373 39.706 7990.722 0.216 B- 1340.000 30.000 183 955448.587 42.625 + 38 111 73 184 Ta + -42839.373 26.010 7993.752 0.141 B- 2866.000 26.000 183 954010.038 27.923 + 36 110 74 184 W -45705.373 0.731 8005.077 0.004 B- -1485.739 4.198 183 950933.260 0.785 + 34 109 75 184 Re -44219.634 4.275 7992.750 0.023 B- 32.898 4.140 183 952528.267 4.589 + 32 108 76 184 Os -44252.533 0.827 7988.677 0.005 B- -4641.682 27.957 183 952492.949 0.887 + 30 107 77 184 Ir x -39610.851 27.945 7959.198 0.152 B- -2276.608 31.997 183 957476.000 30.000 + 28 106 78 184 Pt -37334.243 15.584 7942.574 0.085 B- -7015.533 27.185 183 959920.039 16.730 + 26 105 79 184 Au -a -30318.710 22.275 7900.194 0.121 B- -3969.745 24.442 183 967451.524 23.912 + 24 104 80 184 Hg -26348.965 10.062 7874.367 0.055 B- -9465.723 14.200 183 971713.221 10.802 + 22 103 81 184 Tl -16883.242 10.020 7818.671 0.054 B- -5831.720 16.260 183 981875.093 10.757 + 20 102 82 184 Pb -11051.522 12.806 7782.725 0.070 B- -12114.590 79.153 183 988135.702 13.748 + 18 101 83 184 Bi -a 1063.068 78.110 7712.633 0.425 B- * 184 001141.250 83.854 +0 45 115 70 185 Yb x -28500# 503# 7929# 3# B- 5388# 585# 184 969404# 540# + 43 114 71 185 Lu x -33888# 298# 7954# 2# B- 4432# 305# 184 963620# 320# + 41 113 72 185 Hf x -38319.800 64.273 7973.970 0.347 B- 3074.492 65.815 184 958862.000 69.000 + 39 112 73 185 Ta + -41394.293 14.161 7986.360 0.077 B- 1993.500 14.142 184 955561.396 15.202 + 37 111 74 185 W -43387.793 0.733 7992.907 0.004 B- 431.234 0.661 184 953421.286 0.786 + 35 110 75 185 Re -43819.027 0.818 7991.009 0.004 B- -1013.147 0.419 184 952958.337 0.877 + 33 109 76 185 Os -42805.880 0.830 7981.304 0.004 B- -2470.326 27.957 184 954045.995 0.891 + 31 108 77 185 Ir x -40335.553 27.945 7963.722 0.151 B- -3647.414 38.055 184 956698.000 30.000 + 29 107 78 185 Pt -36688.140 25.832 7939.777 0.140 B- -4829.997 25.963 184 960613.659 27.731 + 27 106 79 185 Au x -31858.143 2.608 7909.440 0.014 B- -5674.477 13.886 184 965798.874 2.800 + 25 105 80 185 Hg -26183.666 13.639 7874.538 0.074 B- -6425.925 24.767 184 971890.676 14.641 + 23 104 81 185 Tl IT -19757.741 20.674 7835.575 0.112 B- -8216.521 26.249 184 978789.191 22.194 + 21 103 82 185 Pb -a -11541.220 16.175 7786.932 0.087 B- -9305# 83# 184 987609.989 17.364 + 19 102 83 185 Bi IT -2236# 81# 7732# 0# B- * 184 997600# 87# +0 44 115 71 186 Lu x -30210# 401# 7935# 2# B- 6214# 404# 185 967568# 430# + 42 114 72 186 Hf x -36424.210 51.232 7964.302 0.275 B- 2183.318 78.906 185 960897.000 55.000 + 40 113 73 186 Ta + -38607.528 60.012 7971.835 0.323 B- 3901.000 60.000 185 958553.111 64.425 + 38 112 74 186 W -42508.528 1.212 7988.601 0.007 B- -581.442 1.244 185 954365.215 1.300 + 36 111 75 186 Re -41927.086 0.826 7981.269 0.004 B- 1072.857 0.837 185 954989.419 0.886 + 34 110 76 186 Os -42999.943 0.761 7982.831 0.004 B- -3827.596 16.543 185 953837.660 0.816 + 32 109 77 186 Ir x -39172.346 16.526 7958.047 0.089 B- -1307.903 27.312 185 957946.754 17.740 + 30 108 78 186 Pt -37864.443 21.745 7946.809 0.117 B- -6149.591 30.207 185 959350.846 23.344 + 28 107 79 186 Au -31714.852 20.967 7909.540 0.113 B- -3175.756 23.987 185 965952.703 22.509 + 26 106 80 186 Hg -28539.097 11.650 7888.260 0.063 B- -8652.484 25.209 185 969362.017 12.507 + 24 105 81 186 Tl x -19886.613 22.356 7837.535 0.120 B- -5204.588 25.078 185 978650.841 24.000 + 22 104 82 186 Pb -a -14682.026 11.363 7805.347 0.061 B- -11535.814 20.329 185 984238.196 12.199 + 20 103 83 186 Bi -a -3146.212 16.857 7739.121 0.091 B- -7247.186 24.870 185 996622.402 18.096 + 18 102 84 186 Po -a 4100.974 18.286 7695.951 0.098 B- * 186 004402.577 19.630 +0 45 116 71 187 Lu x -27580# 401# 7922# 2# B- 5237# 499# 186 970392# 430# + 43 115 72 187 Hf x -32817# 298# 7946# 2# B- 4079# 303# 186 964770# 320# + 41 114 73 187 Ta x -36895.546 55.890 7963.212 0.299 B- 3008.424 55.903 186 960391.000 60.000 + 39 113 74 187 W -39903.970 1.212 7975.116 0.006 B- 1312.508 1.122 186 957161.323 1.300 + 37 112 75 187 Re -41216.478 0.736 7977.951 0.004 B- 2.467 0.002 186 955752.288 0.790 + 35 111 76 187 Os -41218.945 0.736 7973.780 0.004 B- -1669.572 27.955 186 955749.640 0.790 + 33 110 77 187 Ir x -39549.372 27.945 7960.668 0.149 B- -2864.323 36.868 186 957542.000 30.000 + 31 109 78 187 Pt -36685.050 24.048 7941.168 0.129 B- -3657.212 27.377 186 960616.976 25.816 + 29 108 79 187 Au -33027.838 22.308 7917.427 0.119 B- -4909.908 26.287 186 964543.155 23.948 + 27 107 80 187 Hg -28117.930 13.905 7886.987 0.074 B- -5673.343 16.067 186 969814.158 14.928 + 25 106 81 187 Tl -22444.587 8.048 7852.464 0.043 B- -7457.628 9.525 186 975904.743 8.640 + 23 105 82 187 Pb -14986.959 5.094 7808.400 0.027 B- -8603.688 11.227 186 983910.836 5.468 + 21 104 83 187 Bi -a -6383.271 10.005 7758.208 0.054 B- -9211.868 33.430 186 993147.276 10.740 + 19 103 84 187 Po -a 2828.597 31.898 7704.763 0.171 B- * 187 003036.624 34.243 +0 46 117 71 188 Lu x -23790# 503# 7902# 3# B- 7089# 585# 187 974460# 540# + 44 116 72 188 Hf x -30879# 298# 7936# 2# B- 2733# 303# 187 966850# 320# + 42 115 73 188 Ta x -33612.030 54.958 7946.321 0.292 B- 5055.781 55.045 187 963916.000 59.000 + 40 114 74 188 W + -38667.811 3.089 7969.052 0.016 B- 349.000 3.000 187 958488.395 3.316 + 38 113 75 188 Re -n -39016.811 0.738 7966.747 0.004 B- 2120.422 0.152 187 958113.728 0.791 + 36 112 76 188 Os -41137.233 0.734 7973.864 0.004 B- -2792.326 9.416 187 955837.361 0.787 + 34 111 77 188 Ir -38344.907 9.423 7954.850 0.050 B- -523.979 8.686 187 958835.046 10.116 + 32 110 78 188 Pt -37820.929 5.304 7947.902 0.028 B- -5449.621 5.953 187 959397.560 5.694 + 30 109 79 188 Au x -32371.308 2.701 7914.753 0.014 B- -2169.394 12.569 187 965247.969 2.900 + 28 108 80 188 Hg -30201.914 12.275 7899.052 0.065 B- -7865.513 32.325 187 967576.910 13.178 + 26 107 81 188 Tl x -22336.400 29.904 7853.053 0.159 B- -4521.198 31.734 187 976020.886 32.103 + 24 106 82 188 Pb -a -17815.202 10.622 7824.843 0.057 B- -10620.515 15.427 187 980874.592 11.403 + 22 105 83 188 Bi -a -7194.687 11.187 7764.189 0.060 B- -6650.374 22.892 187 992276.184 12.009 + 20 104 84 188 Po -a -544.313 19.973 7724.653 0.106 B- * 187 999415.655 21.441 +0 45 117 72 189 Hf x -27162# 298# 7917# 2# B- 4667# 357# 188 970840# 320# + 43 116 73 189 Ta x -31829# 196# 7938# 1# B- 3788# 200# 188 965830# 210# + 41 115 74 189 W x -35617.536 40.054 7953.454 0.212 B- 2361.507 40.883 188 961763.000 43.000 + 39 114 75 189 Re +p -37979.043 8.191 7961.809 0.043 B- 1007.702 8.167 188 959227.817 8.793 + 37 113 76 189 Os -38986.745 0.666 7963.002 0.004 B- -537.159 12.563 188 958146.005 0.715 + 35 112 77 189 Ir -38449.586 12.576 7956.020 0.067 B- -1980.238 13.636 188 958722.669 13.500 + 33 111 78 189 Pt -36469.348 10.090 7941.403 0.053 B- -2887.394 22.474 188 960848.542 10.832 + 31 110 79 189 Au x -33581.955 20.081 7921.987 0.106 B- -3955.554 37.401 188 963948.286 21.558 + 29 109 80 189 Hg -29626.401 31.553 7896.919 0.167 B- -5010.300 32.643 188 968194.748 33.873 + 27 108 81 189 Tl -24616.100 8.368 7866.270 0.044 B- -6772.066 16.364 188 973573.527 8.983 + 25 107 82 189 Pb -17844.035 14.062 7826.299 0.074 B- -7779.374 25.150 188 980843.639 15.096 + 23 106 83 189 Bi -a -10064.660 20.851 7780.999 0.110 B- -8642.656 30.354 188 989195.141 22.384 + 21 105 84 189 Po -a -1422.005 22.059 7731.131 0.117 B- * 188 998473.415 23.681 +0 46 118 72 190 Hf x -25030# 401# 7907# 2# B- 3483# 446# 189 973129# 430# + 44 117 73 190 Ta x -28513# 196# 7921# 1# B- 5869# 200# 189 969390# 210# + 42 116 74 190 W -34382.313 39.726 7947.573 0.209 B- 1253.517 63.522 189 963089.066 42.647 + 40 115 75 190 Re -35635.830 70.852 7950.053 0.373 B- 3071.941 70.854 189 961743.360 76.063 + 38 114 76 190 Os -38707.771 0.650 7962.104 0.003 B- -1954.227 1.213 189 958445.496 0.697 + 36 113 77 190 Ir +n -36753.544 1.370 7947.701 0.007 B- 552.906 1.282 189 960543.445 1.470 + 34 112 78 190 Pt -37306.450 0.657 7946.493 0.003 B- -4472.917 3.509 189 959949.876 0.704 + 32 111 79 190 Au x -32833.533 3.447 7918.834 0.018 B- -1462.836 16.276 189 964751.750 3.700 + 30 110 80 190 Hg -31370.697 15.907 7907.017 0.084 B- -6998.670 17.782 189 966322.169 17.076 + 28 109 81 190 Tl +a -24372.027 7.948 7866.064 0.042 B- -3955.382 14.825 189 973835.551 8.532 + 26 108 82 190 Pb -a -20416.645 12.514 7841.129 0.066 B- -9817.066 25.800 189 978081.828 13.434 + 24 107 83 190 Bi -a -10599.579 22.562 7785.342 0.119 B- -6035.742 26.275 189 988620.883 24.221 + 22 106 84 190 Po -a -4563.837 13.465 7749.458 0.071 B- * 189 995100.519 14.455 +0 45 118 73 191 Ta x -26492# 298# 7911# 2# B- 4684# 301# 190 971560# 320# + 43 117 74 191 W x -31176.173 41.917 7931.435 0.219 B- 3174.124 43.156 190 966531.000 45.000 + 41 116 75 191 Re +p -34350.296 10.265 7943.957 0.054 B- 2044.889 10.244 190 963123.437 11.019 + 39 115 76 191 Os -36395.185 0.659 7950.568 0.003 B- 313.570 1.141 190 960928.159 0.707 + 37 114 77 191 Ir -36708.756 1.311 7948.113 0.007 B- -1010.518 3.636 190 960591.527 1.406 + 35 113 78 191 Pt -35698.237 4.127 7938.727 0.022 B- -1900.333 6.426 190 961676.363 4.430 + 33 112 79 191 Au -33797.904 4.926 7924.681 0.026 B- -3206.008 22.710 190 963716.455 5.288 + 31 111 80 191 Hg -30591.896 22.280 7903.800 0.117 B- -4308.951 23.461 190 967158.247 23.918 + 29 110 81 191 Tl +a -26282.945 7.349 7877.144 0.038 B- -6051.827 37.978 190 971784.096 7.889 + 27 109 82 191 Pb x -20231.118 37.260 7841.363 0.195 B- -6991.772 38.005 190 978281.000 40.000 + 25 108 83 191 Bi -13239.347 7.487 7800.661 0.039 B- -8170.612 10.320 190 985786.975 8.037 + 23 107 84 191 Po -5068.735 7.103 7753.786 0.037 B- -8932.653 17.600 190 994558.488 7.624 + 21 106 85 191 At -a 3863.917 16.103 7702.923 0.084 B- * 191 004148.086 17.287 +0 46 119 73 192 Ta x -23064# 401# 7894# 2# B- 6586# 446# 191 975240# 430# + 44 118 74 192 W x -29649# 196# 7924# 1# B- 1939# 208# 191 968170# 210# + 42 117 75 192 Re x -31588.825 70.794 7930.238 0.369 B- 4293.366 70.831 191 966088.000 76.000 + 40 116 76 192 Os -35882.191 2.315 7948.525 0.012 B- -1046.630 2.397 191 961478.881 2.485 + 38 115 77 192 Ir -34835.561 1.314 7938.999 0.007 B- 1452.896 2.274 191 962602.485 1.410 + 36 114 78 192 Pt -36288.457 2.570 7942.491 0.013 B- -3516.341 15.617 191 961042.736 2.758 + 34 113 79 192 Au - -32772.116 15.827 7920.102 0.082 B- -760.563 22.178 191 964817.684 16.991 + 32 112 80 192 Hg x -32011.553 15.537 7912.066 0.081 B- -6139.307 35.277 191 965634.182 16.679 + 30 111 81 192 Tl x -25872.246 31.671 7876.016 0.165 B- -3316.226 34.348 191 972225.000 34.000 + 28 110 82 192 Pb -a -22556.020 13.295 7854.669 0.069 B- -9021.485 32.917 191 975785.115 14.273 + 26 109 83 192 Bi -a -13534.535 30.112 7803.608 0.157 B- -5463.873 32.096 191 985470.078 32.326 + 24 108 84 192 Po -a -8070.661 11.110 7771.075 0.058 B- -10996.516 30.008 191 991335.788 11.926 + 22 107 85 192 At -a 2925.854 27.876 7709.727 0.145 B- * 192 003141.034 29.926 +0 47 120 73 193 Ta x -20870# 401# 7884# 2# B- 5417# 446# 192 977595# 430# + 45 119 74 193 W x -26287# 196# 7908# 1# B- 3945# 199# 192 971780# 210# + 43 118 75 193 Re x -30231.638 39.123 7923.937 0.203 B- 3162.652 39.192 192 967545.000 42.000 + 41 117 76 193 Os -33394.289 2.321 7936.270 0.012 B- 1141.946 2.400 192 964149.753 2.491 + 39 116 77 193 Ir -34536.235 1.328 7938.133 0.007 B- -56.628 0.300 192 962923.824 1.425 + 37 115 78 193 Pt -34479.608 1.359 7933.786 0.007 B- -1074.787 8.768 192 962984.616 1.458 + 35 114 79 193 Au -33404.821 8.674 7924.164 0.045 B- -2342.642 14.370 192 964138.447 9.311 + 33 113 80 193 Hg -31062.179 15.505 7907.972 0.080 B- -3584.967 16.894 192 966653.377 16.645 + 31 112 81 193 Tl x -27477.212 6.707 7885.344 0.035 B- -5282.723 50.028 192 970501.997 7.200 + 29 111 82 193 Pb x -22194.490 49.577 7853.919 0.257 B- -6309.931 50.152 192 976173.234 53.222 + 27 110 83 193 Bi -15884.559 7.576 7817.171 0.039 B- -7559.241 16.387 192 982947.223 8.132 + 25 109 84 193 Po -a -8325.318 14.531 7773.950 0.075 B- -8257.998 26.059 192 991062.403 15.599 + 23 108 85 193 At -a -67.320 21.632 7727.109 0.112 B- -9110.231 33.144 192 999927.728 23.222 + 21 107 86 193 Rn -a 9042.911 25.112 7675.852 0.130 B- * 193 009707.964 26.958 +0 48 121 73 194 Ta x -17300# 503# 7866# 3# B- 7227# 585# 193 981428# 540# + 46 120 74 194 W x -24526# 298# 7899# 2# B- 2711# 357# 193 973670# 320# + 44 119 75 194 Re x -27237# 196# 7909# 1# B- 5198# 196# 193 970760# 210# + 42 118 76 194 Os + -32435.108 2.403 7932.022 0.012 B- 96.600 2.000 193 965179.477 2.579 + 40 117 77 194 Ir -n -32531.708 1.332 7928.487 0.007 B- 2228.362 1.257 193 965075.773 1.430 + 38 116 78 194 Pt -34760.070 0.496 7935.941 0.003 B- -2548.134 2.117 193 962683.527 0.532 + 36 115 79 194 Au +3n -32211.936 2.118 7918.774 0.011 B- -27.991 3.581 193 965419.062 2.273 + 34 114 80 194 Hg x -32183.945 2.888 7914.597 0.015 B- -5246.454 14.268 193 965449.111 3.100 + 32 113 81 194 Tl x -26937.491 13.972 7883.520 0.072 B- -2729.552 22.343 193 971081.411 15.000 + 30 112 82 194 Pb -24207.940 17.435 7865.418 0.090 B- -8179.128 18.498 193 974011.706 18.717 + 28 111 83 194 Bi +a -16028.811 6.178 7819.225 0.032 B- -5024.156 14.313 193 982792.362 6.632 + 26 110 84 194 Po -a -11004.655 12.911 7789.294 0.067 B- -10284.492 28.076 193 988186.015 13.860 + 24 109 85 194 At -a -720.163 24.931 7732.249 0.129 B- -6443.658 30.119 193 999226.872 26.764 + 22 108 86 194 Rn -a 5723.495 16.899 7695.001 0.087 B- * 194 006144.424 18.141 +0 47 121 74 195 W x -21010# 298# 7882# 2# B- 4569# 422# 194 977445# 320# + 45 120 75 195 Re x -25579# 298# 7902# 2# B- 3933# 303# 194 972540# 320# + 43 119 76 195 Os x -29511.593 55.890 7917.744 0.287 B- 2180.658 55.906 194 968318.000 60.000 + 41 118 77 195 Ir -n -31692.251 1.333 7924.915 0.007 B- 1101.598 1.264 194 965976.967 1.431 + 39 117 78 195 Pt -32793.849 0.503 7926.552 0.003 B- -226.817 1.000 194 964794.353 0.539 + 37 116 79 195 Au -32567.031 1.119 7921.377 0.006 B- -1553.638 23.156 194 965037.851 1.201 + 35 115 80 195 Hg -31013.393 23.142 7909.397 0.119 B- -2858.145 25.657 194 966705.751 24.843 + 33 114 81 195 Tl -28155.248 11.093 7890.728 0.057 B- -4447.555 21.106 194 969774.096 11.909 + 31 113 82 195 Pb -23707.693 17.960 7863.908 0.092 B- -5682.132 18.722 194 974548.743 19.280 + 29 112 83 195 Bi -18025.561 5.287 7830.757 0.027 B- -6969.303 37.737 194 980648.762 5.675 + 27 111 84 195 Po -a -11056.259 37.364 7791.005 0.192 B- -7585.964 38.571 194 988130.617 40.112 + 25 110 85 195 At -a -3470.295 9.573 7748.091 0.049 B- -8520.575 51.401 194 996274.485 10.276 + 23 109 86 195 Rn -a 5050.281 50.502 7700.383 0.259 B- * 195 005421.699 54.216 +0 48 122 74 196 W x -18880# 401# 7872# 2# B- 3662# 499# 195 979731# 430# + 46 121 75 196 Re x -22542# 298# 7887# 2# B- 5735# 301# 195 975800# 320# + 44 120 76 196 Os +pp -28277.105 40.055 7912.229 0.204 B- 1158.388 55.495 195 969643.277 43.000 + 42 119 77 196 Ir + -29435.493 38.414 7914.148 0.196 B- 3209.016 38.411 195 968399.696 41.239 + 40 118 78 196 Pt -32644.510 0.510 7926.529 0.003 B- -1505.803 2.960 195 964954.675 0.547 + 38 117 79 196 Au -31138.706 2.962 7914.855 0.015 B- 687.235 3.118 195 966571.221 3.179 + 36 116 80 196 Hg -31825.941 2.946 7914.369 0.015 B- -4329.349 12.463 195 965833.444 3.163 + 34 115 81 196 Tl x -27496.592 12.109 7888.289 0.062 B- -2148.280 14.356 195 970481.192 13.000 + 32 114 82 196 Pb -25348.312 7.710 7873.337 0.039 B- -7339.281 25.616 195 972787.466 8.277 + 30 113 83 196 Bi x -18009.031 24.428 7831.900 0.125 B- -4535.989 27.916 195 980666.509 26.224 + 28 112 84 196 Po -a -13473.042 13.512 7804.766 0.069 B- -9558.365 33.162 195 985536.094 14.506 + 26 111 85 196 At -a -3914.677 30.284 7752.007 0.155 B- -5885.668 33.540 195 995797.421 32.511 + 24 110 86 196 Rn -a 1970.991 14.417 7717.987 0.074 B- * 196 002115.945 15.476 +0 49 123 74 197 W x -15140# 401# 7854# 2# B- 5363# 499# 196 983747# 430# + 47 122 75 197 Re x -20502# 298# 7878# 2# B- 4807# 357# 196 977990# 320# + 45 121 76 197 Os x -25309# 196# 7898# 1# B- 2955# 197# 196 972830# 210# + 43 120 77 197 Ir +p -28264.105 20.110 7908.999 0.102 B- 2155.645 20.106 196 969657.233 21.588 + 41 119 78 197 Pt -30419.750 0.536 7915.971 0.003 B- 719.988 0.502 196 967343.053 0.575 + 39 118 79 197 Au -31139.738 0.542 7915.654 0.003 B- -599.509 3.202 196 966570.114 0.581 + 37 117 80 197 Hg -30540.229 3.207 7908.640 0.016 B- -2198.580 16.637 196 967213.713 3.442 + 35 116 81 197 Tl +a -28341.649 16.325 7893.508 0.083 B- -3596.247 17.014 196 969573.986 17.526 + 33 115 82 197 Pb -24745.401 4.804 7871.282 0.024 B- -5058.210 9.619 196 973434.717 5.157 + 31 114 83 197 Bi +a -19687.191 8.333 7841.634 0.042 B- -6329.202 50.373 196 978864.929 8.946 + 29 113 84 197 Po -a -13357.990 49.679 7805.535 0.252 B- -7002.739 50.317 196 985659.607 53.332 + 27 112 85 197 At -6355.250 7.983 7766.017 0.041 B- -7865.603 18.054 196 993177.357 8.570 + 25 111 86 197 Rn -a 1510.353 16.193 7722.118 0.082 B- -8743.618 56.762 197 001621.430 17.383 + 23 110 87 197 Fr -a 10253.971 54.404 7673.763 0.276 B- * 197 011008.090 58.404 +0 48 123 75 198 Re x -17139# 401# 7862# 2# B- 6697# 446# 197 981600# 430# + 46 122 76 198 Os x -23837# 196# 7891# 1# B- 1984# 277# 197 974410# 210# + 44 121 77 198 Ir x -25821# 196# 7897# 1# B- 4083# 196# 197 972280# 210# + 42 120 78 198 Pt -29903.999 2.100 7914.150 0.011 B- -323.219 2.059 197 967896.734 2.254 + 40 119 79 198 Au -29580.781 0.540 7908.567 0.003 B- 1373.530 0.490 197 968243.724 0.579 + 38 118 80 198 Hg -30954.310 0.458 7911.552 0.002 B- -3425.564 7.559 197 966769.179 0.491 + 36 117 81 198 Tl x -27528.746 7.545 7890.300 0.038 B- -1461.257 11.554 197 970446.673 8.100 + 34 116 82 198 Pb -26067.489 8.750 7878.969 0.044 B- -6698.003 29.283 197 972015.397 9.393 + 32 115 83 198 Bi x -19369.486 27.945 7841.189 0.141 B- -3896.134 32.932 197 979206.000 30.000 + 30 114 84 198 Po -15473.352 17.424 7817.561 0.088 B- -8758.839 18.386 197 983388.672 18.705 + 28 113 85 198 At x -6714.513 5.868 7769.373 0.030 B- -5484.155 14.647 197 992791.673 6.300 + 26 112 86 198 Rn -a -1230.358 13.420 7737.724 0.068 B- -10804.382 34.905 197 998679.156 14.406 + 24 111 87 198 Fr -a 9574.024 32.222 7679.205 0.163 B- * 198 010278.138 34.591 +0 49 124 75 199 Re x -14860# 401# 7851# 2# B- 5623# 446# 198 984047# 430# + 47 123 76 199 Os x -20484# 196# 7875# 1# B- 3915# 200# 198 978010# 210# + 45 122 77 199 Ir p-2n -24398.515 41.054 7891.206 0.206 B- 2990.167 41.003 198 973807.115 44.073 + 43 121 78 199 Pt -n -27388.682 2.159 7902.300 0.011 B- 1705.059 2.120 198 970597.038 2.317 + 41 120 79 199 Au -29093.741 0.542 7906.937 0.003 B- 452.327 0.613 198 968766.582 0.581 + 39 119 80 199 Hg -29546.068 0.526 7905.279 0.003 B- -1486.674 27.950 198 968280.989 0.564 + 37 118 81 199 Tl x -28059.394 27.945 7893.877 0.140 B- -2827.589 29.679 198 969877.000 30.000 + 35 117 82 199 Pb +a -25231.804 9.996 7875.736 0.050 B- -4434.239 14.547 198 972912.542 10.730 + 33 116 83 199 Bi -20797.566 10.568 7849.522 0.053 B- -5589.083 20.919 198 977672.893 11.345 + 31 115 84 199 Po -a -15208.483 18.060 7817.505 0.091 B- -6385.111 18.845 198 983673.021 19.387 + 29 114 85 199 At -8823.372 5.384 7781.488 0.027 B- -7323.921 37.972 198 990527.719 5.780 + 27 113 86 199 Rn -a -1499.451 37.588 7740.753 0.189 B- -8270.844 40.015 198 998390.273 40.352 + 25 112 87 199 Fr -a 6771.393 13.726 7695.259 0.069 B- * 199 007269.389 14.734 +0 48 124 76 200 Os x -18779# 298# 7868# 1# B- 2832# 357# 199 979840# 320# + 46 123 77 200 Ir x -21611# 196# 7878# 1# B- 4988# 197# 199 976800# 210# + 44 122 78 200 Pt -nn -26599.160 20.110 7899.198 0.101 B- 640.932 33.439 199 971444.625 21.588 + 42 121 79 200 Au -27240.092 26.717 7898.491 0.134 B- 2263.178 26.719 199 970756.556 28.681 + 40 120 80 200 Hg -29503.270 0.529 7905.895 0.003 B- -2456.040 5.735 199 968326.934 0.568 + 38 119 81 200 Tl - -27047.230 5.759 7889.703 0.029 B- -796.176 12.340 199 970963.602 6.182 + 36 118 82 200 Pb 4n -26251.054 10.927 7881.810 0.055 B- -5880.299 24.852 199 971818.332 11.730 + 34 117 83 200 Bi +a -20370.755 22.321 7848.497 0.112 B- -3428.994 23.573 199 978131.093 23.962 + 32 116 84 200 Po -16941.761 7.579 7827.440 0.038 B- -7953.869 25.612 199 981812.270 8.135 + 30 115 85 200 At -a -8987.892 24.465 7783.759 0.122 B- -4983.127 28.030 199 990351.100 26.264 + 28 114 86 200 Rn -a -4004.765 13.681 7754.932 0.068 B- -10137.263 33.529 199 995700.707 14.686 + 26 113 87 200 Fr -a 6132.498 30.611 7700.334 0.153 B- * 200 006583.507 32.861 +0 49 125 76 201 Os x -15239# 298# 7851# 1# B- 4657# 357# 200 983640# 320# + 47 124 77 201 Ir x -19897# 196# 7871# 1# B- 3844# 202# 200 978640# 210# + 45 123 78 201 Pt + -23740.714 50.103 7885.833 0.249 B- 2660.000 50.000 200 974513.293 53.788 + 43 122 79 201 Au -26400.714 3.218 7895.175 0.016 B- 1261.827 3.147 200 971657.665 3.454 + 41 121 80 201 Hg -27662.542 0.711 7897.560 0.004 B- -481.704 14.181 200 970303.038 0.763 + 39 120 81 201 Tl -27180.838 14.185 7891.271 0.071 B- -1909.802 18.530 200 970820.168 15.228 + 37 119 82 201 Pb -25271.036 13.747 7877.877 0.068 B- -3854.603 20.481 200 972870.425 14.758 + 35 118 83 201 Bi +a -21416.433 15.183 7854.808 0.076 B- -4895.248 15.962 200 977008.512 16.299 + 33 117 84 201 Po -16521.185 4.942 7826.561 0.025 B- -5731.747 9.561 200 982263.777 5.305 + 31 116 85 201 At +a -10789.438 8.184 7794.153 0.041 B- -6717.113 50.401 200 988417.061 8.786 + 29 115 86 201 Rn -a -4072.324 49.732 7756.842 0.247 B- -7660.902 50.554 200 995628.179 53.389 + 27 114 87 201 Fr -a 3588.577 9.080 7714.836 0.045 B- -8348.224 22.239 201 003852.496 9.747 + 25 113 88 201 Ra -a 11936.801 20.301 7669.410 0.101 B- * 201 012814.683 21.794 +0 50 126 76 202 Os x -13087# 401# 7842# 2# B- 3689# 499# 201 985950# 430# + 48 125 77 202 Ir x -16776# 298# 7856# 1# B- 5916# 299# 201 981990# 320# + 46 124 78 202 Pt x -22692.125 25.150 7881.560 0.125 B- 1660.854 34.276 201 975639.000 27.000 + 44 123 79 202 Au x -24352.979 23.287 7885.909 0.115 B- 2992.345 23.298 201 973856.000 25.000 + 42 122 80 202 Hg -27345.324 0.705 7896.850 0.003 B- -1365.108 1.636 201 970643.585 0.756 + 40 121 81 202 Tl -25980.216 1.606 7886.219 0.008 B- -39.602 4.096 201 972109.089 1.723 + 38 120 82 202 Pb -25940.614 3.796 7882.150 0.019 B- -5199.130 15.856 201 972151.604 4.075 + 36 119 83 202 Bi -20741.484 15.396 7852.539 0.076 B- -2799.868 17.666 201 977733.100 16.528 + 34 118 84 202 Po -17941.616 8.670 7834.805 0.043 B- -7350.884 29.289 201 980738.881 9.307 + 32 117 85 202 At -a -10590.732 27.977 7794.541 0.138 B- -4316.097 33.010 201 988630.380 30.034 + 30 116 86 202 Rn -a -6274.635 17.520 7769.301 0.087 B- -9370.871 18.881 201 993263.902 18.808 + 28 115 87 202 Fr -a 3096.237 7.040 7719.038 0.035 B- -5978.625 16.586 202 003323.946 7.557 + 26 114 88 202 Ra -a 9074.861 15.018 7685.568 0.074 B- * 202 009742.264 16.122 +0 51 127 76 203 Os x -7640# 401# 7816# 2# B- 7050# 566# 202 991798# 430# + 49 126 77 203 Ir x -14690# 401# 7847# 2# B- 4937# 446# 202 984230# 430# + 47 125 78 203 Pt x -19627# 196# 7867# 1# B- 3517# 196# 202 978930# 210# + 45 124 79 203 Au -23143.436 3.083 7880.864 0.015 B- 2125.829 3.451 202 975154.498 3.309 + 43 123 80 203 Hg -25269.265 1.627 7887.482 0.008 B- 492.112 1.225 202 972872.326 1.746 + 41 122 81 203 Tl -25761.377 1.166 7886.053 0.006 B- -974.820 6.461 202 972344.022 1.252 + 39 121 82 203 Pb -24786.557 6.554 7877.397 0.032 B- -3261.729 14.356 202 973390.535 7.036 + 37 120 83 203 Bi +a -21524.827 12.778 7857.475 0.063 B- -4213.939 15.433 202 976892.145 13.717 + 35 119 84 203 Po +a -17310.889 8.655 7832.863 0.043 B- -5148.332 13.666 202 981415.995 9.291 + 33 118 85 203 At -12162.557 10.576 7803.648 0.052 B- -6008.858 21.027 202 986942.957 11.353 + 31 117 86 203 Rn -a -6153.699 18.179 7770.193 0.090 B- -7030.116 19.218 202 993393.732 19.516 + 29 116 87 203 Fr 876.417 6.232 7731.708 0.031 B- -7785.309 38.630 203 000940.872 6.689 + 27 115 88 203 Ra -a 8661.726 38.124 7689.503 0.188 B- * 203 009298.745 40.928 +0 50 127 77 204 Ir x -9688# 401# 7824# 2# B- 8234# 446# 203 989600# 430# + 48 126 78 204 Pt x -17922# 196# 7860# 1# B- 2728# 280# 203 980760# 210# + 46 125 79 204 Au + -20650# 200# 7870# 1# B- 4040# 200# 203 977831# 215# + 44 124 80 204 Hg -24690.145 0.498 7885.545 0.002 B- -344.000 1.186 203 973494.037 0.534 + 42 123 81 204 Tl -24346.145 1.152 7880.023 0.006 B- 763.748 0.177 203 973863.337 1.236 + 40 122 82 204 Pb -25109.892 1.146 7879.932 0.006 B- -4463.996 9.248 203 973043.420 1.230 + 38 121 83 204 Bi +a -20645.896 9.180 7854.215 0.045 B- -2304.652 14.335 203 977835.717 9.854 + 36 120 84 204 Po -a -18341.244 11.013 7839.083 0.054 B- -6465.811 24.860 203 980309.863 11.822 + 34 119 85 204 At -11875.433 22.288 7803.552 0.109 B- -3905.240 23.498 203 987251.197 23.926 + 32 118 86 204 Rn -7970.193 7.444 7780.574 0.036 B- -8577.503 25.684 203 991443.644 7.991 + 30 117 87 204 Fr -a 607.310 24.581 7734.692 0.120 B- -5449.477 28.940 204 000651.974 26.389 + 28 116 88 204 Ra -a 6056.787 15.273 7704.144 0.075 B- * 204 006502.228 16.396 +0 51 128 77 205 Ir x -5960# 503# 7807# 2# B- 7007# 585# 204 993602# 540# + 49 127 78 205 Pt x -12966# 298# 7837# 1# B- 5803# 357# 204 986080# 320# + 47 126 79 205 Au x -18770# 196# 7861# 1# B- 3518# 196# 204 979850# 210# + 45 125 80 205 Hg -22287.740 3.654 7874.732 0.018 B- 1533.135 3.724 204 976073.125 3.923 + 43 124 81 205 Tl -23820.874 1.237 7878.394 0.006 B- -50.636 0.503 204 974427.237 1.328 + 41 123 82 205 Pb -23770.239 1.144 7874.331 0.006 B- -2705.734 5.107 204 974481.597 1.228 + 39 122 83 205 Bi -21064.504 5.111 7857.316 0.025 B- -3543.106 11.280 204 977386.323 5.487 + 37 121 84 205 Po -17521.398 10.059 7836.216 0.049 B- -4549.452 18.130 204 981190.004 10.798 + 35 120 85 205 At +a -12971.946 15.085 7810.207 0.074 B- -5262.161 15.913 204 986074.041 16.194 + 33 119 86 205 Rn -7709.786 5.080 7780.722 0.025 B- -6399.973 9.329 204 991723.204 5.453 + 31 118 87 205 Fr x -1309.813 7.824 7745.686 0.038 B- -7148.804 70.954 204 998593.858 8.399 + 29 117 88 205 Ra -a 5838.991 70.521 7706.998 0.344 B- -8267.702 86.923 205 006268.415 75.707 + 27 116 89 205 Ac -a 14106.693 50.818 7662.851 0.248 B- * 205 015144.158 54.555 +0 50 128 78 206 Pt x -9632# 298# 7822# 1# B- 4583# 422# 205 989660# 320# + 48 127 79 206 Au x -14215# 298# 7840# 1# B- 6731# 299# 205 984740# 320# + 46 126 80 206 Hg +a -20945.801 20.440 7869.172 0.099 B- 1307.566 20.410 205 977513.756 21.943 + 44 125 81 206 Tl -22253.367 1.284 7871.721 0.006 B- 1532.217 0.612 205 976110.026 1.378 + 42 124 82 206 Pb -23785.584 1.144 7875.362 0.006 B- -3757.306 7.546 205 974465.124 1.227 + 40 123 83 206 Bi - -20028.278 7.632 7853.324 0.037 B- -1839.604 8.600 205 978498.757 8.193 + 38 122 84 206 Po -a -18188.674 4.012 7840.597 0.019 B- -5758.956 15.580 205 980473.654 4.306 + 36 121 85 206 At -12429.718 15.056 7808.843 0.073 B- -3296.753 17.330 205 986656.148 16.162 + 34 120 86 206 Rn -9132.965 8.591 7789.041 0.042 B- -7890.549 29.475 205 990195.358 9.223 + 32 119 87 206 Fr -a -1242.416 28.195 7746.940 0.137 B- -4807.955 33.455 205 998666.211 30.268 + 30 118 88 206 Ra -a 3565.539 18.008 7719.802 0.087 B- -9913.913 53.608 206 003827.763 19.332 + 28 117 89 206 Ac -a 13479.452 50.493 7667.879 0.245 B- * 206 014470.787 54.206 +0 51 129 78 207 Pt x -4540# 401# 7798# 2# B- 6270# 500# 206 995126# 430# + 49 128 79 207 Au x -10810# 300# 7825# 1# B- 5677# 301# 206 988395# 322# + 47 127 80 207 Hg x -16487.444 29.808 7848.610 0.144 B- 4547.008 30.300 206 982300.000 32.000 + 45 126 81 207 Tl -21034.451 5.439 7866.797 0.026 B- 1417.595 5.402 206 977418.586 5.839 + 43 125 82 207 Pb -22452.047 1.147 7869.866 0.006 B- -2397.420 2.118 206 975896.735 1.230 + 41 124 83 207 Bi -20054.627 2.397 7854.505 0.012 B- -2908.852 6.614 206 978470.471 2.573 + 39 123 84 207 Po -17145.775 6.659 7836.673 0.032 B- -3918.358 14.075 206 981593.252 7.148 + 37 122 85 207 At +a -13227.416 12.406 7813.964 0.060 B- -4592.654 15.037 206 985799.783 13.318 + 35 121 86 207 Rn +a -8634.762 8.497 7787.998 0.041 B- -5790.421 19.458 206 990730.200 9.121 + 33 120 87 207 Fr -2844.341 17.505 7756.246 0.085 B- -6388.826 56.008 206 996946.474 18.792 + 31 119 88 207 Ra -a 3544.485 53.202 7721.602 0.257 B- -7601.748 73.276 207 003805.161 57.115 + 29 118 89 207 Ac -a 11146.233 50.387 7681.099 0.243 B- * 207 011965.973 54.092 +0 52 130 78 208 Pt x -990# 400# 7783# 2# B- 5111# 499# 207 998937# 429# + 50 129 79 208 Au x -6101# 298# 7804# 1# B- 7164# 300# 207 993450# 320# + 48 128 80 208 Hg x -13265.406 30.739 7834.191 0.148 B- 3484.726 30.795 207 985759.000 33.000 + 46 127 81 208 Tl +a -16750.132 1.854 7847.183 0.009 B- 4998.466 1.669 207 982017.992 1.990 + 44 126 82 208 Pb -21748.598 1.148 7867.453 0.006 B- -2878.375 2.013 207 976651.918 1.231 + 42 125 83 208 Bi +n -18870.223 2.304 7849.853 0.011 B- -1400.628 2.397 207 979741.981 2.473 + 40 124 84 208 Po -a -17469.596 1.737 7839.358 0.008 B- -4999.725 9.086 207 981245.616 1.864 + 38 123 85 208 At +a -12469.871 8.921 7811.560 0.043 B- -2814.279 14.269 207 986613.042 9.577 + 36 122 86 208 Rn -a -9655.591 11.138 7794.268 0.054 B- -6989.672 16.251 207 989634.295 11.957 + 34 121 87 208 Fr -2665.919 11.834 7756.903 0.057 B- -4393.774 14.881 207 997138.018 12.704 + 32 120 88 208 Ra -a 1727.856 9.023 7732.017 0.043 B- -9025.380 56.442 208 001854.929 9.686 + 30 119 89 208 Ac -a 10753.235 55.716 7684.865 0.268 B- -5930.495 65.370 208 011544.073 59.813 + 28 118 90 208 Th -a 16683.730 34.190 7652.592 0.164 B- * 208 017910.722 36.704 +0 51 130 79 209 Au x -2540# 400# 7788# 2# B- 6104# 426# 208 997273# 429# + 49 129 80 209 Hg x -8644# 149# 7813# 1# B- 5000# 149# 208 990720# 160# + 47 128 81 209 Tl +a -13644.757 6.110 7833.397 0.029 B- 3969.889 6.211 208 985351.750 6.559 + 45 127 82 209 Pb -17614.646 1.747 7848.648 0.008 B- 644.016 1.146 208 981089.898 1.875 + 43 126 83 209 Bi -18258.662 1.364 7847.987 0.007 B- -1892.570 1.564 208 980398.519 1.464 + 41 125 84 209 Po -a -16366.092 1.778 7835.188 0.009 B- -3483.478 5.287 208 982430.276 1.908 + 39 124 85 209 At -12882.613 5.102 7814.777 0.024 B- -3941.564 11.188 208 986169.944 5.477 + 37 123 86 209 Rn -8941.049 9.960 7792.175 0.048 B- -5171.477 17.713 208 990401.388 10.692 + 35 122 87 209 Fr x -3769.572 14.648 7763.688 0.070 B- -5627.791 15.730 208 995953.197 15.725 + 33 121 88 209 Ra -a 1858.219 5.747 7733.017 0.027 B- -6985.590 50.934 209 001994.879 6.169 + 31 120 89 209 Ac -a 8843.809 50.608 7695.850 0.242 B- -7523# 148# 209 009494.220 54.330 + 29 119 90 209 Th IT 16367# 140# 7656# 1# B- * 209 017571# 150# +0 52 131 79 210 Au x 2329# 401# 7766# 2# B- 7694# 446# 210 002500# 430# + 50 130 80 210 Hg x -5365# 196# 7799# 1# B- 3882# 196# 209 994240# 210# + 48 129 81 210 Tl +a -9246.969 11.604 7813.588 0.055 B- 5481.534 11.561 209 990072.970 12.456 + 46 128 82 210 Pb -14728.502 1.447 7835.965 0.007 B- 63.476 0.499 209 984188.301 1.553 + 44 127 83 210 Bi -14791.979 1.363 7832.542 0.006 B- 1161.159 0.766 209 984120.156 1.462 + 42 126 84 210 Po -15953.137 1.146 7834.346 0.005 B- -3980.960 7.610 209 982873.601 1.230 + 40 125 85 210 At -a -11972.177 7.695 7811.663 0.037 B- -2367.407 8.922 209 987147.338 8.261 + 38 124 86 210 Rn -a -9604.770 4.557 7796.665 0.022 B- -6271.565 15.824 209 989688.854 4.892 + 36 123 87 210 Fr -3333.205 15.154 7763.075 0.072 B- -3775.997 17.720 209 996421.657 16.268 + 34 122 88 210 Ra -a 442.792 9.193 7741.368 0.044 B- -8346.908 58.133 210 000475.356 9.868 + 32 121 89 210 Ac -a 8789.699 57.402 7697.896 0.273 B- -5269.747 60.436 210 009436.130 61.623 + 30 120 90 210 Th -a 14059.446 18.909 7669.076 0.090 B- * 210 015093.437 20.299 +0 51 131 80 211 Hg x -624# 196# 7778# 1# B- 5454# 200# 210 999330# 210# + 49 130 81 211 Tl x -6077.998 41.917 7799.791 0.199 B- 4414.950 41.978 210 993475.000 45.000 + 47 129 82 211 Pb -10492.948 2.261 7817.007 0.011 B- 1366.183 5.471 210 988735.356 2.426 + 45 128 83 211 Bi -11859.131 5.442 7819.774 0.026 B- 573.439 5.430 210 987268.698 5.842 + 43 127 84 211 Po -a -12432.571 1.255 7818.784 0.006 B- -785.307 2.539 210 986653.085 1.347 + 41 126 85 211 At -a -11647.264 2.729 7811.354 0.013 B- -2891.860 6.894 210 987496.147 2.929 + 39 125 86 211 Rn -a -8755.404 6.813 7793.941 0.032 B- -4615.155 13.786 210 990600.686 7.314 + 37 124 87 211 Fr -4140.249 11.991 7768.360 0.057 B- -4972.272 14.369 210 995555.259 12.872 + 35 123 88 211 Ra x 832.023 7.918 7741.087 0.038 B- -6370.191 53.564 211 000893.213 8.500 + 33 122 89 211 Ac -a 7202.214 52.976 7707.189 0.251 B- -6707.958 90.205 211 007731.894 56.871 + 31 121 90 211 Th -a 13910.171 73.010 7671.690 0.346 B- -8170# 126# 211 014933.183 78.379 + 29 120 91 211 Pa x 22080# 102# 7629# 0# B- * 211 023704# 110# +0 52 132 80 212 Hg x 2757# 298# 7763# 1# B- 4308# 359# 212 002960# 320# + 50 131 81 212 Tl +a -1551# 200# 7780# 1# B- 5998# 200# 211 998335# 215# + 48 130 82 212 Pb -7548.850 1.842 7804.319 0.009 B- 569.104 1.825 211 991895.975 1.977 + 46 129 83 212 Bi -8117.954 1.854 7803.313 0.009 B- 2251.533 1.667 211 991285.016 1.989 + 44 128 84 212 Po -10369.487 1.152 7810.243 0.005 B- -1741.266 2.107 211 988867.896 1.236 + 42 127 85 212 At -a -8628.221 2.384 7798.340 0.011 B- 31.387 3.605 211 990737.223 2.559 + 40 126 86 212 Rn -a -8659.608 3.145 7794.797 0.015 B- -5143.640 9.318 211 990703.528 3.376 + 38 125 87 212 Fr -3515.968 8.775 7766.845 0.041 B- -3317.000 14.276 211 996225.453 9.420 + 36 124 88 212 Ra -a -198.968 11.263 7747.508 0.053 B- -7476.266 52.601 211 999786.399 12.091 + 34 123 89 212 Ac -a 7277.298 51.381 7708.552 0.242 B- -4833.510 52.366 212 007812.501 55.160 + 32 122 90 212 Th -a 12110.808 10.109 7682.062 0.048 B- -9482.551 75.541 212 013001.487 10.852 + 30 121 91 212 Pa -a 21593.358 74.862 7633.643 0.353 B- * 212 023181.425 80.367 +0 53 133 80 213 Hg x 7666# 298# 7741# 1# B- 5882# 299# 213 008230# 320# + 51 132 81 213 Tl x 1783.811 27.013 7765.430 0.127 B- 4987.343 27.894 213 001915.000 29.000 + 49 131 82 213 Pb +a -3203.532 6.954 7785.172 0.033 B- 2028.103 8.371 212 996560.867 7.465 + 47 130 83 213 Bi -5231.635 5.082 7791.021 0.024 B- 1421.949 5.490 212 994383.608 5.456 + 45 129 84 213 Po -6653.584 3.053 7794.024 0.014 B- -73.989 5.465 212 992857.083 3.277 + 43 128 85 213 At -a -6579.595 4.898 7790.003 0.023 B- -883.569 5.724 212 992936.514 5.257 + 41 127 86 213 Rn -a -5696.026 3.370 7782.182 0.016 B- -2143.179 6.006 212 993885.064 3.617 + 39 126 87 213 Fr -3552.848 5.091 7768.447 0.024 B- -3898.405 11.057 212 996185.861 5.465 + 37 125 88 213 Ra 345.557 9.818 7746.472 0.046 B- -5809.134 18.156 213 000370.970 10.540 + 35 124 89 213 Ac -a 6154.692 15.272 7715.526 0.072 B- -5965.394 17.834 213 006607.333 16.395 + 33 123 90 213 Th -a 12120.086 9.217 7683.846 0.043 B- -7542.539 71.737 213 013011.447 9.895 + 31 122 91 213 Pa -a 19662.625 71.142 7644.762 0.334 B- * 213 021108.697 76.374 +0 54 134 80 214 Hg x 11178# 401# 7727# 2# B- 4713# 446# 214 012000# 430# + 52 133 81 214 Tl x 6465# 196# 7745# 1# B- 6647# 196# 214 006940# 210# + 50 132 82 214 Pb -182.769 1.975 7772.394 0.009 B- 1017.984 11.256 213 999803.788 2.120 + 48 131 83 214 Bi -1200.753 11.209 7773.495 0.052 B- 3269.293 11.165 213 998710.938 12.033 + 46 130 84 214 Po -4470.046 1.449 7785.116 0.007 B- -1090.215 4.107 213 995201.208 1.555 + 44 129 85 214 At -a -3379.831 4.298 7776.366 0.020 B- 939.911 10.014 213 996371.601 4.614 + 42 128 86 214 Rn -a -4319.742 9.187 7777.102 0.043 B- -3361.035 12.503 213 995362.566 9.862 + 40 127 87 214 Fr -a -958.707 8.634 7757.740 0.040 B- -1051.441 10.086 213 998970.785 9.268 + 38 126 88 214 Ra -a 92.734 5.250 7749.171 0.025 B- -6351.120 16.232 214 000099.554 5.636 + 36 125 89 214 Ac -a 6443.854 15.360 7715.837 0.072 B- -4251.030 18.693 214 006917.762 16.489 + 34 124 90 214 Th -a 10694.885 10.661 7692.317 0.050 B- -8790.630 76.867 214 011481.431 11.445 + 32 123 91 214 Pa -a 19485.515 76.125 7647.583 0.356 B- * 214 020918.561 81.723 +0 55 135 80 215 Hg x 16208# 401# 7705# 2# B- 6297# 499# 215 017400# 430# + 53 134 81 215 Tl x 9911# 298# 7730# 1# B- 5569# 303# 215 010640# 320# + 51 133 82 215 Pb +a 4342.244 52.448 7752.737 0.244 B- 2712.922 52.748 215 004661.590 56.304 + 49 132 83 215 Bi 1629.322 5.624 7761.717 0.026 B- 2171.028 5.530 215 001749.149 6.037 + 47 131 84 215 Po -541.706 2.121 7768.176 0.010 B- 714.049 6.819 214 999418.454 2.276 + 45 130 85 215 At -a -1255.756 6.799 7767.858 0.032 B- -87.195 10.168 214 998651.890 7.299 + 43 129 86 215 Rn -a -1168.561 7.672 7763.814 0.036 B- -1486.625 10.306 214 998745.498 8.236 + 41 128 87 215 Fr -a 318.065 7.066 7753.260 0.033 B- -2215.674 10.077 215 000341.456 7.585 + 39 127 88 215 Ra -a 2533.739 7.613 7739.316 0.035 B- -3496.877 14.551 215 002720.080 8.172 + 37 126 89 215 Ac -a 6030.615 12.406 7719.413 0.058 B- -4890.971 15.234 215 006474.132 13.318 + 35 125 90 215 Th -a 10921.586 8.840 7693.025 0.041 B- -6942.353 73.380 215 011724.805 9.490 + 33 124 91 215 Pa -a 17863.939 72.845 7657.096 0.339 B- -7059.147 114.616 215 019177.728 78.202 + 31 123 92 215 U -a 24923.087 88.490 7620.624 0.412 B- * 215 026756.035 94.997 +0 56 136 80 216 Hg x 19859# 401# 7690# 2# B- 5142# 499# 216 021320# 430# + 54 135 81 216 Tl x 14718# 298# 7710# 1# B- 7238# 357# 216 015800# 320# + 52 134 82 216 Pb x 7480# 196# 7740# 1# B- 1606# 196# 216 008030# 210# + 50 133 83 216 Bi x 5873.991 11.178 7743.499 0.052 B- 4091.571 11.324 216 006305.989 12.000 + 48 132 84 216 Po 1782.420 1.816 7758.819 0.008 B- -474.246 3.571 216 001913.506 1.949 + 46 131 85 216 At -a 2256.666 3.575 7753.002 0.017 B- 2003.799 6.836 216 002422.631 3.837 + 44 130 86 216 Rn -a 252.868 5.994 7758.657 0.028 B- -2718.082 7.126 216 000271.464 6.435 + 42 129 87 216 Fr -a 2970.950 4.173 7742.451 0.019 B- -320.128 9.548 216 003189.445 4.480 + 40 128 88 216 Ra -a 3291.077 8.737 7737.347 0.040 B- -4853.317 13.921 216 003533.117 9.379 + 38 127 89 216 Ac -a 8144.395 10.840 7711.256 0.050 B- -2153.937 16.201 216 008743.367 11.637 + 36 126 90 216 Th -a 10298.332 12.042 7697.662 0.056 B- -7500.882 54.864 216 011055.714 12.928 + 34 125 91 216 Pa -a 17799.214 53.526 7659.314 0.248 B- -5267.137 60.450 216 019108.242 57.462 + 32 124 92 216 U -a 23066.351 28.093 7631.307 0.130 B- * 216 024762.747 30.158 +0 55 136 81 217 Tl x 18313# 401# 7695# 2# B- 6073# 499# 217 019660# 430# + 53 135 82 217 Pb x 12240# 298# 7719# 1# B- 3510# 299# 217 013140# 320# + 51 134 83 217 Bi x 8729.962 17.698 7731.848 0.082 B- 2846.444 18.870 217 009372.000 19.000 + 49 133 84 217 Po +a 5883.518 6.544 7741.360 0.030 B- 1488.883 7.979 217 006316.216 7.025 + 47 132 85 217 At 4394.635 5.001 7744.616 0.023 B- 736.135 6.151 217 004717.835 5.369 + 45 131 86 217 Rn -a 3658.501 4.198 7744.403 0.019 B- -656.089 7.538 217 003927.562 4.506 + 43 130 87 217 Fr -a 4314.590 6.531 7737.775 0.030 B- -1575.067 9.588 217 004631.902 7.010 + 41 129 88 217 Ra -a 5889.656 7.202 7726.911 0.033 B- -2814.017 13.430 217 006322.806 7.731 + 39 128 89 217 Ac -a 8703.673 11.389 7710.338 0.052 B- -3502.107 15.566 217 009343.777 12.226 + 37 127 90 217 Th -a 12205.780 10.614 7690.594 0.049 B- -4862.630 19.132 217 013103.444 11.394 + 35 126 91 217 Pa -a 17068.410 15.918 7664.580 0.073 B- -5905# 73# 217 018323.692 17.089 + 33 125 92 217 U -a 22973# 71# 7634# 0# B- * 217 024663# 77# +0 56 137 81 218 Tl x 23180# 400# 7674# 2# B- 7727# 499# 218 024885# 429# + 54 136 82 218 Pb x 15453# 298# 7706# 1# B- 2237# 299# 218 016590# 320# + 52 135 83 218 Bi x 13216.037 27.013 7712.827 0.124 B- 4859.136 27.085 218 014188.000 29.000 + 50 134 84 218 Po 8356.901 1.973 7731.528 0.009 B- 258.738 11.649 218 008971.502 2.118 + 48 133 85 218 At -a 8098.162 11.604 7729.126 0.053 B- 2880.816 11.705 218 008693.735 12.456 + 46 132 86 218 Rn 5217.347 2.316 7738.752 0.011 B- -1841.770 4.942 218 005601.052 2.486 + 44 131 87 218 Fr -a 7059.117 4.757 7726.715 0.022 B- 407.947 12.039 218 007578.274 5.106 + 42 130 88 218 Ra -a 6651.170 11.176 7724.998 0.051 B- -4192.439 51.931 218 007140.325 11.997 + 40 129 89 218 Ac -a 10843.609 50.740 7702.177 0.233 B- -1523.132 51.815 218 011641.093 54.471 + 38 128 90 218 Th -a 12366.741 10.516 7691.602 0.048 B- -6317.029 21.130 218 013276.242 11.289 + 36 127 91 218 Pa -a 18683.770 18.329 7659.036 0.084 B- -3210.838 22.888 218 020057.853 19.676 + 34 126 92 218 U -a 21894.608 13.714 7640.719 0.063 B- * 218 023504.829 14.722 +0 55 137 82 219 Pb x 20279# 401# 7686# 2# B- 3996# 446# 219 021770# 430# + 53 136 83 219 Bi x 16283# 196# 7700# 1# B- 3601# 196# 219 017480# 210# + 51 135 84 219 Po x 12681.359 15.835 7713.333 0.072 B- 2285.283 16.163 219 013614.000 17.000 + 49 134 85 219 At 10396.076 3.237 7720.196 0.015 B- 1566.675 2.947 219 011160.647 3.474 + 47 133 86 219 Rn 8829.402 2.100 7723.777 0.010 B- 211.635 7.058 219 009478.753 2.254 + 45 132 87 219 Fr -a 8617.767 7.039 7721.171 0.032 B- -776.515 10.772 219 009251.553 7.556 + 43 131 88 219 Ra -a 9394.282 8.258 7714.053 0.038 B- -2175.199 51.142 219 010085.176 8.865 + 41 130 89 219 Ac -a 11569.480 50.497 7700.549 0.231 B- -2901.910 71.425 219 012420.348 54.210 + 39 129 90 219 Th -a 14471.390 50.576 7683.725 0.231 B- -4068.741 72.192 219 015535.677 54.295 + 37 128 91 219 Pa -a 18540.131 51.516 7661.574 0.235 B- -4746.439 72.333 219 019903.650 55.304 + 35 127 92 219 U -a 23286.569 50.775 7636.329 0.232 B- -6170.086 101.905 219 024999.161 54.509 + 33 126 93 219 Np -a 29456.655 88.354 7604.583 0.403 B- * 219 031623.021 94.851 +0 56 138 82 220 Pb x 23669# 401# 7672# 2# B- 2850# 499# 220 025410# 430# + 54 137 83 220 Bi x 20819# 298# 7682# 1# B- 5555# 299# 220 022350# 320# + 52 136 84 220 Po x 15263.461 17.698 7703.224 0.080 B- 887.714 22.549 220 016386.000 19.000 + 50 135 85 220 At x 14375.747 13.972 7703.703 0.064 B- 3763.670 14.090 220 015433.000 15.000 + 48 134 86 220 Rn 10612.077 1.815 7717.254 0.008 B- -870.242 4.026 220 011392.534 1.948 + 46 133 87 220 Fr -a 11482.320 4.028 7709.742 0.018 B- 1212.075 9.061 220 012326.778 4.324 + 44 132 88 220 Ra -a 10270.245 8.237 7711.696 0.037 B- -3473.437 10.141 220 011025.562 8.843 + 42 131 89 220 Ac -a 13743.682 6.129 7692.351 0.028 B- -925.417 22.941 220 014754.450 6.579 + 40 130 90 220 Th -a 14669.100 22.166 7684.589 0.101 B- -5549# 56# 220 015747.926 23.795 + 38 129 91 220 Pa -a 20218# 51# 7656# 0# B- -2715# 113# 220 021705# 55# + 36 128 92 220 U -a 22933# 101# 7640# 0# B- -7378# 220# 220 024620# 108# + 34 127 93 220 Np x 30311# 196# 7603# 1# B- * 220 032540# 210# +0 55 138 83 221 Bi x 24098# 298# 7668# 1# B- 4324# 299# 221 025870# 320# + 53 137 84 221 Po x 19773.755 19.561 7684.481 0.089 B- 2991.027 24.039 221 021228.000 21.000 + 51 136 85 221 At x 16782.727 13.972 7694.475 0.063 B- 2311.308 15.096 221 018017.000 15.000 + 49 135 86 221 Rn +a 14471.420 5.714 7701.393 0.026 B- 1194.130 7.231 221 015535.709 6.134 + 47 134 87 221 Fr 13277.290 4.886 7703.256 0.022 B- 313.479 6.386 221 014253.757 5.245 + 45 133 88 221 Ra -a 12963.811 4.630 7701.135 0.021 B- -1559.298 50.603 221 013917.224 4.970 + 43 132 89 221 Ac -a 14523.109 50.425 7690.539 0.228 B- -2417.261 51.056 221 015591.199 54.133 + 41 131 90 221 Th -a 16940.371 8.166 7676.061 0.037 B- -3435.918 51.915 221 018186.236 8.766 + 39 130 91 221 Pa -a 20376.288 51.281 7656.974 0.232 B- -4143.707 72.404 221 021874.846 55.052 + 37 129 92 221 U -a 24519.995 51.114 7634.684 0.231 B- -5330# 207# 221 026323.299 54.873 + 35 128 93 221 Np x 29850# 200# 7607# 1# B- * 221 032045# 215# +0 56 139 83 222 Bi x 28729# 300# 7649# 1# B- 6243# 303# 222 030842# 322# + 54 138 84 222 Po x 22486.265 40.054 7674.005 0.180 B- 1533.239 43.071 222 024140.000 43.000 + 52 137 85 222 At x 20953.026 15.835 7677.387 0.071 B- 4580.820 15.955 222 022494.000 17.000 + 50 136 86 222 Rn 16372.206 1.950 7694.497 0.009 B- -5.900 7.703 222 017576.286 2.093 + 48 135 87 222 Fr x 16378.105 7.452 7690.947 0.034 B- 2057.917 8.682 222 017582.620 8.000 + 46 134 88 222 Ra 14320.188 4.454 7696.692 0.020 B- -2301.285 6.637 222 015373.355 4.781 + 44 133 89 222 Ac -a 16621.474 5.174 7682.802 0.023 B- -581.637 13.228 222 017843.887 5.554 + 42 132 90 222 Th -a 17203.111 12.279 7676.658 0.055 B- -4951# 74# 222 018468.300 13.182 + 40 131 91 222 Pa -a 22155# 72# 7651# 0# B- -2118# 89# 222 023784# 78# + 38 130 92 222 U -a 24272.827 51.994 7637.764 0.234 B- -6746# 202# 222 026057.953 55.817 + 36 129 93 222 Np x 31019# 196# 7604# 1# B- * 222 033300# 210# +0 57 140 83 223 Bi x 32137# 401# 7636# 2# B- 5058# 446# 223 034500# 430# + 55 139 84 223 Po x 27079# 196# 7655# 1# B- 3651# 196# 223 029070# 210# + 53 138 85 223 At x 23428.006 13.972 7668.055 0.063 B- 3038.267 16.013 223 025151.000 15.000 + 51 137 86 223 Rn 20389.739 7.822 7678.171 0.035 B- 2007.344 8.057 223 021889.285 8.397 + 49 136 87 223 Fr 18382.394 1.932 7683.664 0.009 B- 1149.085 0.848 223 019734.313 2.073 + 47 135 88 223 Ra 17233.309 2.090 7685.309 0.009 B- -592.573 7.128 223 018500.719 2.244 + 45 134 89 223 Ac -a 17825.882 7.110 7679.143 0.032 B- -1559.948 11.563 223 019136.872 7.632 + 43 133 90 223 Th -a 19385.831 9.212 7668.640 0.041 B- -2934.845 71.639 223 020811.546 9.889 + 41 132 91 223 Pa -a 22320.676 71.063 7651.971 0.319 B- -3516.330 100.506 223 023962.232 76.289 + 39 131 92 223 U -a 25837.006 71.119 7632.694 0.319 B- -4763# 208# 223 027737.168 76.349 + 37 130 93 223 Np x 30600# 196# 7608# 1# B- * 223 032850# 210# +0 58 141 83 224 Bi x 36830# 400# 7617# 2# B- 6920# 445# 224 039539# 429# + 56 140 84 224 Po x 29910# 196# 7644# 1# B- 2199# 197# 224 032110# 210# + 54 139 85 224 At x 27711.015 22.356 7650.735 0.100 B- 5265.917 24.415 224 029749.000 24.000 + 52 138 86 224 Rn 22445.098 9.814 7670.751 0.044 B- 696.482 14.875 224 024095.804 10.536 + 50 137 87 224 Fr x 21748.616 11.178 7670.367 0.050 B- 2922.699 11.324 224 023348.100 12.000 + 48 136 88 224 Ra 18825.917 1.813 7679.922 0.008 B- -1408.219 4.087 224 020210.453 1.945 + 46 135 89 224 Ac -a 20234.135 4.089 7670.143 0.018 B- 240.401 10.823 224 021722.239 4.389 + 44 134 90 224 Th -a 19993.734 10.120 7667.724 0.045 B- -3868.544 12.546 224 021464.157 10.864 + 42 133 91 224 Pa -a 23862.278 7.587 7646.961 0.034 B- -1859.974 24.329 224 025617.210 8.145 + 40 132 92 224 U -a 25722.252 23.171 7635.165 0.103 B- -6153# 197# 224 027613.974 24.875 + 38 131 93 224 Np x 31876# 196# 7604# 1# B- * 224 034220# 210# +0 57 141 84 225 Po x 34530# 298# 7626# 1# B- 4136# 422# 225 037070# 320# + 55 140 85 225 At x 30395# 298# 7641# 1# B- 3861# 298# 225 032630# 320# + 53 139 86 225 Rn 26534.141 11.140 7654.357 0.050 B- 2713.531 16.349 225 028485.574 11.958 + 51 138 87 225 Fr 23820.610 11.967 7662.940 0.053 B- 1827.501 12.158 225 025572.478 12.847 + 49 137 88 225 Ra 21993.109 2.596 7667.586 0.012 B- 355.763 5.007 225 023610.574 2.787 + 47 136 89 225 Ac 21637.346 4.758 7665.690 0.021 B- -672.781 6.658 225 023228.647 5.107 + 45 135 90 225 Th -a 22310.127 5.093 7659.222 0.023 B- -2030.598 71.170 225 023950.907 5.467 + 43 134 91 225 Pa -a 24340.725 71.012 7646.720 0.316 B- -3039.196 71.827 225 026130.844 76.234 + 41 133 92 225 U -a 27379.921 10.909 7629.736 0.048 B- -4207.783 72.440 225 029393.555 11.711 + 39 132 93 225 Np -a 31587.704 71.622 7607.557 0.318 B- * 225 033910.797 76.889 +0 58 142 84 226 Po x 37549# 401# 7614# 2# B- 2934# 499# 226 040310# 430# + 56 141 85 226 At x 34614# 298# 7624# 1# B- 5867# 298# 226 037160# 320# + 54 140 86 226 Rn 28747.192 10.477 7646.410 0.046 B- 1226.653 12.190 226 030861.382 11.247 + 52 139 87 226 Fr 27520.539 6.230 7648.376 0.028 B- 3852.715 6.523 226 029544.515 6.688 + 50 138 88 226 Ra 23667.824 1.933 7661.962 0.009 B- -641.440 3.274 226 025408.455 2.075 + 48 137 89 226 Ac 24309.264 3.100 7655.662 0.014 B- 1111.630 4.563 226 026097.069 3.328 + 46 136 90 226 Th 23197.634 4.481 7657.119 0.020 B- -2835.642 12.165 226 024903.686 4.810 + 44 135 91 226 Pa -a 26033.276 11.420 7641.110 0.051 B- -1295.593 17.228 226 027947.872 12.259 + 42 134 92 226 U -a 27328.869 12.999 7631.916 0.058 B- -5448# 89# 226 029338.749 13.955 + 40 133 93 226 Np -a 32777# 88# 7604# 0# B- * 226 035188# 95# +0 59 143 84 227 Po x 42281# 401# 7596# 2# B- 4797# 499# 227 045390# 430# + 57 142 85 227 At x 37483# 298# 7613# 1# B- 4597# 298# 227 040240# 320# + 55 141 86 227 Rn 32885.834 14.091 7630.050 0.062 B- 3203.388 15.276 227 035304.396 15.127 + 53 140 87 227 Fr 29682.445 5.898 7640.715 0.026 B- 2504.734 6.213 227 031865.417 6.332 + 51 139 88 227 Ra -n 27177.711 1.952 7648.303 0.009 B- 1328.132 2.265 227 029176.474 2.095 + 49 138 89 227 Ac 25849.580 1.927 7650.707 0.008 B- 44.757 0.830 227 027750.666 2.068 + 47 137 90 227 Th 25804.823 2.088 7647.458 0.009 B- -1026.375 7.437 227 027702.618 2.241 + 45 136 91 227 Pa -a 26831.198 7.420 7639.490 0.033 B- -2214.264 12.146 227 028804.477 7.965 + 43 135 92 227 U -a 29045.462 9.705 7626.289 0.043 B- -3516.618 73.135 227 031181.587 10.419 + 41 134 93 227 Np -a 32562.080 72.506 7607.351 0.319 B- -4208# 123# 227 034956.832 77.838 + 39 133 94 227 Pu x 36770# 100# 7585# 0# B- * 227 039474# 107# +0 58 143 85 228 At x 41684# 401# 7597# 2# B- 6441# 401# 228 044750# 430# + 56 142 86 228 Rn 35243.465 17.677 7621.645 0.078 B- 1859.244 18.916 228 037835.418 18.977 + 54 141 87 228 Fr 33384.221 6.732 7626.368 0.030 B- 4443.953 7.021 228 035839.437 7.226 + 52 140 88 228 Ra +a 28940.268 1.996 7642.428 0.009 B- 45.540 0.634 228 031068.657 2.142 + 50 139 89 228 Ac - 28894.728 2.094 7639.196 0.009 B- 2123.743 2.645 228 031019.767 2.247 + 48 138 90 228 Th 26770.984 1.807 7645.080 0.008 B- -2152.602 4.340 228 028739.835 1.940 + 46 137 91 228 Pa -a 28923.586 4.340 7632.207 0.019 B- -298.640 14.929 228 031050.748 4.659 + 44 136 92 228 U -a 29222.226 14.354 7627.466 0.063 B- -4373.468 52.545 228 031371.351 15.409 + 42 135 93 228 Np -a 33595.694 50.572 7604.853 0.222 B- -2491.677 58.346 228 036066.462 54.291 + 40 134 94 228 Pu -a 36087.370 29.143 7590.493 0.128 B- * 228 038741.387 31.286 +0 59 144 85 229 At x 44823# 401# 7585# 2# B- 5461# 401# 229 048120# 430# + 57 143 86 229 Rn x 39362.400 13.041 7605.622 0.057 B- 3694.138 13.967 229 042257.276 14.000 + 55 142 87 229 Fr 35668.262 5.001 7618.337 0.022 B- 3106.298 16.231 229 038291.455 5.368 + 53 141 88 229 Ra x 32561.963 15.441 7628.485 0.067 B- 1872.030 19.623 229 034956.707 16.576 + 51 140 89 229 Ac x 30689.933 12.109 7633.244 0.053 B- 1104.350 12.346 229 032947.000 13.000 + 49 139 90 229 Th 29585.583 2.405 7634.650 0.011 B- -311.325 3.715 229 031761.431 2.581 + 47 138 91 229 Pa 29896.908 3.280 7629.874 0.014 B- -1313.646 6.655 229 032095.652 3.521 + 45 137 92 229 U -a 31210.554 5.938 7620.721 0.026 B- -2569.122 87.031 229 033505.909 6.374 + 43 136 93 229 Np -a 33779.675 86.848 7606.086 0.379 B- -3615.915 100.792 229 036263.974 93.235 + 41 135 94 229 Pu -a 37395.590 51.176 7586.880 0.223 B- -4754.430 101.230 229 040145.819 54.939 + 39 134 95 229 Am -a 42150.020 87.348 7562.702 0.381 B- * 229 045249.909 93.772 +0 58 144 86 230 Rn x 42048# 196# 7596# 1# B- 2561# 196# 230 045140# 210# + 56 143 87 230 Fr 39486.768 6.541 7603.704 0.028 B- 4970.462 12.198 230 042390.791 7.022 + 54 142 88 230 Ra x 34516.306 10.296 7621.914 0.045 B- 677.924 18.888 230 037054.780 11.053 + 52 141 89 230 Ac x 33838.383 15.835 7621.460 0.069 B- 2975.789 15.882 230 036327.000 17.000 + 50 140 90 230 Th 30862.593 1.210 7630.996 0.005 B- -1311.014 2.833 230 033132.358 1.299 + 48 139 91 230 Pa 32173.607 3.038 7621.895 0.013 B- 558.605 4.592 230 034539.789 3.261 + 46 138 92 230 U -a 31615.002 4.509 7620.922 0.020 B- -3621.290 51.461 230 033940.102 4.841 + 44 137 93 230 Np -a 35236.291 51.288 7601.776 0.223 B- -1698.101 53.363 230 037827.716 55.059 + 42 136 94 230 Pu -a 36934.392 14.824 7590.991 0.064 B- -5998# 134# 230 039650.703 15.913 + 40 135 95 230 Am -a 42932# 133# 7562# 1# B- * 230 046089# 143# +0 59 145 86 231 Rn x 46454# 298# 7579# 1# B- 4373# 298# 231 049870# 320# + 57 144 87 231 Fr x 42080.575 7.731 7594.500 0.033 B- 3864.089 13.749 231 045175.357 8.300 + 55 143 88 231 Ra 38216.486 11.370 7607.841 0.049 B- 2453.636 17.301 231 041027.086 12.206 + 53 142 89 231 Ac x 35762.849 13.041 7615.076 0.056 B- 1946.959 13.098 231 038393.000 14.000 + 51 141 90 231 Th 33815.891 1.218 7620.118 0.005 B- 391.487 1.460 231 036302.853 1.308 + 49 140 91 231 Pa 33424.404 1.772 7618.426 0.008 B- -381.611 2.033 231 035882.575 1.902 + 47 139 92 231 U -a 33806.015 2.670 7613.387 0.012 B- -1818.498 50.577 231 036292.252 2.866 + 45 138 93 231 Np -a 35624.513 50.547 7602.128 0.219 B- -2684.492 55.333 231 038244.490 54.264 + 43 137 94 231 Pu -a 38309.005 22.549 7587.120 0.098 B- -4101# 301# 231 041126.410 24.206 + 41 136 95 231 Am x 42410# 300# 7566# 1# B- -4860# 424# 231 045529# 322# + 39 135 96 231 Cm x 47270# 300# 7542# 1# B- * 231 050746# 322# +0 58 145 87 232 Fr x 46072.834 13.972 7579.347 0.060 B- 5575.880 16.702 232 049461.224 15.000 + 56 144 88 232 Ra 40496.953 9.151 7600.009 0.039 B- 1342.534 15.931 232 043475.270 9.823 + 54 143 89 232 Ac x 39154.419 13.041 7602.424 0.056 B- 3707.635 13.118 232 042034.000 14.000 + 52 142 90 232 Th 35446.784 1.422 7615.033 0.006 B- -499.850 7.734 232 038053.689 1.526 + 50 141 91 232 Pa + 35946.633 7.645 7609.506 0.033 B- 1337.103 7.428 232 038590.300 8.207 + 48 140 92 232 U 34609.530 1.809 7611.897 0.008 B- -2750# 100# 232 037154.860 1.942 + 46 139 93 232 Np - 37360# 100# 7597# 0# B- -1004# 102# 232 040107# 107# + 44 138 94 232 Pu -a 38363.140 17.595 7588.974 0.076 B- -4976# 300# 232 041184.526 18.888 + 42 137 95 232 Am x 43340# 300# 7564# 1# B- -2973# 362# 232 046527# 322# + 40 136 96 232 Cm -a 46312# 202# 7548# 1# B- * 232 049718# 217# +0 59 146 87 233 Fr x 48920.051 19.561 7569.239 0.084 B- 4585.991 21.369 233 052517.838 21.000 + 57 145 88 233 Ra 44334.060 8.603 7585.564 0.037 B- 3026.027 15.623 233 047594.573 9.235 + 55 144 89 233 Ac x 41308.033 13.041 7595.193 0.056 B- 2576.318 13.118 233 044346.000 14.000 + 53 143 90 233 Th 38731.715 1.425 7602.893 0.006 B- 1242.243 1.122 233 041580.208 1.529 + 51 142 91 233 Pa 37489.472 1.336 7604.866 0.006 B- 570.296 1.975 233 040246.605 1.434 + 49 141 92 233 U 36919.176 2.255 7603.956 0.010 B- -1029.415 51.005 233 039634.367 2.420 + 47 140 93 233 Np -a 37948.590 50.981 7596.181 0.219 B- -2103.179 71.642 233 040739.489 54.729 + 45 139 94 233 Pu -a 40051.769 50.351 7583.796 0.216 B- -3211# 113# 233 042997.345 54.054 + 43 138 95 233 Am -a 43263# 102# 7567# 0# B- -4031# 124# 233 046445# 109# + 41 137 96 233 Cm -a 47294.006 71.547 7545.998 0.307 B- -5567# 235# 233 050772.206 76.809 + 39 136 97 233 Bk -a 52861# 224# 7519# 1# B- * 233 056748# 240# +0 58 146 88 234 Ra x 46930.629 8.383 7576.543 0.036 B- 2089.439 16.294 234 050382.104 9.000 + 56 145 89 234 Ac x 44841.190 13.972 7582.129 0.060 B- 4228.181 14.210 234 048139.000 15.000 + 54 144 90 234 Th +a 40613.009 2.589 7596.855 0.011 B- 274.088 3.172 234 043599.860 2.779 + 52 143 91 234 Pa IT 40338.921 4.094 7594.683 0.017 B- 2193.896 4.000 234 043305.615 4.395 + 50 142 92 234 U 38145.025 1.130 7600.715 0.005 B- -1809.846 8.321 234 040950.370 1.213 + 48 141 93 234 Np - 39954.871 8.397 7589.637 0.036 B- -395.100 10.752 234 042893.320 9.014 + 46 140 94 234 Pu -a 40349.971 6.798 7584.605 0.029 B- -4111# 159# 234 043317.478 7.298 + 44 139 95 234 Am -a 44461# 159# 7564# 1# B- -2263# 159# 234 047731# 170# + 42 138 96 234 Cm -a 46724.633 17.394 7550.677 0.074 B- -6731# 143# 234 050160.959 18.673 + 40 137 97 234 Bk -a 53455# 142# 7519# 1# B- * 234 057387# 153# +0 59 147 88 235 Ra x 51130# 300# 7561# 1# B- 3773# 300# 235 054890# 322# + 57 146 89 235 Ac x 47357.155 13.972 7573.504 0.059 B- 3339.406 19.113 235 050840.000 15.000 + 55 145 90 235 Th x 44017.749 13.041 7584.385 0.055 B- 1728.853 19.113 235 047255.000 14.000 + 53 144 91 235 Pa x 42288.896 13.972 7588.413 0.059 B- 1370.050 14.017 235 045399.000 15.000 + 51 143 92 235 U 40918.846 1.117 7590.914 0.005 B- -124.262 0.852 235 043928.190 1.199 + 49 142 93 235 Np 41043.108 1.389 7587.056 0.006 B- -1139.302 20.499 235 044061.591 1.491 + 47 141 94 235 Pu -a 42182.410 20.521 7578.879 0.087 B- -2443.019 56.045 235 045284.682 22.030 + 45 140 95 235 Am -a 44625.429 52.192 7565.154 0.222 B- -3408# 208# 235 047907.371 56.030 + 43 139 96 235 Cm -a 48034# 201# 7547# 1# B- -4670# 448# 235 051567# 216# + 41 138 97 235 Bk x 52704# 401# 7524# 2# B- * 235 056580# 430# +0 58 147 89 236 Ac x 51220.992 38.191 7559.242 0.162 B- 4965.795 40.667 236 054988.000 41.000 + 56 146 90 236 Th x 46255.198 13.972 7576.968 0.059 B- 921.248 19.760 236 049657.000 15.000 + 54 145 91 236 Pa x 45333.950 13.972 7577.557 0.059 B- 2889.306 14.017 236 048668.000 15.000 + 52 144 92 236 U 42444.644 1.113 7586.484 0.005 B- -933.534 50.415 236 045566.201 1.194 + 50 143 93 236 Np IT 43378.178 50.421 7579.214 0.214 B- 476.585 50.389 236 046568.392 54.129 + 48 142 94 236 Pu 42901.593 1.811 7577.918 0.008 B- -3139# 112# 236 046056.756 1.944 + 46 141 95 236 Am -a 46041# 112# 7561# 0# B- -1814# 113# 236 049427# 120# + 44 140 96 236 Cm -a 47855.045 18.315 7550.299 0.078 B- -5687# 401# 236 051374.506 19.662 + 42 139 97 236 Bk x 53542# 401# 7523# 2# B- * 236 057480# 430# +0 59 148 89 237 Ac x 54020# 400# 7550# 2# B- 4065# 400# 237 057993# 429# + 57 147 90 237 Th x 49955.092 15.835 7563.443 0.067 B- 2427.473 20.514 237 053629.000 17.000 + 55 146 91 237 Pa x 47527.619 13.041 7570.384 0.055 B- 2137.425 13.096 237 051023.000 14.000 + 53 145 92 237 U 45390.194 1.203 7576.102 0.005 B- 518.534 0.520 237 048728.380 1.291 + 51 144 93 237 Np 44871.659 1.120 7574.989 0.005 B- -220.063 1.294 237 048171.710 1.202 + 49 143 94 237 Pu 45091.722 1.697 7570.759 0.007 B- -1478# 59# 237 048407.957 1.822 + 47 142 95 237 Am -a 46570# 59# 7561# 0# B- -2677# 93# 237 049995# 64# + 45 141 96 237 Cm -a 49247.085 70.960 7546.624 0.299 B- -3941# 235# 237 052868.923 76.178 + 43 140 97 237 Bk -a 53188# 224# 7527# 1# B- -4751# 241# 237 057100# 241# + 41 139 98 237 Cf -a 57938.921 87.287 7503.347 0.368 B- * 237 062199.993 93.706 +0 58 148 90 238 Th +a 52525# 283# 7555# 1# B- 1631# 284# 238 056388# 304# + 56 147 91 238 Pa x 50894.038 15.835 7558.344 0.067 B- 3586.255 15.906 238 054637.000 17.000 + 54 146 92 238 U 47307.783 1.493 7570.125 0.006 B- -146.874 1.201 238 050786.996 1.602 + 52 145 93 238 Np -n 47454.656 1.138 7566.221 0.005 B- 1291.443 0.457 238 050944.671 1.221 + 50 144 94 238 Pu 46163.213 1.139 7568.360 0.005 B- -2258.273 50.688 238 049558.250 1.222 + 48 143 95 238 Am -a 48421.487 50.700 7555.584 0.213 B- -1023.701 52.145 238 051982.607 54.428 + 46 142 96 238 Cm -a 49445.188 12.234 7547.996 0.051 B- -4771# 255# 238 053081.595 13.133 + 44 141 97 238 Bk -a 54216# 255# 7525# 1# B- -3061# 392# 238 058203# 274# + 42 140 98 238 Cf x 57278# 298# 7509# 1# B- * 238 061490# 320# +0 59 149 90 239 Th x 56450# 400# 7541# 2# B- 3113# 445# 239 060602# 429# + 57 148 91 239 Pa x 53337# 196# 7550# 1# B- 2765# 196# 239 057260# 210# + 55 147 92 239 U -n 50572.718 1.503 7558.561 0.006 B- 1261.661 1.493 239 054292.048 1.613 + 53 146 93 239 Np 49311.057 1.311 7560.567 0.005 B- 722.774 0.930 239 052937.599 1.407 + 51 145 94 239 Pu 48588.282 1.113 7560.318 0.005 B- -802.142 1.664 239 052161.669 1.195 + 49 144 95 239 Am -a 49390.424 1.982 7553.688 0.008 B- -1756.602 54.058 239 053022.803 2.128 + 47 143 96 239 Cm -a 51147.025 54.047 7543.065 0.226 B- -3103# 214# 239 054908.593 58.022 + 45 142 97 239 Bk -a 54250# 207# 7527# 1# B- -4019# 294# 239 058240# 222# + 43 141 98 239 Cf -a 58269# 209# 7507# 1# B- -5287# 364# 239 062554# 224# + 41 140 99 239 Es x 63556# 298# 7481# 1# B- * 239 068230# 320# +0 58 149 91 240 Pa x 56910# 200# 7538# 1# B- 4194# 200# 240 061095# 215# + 56 148 92 240 U 52715.505 2.553 7551.770 0.011 B- 399.233 17.083 240 056592.425 2.740 + 54 147 93 240 Np 52316.272 17.032 7550.173 0.071 B- 2190.891 17.015 240 056163.830 18.284 + 52 146 94 240 Pu 50125.380 1.106 7556.042 0.005 B- -1384.789 13.788 240 053811.812 1.187 + 50 145 95 240 Am +n 51510.169 13.832 7547.013 0.058 B- -214.137 13.897 240 055298.444 14.849 + 48 144 96 240 Cm 51724.306 1.906 7542.861 0.008 B- -3940# 150# 240 055528.329 2.046 + 46 143 97 240 Bk - 55664# 150# 7523# 1# B- -2327# 151# 240 059758# 161# + 44 142 98 240 Cf -a 57990.944 18.700 7510.230 0.078 B- -6208# 401# 240 062255.842 20.075 + 42 141 99 240 Es x 64199# 401# 7481# 2# B- * 240 068920# 430# +0 59 150 91 241 Pa x 59640# 300# 7528# 1# B- 3443# 358# 241 064026# 322# + 57 149 92 241 U x 56197# 196# 7539# 1# B- 1937# 208# 241 060330# 210# + 55 148 93 241 Np + 54260.175 70.719 7544.270 0.293 B- 1305.000 70.711 241 058250.697 75.920 + 53 147 94 241 Pu 52955.175 1.106 7546.439 0.005 B- 20.780 0.166 241 056849.722 1.187 + 51 146 95 241 Am 52934.395 1.114 7543.278 0.005 B- -767.434 1.168 241 056827.413 1.195 + 49 145 96 241 Cm 53701.830 1.608 7536.848 0.007 B- -2330# 200# 241 057651.288 1.726 + 47 144 97 241 Bk - 56032# 200# 7524# 1# B- -3295# 260# 241 060153# 215# + 45 143 98 241 Cf -a 59327# 166# 7507# 1# B- -4537# 280# 241 063690# 178# + 43 142 99 241 Es -a 63863# 225# 7485# 1# B- -5263# 374# 241 068560# 242# + 41 141 100 241 Fm x 69126# 298# 7460# 1# B- * 241 074210# 320# +0 58 150 92 242 U +a 58620# 201# 7532# 1# B- 1203# 283# 242 062931# 215# + 56 149 93 242 Np + 57416.932 200.004 7533.403 0.826 B- 2700.000 200.000 242 061639.615 214.713 + 54 148 94 242 Pu 54716.932 1.245 7541.327 0.005 B- -751.140 0.708 242 058741.045 1.336 + 52 147 95 242 Am -n 55468.072 1.119 7534.991 0.005 B- 664.309 0.414 242 059547.428 1.200 + 50 146 96 242 Cm 54803.764 1.142 7534.503 0.005 B- -2930# 200# 242 058834.263 1.225 + 48 145 97 242 Bk - 57734# 200# 7519# 1# B- -1653# 200# 242 061980# 215# + 46 144 98 242 Cf -a 59386.966 12.892 7509.098 0.053 B- -5414# 256# 242 063754.533 13.840 + 44 143 99 242 Es -a 64801# 256# 7483# 1# B- -3598# 475# 242 069567# 275# + 42 142 100 242 Fm x 68400# 401# 7465# 2# B- * 242 073430# 430# +0 59 151 92 243 U x 62360# 300# 7518# 1# B- 2484# 302# 243 066946# 322# + 57 150 93 243 Np IT 59876# 32# 7525# 0# B- 2121# 32# 243 064279# 34# + 55 149 94 243 Pu 57754.602 2.542 7531.008 0.010 B- 579.556 2.622 243 062002.119 2.728 + 53 148 95 243 Am 57175.046 1.388 7530.173 0.006 B- -6.952 1.569 243 061379.940 1.490 + 51 147 96 243 Cm -a 57181.998 1.496 7526.925 0.006 B- -1507.695 4.506 243 061387.403 1.606 + 49 146 97 243 Bk -a 58689.693 4.524 7517.501 0.019 B- -2300# 114# 243 063005.980 4.857 + 47 145 98 243 Cf -a 60990# 114# 7505# 0# B- -3757# 236# 243 065475# 123# + 45 144 99 243 Es -a 64747# 207# 7486# 1# B- -4640# 298# 243 069509# 222# + 43 143 100 243 Fm -a 69387# 215# 7464# 1# B- * 243 074490# 231# +0 58 151 93 244 Np x 63202# 298# 7514# 1# B- 3396# 298# 244 067850# 320# + 56 150 94 244 Pu 59806.028 2.346 7524.815 0.010 B- -73.168 2.686 244 064204.415 2.518 + 54 149 95 244 Am + 59879.196 1.492 7521.308 0.006 B- 1427.300 1.000 244 064282.964 1.601 + 52 148 96 244 Cm -a 58451.896 1.107 7523.952 0.005 B- -2261.989 14.357 244 062750.694 1.188 + 50 147 97 244 Bk -a 60713.885 14.399 7511.475 0.059 B- -764.294 14.572 244 065179.039 15.457 + 48 146 98 244 Cf 61478.179 2.618 7505.136 0.011 B- -4547# 181# 244 065999.543 2.810 + 46 145 99 244 Es -a 66026# 181# 7483# 1# B- -2940# 271# 244 070881# 195# + 44 144 100 244 Fm -a 68966# 201# 7468# 1# B- * 244 074038# 216# +0 59 152 93 245 Np x 65890# 300# 7505# 1# B- 2712# 300# 245 070736# 322# + 57 151 94 245 Pu -n 63178.179 13.620 7513.281 0.056 B- 1277.710 13.733 245 067824.568 14.621 + 55 150 95 245 Am +a 61900.469 1.887 7515.303 0.008 B- 895.889 1.549 245 066452.890 2.025 + 53 149 96 245 Cm 61004.580 1.150 7515.767 0.005 B- -809.256 1.496 245 065491.113 1.234 + 51 148 97 245 Bk -a 61813.836 1.793 7509.270 0.007 B- -1571.374 2.586 245 066359.885 1.924 + 49 147 98 245 Cf 63385.210 2.428 7499.663 0.010 B- -2981# 200# 245 068046.825 2.606 + 47 146 99 245 Es -a 66366# 200# 7484# 1# B- -3821# 279# 245 071247# 215# + 45 145 100 245 Fm -a 70187# 195# 7466# 1# B- -5085# 362# 245 075349# 209# + 43 144 101 245 Md -a 75272# 305# 7442# 1# B- * 245 080808# 328# +0 58 152 94 246 Pu 65394.801 14.985 7506.539 0.061 B- 401# 14# 246 070204.209 16.087 + 56 151 95 246 Am IT 64994# 18# 7505# 0# B- 2377# 18# 246 069774# 19# + 54 150 96 246 Cm 62616.967 1.526 7511.471 0.006 B- -1350.000 60.000 246 067222.082 1.638 + 52 149 97 246 Bk - 63966.967 60.019 7502.803 0.244 B- -123.325 60.020 246 068671.367 64.433 + 50 148 98 246 Cf 64090.292 1.515 7499.121 0.006 B- -3810# 224# 246 068803.762 1.626 + 48 147 99 246 Es -a 67901# 224# 7480# 1# B- -2288# 224# 246 072894# 240# + 46 146 100 246 Fm -a 70188.833 15.333 7467.970 0.062 B- -5926# 260# 246 075350.815 16.460 + 44 145 101 246 Md -a 76115# 259# 7441# 1# B- * 246 081713# 278# +0 59 153 94 247 Pu x 69108# 196# 7494# 1# B- 1954# 220# 247 074190# 210# + 57 152 95 247 Am + 67153# 100# 7499# 0# B- 1620# 100# 247 072092# 107# + 55 151 96 247 Cm 65533.143 3.797 7501.931 0.015 B- 43.581 6.324 247 070352.726 4.076 + 53 150 97 247 Bk -a 65489.562 5.189 7498.940 0.021 B- -614.341 16.188 247 070305.940 5.570 + 51 149 98 247 Cf +a 66103.903 15.334 7493.285 0.062 B- -2474.485 24.760 247 070965.462 16.461 + 49 148 99 247 Es +a 68578.388 19.441 7480.100 0.079 B- -3094# 116# 247 073621.932 20.870 + 47 147 100 247 Fm +a 71673# 115# 7464# 0# B- -4264# 237# 247 076944# 123# + 45 146 101 247 Md -a 75937# 207# 7444# 1# B- * 247 081521# 222# +0 58 153 95 248 Am + 70563# 200# 7487# 1# B- 3170# 200# 248 075752# 215# + 56 152 96 248 Cm 67392.755 2.358 7496.728 0.010 B- -687# 71# 248 072349.101 2.531 + 54 151 97 248 Bk IT 68080# 71# 7491# 0# B- 842# 71# 248 073087# 76# + 52 150 98 248 Cf -a 67238.012 5.121 7491.043 0.021 B- -3061# 53# 248 072182.978 5.497 + 50 149 99 248 Es -a 70299# 52# 7476# 0# B- -1599# 53# 248 075469# 56# + 48 148 100 248 Fm 71897.857 8.497 7465.944 0.034 B- -5250# 238# 248 077185.528 9.122 + 46 147 101 248 Md -a 77148# 237# 7442# 1# B- -3473# 327# 248 082822# 255# + 44 146 102 248 No -a 80621# 224# 7424# 1# B- * 248 086550# 241# +0 59 154 95 249 Am x 73104# 298# 7479# 1# B- 2353# 298# 249 078480# 320# + 57 153 96 249 Cm -n 70750.702 2.371 7485.550 0.010 B- 904.317 2.594 249 075954.006 2.545 + 55 152 97 249 Bk + 69846.384 1.249 7486.040 0.005 B- 123.600 0.400 249 074983.182 1.340 + 53 151 98 249 Cf 69722.784 1.183 7483.394 0.005 B- -1452# 30# 249 074850.491 1.270 + 51 150 99 249 Es -a 71175# 30# 7474# 0# B- -2344# 31# 249 076409# 32# + 49 149 100 249 Fm 73519.188 6.212 7461.864 0.025 B- -3713# 201# 249 078926.098 6.668 + 47 148 101 249 Md -a 77232# 201# 7444# 1# B- -4550# 344# 249 082912# 216# + 45 147 102 249 No -a 81782# 279# 7422# 1# B- * 249 087797# 300# +0 58 154 96 250 Cm -nn 72989.594 10.274 7478.938 0.041 B- 39.616 10.894 250 078357.556 11.029 + 56 153 97 250 Bk +a 72949.978 3.719 7475.967 0.015 B- 1779.587 3.386 250 078315.027 3.992 + 54 152 98 250 Cf -a 71170.391 1.538 7479.956 0.006 B- -2055# 100# 250 076404.561 1.651 + 52 151 99 250 Es - 73225# 100# 7469# 0# B- -847# 100# 250 078611# 107# + 50 150 100 250 Fm 74072.243 7.888 7462.090 0.032 B- -4558# 301# 250 079519.828 8.468 + 48 149 101 250 Md -a 78630# 301# 7441# 1# B- -2933# 362# 250 084413# 323# + 46 148 102 250 No -a 81564# 201# 7426# 1# B- * 250 087562# 215# +0 59 155 96 251 Cm + 76648.018 22.698 7466.722 0.090 B- 1420.000 20.000 251 082285.036 24.367 + 57 154 97 251 Bk + 75228.018 10.734 7469.263 0.043 B- 1093.000 10.000 251 080760.603 11.523 + 55 153 98 251 Cf -a 74135.018 3.901 7470.500 0.016 B- -377.259 7.057 251 079587.219 4.187 + 53 152 99 251 Es -a 74512.277 5.994 7465.881 0.024 B- -1441.641 16.342 251 079992.224 6.434 + 51 151 100 251 Fm +a 75953.919 15.203 7457.020 0.061 B- -3012.825 24.271 251 081539.889 16.320 + 49 150 101 251 Md +a 78966.744 18.919 7441.900 0.075 B- -3882# 116# 251 084774.291 20.310 + 47 149 102 251 No IT 82849# 114# 7423# 0# B- -4879# 319# 251 088942# 123# + 45 148 103 251 Lr x 87728# 298# 7401# 1# B- * 251 094180# 320# +0 60 156 96 252 Cm x 79056# 298# 7460# 1# B- 521# 359# 252 084870# 320# + 58 155 97 252 Bk + 78535# 200# 7459# 1# B- 2500# 200# 252 084310# 215# + 56 154 98 252 Cf -a 76034.617 2.358 7465.347 0.009 B- -1260.000 50.000 252 081626.523 2.531 + 54 153 99 252 Es - 77294.617 50.056 7457.242 0.199 B- 478.990 50.351 252 082979.189 53.736 + 52 152 100 252 Fm -a 76815.627 5.498 7456.038 0.022 B- -3695# 130# 252 082464.972 5.902 + 50 151 101 252 Md IT 80510# 130# 7438# 1# B- -2361# 131# 252 086432# 140# + 48 150 102 252 No 82871.427 9.292 7425.798 0.037 B- -5866# 238# 252 088966.141 9.975 + 46 149 103 252 Lr -a 88737# 238# 7399# 1# B- * 252 095263# 255# +0 59 156 97 253 Bk -a 80929# 359# 7451# 1# B- 1627# 359# 253 086880# 385# + 57 155 98 253 Cf -a 79301.567 4.257 7454.829 0.017 B- 291.030 4.385 253 085133.738 4.570 + 55 154 99 253 Es -a 79010.538 1.250 7452.887 0.005 B- -335.202 2.713 253 084821.305 1.341 + 53 153 100 253 Fm -a 79345.740 2.932 7448.470 0.012 B- -1827# 31# 253 085181.160 3.148 + 51 152 101 253 Md -a 81173# 31# 7438# 0# B- -3186# 32# 253 087143# 34# + 49 151 102 253 No 84358.735 6.912 7422.471 0.027 B- -4217# 202# 253 090562.831 7.420 + 47 150 103 253 Lr -a 88575# 202# 7403# 1# B- -4982# 457# 253 095089# 217# + 45 149 104 253 Rf -a 93557# 410# 7380# 2# B- * 253 100438# 440# +0 60 157 97 254 Bk x 84393# 298# 7440# 1# B- 3052# 298# 254 090600# 320# + 58 156 98 254 Cf -a 81341.401 11.462 7449.225 0.045 B- -649.193 12.113 254 087323.590 12.304 + 56 155 99 254 Es -a 81990.594 4.010 7443.589 0.016 B- 1087.800 3.202 254 088020.527 4.304 + 54 154 100 254 Fm -a 80902.794 2.414 7444.792 0.010 B- -2550# 100# 254 086852.726 2.591 + 52 153 101 254 Md - 83453# 100# 7432# 0# B- -1271# 100# 254 089590# 107# + 50 152 102 254 No 84723.347 9.658 7423.590 0.038 B- -5148# 301# 254 090954.259 10.367 + 48 151 103 254 Lr -a 89871# 301# 7400# 1# B- -3327# 414# 254 096481# 323# + 46 150 104 254 Rf -a 93199# 283# 7384# 1# B- * 254 100053# 304# +0 59 157 98 255 Cf + 84809# 200# 7438# 1# B- 720# 200# 255 091047# 215# + 57 156 99 255 Es -a 84089.274 10.817 7437.821 0.042 B- 289.620 10.247 255 090273.553 11.612 + 55 155 100 255 Fm -a 83799.654 4.291 7435.888 0.017 B- -1043.416 7.747 255 089962.633 4.607 + 53 154 101 255 Md -a 84843.070 6.553 7428.729 0.026 B- -1964.164 16.281 255 091082.787 7.035 + 51 153 102 255 No x 86807.234 14.904 7417.958 0.058 B- -3140.066 23.138 255 093191.404 16.000 + 49 152 103 255 Lr x 89947.300 17.698 7402.576 0.069 B- -4382# 116# 255 096562.404 19.000 + 47 151 104 255 Rf -a 94330# 115# 7382# 0# B- -5263# 377# 255 101267# 123# + 45 150 105 255 Db -a 99593# 359# 7359# 1# B- * 255 106918# 385# +0 60 158 98 256 Cf -a 87041# 314# 7432# 1# B- -146# 330# 256 093442# 338# + 58 157 99 256 Es + 87187# 100# 7428# 0# B- 1700# 100# 256 093599# 108# + 56 156 100 256 Fm -a 85486.817 5.600 7431.780 0.022 B- -1969# 123# 256 091773.878 6.012 + 54 155 101 256 Md IT 87456# 122# 7421# 0# B- -366# 123# 256 093888# 132# + 52 154 102 256 No -a 87822.062 7.743 7416.546 0.030 B- -3924.536 83.264 256 094280.866 8.312 + 50 153 103 256 Lr x 91746.598 82.903 7398.160 0.324 B- -2475.451 84.802 256 098494.029 89.000 + 48 152 104 256 Rf -a 94222.049 17.848 7385.434 0.070 B- -6276# 241# 256 101151.535 19.160 + 46 151 105 256 Db -a 100498# 240# 7358# 1# B- * 256 107889# 258# +0 59 158 99 257 Es -a 89403# 411# 7422# 2# B- 813# 411# 257 095979# 441# + 57 157 100 257 Fm -a 88590.033 4.486 7422.194 0.017 B- -403.020 4.715 257 095105.317 4.815 + 55 156 101 257 Md -a 88993.053 1.601 7417.582 0.006 B- -1254.202 6.661 257 095537.977 1.718 + 53 155 102 257 No -a 90247.256 6.678 7409.657 0.026 B- -2418# 45# 257 096884.419 7.169 + 51 154 103 257 Lr -a 92665# 44# 7397# 0# B- -3201# 45# 257 099480# 47# + 49 153 104 257 Rf -a 95866.427 10.817 7381.704 0.042 B- -4340# 203# 257 102916.848 11.612 + 47 152 105 257 Db -a 100207# 203# 7362# 1# B- * 257 107576# 218# +0 60 159 99 258 Es x 92702# 401# 7412# 2# B- 2276# 448# 258 099520# 430# + 58 158 100 258 Fm -a 90426# 200# 7418# 1# B- -1260# 200# 258 097077# 215# + 56 157 101 258 Md -a 91686.792 4.419 7409.675 0.017 B- 209# 100# 258 098429.825 4.743 + 54 156 102 258 No -a 91478# 100# 7407# 0# B- -3304# 143# 258 098205# 107# + 52 155 103 258 Lr -a 94782# 102# 7392# 0# B- -1559# 107# 258 101753# 109# + 50 154 104 258 Rf -a 96341.036 31.967 7382.538 0.124 B- -5456# 307# 258 103426.362 34.317 + 48 153 105 258 Db -a 101797# 305# 7358# 1# B- -3447# 513# 258 109284# 328# + 46 152 106 258 Sg -a 105244# 413# 7342# 2# B- * 258 112984# 443# +0 59 159 100 259 Fm -a 93704# 283# 7407# 1# B- 80# 346# 259 100596# 304# + 57 158 101 259 Md -a 93624# 200# 7405# 1# B- -454# 200# 259 100510# 215# + 55 157 102 259 No -a 94078.569 6.589 7399.974 0.025 B- -1773# 71# 259 100997.503 7.073 + 53 156 103 259 Lr -a 95852# 71# 7390# 0# B- -2510# 101# 259 102901# 76# + 51 155 104 259 Rf -a 98362# 72# 7377# 0# B- -3629# 90# 259 105596# 78# + 49 154 105 259 Db -a 101991.016 53.040 7360.362 0.205 B- -4529# 126# 259 109491.865 56.940 + 47 153 106 259 Sg -a 106520# 115# 7340# 0# B- * 259 114353# 123# +0 60 160 100 260 Fm -a 95766# 435# 7402# 2# B- -786# 537# 260 102809# 467# + 58 159 101 260 Md -a 96552# 316# 7396# 1# B- 940# 374# 260 103653# 340# + 56 158 102 260 No -a 95612# 200# 7397# 1# B- -2665# 235# 260 102643# 215# + 54 157 103 260 Lr -a 98277# 124# 7383# 0# B- -870# 236# 260 105504# 133# + 52 156 104 260 Rf -a 99147# 200# 7377# 1# B- -4526# 221# 260 106439# 215# + 50 155 105 260 Db -a 103673# 93# 7357# 0# B- -2875# 95# 260 111297# 100# + 48 154 106 260 Sg -a 106547.552 20.536 7342.562 0.079 B- -6776# 246# 260 114383.508 22.045 + 46 153 107 260 Bh -a 113323# 245# 7313# 1# B- * 260 121658# 263# +0 59 160 101 261 Md -a 98578# 509# 7391# 2# B- 123# 547# 261 105828# 546# + 57 159 102 261 No -a 98455# 200# 7388# 1# B- -1103# 283# 261 105696# 215# + 55 158 103 261 Lr -a 99558# 200# 7381# 1# B- -1761# 206# 261 106880# 215# + 53 157 104 261 Rf -a 101318.594 50.444 7371.384 0.193 B- -2990# 121# 261 108769.990 54.153 + 51 156 105 261 Db -a 104308# 110# 7357# 0# B- -3697# 112# 261 111980# 118# + 49 155 106 261 Sg -a 108005.043 18.494 7339.770 0.071 B- -5128# 210# 261 115948.188 19.853 + 47 154 107 261 Bh -a 113133# 209# 7317# 1# B- * 261 121454# 224# +0 60 161 101 262 Md -a 101627# 500# 7382# 2# B- 1526# 617# 262 109101# 537# + 58 160 102 262 No -a 100101# 361# 7385# 1# B- -2000# 412# 262 107463# 387# + 56 159 103 262 Lr -a 102102# 200# 7374# 1# B- -291# 300# 262 109611# 215# + 54 158 104 262 Rf -a 102393# 224# 7370# 1# B- -3861# 265# 262 109923# 240# + 52 157 105 262 Db -a 106253# 143# 7352# 1# B- -2112# 147# 262 114068# 154# + 50 156 106 262 Sg -a 108365.771 35.411 7341.185 0.135 B- -6176# 308# 262 116335.446 38.015 + 48 155 107 262 Bh -a 114541# 306# 7315# 1# B- * 262 122965# 328# +0 59 161 102 263 No -a 103129# 490# 7376# 2# B- -600# 566# 263 110714# 526# + 57 160 103 263 Lr -a 103729# 283# 7371# 1# B- -1027# 322# 263 111358# 304# + 55 159 104 263 Rf -a 104756# 153# 7364# 1# B- -2355# 227# 263 112460# 164# + 53 158 105 263 Db -a 107111# 168# 7352# 1# B- -3079# 193# 263 114988# 181# + 51 157 106 263 Sg -a 110190# 95# 7337# 0# B- -4306# 319# 263 118294# 102# + 49 156 107 263 Bh -a 114496# 305# 7318# 1# B- -5182# 329# 263 122916# 327# + 47 155 108 263 Hs -a 119678# 125# 7295# 0# B- * 263 128480# 134# +0 60 162 102 264 No -a 105011# 591# 7371# 2# B- -1366# 734# 264 112734# 634# + 58 161 103 264 Lr -a 106377# 436# 7363# 2# B- 300# 566# 264 114200# 468# + 56 160 104 264 Rf -a 106077# 361# 7361# 1# B- -3285# 431# 264 113878# 387# + 54 159 105 264 Db -a 109362# 235# 7346# 1# B- -1420# 368# 264 117405# 253# + 52 158 106 264 Sg -a 110782# 283# 7338# 1# B- -5276# 334# 264 118929# 304# + 50 157 107 264 Bh -a 116058# 177# 7315# 1# B- -3506# 180# 264 124593# 190# + 48 156 108 264 Hs -a 119563.222 28.881 7298.375 0.109 B- * 264 128356.405 31.005 +0 59 162 103 265 Lr -a 108233# 547# 7359# 2# B- -457# 655# 265 116193# 587# + 57 161 104 265 Rf -a 108690# 361# 7354# 1# B- -1793# 424# 265 116683# 387# + 55 160 105 265 Db -a 110483# 224# 7344# 1# B- -2312# 255# 265 118608# 240# + 53 159 106 265 Sg -a 112794# 123# 7333# 0# B- -3621# 264# 265 121090# 132# + 51 158 107 265 Bh -a 116415# 234# 7316# 1# B- -4485# 235# 265 124977# 251# + 49 157 108 265 Hs -a 120900.283 23.958 7296.247 0.090 B- -5778# 452# 265 129791.799 25.719 + 47 156 109 265 Mt -a 126678# 451# 7271# 2# B- * 265 135995# 484# +0 60 163 103 266 Lr -a 111622# 583# 7349# 2# B- 1546# 749# 266 119831# 626# + 58 162 104 266 Rf -a 110076# 469# 7352# 2# B- -2660# 548# 266 118172# 504# + 56 161 105 266 Db -a 112737# 283# 7339# 1# B- -881# 374# 266 121028# 304# + 54 160 106 266 Sg -a 113618# 245# 7332# 1# B- -4487# 294# 266 121973# 263# + 52 159 107 266 Bh -a 118104# 163# 7313# 1# B- -3032# 167# 266 126790# 175# + 50 158 108 266 Hs -a 121136.373 38.695 7298.273 0.145 B- -6826# 309# 266 130045.252 41.540 + 48 157 109 266 Mt -a 127962# 307# 7270# 1# B- * 266 137373# 329# +0 59 163 104 267 Rf -a 113444# 575# 7342# 2# B- -630# 707# 267 121787# 617# + 57 162 105 267 Db -a 114074# 412# 7336# 2# B- -1732# 486# 267 122464# 443# + 55 161 106 267 Sg -a 115806# 257# 7327# 1# B- -2960# 367# 267 124322# 276# + 53 160 107 267 Bh -a 118766# 263# 7313# 1# B- -3887# 279# 267 127500# 282# + 51 159 108 267 Hs -a 122653# 96# 7295# 0# B- -5138# 512# 267 131673# 103# + 49 158 109 267 Mt -a 127791# 503# 7273# 2# B- -6089# 521# 267 137189# 540# + 47 157 110 267 Ds -a 133880# 135# 7248# 1# B- * 267 143726# 145# +0 60 164 104 268 Rf -a 115476# 662# 7337# 2# B- -1586# 848# 268 123968# 711# + 58 163 105 268 Db -a 117062# 529# 7328# 2# B- 260# 707# 268 125671# 568# + 56 162 106 268 Sg -a 116802# 469# 7326# 2# B- -4005# 605# 268 125392# 504# + 54 161 107 268 Bh -a 120807# 381# 7308# 1# B- -2023# 475# 268 129691# 409# + 52 160 108 268 Hs -a 122830# 283# 7298# 1# B- -6321# 367# 268 131863# 304# + 50 159 109 268 Mt -a 129151# 233# 7271# 1# B- -4497# 381# 268 138649# 250# + 48 158 110 268 Ds -a 133648# 301# 7252# 1# B- * 268 143477# 324# +0 59 164 105 269 Db -a 119148# 624# 7323# 2# B- -614# 722# 269 127911# 669# + 57 163 106 269 Sg -a 119763# 364# 7318# 1# B- -1715# 522# 269 128570# 391# + 55 162 107 269 Bh -a 121478# 374# 7309# 1# B- -3086# 394# 269 130412# 402# + 53 161 108 269 Hs -a 124564# 124# 7294# 0# B- -4806# 480# 269 133725# 133# + 51 160 109 269 Mt -a 129370# 463# 7273# 2# B- -5465# 464# 269 138884# 497# + 49 159 110 269 Ds -a 134834.709 31.403 7250.154 0.117 B- * 269 144751.021 33.712 +0 60 165 105 270 Db -a 122307# 617# 7314# 2# B- 816# 831# 270 131302# 662# + 58 164 106 270 Sg -a 121491# 557# 7314# 2# B- -2735# 627# 270 130426# 598# + 56 163 107 270 Bh -a 124226# 287# 7301# 1# B- -886# 379# 270 133362# 308# + 54 162 108 270 Hs -a 125112# 248# 7295# 1# B- -5598# 301# 270 134314# 266# + 52 161 109 270 Mt -a 130710# 170# 7271# 1# B- -3968# 177# 270 140323# 183# + 50 160 110 270 Ds -a 134678.282 48.011 7253.775 0.178 B- * 270 144583.090 51.542 +0 59 165 106 271 Sg -a 124757# 585# 7305# 2# B- -1164# 718# 271 133932# 628# + 57 164 107 271 Bh -a 125921# 415# 7298# 2# B- -1819# 501# 271 135182# 446# + 55 163 108 271 Hs -a 127740# 280# 7288# 1# B- -3361# 433# 271 137135# 301# + 53 162 109 271 Mt -a 131101# 330# 7273# 1# B- -4847# 344# 271 140742# 354# + 51 161 110 271 Ds -a 135948# 97# 7252# 0# B- * 271 145946# 104# +0 60 166 106 272 Sg -a 126580# 727# 7301# 3# B- -2209# 901# 272 135890# 781# + 58 165 107 272 Bh -a 128789# 532# 7290# 2# B- -217# 737# 272 138261# 571# + 56 164 108 272 Hs 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    \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Another useful Python package is\n", + "[pandas](https://pandas.pydata.org/), which is an open source library\n", + "providing high-performance, easy-to-use data structures and data\n", + "analysis tools for Python. **pandas** stands for panel data, a term borrowed from econometrics and is an efficient library for data analysis with an emphasis on tabular data.\n", + "**pandas** has two major classes, the **DataFrame** class with two-dimensional data objects and tabular data organized in columns and the class **Series** with a focus on one-dimensional data objects. Both classes allow you to index data easily as we will see in the examples below. \n", + "**pandas** allows you also to perform mathematical operations on the data, spanning from simple reshapings of vectors and matrices to statistical operations. \n", + "\n", + "The following simple example shows how we can, in an easy way make tables of our data. Here we define a data set which includes names, place of birth and date of birth, and displays the data in an easy to read way. We will see repeated use of **pandas**, in particular in connection with classification of data." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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non-null float64\n", + " 2 Third 10 non-null float64\n", + " 3 Fourth 10 non-null float64\n", + " 4 Fifth 10 non-null float64\n", + "dtypes: float64(5)\n", + "memory usage: 480.0 bytes\n", + "None\n", + " First Second Third Fourth Fifth\n", + "count 10.000000 10.000000 10.000000 10.000000 10.000000\n", + "mean -0.175300 0.083527 -0.044334 -0.399836 0.331939\n", + "std 1.069584 0.965548 1.018232 0.793167 0.918992\n", + "min -1.749765 -1.443217 -1.690617 -1.613579 -1.232435\n", + "25% -0.522836 -0.633949 -0.713163 -0.785061 0.087887\n", + "50% -0.280179 0.281930 -0.122282 -0.382187 0.463861\n", + "75% 0.441264 0.657041 0.861676 -0.205231 0.923602\n", + "max 1.618982 1.541605 1.361556 0.816847 1.470714\n" + ] + }, + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/gettingstarted_54_3.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "df.columns = ['First', 'Second', 'Third', 'Fourth', 'Fifth']\n", + "df.index = np.arange(10)\n", + "\n", + "display(df)\n", + "print(df['Second'].mean() )\n", + "print(df.info())\n", + "print(df.describe())\n", + "\n", + "from pylab import plt, mpl\n", + "plt.style.use('seaborn')\n", + "mpl.rcParams['font.family'] = 'serif'\n", + "\n", + "df.cumsum().plot(lw=2.0, figsize=(10,6))\n", + "plt.show()\n", + "\n", + "\n", + "df.plot.bar(figsize=(10,6), rot=15)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can produce a $4\\times 4$ matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 1 2 3]\n", + " [ 4 5 6 7]\n", + " [ 8 9 10 11]\n", + " [12 13 14 15]]\n", + " 0 1 2 3\n", + "0 0 1 2 3\n", + "1 4 5 6 7\n", + "2 8 9 10 11\n", + "3 12 13 14 15\n" + ] + } + ], + "source": [ + "b = np.arange(16).reshape((4,4))\n", + "print(b)\n", + "df1 = pd.DataFrame(b)\n", + "print(df1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and many other operations. \n", + "\n", + "The **Series** class is another important class included in\n", + "**pandas**. You can view it as a specialization of **DataFrame** but where\n", + "we have just a single column of data. It shares many of the same features as _DataFrame. As with **DataFrame**,\n", + "most operations are vectorized, achieving thereby a high performance when dealing with computations of arrays, in particular labeled arrays.\n", + "As we will see below it leads also to a very concice code close to the mathematical operations we may be interested in.\n", + "For multidimensional arrays, we recommend strongly [xarray](http://xarray.pydata.org/en/stable/). **xarray** has much of the same flexibility as **pandas**, but allows for the extension to higher dimensions than two. We will see examples later of the usage of both **pandas** and **xarray**. \n", + "\n", + "\n", + "\n", + "## Reading Data and fitting\n", + "\n", + "In order to study various Machine Learning algorithms, we need to\n", + "access data. Acccessing data is an essential step in all machine\n", + "learning algorithms. In particular, setting up the so-called **design\n", + "matrix** (to be defined below) is often the first element we need in\n", + "order to perform our calculations. To set up the design matrix means\n", + "reading (and later, when the calculations are done, writing) data\n", + "in various formats, The formats span from reading files from disk,\n", + "loading data from databases and interacting with online sources\n", + "like web application programming interfaces (APIs).\n", + "\n", + "In handling various input formats, as discussed above, we will mainly stay with **pandas**,\n", + "a Python package which allows us, in a seamless and painless way, to\n", + "deal with a multitude of formats, from standard **csv** (comma separated\n", + "values) files, via **excel**, **html** to **hdf5** formats. With **pandas**\n", + "and the **DataFrame** and **Series** functionalities we are able to convert text data\n", + "into the calculational formats we need for a specific algorithm. And our code is going to be \n", + "pretty close the basic mathematical expressions.\n", + "\n", + "Our first data set is going to be a classic from nuclear physics, namely all\n", + "available data on binding energies. Don't be intimidated if you are not familiar with nuclear physics. It serves simply as an example here of a data set. \n", + "\n", + "We will show some of the\n", + "strengths of packages like **Scikit-Learn** in fitting nuclear binding energies to\n", + "specific functions using linear regression first. Then, as a teaser, we will show you how \n", + "you can easily implement other algorithms like decision trees and random forests and neural networks.\n", + "\n", + "But before we really start with nuclear physics data, let's just look at some simpler polynomial fitting cases, such as,\n", + "(don't be offended) fitting straight lines!\n", + "\n", + "\n", + "### Simple linear regression model using **scikit-learn**\n", + "\n", + "We start with perhaps our simplest possible example, using **Scikit-Learn** to perform linear regression analysis on a data set produced by us. \n", + "\n", + "What follows is a simple Python code where we have defined a function\n", + "$y$ in terms of the variable $x$. Both are defined as vectors with $100$ entries. \n", + "The numbers in the vector $\\hat{x}$ are given\n", + "by random numbers generated with a uniform distribution with entries\n", + "$x_i \\in [0,1]$ (more about probability distribution functions\n", + "later). These values are then used to define a function $y(x)$\n", + "(tabulated again as a vector) with a linear dependence on $x$ plus a\n", + "random noise added via the normal distribution.\n", + "\n", + "\n", + "The Numpy functions are imported used the **import numpy as np**\n", + "statement and the random number generator for the uniform distribution\n", + "is called using the function **np.random.rand()**, where we specificy\n", + "that we want $100$ random variables. Using Numpy we define\n", + "automatically an array with the specified number of elements, $100$ in\n", + "our case. With the Numpy function **randn()** we can compute random\n", + "numbers with the normal distribution (mean value $\\mu$ equal to zero and\n", + "variance $\\sigma^2$ set to one) and produce the values of $y$ assuming a linear\n", + "dependence as function of $x$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "y = 2x+N(0,1),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $N(0,1)$ represents random numbers generated by the normal\n", + "distribution. From **Scikit-Learn** we import then the\n", + "**LinearRegression** functionality and make a prediction $\\tilde{y} =\n", + "\\alpha + \\beta x$ using the function **fit(x,y)**. We call the set of\n", + "data $(\\hat{x},\\hat{y})$ for our training data. The Python package\n", + "**scikit-learn** has also a functionality which extracts the above\n", + "fitting parameters $\\alpha$ and $\\beta$ (see below). Later we will\n", + "distinguish between training data and test data.\n", + "\n", + "For plotting we use the Python package\n", + "[matplotlib](https://matplotlib.org/) which produces publication\n", + "quality figures. Feel free to explore the extensive\n", + "[gallery](https://matplotlib.org/gallery/index.html) of examples. In\n", + "this example we plot our original values of $x$ and $y$ as well as the\n", + "prediction **ypredict** ($\\tilde{y}$), which attempts at fitting our\n", + "data with a straight line.\n", + "\n", + "The Python code follows here." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/gettingstarted_60_0.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# Importing various packages\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.linear_model import LinearRegression\n", + "\n", + "x = np.random.rand(100,1)\n", + "y = 2*x+0.01*np.random.randn(100,1)\n", + "linreg = LinearRegression()\n", + "linreg.fit(x,y)\n", + "#ynew = linreg.predict(x)\n", + "#xnew = np.array([[0],[1]])\n", + "ypredict = linreg.predict(x)\n", + "\n", + "plt.plot(x, ypredict, \"r-\")\n", + "plt.plot(x, y ,'ro')\n", + "plt.axis([0,1.0,0, 5.0])\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "plt.title(r'Simple Linear Regression')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This example serves several aims. It allows us to demonstrate several\n", + "aspects of data analysis and later machine learning algorithms. The\n", + "immediate visualization shows that our linear fit is not\n", + "impressive. It goes through the data points, but there are many\n", + "outliers which are not reproduced by our linear regression. We could\n", + "now play around with this small program and change for example the\n", + "factor in front of $x$ and the normal distribution. Try to change the\n", + "function $y$ to" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "y = 10x+0.01 \\times N(0,1),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $x$ is defined as before. Does the fit look better? Indeed, by\n", + "reducing the role of the noise given by the normal distribution we see immediately that\n", + "our linear prediction seemingly reproduces better the training\n", + "set. However, this testing 'by the eye' is obviouly not satisfactory in the\n", + "long run. Here we have only defined the training data and our model, and \n", + "have not discussed a more rigorous approach to the **cost** function.\n", + "\n", + "We need more rigorous criteria in defining whether we have succeeded or\n", + "not in modeling our training data. You will be surprised to see that\n", + "many scientists seldomly venture beyond this 'by the eye' approach. A\n", + "standard approach for the *cost* function is the so-called $\\chi^2$\n", + "function (a variant of the mean-squared error (MSE))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\chi^2 = \\frac{1}{n}\n", + "\\sum_{i=0}^{n-1}\\frac{(y_i-\\tilde{y}_i)^2}{\\sigma_i^2},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $\\sigma_i^2$ is the variance (to be defined later) of the entry\n", + "$y_i$. We may not know the explicit value of $\\sigma_i^2$, it serves\n", + "however the aim of scaling the equations and make the cost function\n", + "dimensionless. \n", + "\n", + "Minimizing the cost function is a central aspect of\n", + "our discussions to come. Finding its minima as function of the model\n", + "parameters ($\\alpha$ and $\\beta$ in our case) will be a recurring\n", + "theme in these series of lectures. Essentially all machine learning\n", + "algorithms we will discuss center around the minimization of the\n", + "chosen cost function. This depends in turn on our specific\n", + "model for describing the data, a typical situation in supervised\n", + "learning. Automatizing the search for the minima of the cost function is a\n", + "central ingredient in all algorithms. Typical methods which are\n", + "employed are various variants of **gradient** methods. These will be\n", + "discussed in more detail later. Again, you'll be surprised to hear that\n", + "many practitioners minimize the above function ''by the eye', popularly dubbed as \n", + "'chi by the eye'. That is, change a parameter and see (visually and numerically) that \n", + "the $\\chi^2$ function becomes smaller. \n", + "\n", + "There are many ways to define the cost function. A simpler approach is to look at the relative difference between the training data and the predicted data, that is we define \n", + "the relative error (why would we prefer the MSE instead of the relative error?) as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\epsilon_{\\mathrm{relative}}= \\frac{\\vert \\hat{y} -\\hat{\\tilde{y}}\\vert}{\\vert \\hat{y}\\vert}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The squared cost function results in an arithmetic mean-unbiased\n", + "estimator, and the absolute-value cost function results in a\n", + "median-unbiased estimator (in the one-dimensional case, and a\n", + "geometric median-unbiased estimator for the multi-dimensional\n", + "case). The squared cost function has the disadvantage that it has the tendency\n", + "to be dominated by outliers.\n", + "\n", + "We can modify easily the above Python code and plot the relative error instead" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/gettingstarted_68_0.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.linear_model import LinearRegression\n", + "\n", + "x = np.random.rand(100,1)\n", + "y = 5*x+0.01*np.random.randn(100,1)\n", + "linreg = LinearRegression()\n", + "linreg.fit(x,y)\n", + "ypredict = linreg.predict(x)\n", + "\n", + "plt.plot(x, np.abs(ypredict-y)/abs(y), \"ro\")\n", + "plt.axis([0,1.0,0.0, 0.5])\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$\\epsilon_{\\mathrm{relative}}$')\n", + "plt.title(r'Relative error')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Depending on the parameter in front of the normal distribution, we may\n", + "have a small or larger relative error. Try to play around with\n", + "different training data sets and study (graphically) the value of the\n", + "relative error.\n", + "\n", + "As mentioned above, **Scikit-Learn** has an impressive functionality.\n", + "We can for example extract the values of $\\alpha$ and $\\beta$ and\n", + "their error estimates, or the variance and standard deviation and many\n", + "other properties from the statistical data analysis. \n", + "\n", + "Here we show an\n", + "example of the functionality of **Scikit-Learn**." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The intercept alpha: \n", + " [2.18780801]\n", + "Coefficient beta : \n", + " [[4.72228205]]\n", + "Mean squared error: 0.37\n", + "Variance score: 0.83\n", + "Mean squared log error: 0.01\n", + "Mean absolute error: 0.47\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/gettingstarted_70_1.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np \n", + "import matplotlib.pyplot as plt \n", + "from sklearn.linear_model import LinearRegression \n", + "from sklearn.metrics import mean_squared_error, r2_score, mean_squared_log_error, mean_absolute_error\n", + "\n", + "x = np.random.rand(100,1)\n", + "y = 2.0+ 5*x+0.5*np.random.randn(100,1)\n", + "linreg = LinearRegression()\n", + "linreg.fit(x,y)\n", + "ypredict = linreg.predict(x)\n", + "print('The intercept alpha: \\n', linreg.intercept_)\n", + "print('Coefficient beta : \\n', linreg.coef_)\n", + "# The mean squared error \n", + "print(\"Mean squared error: %.2f\" % mean_squared_error(y, ypredict))\n", + "# Explained variance score: 1 is perfect prediction \n", + "print('Variance score: %.2f' % r2_score(y, ypredict))\n", + "# Mean squared log error \n", + "print('Mean squared log error: %.2f' % mean_squared_log_error(y, ypredict) )\n", + "# Mean absolute error \n", + "print('Mean absolute error: %.2f' % mean_absolute_error(y, ypredict))\n", + "plt.plot(x, ypredict, \"r-\")\n", + "plt.plot(x, y ,'ro')\n", + "plt.axis([0.0,1.0,1.5, 7.0])\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "plt.title(r'Linear Regression fit ')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The function **coef** gives us the parameter $\\beta$ of our fit while **intercept** yields \n", + "$\\alpha$. Depending on the constant in front of the normal distribution, we get values near or far from $alpha =2$ and $\\beta =5$. Try to play around with different parameters in front of the normal distribution. The function **meansquarederror** gives us the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "MSE(\\hat{y},\\hat{\\tilde{y}}) = \\frac{1}{n}\n", + "\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The smaller the value, the better the fit. Ideally we would like to\n", + "have an MSE equal zero. The attentive reader has probably recognized\n", + "this function as being similar to the $\\chi^2$ function defined above.\n", + "\n", + "The **r2score** function computes $R^2$, the coefficient of\n", + "determination. It provides a measure of how well future samples are\n", + "likely to be predicted by the model. Best possible score is 1.0 and it\n", + "can be negative (because the model can be arbitrarily worse). A\n", + "constant model that always predicts the expected value of $\\hat{y}$,\n", + "disregarding the input features, would get a $R^2$ score of $0.0$.\n", + "\n", + "If $\\tilde{\\hat{y}}_i$ is the predicted value of the $i-th$ sample and $y_i$ is the corresponding true value, then the score $R^2$ is defined as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "R^2(\\hat{y}, \\tilde{\\hat{y}}) = 1 - \\frac{\\sum_{i=0}^{n - 1} (y_i - \\tilde{y}_i)^2}{\\sum_{i=0}^{n - 1} (y_i - \\bar{y})^2},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where we have defined the mean value of $\\hat{y}$ as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\bar{y} = \\frac{1}{n} \\sum_{i=0}^{n - 1} y_i.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another quantity taht we will meet again in our discussions of regression analysis is \n", + " the mean absolute error (MAE), a risk metric corresponding to the expected value of the absolute error loss or what we call the $l1$-norm loss. In our discussion above we presented the relative error.\n", + "The MAE is defined as follows" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\text{MAE}(\\hat{y}, \\hat{\\tilde{y}}) = \\frac{1}{n} \\sum_{i=0}^{n-1} \\left| y_i - \\tilde{y}_i \\right|.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We present the \n", + "squared logarithmic (quadratic) error" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\text{MSLE}(\\hat{y}, \\hat{\\tilde{y}}) = \\frac{1}{n} \\sum_{i=0}^{n - 1} (\\log_e (1 + y_i) - \\log_e (1 + \\tilde{y}_i) )^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $\\log_e (x)$ stands for the natural logarithm of $x$. This error\n", + "estimate is best to use when targets having exponential growth, such\n", + "as population counts, average sales of a commodity over a span of\n", + "years etc. \n", + "\n", + "\n", + "Finally, another cost function is the Huber cost function used in robust regression.\n", + "\n", + "The rationale behind this possible cost function is its reduced\n", + "sensitivity to outliers in the data set. In our discussions on\n", + "dimensionality reduction and normalization of data we will meet other\n", + "ways of dealing with outliers.\n", + "\n", + "The Huber cost function is defined as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "H_{\\delta}(a)={\\begin{cases}{\\frac {1}{2}}{a^{2}}&{\\text{for }}|a|\\leq \\delta ,\\\\\\delta (|a|-{\\frac {1}{2}}\\delta ),&{\\text{otherwise.}}\\end{cases}}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here $a=\\boldsymbol{y} - \\boldsymbol{\\tilde{y}}$.\n", + "We will discuss in more\n", + "detail these and other functions in the various lectures. We conclude this part with another example. Instead of \n", + "a linear $x$-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/gettingstarted_84_0.png" + } + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0050000000000000044\n" + ] + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import random\n", + "from sklearn.linear_model import Ridge\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.pipeline import make_pipeline\n", + "from sklearn.linear_model import LinearRegression\n", + "\n", + "x=np.linspace(0.02,0.98,200)\n", + "noise = np.asarray(random.sample((range(200)),200))\n", + "y=x**3*noise\n", + "yn=x**3*100\n", + "poly3 = PolynomialFeatures(degree=3)\n", + "X = poly3.fit_transform(x[:,np.newaxis])\n", + "clf3 = LinearRegression()\n", + "clf3.fit(X,y)\n", + "\n", + "Xplot=poly3.fit_transform(x[:,np.newaxis])\n", + "poly3_plot=plt.plot(x, clf3.predict(Xplot), label='Cubic Fit')\n", + "plt.plot(x,yn, color='red', label=\"True Cubic\")\n", + "plt.scatter(x, y, label='Data', color='orange', s=15)\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "def error(a):\n", + " for i in y:\n", + " err=(y-yn)/yn\n", + " return abs(np.sum(err))/len(err)\n", + "\n", + "print (error(y))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### To our real data: nuclear binding energies. Brief reminder on masses and binding energies\n", + "\n", + "Let us now dive into nuclear physics and remind ourselves briefly about some basic features about binding\n", + "energies. A basic quantity which can be measured for the ground\n", + "states of nuclei is the atomic mass $M(N, Z)$ of the neutral atom with\n", + "atomic mass number $A$ and charge $Z$. The number of neutrons is $N$. There are indeed several sophisticated experiments worldwide which allow us to measure this quantity to high precision (parts per million even). \n", + "\n", + "Atomic masses are usually tabulated in terms of the mass excess defined by" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\Delta M(N, Z) = M(N, Z) - uA,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $u$ is the Atomic Mass Unit" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "u = M(^{12}\\mathrm{C})/12 = 931.4940954(57) \\hspace{0.1cm} \\mathrm{MeV}/c^2.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The nucleon masses are" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "m_p = 1.00727646693(9)u,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "m_n = 939.56536(8)\\hspace{0.1cm} \\mathrm{MeV}/c^2 = 1.0086649156(6)u.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the [2016 mass evaluation of by W.J.Huang, G.Audi, M.Wang, F.G.Kondev, S.Naimi and X.Xu](http://nuclearmasses.org/resources_folder/Wang_2017_Chinese_Phys_C_41_030003.pdf)\n", + "there are data on masses and decays of 3437 nuclei.\n", + "\n", + "The nuclear binding energy is defined as the energy required to break\n", + "up a given nucleus into its constituent parts of $N$ neutrons and $Z$\n", + "protons. In terms of the atomic masses $M(N, Z)$ the binding energy is\n", + "defined by" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "BE(N, Z) = ZM_H c^2 + Nm_n c^2 - M(N, Z)c^2 ,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $M_H$ is the mass of the hydrogen atom and $m_n$ is the mass of the neutron.\n", + "In terms of the mass excess the binding energy is given by" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "BE(N, Z) = Z\\Delta_H c^2 + N\\Delta_n c^2 -\\Delta(N, Z)c^2 ,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $\\Delta_H c^2 = 7.2890$ MeV and $\\Delta_n c^2 = 8.0713$ MeV.\n", + "\n", + "\n", + "A popular and physically intuitive model which can be used to parametrize \n", + "the experimental binding energies as function of $A$, is the so-called \n", + "**liquid drop model**. The ansatz is based on the following expression" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "BE(N,Z) = a_1A-a_2A^{2/3}-a_3\\frac{Z^2}{A^{1/3}}-a_4\\frac{(N-Z)^2}{A},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $A$ stands for the number of nucleons and the $a_i$s are parameters which are determined by a fit \n", + "to the experimental data. \n", + "\n", + "\n", + "\n", + "\n", + "To arrive at the above expression we have assumed that we can make the following assumptions:\n", + "\n", + " * There is a volume term $a_1A$ proportional with the number of nucleons (the energy is also an extensive quantity). When an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it. This contribution is proportional to the volume.\n", + "\n", + " * There is a surface energy term $a_2A^{2/3}$. The assumption here is that a nucleon at the surface of a nucleus interacts with fewer other nucleons than one in the interior of the nucleus and hence its binding energy is less. This surface energy term takes that into account and is therefore negative and is proportional to the surface area.\n", + "\n", + " * There is a Coulomb energy term $a_3\\frac{Z^2}{A^{1/3}}$. The electric repulsion between each pair of protons in a nucleus yields less binding. \n", + "\n", + " * There is an asymmetry term $a_4\\frac{(N-Z)^2}{A}$. This term is associated with the Pauli exclusion principle and reflects the fact that the proton-neutron interaction is more attractive on the average than the neutron-neutron and proton-proton interactions.\n", + "\n", + "We could also add a so-called pairing term, which is a correction term that\n", + "arises from the tendency of proton pairs and neutron pairs to\n", + "occur. An even number of particles is more stable than an odd number. \n", + "\n", + "\n", + "### Organizing our data\n", + "\n", + "Let us start with reading and organizing our data. \n", + "We start with the compilation of masses and binding energies from 2016.\n", + "After having downloaded this file to our own computer, we are now ready to read the file and start structuring our data.\n", + "\n", + "\n", + "We start with preparing folders for storing our calculations and the data file over masses and binding energies. We import also various modules that we will find useful in order to present various Machine Learning methods. Here we focus mainly on the functionality of **scikit-learn**." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "# Common imports\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "import sklearn.linear_model as skl\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error\n", + "import os\n", + "\n", + "# Where to save the figures and data files\n", + "PROJECT_ROOT_DIR = \"Results\"\n", + "FIGURE_ID = \"Results/FigureFiles\"\n", + "DATA_ID = \"DataFiles/\"\n", + "\n", + "if not os.path.exists(PROJECT_ROOT_DIR):\n", + " os.mkdir(PROJECT_ROOT_DIR)\n", + "\n", + "if not os.path.exists(FIGURE_ID):\n", + " os.makedirs(FIGURE_ID)\n", + "\n", + "if not os.path.exists(DATA_ID):\n", + " os.makedirs(DATA_ID)\n", + "\n", + "def image_path(fig_id):\n", + " return os.path.join(FIGURE_ID, fig_id)\n", + "\n", + "def data_path(dat_id):\n", + " return os.path.join(DATA_ID, dat_id)\n", + "\n", + "def save_fig(fig_id):\n", + " plt.savefig(image_path(fig_id) + \".png\", format='png')\n", + "\n", + "infile = open(data_path(\"MassEval2016.dat\"),'r')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before we proceed, we define also a function for making our plots. You can obviously avoid this and simply set up various **matplotlib** commands every time you need them. You may however find it convenient to collect all such commands in one function and simply call this function." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "from pylab import plt, mpl\n", + "plt.style.use('seaborn')\n", + "mpl.rcParams['font.family'] = 'serif'\n", + "\n", + "def MakePlot(x,y, styles, labels, axlabels):\n", + " plt.figure(figsize=(10,6))\n", + " for i in range(len(x)):\n", + " plt.plot(x[i], y[i], styles[i], label = labels[i])\n", + " plt.xlabel(axlabels[0])\n", + " plt.ylabel(axlabels[1])\n", + " plt.legend(loc=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our next step is to read the data on experimental binding energies and\n", + "reorganize them as functions of the mass number $A$, the number of\n", + "protons $Z$ and neutrons $N$ using **pandas**. Before we do this it is\n", + "always useful (unless you have a binary file or other types of compressed\n", + "data) to actually open the file and simply take a look at it!\n", + "\n", + "\n", + "In particular, the program that outputs the final nuclear masses is written in Fortran with a specific format. It means that we need to figure out the format and which columns contain the data we are interested in. Pandas comes with a function that reads formatted output. After having admired the file, we are now ready to start massaging it with **pandas**. The file begins with some basic format information." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "' \\nThis is taken from the data file of the mass 2016 evaluation. \\nAll files are 3436 lines long with 124 character per line. \\n Headers are 39 lines long. \\n col 1 : Fortran character control: 1 = page feed 0 = line feed \\n format : a1,i3,i5,i5,i5,1x,a3,a4,1x,f13.5,f11.5,f11.3,f9.3,1x,a2,f11.3,f9.3,1x,i3,1x,f12.5,f11.5 \\n These formats are reflected in the pandas widths variable below, see the statement \\n widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1), \\n Pandas has also a variable header, with length 39 in this case. \\n'" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\" \n", + "This is taken from the data file of the mass 2016 evaluation. \n", + "All files are 3436 lines long with 124 character per line. \n", + " Headers are 39 lines long. \n", + " col 1 : Fortran character control: 1 = page feed 0 = line feed \n", + " format : a1,i3,i5,i5,i5,1x,a3,a4,1x,f13.5,f11.5,f11.3,f9.3,1x,a2,f11.3,f9.3,1x,i3,1x,f12.5,f11.5 \n", + " These formats are reflected in the pandas widths variable below, see the statement \n", + " widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1), \n", + " Pandas has also a variable header, with length 39 in this case. \n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The data we are interested in are in columns 2, 3, 4 and 11, giving us\n", + "the number of neutrons, protons, mass numbers and binding energies,\n", + "respectively. We add also for the sake of completeness the element name. The data are in fixed-width formatted lines and we will\n", + "covert them into the **pandas** DataFrame structure." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "# Read the experimental data with Pandas\n", + "Masses = pd.read_fwf(infile, usecols=(2,3,4,6,11),\n", + " names=('N', 'Z', 'A', 'Element', 'Ebinding'),\n", + " widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1),\n", + " header=39,\n", + " index_col=False)\n", + "\n", + "# Extrapolated values are indicated by '#' in place of the decimal place, so\n", + "# the Ebinding column won't be numeric. Coerce to float and drop these entries.\n", + "Masses['Ebinding'] = pd.to_numeric(Masses['Ebinding'], errors='coerce')\n", + "Masses = Masses.dropna()\n", + "# Convert from keV to MeV.\n", + "Masses['Ebinding'] /= 1000\n", + "\n", + "# Group the DataFrame by nucleon number, A.\n", + "Masses = Masses.groupby('A')\n", + "# Find the rows of the grouped DataFrame with the maximum binding energy.\n", + "Masses = Masses.apply(lambda t: t[t.Ebinding==t.Ebinding.max()])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have now read in the data, grouped them according to the variables we are interested in. \n", + "We see how easy it is to reorganize the data using **pandas**. If we\n", + "were to do these operations in C/C++ or Fortran, we would have had to\n", + "write various functions/subroutines which perform the above\n", + "reorganizations for us. Having reorganized the data, we can now start\n", + "to make some simple fits using both the functionalities in **numpy** and\n", + "**Scikit-Learn** afterwards. \n", + "\n", + "Now we define five variables which contain\n", + "the number of nucleons $A$, the number of protons $Z$ and the number of neutrons $N$, the element name and finally the energies themselves." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " N Z A Element Ebinding\n", + "A \n", + "1 0 0 1 1 H 0.000000\n", + "2 1 1 1 2 H 1.112283\n", + "3 2 2 1 3 H 2.827265\n", + "4 6 2 2 4 He 7.073915\n", + "5 9 3 2 5 He 5.512132\n", + "... ... ... ... ... ...\n", + "264 3304 156 108 264 Hs 7.298375\n", + "265 3310 157 108 265 Hs 7.296247\n", + "266 3317 158 108 266 Hs 7.298273\n", + "269 3338 159 110 269 Ds 7.250154\n", + "270 3344 160 110 270 Ds 7.253775\n", + "\n", + "[267 rows x 5 columns]\n" + ] + } + ], + "source": [ + "A = Masses['A']\n", + "Z = Masses['Z']\n", + "N = Masses['N']\n", + "Element = Masses['Element']\n", + "Energies = Masses['Ebinding']\n", + "print(Masses)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The next step, and we will define this mathematically later, is to set up the so-called **design matrix**. We will throughout call this matrix $\\boldsymbol{X}$.\n", + "It has dimensionality $p\\times n$, where $n$ is the number of data points and $p$ are the so-called predictors. In our case here they are given by the number of polynomials in $A$ we wish to include in the fit." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "# Now we set up the design matrix X\n", + "X = np.zeros((len(A),5))\n", + "X[:,0] = 1\n", + "X[:,1] = A\n", + "X[:,2] = A**(2.0/3.0)\n", + "X[:,3] = A**(-1.0/3.0)\n", + "X[:,4] = A**(-1.0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With **scikitlearn** we are now ready to use linear regression and fit our data." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [], + "source": [ + "clf = skl.LinearRegression().fit(X, Energies)\n", + "fity = clf.predict(X)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pretty simple! \n", + "Now we can print measures of how our fit is doing, the coefficients from the fits and plot the final fit together with our data." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean squared error: 0.04\n", + "Variance score: 0.95\n", + "Mean absolute error: 0.05\n", + "[ 0.00000000e+00 7.06492086e-03 -1.73091052e-01 -1.66020213e+01\n", + " 1.17385778e+00] 15.212327334149508\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/gettingstarted_114_1.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# The mean squared error \n", + "print(\"Mean squared error: %.2f\" % mean_squared_error(Energies, fity))\n", + "# Explained variance score: 1 is perfect prediction \n", + "print('Variance score: %.2f' % r2_score(Energies, fity))\n", + "# Mean absolute error \n", + "print('Mean absolute error: %.2f' % mean_absolute_error(Energies, fity))\n", + "print(clf.coef_, clf.intercept_)\n", + "\n", + "Masses['Eapprox'] = fity\n", + "# Generate a plot comparing the experimental with the fitted values values.\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel(r'$A = N + Z$')\n", + "ax.set_ylabel(r'$E_\\mathrm{bind}\\,/\\mathrm{MeV}$')\n", + "ax.plot(Masses['A'], Masses['Ebinding'], alpha=0.7, lw=2,\n", + " label='Ame2016')\n", + "ax.plot(Masses['A'], Masses['Eapprox'], alpha=0.7, lw=2, c='m',\n", + " label='Fit')\n", + "ax.legend()\n", + "save_fig(\"Masses2016\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Seeing the wood for the trees\n", + "\n", + "As a teaser, let us now see how we can do this with decision trees using **scikit-learn**. Later we will switch to so-called **random forests**!" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/gettingstarted_116_0.png" + } + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " N Z A Element Ebinding Eapprox\n", + "A \n", + "1 0 0 1 1 H 0.000000 0.000000\n", + "2 1 1 1 2 H 1.112283 1.112283\n", + "3 2 2 1 3 H 2.827265 2.827265\n", + "4 6 2 2 4 He 7.073915 7.073915\n", + "5 9 3 2 5 He 5.512132 5.512132\n", + "... ... ... ... ... ... ...\n", + "264 3304 156 108 264 Hs 7.298375 7.298375\n", + "265 3310 157 108 265 Hs 7.296247 7.297260\n", + "266 3317 158 108 266 Hs 7.298273 7.297260\n", + "269 3338 159 110 269 Ds 7.250154 7.250154\n", + "270 3344 160 110 270 Ds 7.253775 7.253775\n", + "\n", + "[267 rows x 6 columns]\n", + "0.00988361564671618\n" + ] + } + ], + "source": [ + "\n", + "#Decision Tree Regression\n", + "from sklearn.tree import DecisionTreeRegressor\n", + "regr_1=DecisionTreeRegressor(max_depth=5)\n", + "regr_2=DecisionTreeRegressor(max_depth=7)\n", + "regr_3=DecisionTreeRegressor(max_depth=9)\n", + "regr_1.fit(X, Energies)\n", + "regr_2.fit(X, Energies)\n", + "regr_3.fit(X, Energies)\n", + "\n", + "\n", + "y_1 = regr_1.predict(X)\n", + "y_2 = regr_2.predict(X)\n", + "y_3=regr_3.predict(X)\n", + "Masses['Eapprox'] = y_3\n", + "# Plot the results\n", + "plt.figure()\n", + "plt.plot(A, Energies, color=\"blue\", label=\"Data\", linewidth=2)\n", + "plt.plot(A, y_1, color=\"red\", label=\"max_depth=5\", linewidth=2)\n", + "plt.plot(A, y_2, color=\"green\", label=\"max_depth=7\", linewidth=2)\n", + "plt.plot(A, y_3, color=\"m\", label=\"max_depth=9\", linewidth=2)\n", + "\n", + "plt.xlabel(\"$A$\")\n", + "plt.ylabel(\"$E$[MeV]\")\n", + "plt.title(\"Decision Tree Regression\")\n", + "plt.legend()\n", + "save_fig(\"Masses2016Trees\")\n", + "plt.show()\n", + "print(Masses)\n", + "print(np.mean( (Energies-y_1)**2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### And what about using neural networks?\n", + "\n", + "The **seaborn** package allows us to visualize data in an efficient way. Note that we use **scikit-learn**'s multi-layer perceptron (or feed forward neural network) \n", + "functionality." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/gettingstarted_118_16.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.neural_network import MLPRegressor\n", + "from sklearn.metrics import accuracy_score\n", + "import seaborn as sns\n", + "\n", + "X_train = X\n", + "Y_train = Energies\n", + "n_hidden_neurons = 100\n", + "epochs = 100\n", + "# store models for later use\n", + "eta_vals = np.logspace(-5, 1, 7)\n", + "lmbd_vals = np.logspace(-5, 1, 7)\n", + "# store the models for later use\n", + "DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n", + "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "sns.set()\n", + "for i, eta in enumerate(eta_vals):\n", + " for j, lmbd in enumerate(lmbd_vals):\n", + " dnn = MLPRegressor(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',\n", + " alpha=lmbd, learning_rate_init=eta, max_iter=epochs)\n", + " dnn.fit(X_train, Y_train)\n", + " DNN_scikit[i][j] = dnn\n", + " train_accuracy[i][j] = dnn.score(X_train, Y_train)\n", + "\n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Training Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A first summary\n", + "\n", + "The aim behind these introductory words was to present to you various\n", + "Python libraries and their functionalities, in particular libraries like\n", + "**numpy**, **pandas**, **xarray** and **matplotlib** and other that make our life much easier\n", + "in handling various data sets and visualizing data. \n", + "\n", + "Furthermore,\n", + "**Scikit-Learn** allows us with few lines of code to implement popular\n", + "Machine Learning algorithms for supervised learning. Later we will meet **Tensorflow**, a powerful library for deep learning. \n", + "Now it is time to dive more into the details of various methods. We will start with linear regression and try to take a deeper look at what it entails." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} \ No newline at end of file diff --git a/doc/src/LectureNotes/_build/jupyter_execute/gettingstarted.py b/doc/src/LectureNotes/_build/jupyter_execute/gettingstarted.py new file mode 100644 index 000000000..e08247f7d --- /dev/null +++ b/doc/src/LectureNotes/_build/jupyter_execute/gettingstarted.py @@ -0,0 +1,1320 @@ + +# Data Analysis and Machine Learning: Getting started, our first data and Machine Learning encounters + + +**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University + +Date: **Dec 25, 2019** + +Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license + + + + + + +## Introduction + +Our emphasis throughout this series of lectures +is on understanding the mathematical aspects of +different algorithms used in the fields of data analysis and machine learning. + +However, where possible we will emphasize the +importance of using available software. We start thus with a hands-on +and top-down approach to machine learning. The aim is thus to start with +relevant data or data we have produced +and use these to introduce statistical data analysis +concepts and machine learning algorithms before we delve into the +algorithms themselves. The examples we will use in the beginning, start with simple +polynomials with random noise added. We will use the Python +software package [Scikit-Learn](http://scikit-learn.org/stable/) and +introduce various machine learning algorithms to make fits of +the data and predictions. We move thereafter to more interesting +cases such as data from say experiments (below we will look at experimental nuclear binding energies as an example). +These are examples where we can easily set up the data and +then use machine learning algorithms included in for example +**Scikit-Learn**. + +These examples will serve us the purpose of getting +started. Furthermore, they allow us to catch more than two birds with +a stone. They will allow us to bring in some programming specific +topics and tools as well as showing the power of various Python +libraries for machine learning and statistical data analysis. + +Here, we will mainly focus on two +specific Python packages for Machine Learning, Scikit-Learn and +Tensorflow (see below for links etc). Moreover, the examples we +introduce will serve as inputs to many of our discussions later, as +well as allowing you to set up models and produce your own data and +get started with programming. + + + +## What is Machine Learning? + +Statistics, data science and machine learning form important fields of +research in modern science. They describe how to learn and make +predictions from data, as well as allowing us to extract important +correlations about physical process and the underlying laws of motion +in large data sets. The latter, big data sets, appear frequently in +essentially all disciplines, from the traditional Science, Technology, +Mathematics and Engineering fields to Life Science, Law, education +research, the Humanities and the Social Sciences. + +It has become more +and more common to see research projects on big data in for example +the Social Sciences where extracting patterns from complicated survey +data is one of many research directions. Having a solid grasp of data +analysis and machine learning is thus becoming central to scientific +computing in many fields, and competences and skills within the fields +of machine learning and scientific computing are nowadays strongly +requested by many potential employers. The latter cannot be +overstated, familiarity with machine learning has almost become a +prerequisite for many of the most exciting employment opportunities, +whether they are in bioinformatics, life science, physics or finance, +in the private or the public sector. This author has had several +students or met students who have been hired recently based on their +skills and competences in scientific computing and data science, often +with marginal knowledge of machine learning. + +Machine learning is a subfield of computer science, and is closely +related to computational statistics. It evolved from the study of +pattern recognition in artificial intelligence (AI) research, and has +made contributions to AI tasks like computer vision, natural language +processing and speech recognition. Many of the methods we will study are also +strongly rooted in basic mathematics and physics research. + +Ideally, machine learning represents the science of giving computers +the ability to learn without being explicitly programmed. The idea is +that there exist generic algorithms which can be used to find patterns +in a broad class of data sets without having to write code +specifically for each problem. The algorithm will build its own logic +based on the data. You should however always keep in mind that +machines and algorithms are to a large extent developed by humans. The +insights and knowledge we have about a specific system, play a central +role when we develop a specific machine learning algorithm. + +Machine learning is an extremely rich field, in spite of its young +age. The increases we have seen during the last three decades in +computational capabilities have been followed by developments of +methods and techniques for analyzing and handling large date sets, +relying heavily on statistics, computer science and mathematics. The +field is rather new and developing rapidly. Popular software packages +written in Python for machine learning like +[Scikit-learn](http://scikit-learn.org/stable/), +[Tensorflow](https://www.tensorflow.org/), +[PyTorch](http://pytorch.org/) and [Keras](https://keras.io/), all +freely available at their respective GitHub sites, encompass +communities of developers in the thousands or more. And the number of +code developers and contributors keeps increasing. Not all the +algorithms and methods can be given a rigorous mathematical +justification, opening up thereby large rooms for experimenting and +trial and error and thereby exciting new developments. However, a +solid command of linear algebra, multivariate theory, probability +theory, statistical data analysis, understanding errors and Monte +Carlo methods are central elements in a proper understanding of many +of algorithms and methods we will discuss. + + + +## Types of Machine Learning + + +The approaches to machine learning are many, but are often split into +two main categories. In *supervised learning* we know the answer to a +problem, and let the computer deduce the logic behind it. On the other +hand, *unsupervised learning* is a method for finding patterns and +relationship in data sets without any prior knowledge of the system. +Some authours also operate with a third category, namely +*reinforcement learning*. This is a paradigm of learning inspired by +behavioral psychology, where learning is achieved by trial-and-error, +solely from rewards and punishment. + +Another way to categorize machine learning tasks is to consider the +desired output of a system. Some of the most common tasks are: + + * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning. + + * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values. + + * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning. + +The methods we cover have three main topics in common, irrespective of +whether we deal with supervised or unsupervised learning. The first +ingredient is normally our data set (which can be subdivided into +training and test data), the second item is a model which is normally a +function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model. + +The last ingredient is a so-called **cost** +function which allows us to present an estimate on how good our model +is in reproducing the data it is supposed to train. +At the heart of basically all ML algorithms there are so-called minimization algorithms, often we end up with various variants of **gradient** methods. + + + + + + + +## Software and needed installations + +We will make extensive use of Python as programming language and its +myriad of available libraries. You will find +Jupyter notebooks invaluable in your work. You can run **R** +codes in the Jupyter/IPython notebooks, with the immediate benefit of +visualizing your data. You can also use compiled languages like C++, +Rust, Julia, Fortran etc if you prefer. The focus in these lectures will be +on Python. + + +If you have Python installed (we strongly recommend Python3) and you feel +pretty familiar with installing different packages, we recommend that +you install the following Python packages via **pip** as + +1. pip install numpy scipy matplotlib ipython scikit-learn mglearn sympy pandas pillow + +For Python3, replace **pip** with **pip3**. + +For OSX users we recommend, after having installed Xcode, to +install **brew**. Brew allows for a seamless installation of additional +software via for example + +1. brew install python3 + +For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution, +you can use **pip** as well and simply install Python as + +1. sudo apt-get install python3 (or python for pyhton2.7) + +etc etc. + + + +## Python installers + +If you don't want to perform these operations separately and venture +into the hassle of exploring how to set up dependencies and paths, we +recommend two widely used distrubutions which set up all relevant +dependencies for Python, namely + +* [Anaconda](https://docs.anaconda.com/), + +which is an open source +distribution of the Python and R programming languages for large-scale +data processing, predictive analytics, and scientific computing, that +aims to simplify package management and deployment. Package versions +are managed by the package management system **conda**. + +* [Enthought canopy](https://www.enthought.com/product/canopy/) + +is a Python +distribution for scientific and analytic computing distribution and +analysis environment, available for free and under a commercial +license. + +Furthermore, [Google's Colab](https://colab.research.google.com/notebooks/welcome.ipynb) is a free Jupyter notebook environment that requires +no setup and runs entirely in the cloud. Try it out! + +## Useful Python libraries +Here we list several useful Python libraries we strongly recommend (if you use anaconda many of these are already there) + +* [NumPy](https://www.numpy.org/) is a highly popular library for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays + +* [The pandas](https://pandas.pydata.org/) library provides high-performance, easy-to-use data structures and data analysis tools + +* [Xarray](http://xarray.pydata.org/en/stable/) is a Python package that makes working with labelled multi-dimensional arrays simple, efficient, and fun! + +* [Scipy](https://www.scipy.org/) (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering. + +* [Matplotlib](https://matplotlib.org/) is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms. + +* [Autograd](https://github.com/HIPS/autograd) can automatically differentiate native Python and Numpy code. It can handle a large subset of Python's features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives + +* [SymPy](https://www.sympy.org/en/index.html) is a Python library for symbolic mathematics. + +* [scikit-learn](https://scikit-learn.org/stable/) has simple and efficient tools for machine learning, data mining and data analysis + +* [TensorFlow](https://www.tensorflow.org/) is a Python library for fast numerical computing created and released by Google + +* [Keras](https://keras.io/) is a high-level neural networks API, written in Python and capable of running on top of TensorFlow, CNTK, or Theano + +* And many more such as [pytorch](https://pytorch.org/), [Theano](https://pypi.org/project/Theano/) etc + +## Installing R, C++, cython or Julia + +You will also find it convenient to utilize **R**. We will mainly +use Python during our lectures and in various projects and exercises. +Those of you +already familiar with **R** should feel free to continue using **R**, keeping +however an eye on the parallel Python set ups. Similarly, if you are a +Python afecionado, feel free to explore **R** as well. Jupyter/Ipython +notebook allows you to run **R** codes interactively in your +browser. The software library **R** is really tailored for statistical data analysis +and allows for an easy usage of the tools and algorithms we will discuss in these +lectures. + +To install **R** with Jupyter notebook +[follow the link here](https://mpacer.org/maths/r-kernel-for-ipython-notebook) + + + + +## Installing R, C++, cython, Numba etc + + +For the C++ aficionados, Jupyter/IPython notebook allows you also to +install C++ and run codes written in this language interactively in +the browser. Since we will emphasize writing many of the algorithms +yourself, you can thus opt for either Python or C++ (or Fortran or other compiled languages) as programming +languages. + +To add more entropy, **cython** can also be used when running your +notebooks. It means that Python with the jupyter notebook +setup allows you to integrate widely popular softwares and tools for +scientific computing. Similarly, the +[Numba Python package](https://numba.pydata.org/) delivers increased performance +capabilities with minimal rewrites of your codes. With its +versatility, including symbolic operations, Python offers a unique +computational environment. Your jupyter notebook can easily be +converted into a nicely rendered **PDF** file or a Latex file for +further processing. For example, convert to latex as + + pycod jupyter nbconvert filename.ipynb --to latex + + +And to add more versatility, the Python package [SymPy](http://www.sympy.org/en/index.html) is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) and is entirely written in Python. + +Finally, if you wish to use the light mark-up language +[doconce](https://github.com/hplgit/doconce) you can convert a standard ascii text file into various HTML +formats, ipython notebooks, latex files, pdf files etc with minimal edits. These lectures were generated using **doconce**. + + + +## Numpy examples and Important Matrix and vector handling packages + +There are several central software libraries for linear algebra and eigenvalue problems. Several of the more +popular ones have been wrapped into ofter software packages like those from the widely used text **Numerical Recipes**. The original source codes in many of the available packages are often taken from the widely used +software package LAPACK, which follows two other popular packages +developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly here. + + * LINPACK: package for linear equations and least square problems. + + * LAPACK:package for solving symmetric, unsymmetric and generalized eigenvalue problems. From LAPACK's website it is possible to download for free all source codes from this library. Both C/C++ and Fortran versions are available. + + * BLAS (I, II and III): (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. Blas I is vector operations, II vector-matrix operations and III matrix-matrix operations. Highly parallelized and efficient codes, all available for download from . + +## Basic Matrix Features + +**Matrix properties reminder.** + +$$ +\mathbf{A} = + \begin{bmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\ + a_{21} & a_{22} & a_{23} & a_{24} \\ + a_{31} & a_{32} & a_{33} & a_{34} \\ + a_{41} & a_{42} & a_{43} & a_{44} + \end{bmatrix}\qquad +\mathbf{I} = + \begin{bmatrix} 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 1 + \end{bmatrix} +$$ + +The inverse of a matrix is defined by + +$$ +\mathbf{A}^{-1} \cdot \mathbf{A} = I +$$ + + + + + + + + + + + + +
    Relations Name matrix elements
    $A = A^{T}$ symmetric $a_{ij} = a_{ji}$
    $A = \left (A^{T} \right )^{-1}$ real orthogonal $\sum_k a_{ik} a_{jk} = \sum_k a_{ki} a_{kj} = \delta_{ij}$
    $A = A^{ * }$ real matrix $a_{ij} = a_{ij}^{ * }$
    $A = A^{\dagger}$ hermitian $a_{ij} = a_{ji}^{ * }$
    $A = \left (A^{\dagger} \right )^{-1}$ unitary $\sum_k a_{ik} a_{jk}^{ * } = \sum_k a_{ki}^{ * } a_{kj} = \delta_{ij}$
    + + + + +### Some famous Matrices + + * Diagonal if $a_{ij}=0$ for $i\ne j$ + + * Upper triangular if $a_{ij}=0$ for $i > j$ + + * Lower triangular if $a_{ij}=0$ for $i < j$ + + * Upper Hessenberg if $a_{ij}=0$ for $i > j+1$ + + * Lower Hessenberg if $a_{ij}=0$ for $i < j+1$ + + * Tridiagonal if $a_{ij}=0$ for $|i -j| > 1$ + + * Lower banded with bandwidth $p$: $a_{ij}=0$ for $i > j+p$ + + * Upper banded with bandwidth $p$: $a_{ij}=0$ for $i < j+p$ + + * Banded, block upper triangular, block lower triangular.... + +### More Basic Matrix Features + +**Some Equivalent Statements.** + +For an $N\times N$ matrix $\mathbf{A}$ the following properties are all equivalent + + * If the inverse of $\mathbf{A}$ exists, $\mathbf{A}$ is nonsingular. + + * The equation $\mathbf{Ax}=0$ implies $\mathbf{x}=0$. + + * The rows of $\mathbf{A}$ form a basis of $R^N$. + + * The columns of $\mathbf{A}$ form a basis of $R^N$. + + * $\mathbf{A}$ is a product of elementary matrices. + + * $0$ is not eigenvalue of $\mathbf{A}$. + + + + +## Numpy and arrays +[Numpy](http://www.numpy.org/) provides an easy way to handle arrays in Python. The standard way to import this library is as + +import numpy as np + +Here follows a simple example where we set up an array of ten elements, all determined by random numbers drawn according to the normal distribution, + +n = 10 +x = np.random.normal(size=n) +print(x) +print(x[1]) + +We defined a vector $x$ with $n=10$ elements with its values given by the Normal distribution $N(0,1)$. +Another alternative is to declare a vector as follows + +import numpy as np +x = np.array([1, 2, 3]) +print(x) + +Here we have defined a vector with three elements, with $x_0=1$, $x_1=2$ and $x_2=3$. Note that both Python and C++ +start numbering array elements from $0$ and on. This means that a vector with $n$ elements has a sequence of entities $x_0, x_1, x_2, \dots, x_{n-1}$. We could also let (recommended) Numpy to compute the logarithms of a specific array as + +import numpy as np +x = np.log(np.array([4, 7, 8])) +print(x) + +In the last example we used Numpy's unary function $np.log$. This function is +highly tuned to compute array elements since the code is vectorized +and does not require looping. We normaly recommend that you use the +Numpy intrinsic functions instead of the corresponding **log** function +from Python's **math** module. The looping is done explicitely by the +**np.log** function. The alternative, and slower way to compute the +logarithms of a vector would be to write + +import numpy as np +from math import log +x = np.array([4, 7, 8]) +for i in range(0, len(x)): + x[i] = log(x[i]) +print(x) + +We note that our code is much longer already and we need to import the **log** function from the **math** module. +The attentive reader will also notice that the output is $[1, 1, 2]$. Python interprets automagically our numbers as integers (like the **automatic** keyword in C++). To change this we could define our array elements to be double precision numbers as + +import numpy as np +x = np.log(np.array([4, 7, 8], dtype = np.float64)) +print(x) + +or simply write them as double precision numbers (Python uses 64 bits as default for floating point type variables), that is + +import numpy as np +x = np.log(np.array([4.0, 7.0, 8.0])) +print(x) + +To check the number of bytes (remember that one byte contains eight bits for double precision variables), you can use simple use the **itemsize** functionality (the array $x$ is actually an object which inherits the functionalities defined in Numpy) as + +import numpy as np +x = np.log(np.array([4.0, 7.0, 8.0])) +print(x.itemsize) + +## Matrices in Python + +Having defined vectors, we are now ready to try out matrices. We can +define a $3 \times 3 $ real matrix $\hat{A}$ as (recall that we user +lowercase letters for vectors and uppercase letters for matrices) + +import numpy as np +A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ])) +print(A) + +If we use the **shape** function we would get $(3, 3)$ as output, that is verifying that our matrix is a $3\times 3$ matrix. We can slice the matrix and print for example the first column (Python organized matrix elements in a row-major order, see below) as + +import numpy as np +A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ])) +# print the first column, row-major order and elements start with 0 +print(A[:,0]) + +We can continue this was by printing out other columns or rows. The example here prints out the second column + +import numpy as np +A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ])) +# print the first column, row-major order and elements start with 0 +print(A[1,:]) + +Numpy contains many other functionalities that allow us to slice, subdivide etc etc arrays. We strongly recommend that you look up the [Numpy website for more details](http://www.numpy.org/). Useful functions when defining a matrix are the **np.zeros** function which declares a matrix of a given dimension and sets all elements to zero + +import numpy as np +n = 10 +# define a matrix of dimension 10 x 10 and set all elements to zero +A = np.zeros( (n, n) ) +print(A) + +or initializing all elements to + +import numpy as np +n = 10 +# define a matrix of dimension 10 x 10 and set all elements to one +A = np.eye( n ) +print(A) + +or as unitarily distributed random numbers (see the material on random number generators in the statistics part) + +import numpy as np +n = 10 +# define a matrix of dimension 10 x 10 and set all elements to random numbers with x \in [0, 1] +A = np.random.rand(n, n) +print(A) + +As we will see throughout these lectures, there are several extremely useful functionalities in Numpy. +As an example, consider the discussion of the covariance matrix. Suppose we have defined three vectors +$\hat{x}, \hat{y}, \hat{z}$ with $n$ elements each. The covariance matrix is defined as + +$$ +\hat{\Sigma} = \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz} \\ + \sigma_{yx} & \sigma_{yy} & \sigma_{yz} \\ + \sigma_{zx} & \sigma_{zy} & \sigma_{zz} + \end{bmatrix}, +$$ + +where for example + +$$ +\sigma_{xy} =\frac{1}{n} \sum_{i=0}^{n-1}(x_i- \overline{x})(y_i- \overline{y}). +$$ + +The Numpy function **np.cov** calculates the covariance elements using the factor $1/(n-1)$ instead of $1/n$ since it assumes we do not have the exact mean values. +The following simple function uses the **np.vstack** function which takes each vector of dimension $1\times n$ and produces a $3\times n$ matrix $\hat{W}$ + +$$ +\hat{W} = \begin{bmatrix} x_0 & y_0 & z_0 \\ + x_1 & y_1 & z_1 \\ + x_2 & y_2 & z_2 \\ + \dots & \dots & \dots \\ + x_{n-2} & y_{n-2} & z_{n-2} \\ + x_{n-1} & y_{n-1} & z_{n-1} + \end{bmatrix}, +$$ + +which in turn is converted into into the $3\times 3$ covariance matrix +$\hat{\Sigma}$ via the Numpy function **np.cov()**. We note that we can also calculate +the mean value of each set of samples $\hat{x}$ etc using the Numpy +function **np.mean(x)**. We can also extract the eigenvalues of the +covariance matrix through the **np.linalg.eig()** function. + +# Importing various packages +import numpy as np + +n = 100 +x = np.random.normal(size=n) +print(np.mean(x)) +y = 4+3*x+np.random.normal(size=n) +print(np.mean(y)) +z = x**3+np.random.normal(size=n) +print(np.mean(z)) +W = np.vstack((x, y, z)) +Sigma = np.cov(W) +print(Sigma) +Eigvals, Eigvecs = np.linalg.eig(Sigma) +print(Eigvals) + +%matplotlib inline + +import numpy as np +import matplotlib.pyplot as plt +from scipy import sparse +eye = np.eye(4) +print(eye) +sparse_mtx = sparse.csr_matrix(eye) +print(sparse_mtx) +x = np.linspace(-10,10,100) +y = np.sin(x) +plt.plot(x,y,marker='x') +plt.show() + +## Meet the Pandas + + + + + +

    + + + + + +Another useful Python package is +[pandas](https://pandas.pydata.org/), which is an open source library +providing high-performance, easy-to-use data structures and data +analysis tools for Python. **pandas** stands for panel data, a term borrowed from econometrics and is an efficient library for data analysis with an emphasis on tabular data. +**pandas** has two major classes, the **DataFrame** class with two-dimensional data objects and tabular data organized in columns and the class **Series** with a focus on one-dimensional data objects. Both classes allow you to index data easily as we will see in the examples below. +**pandas** allows you also to perform mathematical operations on the data, spanning from simple reshapings of vectors and matrices to statistical operations. + +The following simple example shows how we can, in an easy way make tables of our data. Here we define a data set which includes names, place of birth and date of birth, and displays the data in an easy to read way. We will see repeated use of **pandas**, in particular in connection with classification of data. + +import pandas as pd +from IPython.display import display +data = {'First Name': ["Frodo", "Bilbo", "Aragorn II", "Samwise"], + 'Last Name': ["Baggins", "Baggins","Elessar","Gamgee"], + 'Place of birth': ["Shire", "Shire", "Eriador", "Shire"], + 'Date of Birth T.A.': [2968, 2890, 2931, 2980] + } +data_pandas = pd.DataFrame(data) +display(data_pandas) + +In the above we have imported **pandas** with the shorthand **pd**, the latter has become the standard way we import **pandas**. We make then a list of various variables +and reorganize the aboves lists into a **DataFrame** and then print out a neat table with specific column labels as *Name*, *place of birth* and *date of birth*. +Displaying these results, we see that the indices are given by the default numbers from zero to three. +**pandas** is extremely flexible and we can easily change the above indices by defining a new type of indexing as + +data_pandas = pd.DataFrame(data,index=['Frodo','Bilbo','Aragorn','Sam']) +display(data_pandas) + +Thereafter we display the content of the row which begins with the index **Aragorn** + +display(data_pandas.loc['Aragorn']) + +We can easily append data to this, for example + +new_hobbit = {'First Name': ["Peregrin"], + 'Last Name': ["Took"], + 'Place of birth': ["Shire"], + 'Date of Birth T.A.': [2990] + } +data_pandas=data_pandas.append(pd.DataFrame(new_hobbit, index=['Pippin'])) +display(data_pandas) + +Here are other examples where we use the **DataFrame** functionality to handle arrays, now with more interesting features for us, namely numbers. We set up a matrix +of dimensionality $10\times 5$ and compute the mean value and standard deviation of each column. Similarly, we can perform mathematial operations like squaring the matrix elements and many other operations. + +import numpy as np +import pandas as pd +from IPython.display import display +np.random.seed(100) +# setting up a 10 x 5 matrix +rows = 10 +cols = 5 +a = np.random.randn(rows,cols) +df = pd.DataFrame(a) +display(df) +print(df.mean()) +print(df.std()) +display(df**2) +print(df-df.mean()) + + +Thereafter we can select specific columns only and plot final results + +df.columns = ['First', 'Second', 'Third', 'Fourth', 'Fifth'] +df.index = np.arange(10) + +display(df) +print(df['Second'].mean() ) +print(df.info()) +print(df.describe()) + +from pylab import plt, mpl +plt.style.use('seaborn') +mpl.rcParams['font.family'] = 'serif' + +df.cumsum().plot(lw=2.0, figsize=(10,6)) +plt.show() + + +df.plot.bar(figsize=(10,6), rot=15) +plt.show() + +We can produce a $4\times 4$ matrix + +b = np.arange(16).reshape((4,4)) +print(b) +df1 = pd.DataFrame(b) +print(df1) + +and many other operations. + +The **Series** class is another important class included in +**pandas**. You can view it as a specialization of **DataFrame** but where +we have just a single column of data. It shares many of the same features as _DataFrame. As with **DataFrame**, +most operations are vectorized, achieving thereby a high performance when dealing with computations of arrays, in particular labeled arrays. +As we will see below it leads also to a very concice code close to the mathematical operations we may be interested in. +For multidimensional arrays, we recommend strongly [xarray](http://xarray.pydata.org/en/stable/). **xarray** has much of the same flexibility as **pandas**, but allows for the extension to higher dimensions than two. We will see examples later of the usage of both **pandas** and **xarray**. + + + +## Reading Data and fitting + +In order to study various Machine Learning algorithms, we need to +access data. Acccessing data is an essential step in all machine +learning algorithms. In particular, setting up the so-called **design +matrix** (to be defined below) is often the first element we need in +order to perform our calculations. To set up the design matrix means +reading (and later, when the calculations are done, writing) data +in various formats, The formats span from reading files from disk, +loading data from databases and interacting with online sources +like web application programming interfaces (APIs). + +In handling various input formats, as discussed above, we will mainly stay with **pandas**, +a Python package which allows us, in a seamless and painless way, to +deal with a multitude of formats, from standard **csv** (comma separated +values) files, via **excel**, **html** to **hdf5** formats. With **pandas** +and the **DataFrame** and **Series** functionalities we are able to convert text data +into the calculational formats we need for a specific algorithm. And our code is going to be +pretty close the basic mathematical expressions. + +Our first data set is going to be a classic from nuclear physics, namely all +available data on binding energies. Don't be intimidated if you are not familiar with nuclear physics. It serves simply as an example here of a data set. + +We will show some of the +strengths of packages like **Scikit-Learn** in fitting nuclear binding energies to +specific functions using linear regression first. Then, as a teaser, we will show you how +you can easily implement other algorithms like decision trees and random forests and neural networks. + +But before we really start with nuclear physics data, let's just look at some simpler polynomial fitting cases, such as, +(don't be offended) fitting straight lines! + + +### Simple linear regression model using **scikit-learn** + +We start with perhaps our simplest possible example, using **Scikit-Learn** to perform linear regression analysis on a data set produced by us. + +What follows is a simple Python code where we have defined a function +$y$ in terms of the variable $x$. Both are defined as vectors with $100$ entries. +The numbers in the vector $\hat{x}$ are given +by random numbers generated with a uniform distribution with entries +$x_i \in [0,1]$ (more about probability distribution functions +later). These values are then used to define a function $y(x)$ +(tabulated again as a vector) with a linear dependence on $x$ plus a +random noise added via the normal distribution. + + +The Numpy functions are imported used the **import numpy as np** +statement and the random number generator for the uniform distribution +is called using the function **np.random.rand()**, where we specificy +that we want $100$ random variables. Using Numpy we define +automatically an array with the specified number of elements, $100$ in +our case. With the Numpy function **randn()** we can compute random +numbers with the normal distribution (mean value $\mu$ equal to zero and +variance $\sigma^2$ set to one) and produce the values of $y$ assuming a linear +dependence as function of $x$ + +$$ +y = 2x+N(0,1), +$$ + +where $N(0,1)$ represents random numbers generated by the normal +distribution. From **Scikit-Learn** we import then the +**LinearRegression** functionality and make a prediction $\tilde{y} = +\alpha + \beta x$ using the function **fit(x,y)**. We call the set of +data $(\hat{x},\hat{y})$ for our training data. The Python package +**scikit-learn** has also a functionality which extracts the above +fitting parameters $\alpha$ and $\beta$ (see below). Later we will +distinguish between training data and test data. + +For plotting we use the Python package +[matplotlib](https://matplotlib.org/) which produces publication +quality figures. Feel free to explore the extensive +[gallery](https://matplotlib.org/gallery/index.html) of examples. In +this example we plot our original values of $x$ and $y$ as well as the +prediction **ypredict** ($\tilde{y}$), which attempts at fitting our +data with a straight line. + +The Python code follows here. + +# Importing various packages +import numpy as np +import matplotlib.pyplot as plt +from sklearn.linear_model import LinearRegression + +x = np.random.rand(100,1) +y = 2*x+0.01*np.random.randn(100,1) +linreg = LinearRegression() +linreg.fit(x,y) +#ynew = linreg.predict(x) +#xnew = np.array([[0],[1]]) +ypredict = linreg.predict(x) + +plt.plot(x, ypredict, "r-") +plt.plot(x, y ,'ro') +plt.axis([0,1.0,0, 5.0]) +plt.xlabel(r'$x$') +plt.ylabel(r'$y$') +plt.title(r'Simple Linear Regression') +plt.show() + +This example serves several aims. It allows us to demonstrate several +aspects of data analysis and later machine learning algorithms. The +immediate visualization shows that our linear fit is not +impressive. It goes through the data points, but there are many +outliers which are not reproduced by our linear regression. We could +now play around with this small program and change for example the +factor in front of $x$ and the normal distribution. Try to change the +function $y$ to + +$$ +y = 10x+0.01 \times N(0,1), +$$ + +where $x$ is defined as before. Does the fit look better? Indeed, by +reducing the role of the noise given by the normal distribution we see immediately that +our linear prediction seemingly reproduces better the training +set. However, this testing 'by the eye' is obviouly not satisfactory in the +long run. Here we have only defined the training data and our model, and +have not discussed a more rigorous approach to the **cost** function. + +We need more rigorous criteria in defining whether we have succeeded or +not in modeling our training data. You will be surprised to see that +many scientists seldomly venture beyond this 'by the eye' approach. A +standard approach for the *cost* function is the so-called $\chi^2$ +function (a variant of the mean-squared error (MSE)) + +$$ +\chi^2 = \frac{1}{n} +\sum_{i=0}^{n-1}\frac{(y_i-\tilde{y}_i)^2}{\sigma_i^2}, +$$ + +where $\sigma_i^2$ is the variance (to be defined later) of the entry +$y_i$. We may not know the explicit value of $\sigma_i^2$, it serves +however the aim of scaling the equations and make the cost function +dimensionless. + +Minimizing the cost function is a central aspect of +our discussions to come. Finding its minima as function of the model +parameters ($\alpha$ and $\beta$ in our case) will be a recurring +theme in these series of lectures. Essentially all machine learning +algorithms we will discuss center around the minimization of the +chosen cost function. This depends in turn on our specific +model for describing the data, a typical situation in supervised +learning. Automatizing the search for the minima of the cost function is a +central ingredient in all algorithms. Typical methods which are +employed are various variants of **gradient** methods. These will be +discussed in more detail later. Again, you'll be surprised to hear that +many practitioners minimize the above function ''by the eye', popularly dubbed as +'chi by the eye'. That is, change a parameter and see (visually and numerically) that +the $\chi^2$ function becomes smaller. + +There are many ways to define the cost function. A simpler approach is to look at the relative difference between the training data and the predicted data, that is we define +the relative error (why would we prefer the MSE instead of the relative error?) as + +$$ +\epsilon_{\mathrm{relative}}= \frac{\vert \hat{y} -\hat{\tilde{y}}\vert}{\vert \hat{y}\vert}. +$$ + +The squared cost function results in an arithmetic mean-unbiased +estimator, and the absolute-value cost function results in a +median-unbiased estimator (in the one-dimensional case, and a +geometric median-unbiased estimator for the multi-dimensional +case). The squared cost function has the disadvantage that it has the tendency +to be dominated by outliers. + +We can modify easily the above Python code and plot the relative error instead + +import numpy as np +import matplotlib.pyplot as plt +from sklearn.linear_model import LinearRegression + +x = np.random.rand(100,1) +y = 5*x+0.01*np.random.randn(100,1) +linreg = LinearRegression() +linreg.fit(x,y) +ypredict = linreg.predict(x) + +plt.plot(x, np.abs(ypredict-y)/abs(y), "ro") +plt.axis([0,1.0,0.0, 0.5]) +plt.xlabel(r'$x$') +plt.ylabel(r'$\epsilon_{\mathrm{relative}}$') +plt.title(r'Relative error') +plt.show() + +Depending on the parameter in front of the normal distribution, we may +have a small or larger relative error. Try to play around with +different training data sets and study (graphically) the value of the +relative error. + +As mentioned above, **Scikit-Learn** has an impressive functionality. +We can for example extract the values of $\alpha$ and $\beta$ and +their error estimates, or the variance and standard deviation and many +other properties from the statistical data analysis. + +Here we show an +example of the functionality of **Scikit-Learn**. + +import numpy as np +import matplotlib.pyplot as plt +from sklearn.linear_model import LinearRegression +from sklearn.metrics import mean_squared_error, r2_score, mean_squared_log_error, mean_absolute_error + +x = np.random.rand(100,1) +y = 2.0+ 5*x+0.5*np.random.randn(100,1) +linreg = LinearRegression() +linreg.fit(x,y) +ypredict = linreg.predict(x) +print('The intercept alpha: \n', linreg.intercept_) +print('Coefficient beta : \n', linreg.coef_) +# The mean squared error +print("Mean squared error: %.2f" % mean_squared_error(y, ypredict)) +# Explained variance score: 1 is perfect prediction +print('Variance score: %.2f' % r2_score(y, ypredict)) +# Mean squared log error +print('Mean squared log error: %.2f' % mean_squared_log_error(y, ypredict) ) +# Mean absolute error +print('Mean absolute error: %.2f' % mean_absolute_error(y, ypredict)) +plt.plot(x, ypredict, "r-") +plt.plot(x, y ,'ro') +plt.axis([0.0,1.0,1.5, 7.0]) +plt.xlabel(r'$x$') +plt.ylabel(r'$y$') +plt.title(r'Linear Regression fit ') +plt.show() + +The function **coef** gives us the parameter $\beta$ of our fit while **intercept** yields +$\alpha$. Depending on the constant in front of the normal distribution, we get values near or far from $alpha =2$ and $\beta =5$. Try to play around with different parameters in front of the normal distribution. The function **meansquarederror** gives us the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as + +$$ +MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n} +\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2, +$$ + +The smaller the value, the better the fit. Ideally we would like to +have an MSE equal zero. The attentive reader has probably recognized +this function as being similar to the $\chi^2$ function defined above. + +The **r2score** function computes $R^2$, the coefficient of +determination. It provides a measure of how well future samples are +likely to be predicted by the model. Best possible score is 1.0 and it +can be negative (because the model can be arbitrarily worse). A +constant model that always predicts the expected value of $\hat{y}$, +disregarding the input features, would get a $R^2$ score of $0.0$. + +If $\tilde{\hat{y}}_i$ is the predicted value of the $i-th$ sample and $y_i$ is the corresponding true value, then the score $R^2$ is defined as + +$$ +R^2(\hat{y}, \tilde{\hat{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i - \tilde{y}_i)^2}{\sum_{i=0}^{n - 1} (y_i - \bar{y})^2}, +$$ + +where we have defined the mean value of $\hat{y}$ as + +$$ +\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i. +$$ + +Another quantity taht we will meet again in our discussions of regression analysis is + the mean absolute error (MAE), a risk metric corresponding to the expected value of the absolute error loss or what we call the $l1$-norm loss. In our discussion above we presented the relative error. +The MAE is defined as follows + +$$ +\text{MAE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n-1} \left| y_i - \tilde{y}_i \right|. +$$ + +We present the +squared logarithmic (quadratic) error + +$$ +\text{MSLE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n - 1} (\log_e (1 + y_i) - \log_e (1 + \tilde{y}_i) )^2, +$$ + +where $\log_e (x)$ stands for the natural logarithm of $x$. This error +estimate is best to use when targets having exponential growth, such +as population counts, average sales of a commodity over a span of +years etc. + + +Finally, another cost function is the Huber cost function used in robust regression. + +The rationale behind this possible cost function is its reduced +sensitivity to outliers in the data set. In our discussions on +dimensionality reduction and normalization of data we will meet other +ways of dealing with outliers. + +The Huber cost function is defined as + +$$ +H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}. +$$ + +Here $a=\boldsymbol{y} - \boldsymbol{\tilde{y}}$. +We will discuss in more +detail these and other functions in the various lectures. We conclude this part with another example. Instead of +a linear $x$-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn. + +import matplotlib.pyplot as plt +import numpy as np +import random +from sklearn.linear_model import Ridge +from sklearn.preprocessing import PolynomialFeatures +from sklearn.pipeline import make_pipeline +from sklearn.linear_model import LinearRegression + +x=np.linspace(0.02,0.98,200) +noise = np.asarray(random.sample((range(200)),200)) +y=x**3*noise +yn=x**3*100 +poly3 = PolynomialFeatures(degree=3) +X = poly3.fit_transform(x[:,np.newaxis]) +clf3 = LinearRegression() +clf3.fit(X,y) + +Xplot=poly3.fit_transform(x[:,np.newaxis]) +poly3_plot=plt.plot(x, clf3.predict(Xplot), label='Cubic Fit') +plt.plot(x,yn, color='red', label="True Cubic") +plt.scatter(x, y, label='Data', color='orange', s=15) +plt.legend() +plt.show() + +def error(a): + for i in y: + err=(y-yn)/yn + return abs(np.sum(err))/len(err) + +print (error(y)) + +### To our real data: nuclear binding energies. Brief reminder on masses and binding energies + +Let us now dive into nuclear physics and remind ourselves briefly about some basic features about binding +energies. A basic quantity which can be measured for the ground +states of nuclei is the atomic mass $M(N, Z)$ of the neutral atom with +atomic mass number $A$ and charge $Z$. The number of neutrons is $N$. There are indeed several sophisticated experiments worldwide which allow us to measure this quantity to high precision (parts per million even). + +Atomic masses are usually tabulated in terms of the mass excess defined by + +$$ +\Delta M(N, Z) = M(N, Z) - uA, +$$ + +where $u$ is the Atomic Mass Unit + +$$ +u = M(^{12}\mathrm{C})/12 = 931.4940954(57) \hspace{0.1cm} \mathrm{MeV}/c^2. +$$ + +The nucleon masses are + +$$ +m_p = 1.00727646693(9)u, +$$ + +and + +$$ +m_n = 939.56536(8)\hspace{0.1cm} \mathrm{MeV}/c^2 = 1.0086649156(6)u. +$$ + +In the [2016 mass evaluation of by W.J.Huang, G.Audi, M.Wang, F.G.Kondev, S.Naimi and X.Xu](http://nuclearmasses.org/resources_folder/Wang_2017_Chinese_Phys_C_41_030003.pdf) +there are data on masses and decays of 3437 nuclei. + +The nuclear binding energy is defined as the energy required to break +up a given nucleus into its constituent parts of $N$ neutrons and $Z$ +protons. In terms of the atomic masses $M(N, Z)$ the binding energy is +defined by + +$$ +BE(N, Z) = ZM_H c^2 + Nm_n c^2 - M(N, Z)c^2 , +$$ + +where $M_H$ is the mass of the hydrogen atom and $m_n$ is the mass of the neutron. +In terms of the mass excess the binding energy is given by + +$$ +BE(N, Z) = Z\Delta_H c^2 + N\Delta_n c^2 -\Delta(N, Z)c^2 , +$$ + +where $\Delta_H c^2 = 7.2890$ MeV and $\Delta_n c^2 = 8.0713$ MeV. + + +A popular and physically intuitive model which can be used to parametrize +the experimental binding energies as function of $A$, is the so-called +**liquid drop model**. The ansatz is based on the following expression + +$$ +BE(N,Z) = a_1A-a_2A^{2/3}-a_3\frac{Z^2}{A^{1/3}}-a_4\frac{(N-Z)^2}{A}, +$$ + +where $A$ stands for the number of nucleons and the $a_i$s are parameters which are determined by a fit +to the experimental data. + + + + +To arrive at the above expression we have assumed that we can make the following assumptions: + + * There is a volume term $a_1A$ proportional with the number of nucleons (the energy is also an extensive quantity). When an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it. This contribution is proportional to the volume. + + * There is a surface energy term $a_2A^{2/3}$. The assumption here is that a nucleon at the surface of a nucleus interacts with fewer other nucleons than one in the interior of the nucleus and hence its binding energy is less. This surface energy term takes that into account and is therefore negative and is proportional to the surface area. + + * There is a Coulomb energy term $a_3\frac{Z^2}{A^{1/3}}$. The electric repulsion between each pair of protons in a nucleus yields less binding. + + * There is an asymmetry term $a_4\frac{(N-Z)^2}{A}$. This term is associated with the Pauli exclusion principle and reflects the fact that the proton-neutron interaction is more attractive on the average than the neutron-neutron and proton-proton interactions. + +We could also add a so-called pairing term, which is a correction term that +arises from the tendency of proton pairs and neutron pairs to +occur. An even number of particles is more stable than an odd number. + + +### Organizing our data + +Let us start with reading and organizing our data. +We start with the compilation of masses and binding energies from 2016. +After having downloaded this file to our own computer, we are now ready to read the file and start structuring our data. + + +We start with preparing folders for storing our calculations and the data file over masses and binding energies. We import also various modules that we will find useful in order to present various Machine Learning methods. Here we focus mainly on the functionality of **scikit-learn**. + +# Common imports +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +import sklearn.linear_model as skl +from sklearn.model_selection import train_test_split +from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error +import os + +# Where to save the figures and data files +PROJECT_ROOT_DIR = "Results" +FIGURE_ID = "Results/FigureFiles" +DATA_ID = "DataFiles/" + +if not os.path.exists(PROJECT_ROOT_DIR): + os.mkdir(PROJECT_ROOT_DIR) + +if not os.path.exists(FIGURE_ID): + os.makedirs(FIGURE_ID) + +if not os.path.exists(DATA_ID): + os.makedirs(DATA_ID) + +def image_path(fig_id): + return os.path.join(FIGURE_ID, fig_id) + +def data_path(dat_id): + return os.path.join(DATA_ID, dat_id) + +def save_fig(fig_id): + plt.savefig(image_path(fig_id) + ".png", format='png') + +infile = open(data_path("MassEval2016.dat"),'r') + +Before we proceed, we define also a function for making our plots. You can obviously avoid this and simply set up various **matplotlib** commands every time you need them. You may however find it convenient to collect all such commands in one function and simply call this function. + +from pylab import plt, mpl +plt.style.use('seaborn') +mpl.rcParams['font.family'] = 'serif' + +def MakePlot(x,y, styles, labels, axlabels): + plt.figure(figsize=(10,6)) + for i in range(len(x)): + plt.plot(x[i], y[i], styles[i], label = labels[i]) + plt.xlabel(axlabels[0]) + plt.ylabel(axlabels[1]) + plt.legend(loc=0) + +Our next step is to read the data on experimental binding energies and +reorganize them as functions of the mass number $A$, the number of +protons $Z$ and neutrons $N$ using **pandas**. Before we do this it is +always useful (unless you have a binary file or other types of compressed +data) to actually open the file and simply take a look at it! + + +In particular, the program that outputs the final nuclear masses is written in Fortran with a specific format. It means that we need to figure out the format and which columns contain the data we are interested in. Pandas comes with a function that reads formatted output. After having admired the file, we are now ready to start massaging it with **pandas**. The file begins with some basic format information. + +""" +This is taken from the data file of the mass 2016 evaluation. +All files are 3436 lines long with 124 character per line. + Headers are 39 lines long. + col 1 : Fortran character control: 1 = page feed 0 = line feed + format : a1,i3,i5,i5,i5,1x,a3,a4,1x,f13.5,f11.5,f11.3,f9.3,1x,a2,f11.3,f9.3,1x,i3,1x,f12.5,f11.5 + These formats are reflected in the pandas widths variable below, see the statement + widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1), + Pandas has also a variable header, with length 39 in this case. +""" + +The data we are interested in are in columns 2, 3, 4 and 11, giving us +the number of neutrons, protons, mass numbers and binding energies, +respectively. We add also for the sake of completeness the element name. The data are in fixed-width formatted lines and we will +covert them into the **pandas** DataFrame structure. + +# Read the experimental data with Pandas +Masses = pd.read_fwf(infile, usecols=(2,3,4,6,11), + names=('N', 'Z', 'A', 'Element', 'Ebinding'), + widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1), + header=39, + index_col=False) + +# Extrapolated values are indicated by '#' in place of the decimal place, so +# the Ebinding column won't be numeric. Coerce to float and drop these entries. +Masses['Ebinding'] = pd.to_numeric(Masses['Ebinding'], errors='coerce') +Masses = Masses.dropna() +# Convert from keV to MeV. +Masses['Ebinding'] /= 1000 + +# Group the DataFrame by nucleon number, A. +Masses = Masses.groupby('A') +# Find the rows of the grouped DataFrame with the maximum binding energy. +Masses = Masses.apply(lambda t: t[t.Ebinding==t.Ebinding.max()]) + +We have now read in the data, grouped them according to the variables we are interested in. +We see how easy it is to reorganize the data using **pandas**. If we +were to do these operations in C/C++ or Fortran, we would have had to +write various functions/subroutines which perform the above +reorganizations for us. Having reorganized the data, we can now start +to make some simple fits using both the functionalities in **numpy** and +**Scikit-Learn** afterwards. + +Now we define five variables which contain +the number of nucleons $A$, the number of protons $Z$ and the number of neutrons $N$, the element name and finally the energies themselves. + +A = Masses['A'] +Z = Masses['Z'] +N = Masses['N'] +Element = Masses['Element'] +Energies = Masses['Ebinding'] +print(Masses) + +The next step, and we will define this mathematically later, is to set up the so-called **design matrix**. We will throughout call this matrix $\boldsymbol{X}$. +It has dimensionality $p\times n$, where $n$ is the number of data points and $p$ are the so-called predictors. In our case here they are given by the number of polynomials in $A$ we wish to include in the fit. + +# Now we set up the design matrix X +X = np.zeros((len(A),5)) +X[:,0] = 1 +X[:,1] = A +X[:,2] = A**(2.0/3.0) +X[:,3] = A**(-1.0/3.0) +X[:,4] = A**(-1.0) + +With **scikitlearn** we are now ready to use linear regression and fit our data. + +clf = skl.LinearRegression().fit(X, Energies) +fity = clf.predict(X) + +Pretty simple! +Now we can print measures of how our fit is doing, the coefficients from the fits and plot the final fit together with our data. + +# The mean squared error +print("Mean squared error: %.2f" % mean_squared_error(Energies, fity)) +# Explained variance score: 1 is perfect prediction +print('Variance score: %.2f' % r2_score(Energies, fity)) +# Mean absolute error +print('Mean absolute error: %.2f' % mean_absolute_error(Energies, fity)) +print(clf.coef_, clf.intercept_) + +Masses['Eapprox'] = fity +# Generate a plot comparing the experimental with the fitted values values. +fig, ax = plt.subplots() +ax.set_xlabel(r'$A = N + Z$') +ax.set_ylabel(r'$E_\mathrm{bind}\,/\mathrm{MeV}$') +ax.plot(Masses['A'], Masses['Ebinding'], alpha=0.7, lw=2, + label='Ame2016') +ax.plot(Masses['A'], Masses['Eapprox'], alpha=0.7, lw=2, c='m', + label='Fit') +ax.legend() +save_fig("Masses2016") +plt.show() + +### Seeing the wood for the trees + +As a teaser, let us now see how we can do this with decision trees using **scikit-learn**. Later we will switch to so-called **random forests**! + + +#Decision Tree Regression +from sklearn.tree import DecisionTreeRegressor +regr_1=DecisionTreeRegressor(max_depth=5) +regr_2=DecisionTreeRegressor(max_depth=7) +regr_3=DecisionTreeRegressor(max_depth=9) +regr_1.fit(X, Energies) +regr_2.fit(X, Energies) +regr_3.fit(X, Energies) + + +y_1 = regr_1.predict(X) +y_2 = regr_2.predict(X) +y_3=regr_3.predict(X) +Masses['Eapprox'] = y_3 +# Plot the results +plt.figure() +plt.plot(A, Energies, color="blue", label="Data", linewidth=2) +plt.plot(A, y_1, color="red", label="max_depth=5", linewidth=2) +plt.plot(A, y_2, color="green", label="max_depth=7", linewidth=2) +plt.plot(A, y_3, color="m", label="max_depth=9", linewidth=2) + +plt.xlabel("$A$") +plt.ylabel("$E$[MeV]") +plt.title("Decision Tree Regression") +plt.legend() +save_fig("Masses2016Trees") +plt.show() +print(Masses) +print(np.mean( (Energies-y_1)**2)) + +### And what about using neural networks? + +The **seaborn** package allows us to visualize data in an efficient way. Note that we use **scikit-learn**'s multi-layer perceptron (or feed forward neural network) +functionality. + +from sklearn.neural_network import MLPRegressor +from sklearn.metrics import accuracy_score +import seaborn as sns + +X_train = X +Y_train = Energies +n_hidden_neurons = 100 +epochs = 100 +# store models for later use +eta_vals = np.logspace(-5, 1, 7) +lmbd_vals = np.logspace(-5, 1, 7) +# store the models for later use +DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object) +train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals))) +sns.set() +for i, eta in enumerate(eta_vals): + for j, lmbd in enumerate(lmbd_vals): + dnn = MLPRegressor(hidden_layer_sizes=(n_hidden_neurons), activation='logistic', + alpha=lmbd, learning_rate_init=eta, max_iter=epochs) + dnn.fit(X_train, Y_train) + DNN_scikit[i][j] = dnn + train_accuracy[i][j] = dnn.score(X_train, Y_train) + +fig, ax = plt.subplots(figsize = (10, 10)) +sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis") +ax.set_title("Training Accuracy") +ax.set_ylabel("$\eta$") +ax.set_xlabel("$\lambda$") +plt.show() + +## A first summary + +The aim behind these introductory words was to present to you various +Python libraries and their functionalities, in particular libraries like +**numpy**, **pandas**, **xarray** and **matplotlib** and other that make our life much easier +in handling various data sets and visualizing data. + +Furthermore, +**Scikit-Learn** allows us with few lines of code to implement popular +Machine Learning algorithms for supervised learning. Later we will meet **Tensorflow**, a powerful library for deep learning. +Now it is time to dive more into the details of various methods. 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Released under CC Attribution-NonCommercial 4.0 license\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## Why Linear Regression (aka Ordinary Least Squares and family)\n", + "\n", + "Fitting a continuous function with linear parameterization in terms of the parameters $\\boldsymbol{\\beta}$.\n", + "* Method of choice for fitting a continuous function!\n", + "\n", + "* Gives an excellent introduction to central Machine Learning features with **understandable pedagogical** links to other methods like **Neural Networks**, **Support Vector Machines** etc\n", + "\n", + "* Analytical expression for the fitting parameters $\\boldsymbol{\\beta}$\n", + "\n", + "* Analytical expressions for statistical propertiers like mean values, variances, confidence intervals and more\n", + "\n", + "* Analytical relation with probabilistic interpretations \n", + "\n", + "* Easy to introduce basic concepts like bias-variance tradeoff, cross-validation, resampling and regularization techniques and many other ML topics\n", + "\n", + "* Easy to code! And links well with classification problems and logistic regression and neural networks\n", + "\n", + "* Allows for **easy** hands-on understanding of gradient descent methods\n", + "\n", + "* and many more features\n", + "\n", + "For more discussions of Ridge and Lasso regression, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended.\n", + "Similarly, [Mehta et al's article](https://arxiv.org/abs/1803.08823) is also recommended.\n", + "\n", + "\n", + "## Regression analysis, overarching aims\n", + "\n", + "Regression modeling deals with the description of the sampling distribution of a given random variable $y$ and how it varies as function of another variable or a set of such variables $\\boldsymbol{x} =[x_0, x_1,\\dots, x_{n-1}]^T$. \n", + "The first variable is called the **dependent**, the **outcome** or the **response** variable while the set of variables $\\boldsymbol{x}$ is called the independent variable, or the predictor variable or the explanatory variable. \n", + "\n", + "A regression model aims at finding a likelihood function $p(\\boldsymbol{y}\\vert \\boldsymbol{x})$, that is the conditional distribution for $\\boldsymbol{y}$ with a given $\\boldsymbol{x}$. The estimation of $p(\\boldsymbol{y}\\vert \\boldsymbol{x})$ is made using a data set with \n", + "* $n$ cases $i = 0, 1, 2, \\dots, n-1$ \n", + "\n", + "* Response (target, dependent or outcome) variable $y_i$ with $i = 0, 1, 2, \\dots, n-1$ \n", + "\n", + "* $p$ so-called explanatory (independent or predictor) variables $\\boldsymbol{x}_i=[x_{i0}, x_{i1}, \\dots, x_{ip-1}]$ with $i = 0, 1, 2, \\dots, n-1$ and explanatory variables running from $0$ to $p-1$. See below for more explicit examples. \n", + "\n", + " The goal of the regression analysis is to extract/exploit relationship between $\\boldsymbol{y}$ and $\\boldsymbol{x}$ in or to infer causal dependencies, approximations to the likelihood functions, functional relationships and to make predictions, making fits and many other things.\n", + "\n", + "\n", + "\n", + "## Regression analysis, overarching aims II\n", + "\n", + "\n", + "Consider an experiment in which $p$ characteristics of $n$ samples are\n", + "measured. The data from this experiment, for various explanatory variables $p$ are normally represented by a matrix \n", + "$\\mathbf{X}$.\n", + "\n", + "The matrix $\\mathbf{X}$ is called the *design\n", + "matrix*. Additional information of the samples is available in the\n", + "form of $\\boldsymbol{y}$ (also as above). The variable $\\boldsymbol{y}$ is\n", + "generally referred to as the *response variable*. The aim of\n", + "regression analysis is to explain $\\boldsymbol{y}$ in terms of\n", + "$\\boldsymbol{X}$ through a functional relationship like $y_i =\n", + "f(\\mathbf{X}_{i,\\ast})$. When no prior knowledge on the form of\n", + "$f(\\cdot)$ is available, it is common to assume a linear relationship\n", + "between $\\boldsymbol{X}$ and $\\boldsymbol{y}$. This assumption gives rise to\n", + "the *linear regression model* where $\\boldsymbol{\\beta} = [\\beta_0, \\ldots,\n", + "\\beta_{p-1}]^{T}$ are the *regression parameters*. \n", + "\n", + "Linear regression gives us a set of analytical equations for the parameters $\\beta_j$.\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## Examples\n", + "In order to understand the relation among the predictors $p$, the set of data $n$ and the target (outcome, output etc) $\\boldsymbol{y}$,\n", + "consider the model we discussed for describing nuclear binding energies. \n", + "\n", + "There we assumed that we could parametrize the data using a polynomial approximation based on the liquid drop model.\n", + "Assuming" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "BE(A) = a_0+a_1A+a_2A^{2/3}+a_3A^{-1/3}+a_4A^{-1},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we have five predictors, that is the intercept, the $A$ dependent term, the $A^{2/3}$ term and the $A^{-1/3}$ and $A^{-1}$ terms.\n", + "This gives $p=0,1,2,3,4$. Furthermore we have $n$ entries for each predictor. It means that our design matrix is a \n", + "$p\\times n$ matrix $\\boldsymbol{X}$.\n", + "\n", + "Here the predictors are based on a model we have made. A popular data set which is widely encountered in ML applications is the\n", + "so-called [credit card default data from Taiwan](https://www.sciencedirect.com/science/article/pii/S0957417407006719?via%3Dihub). The data set contains data on $n=30000$ credit card holders with predictors like gender, marital status, age, profession, education, etc. In total there are $24$ such predictors or attributes leading to a design matrix of dimensionality $24 \\times 30000$. This is however a classification problem and we will come back to it when we discuss Logistic Regression.\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## General linear models\n", + "Before we proceed let us study a case from linear algebra where we aim at fitting a set of data $\\boldsymbol{y}=[y_0,y_1,\\dots,y_{n-1}]$. We could think of these data as a result of an experiment or a complicated numerical experiment. These data are functions of a series of variables $\\boldsymbol{x}=[x_0,x_1,\\dots,x_{n-1}]$, that is $y_i = y(x_i)$ with $i=0,1,2,\\dots,n-1$. The variables $x_i$ could represent physical quantities like time, temperature, position etc. We assume that $y(x)$ is a smooth function. \n", + "\n", + "Since obtaining these data points may not be trivial, we want to use these data to fit a function which can allow us to make predictions for values of $y$ which are not in the present set. The perhaps simplest approach is to assume we can parametrize our function in terms of a polynomial of degree $n-1$ with $n$ points, that is" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "y=y(x) \\rightarrow y(x_i)=\\tilde{y}_i+\\epsilon_i=\\sum_{j=0}^{n-1} \\beta_j x_i^j+\\epsilon_i,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $\\epsilon_i$ is the error in our approximation.\n", + "\n", + "\n", + "\n", + "\n", + "## Rewriting the fitting procedure as a linear algebra problem\n", + "For every set of values $y_i,x_i$ we have thus the corresponding set of equations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*}\n", + "y_0&=\\beta_0+\\beta_1x_0^1+\\beta_2x_0^2+\\dots+\\beta_{n-1}x_0^{n-1}+\\epsilon_0\\\\\n", + "y_1&=\\beta_0+\\beta_1x_1^1+\\beta_2x_1^2+\\dots+\\beta_{n-1}x_1^{n-1}+\\epsilon_1\\\\\n", + "y_2&=\\beta_0+\\beta_1x_2^1+\\beta_2x_2^2+\\dots+\\beta_{n-1}x_2^{n-1}+\\epsilon_2\\\\\n", + "\\dots & \\dots \\\\\n", + "y_{n-1}&=\\beta_0+\\beta_1x_{n-1}^1+\\beta_2x_{n-1}^2+\\dots+\\beta_{n-1}x_{n-1}^{n-1}+\\epsilon_{n-1}.\\\\\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Rewriting the fitting procedure as a linear algebra problem, more details\n", + "Defining the vectors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{y} = [y_0,y_1, y_2,\\dots, y_{n-1}]^T,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\beta} = [\\beta_0,\\beta_1, \\beta_2,\\dots, \\beta_{n-1}]^T,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\epsilon} = [\\epsilon_0,\\epsilon_1, \\epsilon_2,\\dots, \\epsilon_{n-1}]^T,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and the design matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}=\n", + "\\begin{bmatrix} \n", + "1& x_{0}^1 &x_{0}^2& \\dots & \\dots &x_{0}^{n-1}\\\\\n", + "1& x_{1}^1 &x_{1}^2& \\dots & \\dots &x_{1}^{n-1}\\\\\n", + "1& x_{2}^1 &x_{2}^2& \\dots & \\dots &x_{2}^{n-1}\\\\ \n", + "\\dots& \\dots &\\dots& \\dots & \\dots &\\dots\\\\\n", + "1& x_{n-1}^1 &x_{n-1}^2& \\dots & \\dots &x_{n-1}^{n-1}\\\\\n", + "\\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we can rewrite our equations as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta}+\\boldsymbol{\\epsilon}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above design matrix is called a [Vandermonde matrix](https://en.wikipedia.org/wiki/Vandermonde_matrix).\n", + "\n", + "\n", + "\n", + "\n", + "## Generalizing the fitting procedure as a linear algebra problem\n", + "\n", + "We are obviously not limited to the above polynomial expansions. We\n", + "could replace the various powers of $x$ with elements of Fourier\n", + "series or instead of $x_i^j$ we could have $\\cos{(j x_i)}$ or $\\sin{(j\n", + "x_i)}$, or time series or other orthogonal functions. For every set\n", + "of values $y_i,x_i$ we can then generalize the equations to" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*}\n", + "y_0&=\\beta_0x_{00}+\\beta_1x_{01}+\\beta_2x_{02}+\\dots+\\beta_{n-1}x_{0n-1}+\\epsilon_0\\\\\n", + "y_1&=\\beta_0x_{10}+\\beta_1x_{11}+\\beta_2x_{12}+\\dots+\\beta_{n-1}x_{1n-1}+\\epsilon_1\\\\\n", + "y_2&=\\beta_0x_{20}+\\beta_1x_{21}+\\beta_2x_{22}+\\dots+\\beta_{n-1}x_{2n-1}+\\epsilon_2\\\\\n", + "\\dots & \\dots \\\\\n", + "y_{i}&=\\beta_0x_{i0}+\\beta_1x_{i1}+\\beta_2x_{i2}+\\dots+\\beta_{n-1}x_{in-1}+\\epsilon_i\\\\\n", + "\\dots & \\dots \\\\\n", + "y_{n-1}&=\\beta_0x_{n-1,0}+\\beta_1x_{n-1,2}+\\beta_2x_{n-1,2}+\\dots+\\beta_{n-1}x_{n-1,n-1}+\\epsilon_{n-1}.\\\\\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note that we have $p=n$ here. The matrix is symmetric. This is generally not the case!**\n", + "\n", + "\n", + "\n", + "\n", + "## Generalizing the fitting procedure as a linear algebra problem\n", + "We redefine in turn the matrix $\\boldsymbol{X}$ as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}=\n", + "\\begin{bmatrix} \n", + "x_{00}& x_{01} &x_{02}& \\dots & \\dots &x_{0,n-1}\\\\\n", + "x_{10}& x_{11} &x_{12}& \\dots & \\dots &x_{1,n-1}\\\\\n", + "x_{20}& x_{21} &x_{22}& \\dots & \\dots &x_{2,n-1}\\\\ \n", + "\\dots& \\dots &\\dots& \\dots & \\dots &\\dots\\\\\n", + "x_{n-1,0}& x_{n-1,1} &x_{n-1,2}& \\dots & \\dots &x_{n-1,n-1}\\\\\n", + "\\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and without loss of generality we rewrite again our equations as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta}+\\boldsymbol{\\epsilon}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The left-hand side of this equation is kwown. Our error vector $\\boldsymbol{\\epsilon}$ and the parameter vector $\\boldsymbol{\\beta}$ are our unknow quantities. How can we obtain the optimal set of $\\beta_i$ values?\n", + "\n", + "\n", + "\n", + "\n", + "## Optimizing our parameters\n", + "We have defined the matrix $\\boldsymbol{X}$ via the equations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*}\n", + "y_0&=\\beta_0x_{00}+\\beta_1x_{01}+\\beta_2x_{02}+\\dots+\\beta_{n-1}x_{0n-1}+\\epsilon_0\\\\\n", + "y_1&=\\beta_0x_{10}+\\beta_1x_{11}+\\beta_2x_{12}+\\dots+\\beta_{n-1}x_{1n-1}+\\epsilon_1\\\\\n", + "y_2&=\\beta_0x_{20}+\\beta_1x_{21}+\\beta_2x_{22}+\\dots+\\beta_{n-1}x_{2n-1}+\\epsilon_1\\\\\n", + "\\dots & \\dots \\\\\n", + "y_{i}&=\\beta_0x_{i0}+\\beta_1x_{i1}+\\beta_2x_{i2}+\\dots+\\beta_{n-1}x_{in-1}+\\epsilon_1\\\\\n", + "\\dots & \\dots \\\\\n", + "y_{n-1}&=\\beta_0x_{n-1,0}+\\beta_1x_{n-1,2}+\\beta_2x_{n-1,2}+\\dots+\\beta_{n-1}x_{n-1,n-1}+\\epsilon_{n-1}.\\\\\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we noted above, we stayed with a system with the design matrix \n", + " $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times n}$, that is we have $p=n$. For reasons to come later (algorithmic arguments) we will hereafter define \n", + "our matrix as $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$, with the predictors refering to the column numbers and the entries $n$ being the row elements.\n", + "\n", + "\n", + "\n", + "\n", + "## Our model for the nuclear binding energies\n", + "\n", + "In our [introductory notes](https://compphysics.github.io/MachineLearning/doc/pub/How2ReadData/html/How2ReadData.html) we looked at the so-called [liquid drop model](https://en.wikipedia.org/wiki/Semi-empirical_mass_formula). Let us remind ourselves about what we did by looking at the code.\n", + "\n", + "We restate the parts of the code we are most interested in." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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Coerce to float and drop these entries.\n", + "Masses['Ebinding'] = pd.to_numeric(Masses['Ebinding'], errors='coerce')\n", + "Masses = Masses.dropna()\n", + "# Convert from keV to MeV.\n", + "Masses['Ebinding'] /= 1000\n", + "\n", + "# Group the DataFrame by nucleon number, A.\n", + "Masses = Masses.groupby('A')\n", + "# Find the rows of the grouped DataFrame with the maximum binding energy.\n", + "Masses = Masses.apply(lambda t: t[t.Ebinding==t.Ebinding.max()])\n", + "A = Masses['A']\n", + "Z = Masses['Z']\n", + "N = Masses['N']\n", + "Element = Masses['Element']\n", + "Energies = Masses['Ebinding']\n", + "\n", + "# Now we set up the design matrix X\n", + "X = np.zeros((len(A),5))\n", + "X[:,0] = 1\n", + "X[:,1] = A\n", + "X[:,2] = A**(2.0/3.0)\n", + "X[:,3] = A**(-1.0/3.0)\n", + "X[:,4] = A**(-1.0)\n", + "# Then nice printout using pandas\n", + "DesignMatrix = pd.DataFrame(X)\n", + "DesignMatrix.index = A\n", + "DesignMatrix.columns = ['1', 'A', 'A^(2/3)', 'A^(-1/3)', '1/A']\n", + "display(DesignMatrix)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With $\\boldsymbol{\\beta}\\in {\\mathbb{R}}^{p\\times 1}$, it means that we will hereafter write our equations for the approximation as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\tilde{y}}= \\boldsymbol{X}\\boldsymbol{\\beta},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "throughout these lectures. \n", + "\n", + "\n", + "## Optimizing our parameters, more details\n", + "With the above we use the design matrix to define the approximation $\\boldsymbol{\\tilde{y}}$ via the unknown quantity $\\boldsymbol{\\beta}$ as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\tilde{y}}= \\boldsymbol{X}\\boldsymbol{\\beta},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and in order to find the optimal parameters $\\beta_i$ instead of solving the above linear algebra problem, we define a function which gives a measure of the spread between the values $y_i$ (which represent hopefully the exact values) and the parameterized values $\\tilde{y}_i$, namely" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "C(\\boldsymbol{\\beta})=\\frac{1}{n}\\sum_{i=0}^{n-1}\\left(y_i-\\tilde{y}_i\\right)^2=\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}}\\right)^T\\left(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}}\\right)\\right\\},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "or using the matrix $\\boldsymbol{X}$ and in a more compact matrix-vector notation as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "C(\\boldsymbol{\\beta})=\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)\\right\\}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This function is one possible way to define the so-called cost function.\n", + "\n", + "\n", + "\n", + "It is also common to define\n", + "the function $C$ as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "C(\\boldsymbol{\\beta})=\\frac{1}{2n}\\sum_{i=0}^{n-1}\\left(y_i-\\tilde{y}_i\\right)^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "since when taking the first derivative with respect to the unknown parameters $\\beta$, the factor of $2$ cancels out.\n", + "\n", + "\n", + "\n", + "\n", + "## Interpretations and optimizing our parameters\n", + "\n", + "The function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "C(\\boldsymbol{\\beta})=\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)\\right\\},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "can be linked to the variance of the quantity $y_i$ if we interpret the latter as the mean value. \n", + "When linking (see the discussion below) with the maximum likelihood approach below, we will indeed interpret $y_i$ as a mean value" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "y_{i}=\\langle y_i \\rangle = \\beta_0x_{i,0}+\\beta_1x_{i,1}+\\beta_2x_{i,2}+\\dots+\\beta_{n-1}x_{i,n-1}+\\epsilon_i,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $\\langle y_i \\rangle$ is the mean value. Keep in mind also that\n", + "till now we have treated $y_i$ as the exact value. Normally, the\n", + "response (dependent or outcome) variable $y_i$ the outcome of a\n", + "numerical experiment or another type of experiment and is thus only an\n", + "approximation to the true value. It is then always accompanied by an\n", + "error estimate, often limited to a statistical error estimate given by\n", + "the standard deviation discussed earlier. In the discussion here we\n", + "will treat $y_i$ as our exact value for the response variable.\n", + "\n", + "In order to find the parameters $\\beta_i$ we will then minimize the spread of $C(\\boldsymbol{\\beta})$, that is we are going to solve the problem" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n", + "{\\mathbb{R}}^{p}}}\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)\\right\\}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In practical terms it means we will require" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\partial C(\\boldsymbol{\\beta})}{\\partial \\beta_j} = \\frac{\\partial }{\\partial \\beta_j}\\left[ \\frac{1}{n}\\sum_{i=0}^{n-1}\\left(y_i-\\beta_0x_{i,0}-\\beta_1x_{i,1}-\\beta_2x_{i,2}-\\dots-\\beta_{n-1}x_{i,n-1}\\right)^2\\right]=0,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which results in" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\partial C(\\boldsymbol{\\beta})}{\\partial \\beta_j} = -\\frac{2}{n}\\left[ \\sum_{i=0}^{n-1}x_{ij}\\left(y_i-\\beta_0x_{i,0}-\\beta_1x_{i,1}-\\beta_2x_{i,2}-\\dots-\\beta_{n-1}x_{i,n-1}\\right)\\right]=0,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "or in a matrix-vector form as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\partial C(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = 0 = \\boldsymbol{X}^T\\left( \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Interpretations and optimizing our parameters\n", + "We can rewrite" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\partial C(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = 0 = \\boldsymbol{X}^T\\left( \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}^T\\boldsymbol{y} = \\boldsymbol{X}^T\\boldsymbol{X}\\boldsymbol{\\beta},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and if the matrix $\\boldsymbol{X}^T\\boldsymbol{X}$ is invertible we have the solution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\beta} =\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We note also that since our design matrix is defined as $\\boldsymbol{X}\\in\n", + "{\\mathbb{R}}^{n\\times p}$, the product $\\boldsymbol{X}^T\\boldsymbol{X} \\in\n", + "{\\mathbb{R}}^{p\\times p}$. In the above case we have that $p \\ll n$,\n", + "in our case $p=5$ meaning that we end up with inverting a small\n", + "$5\\times 5$ matrix. This is a rather common situation, in many cases we end up with low-dimensional\n", + "matrices to invert. The methods discussed here and for many other\n", + "supervised learning algorithms like classification with logistic\n", + "regression or support vector machines, exhibit dimensionalities which\n", + "allow for the usage of direct linear algebra methods such as **LU** decomposition or **Singular Value Decomposition** (SVD) for finding the inverse of the matrix\n", + "$\\boldsymbol{X}^T\\boldsymbol{X}$.\n", + "\n", + "\n", + "\n", + "**Small question**: Do you think the example we have at hand here (the nuclear binding energies) can lead to problems in inverting the matrix $\\boldsymbol{X}^T\\boldsymbol{X}$? What kind of problems can we expect?\n", + "\n", + "\n", + "\n", + "## Some useful matrix and vector expressions\n", + "\n", + "The following matrix and vector relation will be useful here and for the rest of the course. Vectors are always written as boldfaced lower case letters and \n", + "matrices as upper case boldfaced letters." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\n", + "6\n", + " \n", + "<\n", + "<\n", + "<\n", + "!\n", + "!\n", + "M\n", + "A\n", + "T\n", + "H\n", + "_\n", + "B\n", + "L\n", + "O\n", + "C\n", + "K" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\n", + "7\n", + " \n", + "<\n", + "<\n", + "<\n", + "!\n", + "!\n", + "M\n", + "A\n", + "T\n", + "H\n", + "_\n", + "B\n", + "L\n", + "O\n", + "C\n", + "K" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\n", + "8\n", + " \n", + "<\n", + "<\n", + "<\n", + "!\n", + "!\n", + "M\n", + "A\n", + "T\n", + "H\n", + "_\n", + "B\n", + "L\n", + "O\n", + "C\n", + "K" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\partial \\log{\\vert\\boldsymbol{A}\\vert}}{\\partial \\boldsymbol{A}} = (\\boldsymbol{A}^{-1})^T.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Interpretations and optimizing our parameters\n", + "The residuals $\\boldsymbol{\\epsilon}$ are in turn given by" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\epsilon} = \\boldsymbol{y}-\\boldsymbol{\\tilde{y}} = \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and with" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}^T\\left( \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)= 0,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we have" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}^T\\boldsymbol{\\epsilon}=\\boldsymbol{X}^T\\left( \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)= 0,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "meaning that the solution for $\\boldsymbol{\\beta}$ is the one which minimizes the residuals. Later we will link this with the maximum likelihood approach.\n", + "\n", + "\n", + "\n", + "\n", + "Let us now return to our nuclear binding energies and simply code the above equations. \n", + "\n", + "## Own code for Ordinary Least Squares\n", + "\n", + "It is rather straightforward to implement the matrix inversion and obtain the parameters $\\boldsymbol{\\beta}$. After having defined the matrix $\\boldsymbol{X}$ we simply need to \n", + "write" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# matrix inversion to find beta\n", + "beta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Energies)\n", + "# and then make the prediction\n", + "ytilde = X @ beta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, you can use the least squares functionality in **Numpy** as" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "fit = np.linalg.lstsq(X, Energies, rcond =None)[0]\n", + "ytildenp = np.dot(fit,X.T)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And finally we plot our fit with and compare with data" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/regression_70_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "Masses['Eapprox'] = ytilde\n", + "# Generate a plot comparing the experimental with the fitted values values.\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel(r'$A = N + Z$')\n", + "ax.set_ylabel(r'$E_\\mathrm{bind}\\,/\\mathrm{MeV}$')\n", + "ax.plot(Masses['A'], Masses['Ebinding'], alpha=0.7, lw=2,\n", + " label='Ame2016')\n", + "ax.plot(Masses['A'], Masses['Eapprox'], alpha=0.7, lw=2, c='m',\n", + " label='Fit')\n", + "ax.legend()\n", + "save_fig(\"Masses2016OLS\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Adding error analysis and training set up\n", + "\n", + "We can easily test our fit by computing the $R2$ score that we discussed in connection with the functionality of **Scikit-Learn** in the introductory slides.\n", + "Since we are not using **Scikit-Learn** here we can define our own $R2$ function as" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def R2(y_data, y_model):\n", + " return 1 - np.sum((y_data - y_model) ** 2) / np.sum((y_data - np.mean(y_data)) ** 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and we would be using it as" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.9547578478889096\n" + ] + } + ], + "source": [ + "print(R2(Energies,ytilde))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can easily add our **MSE** score as" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.03787596148305239\n" + ] + } + ], + "source": [ + "def MSE(y_data,y_model):\n", + " n = np.size(y_model)\n", + " return np.sum((y_data-y_model)**2)/n\n", + "\n", + "print(MSE(Energies,ytilde))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and finally the relative error as" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A \n", + "1 0 inf\n", + "2 1 1.123190\n", + "3 2 0.327631\n", + "4 6 0.344172\n", + "5 9 0.044402\n", + " ... \n", + "264 3304 0.009911\n", + "265 3310 0.009154\n", + "266 3317 0.007824\n", + "269 3338 0.011347\n", + "270 3344 0.009790\n", + "Name: Ebinding, Length: 267, dtype: float64\n" + ] + } + ], + "source": [ + "def RelativeError(y_data,y_model):\n", + " return abs((y_data-y_model)/y_data)\n", + "print(RelativeError(Energies, ytilde))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The $\\chi^2$ function\n", + "\n", + "Normally, the response (dependent or outcome) variable $y_i$ is the\n", + "outcome of a numerical experiment or another type of experiment and is\n", + "thus only an approximation to the true value. It is then always\n", + "accompanied by an error estimate, often limited to a statistical error\n", + "estimate given by the standard deviation discussed earlier. In the\n", + "discussion here we will treat $y_i$ as our exact value for the\n", + "response variable.\n", + "\n", + "Introducing the standard deviation $\\sigma_i$ for each measurement\n", + "$y_i$, we define now the $\\chi^2$ function (omitting the $1/n$ term)\n", + "as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\chi^2(\\boldsymbol{\\beta})=\\frac{1}{n}\\sum_{i=0}^{n-1}\\frac{\\left(y_i-\\tilde{y}_i\\right)^2}{\\sigma_i^2}=\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}}\\right)^T\\frac{1}{\\boldsymbol{\\Sigma^2}}\\left(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}}\\right)\\right\\},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where the matrix $\\boldsymbol{\\Sigma}$ is a diagonal matrix with $\\sigma_i$ as matrix elements.\n", + "\n", + "\n", + "\n", + "## The $\\chi^2$ function\n", + "\n", + "In order to find the parameters $\\beta_i$ we will then minimize the spread of $\\chi^2(\\boldsymbol{\\beta})$ by requiring" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\partial \\chi^2(\\boldsymbol{\\beta})}{\\partial \\beta_j} = \\frac{\\partial }{\\partial \\beta_j}\\left[ \\frac{1}{n}\\sum_{i=0}^{n-1}\\left(\\frac{y_i-\\beta_0x_{i,0}-\\beta_1x_{i,1}-\\beta_2x_{i,2}-\\dots-\\beta_{n-1}x_{i,n-1}}{\\sigma_i}\\right)^2\\right]=0,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which results in" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\partial \\chi^2(\\boldsymbol{\\beta})}{\\partial \\beta_j} = -\\frac{2}{n}\\left[ \\sum_{i=0}^{n-1}\\frac{x_{ij}}{\\sigma_i}\\left(\\frac{y_i-\\beta_0x_{i,0}-\\beta_1x_{i,1}-\\beta_2x_{i,2}-\\dots-\\beta_{n-1}x_{i,n-1}}{\\sigma_i}\\right)\\right]=0,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "or in a matrix-vector form as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\partial \\chi^2(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = 0 = \\boldsymbol{A}^T\\left( \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{\\beta}\\right).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where we have defined the matrix $\\boldsymbol{A} =\\boldsymbol{X}/\\boldsymbol{\\Sigma}$ with matrix elements $a_{ij} = x_{ij}/\\sigma_i$ and the vector $\\boldsymbol{b}$ with elements $b_i = y_i/\\sigma_i$.\n", + "\n", + "\n", + "\n", + "## The $\\chi^2$ function\n", + "\n", + "We can rewrite" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\partial \\chi^2(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = 0 = \\boldsymbol{A}^T\\left( \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{\\beta}\\right),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{A}^T\\boldsymbol{b} = \\boldsymbol{A}^T\\boldsymbol{A}\\boldsymbol{\\beta},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and if the matrix $\\boldsymbol{A}^T\\boldsymbol{A}$ is invertible we have the solution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\beta} =\\left(\\boldsymbol{A}^T\\boldsymbol{A}\\right)^{-1}\\boldsymbol{A}^T\\boldsymbol{b}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The $\\chi^2$ function\n", + "\n", + "If we then introduce the matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{H} = \\left(\\boldsymbol{A}^T\\boldsymbol{A}\\right)^{-1},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we have then the following expression for the parameters $\\beta_j$ (the matrix elements of $\\boldsymbol{H}$ are $h_{ij}$)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\beta_j = \\sum_{k=0}^{p-1}h_{jk}\\sum_{i=0}^{n-1}\\frac{y_i}{\\sigma_i}\\frac{x_{ik}}{\\sigma_i} = \\sum_{k=0}^{p-1}h_{jk}\\sum_{i=0}^{n-1}b_ia_{ik}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We state without proof the expression for the uncertainty in the parameters $\\beta_j$ as (we leave this as an exercise)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\sigma^2(\\beta_j) = \\sum_{i=0}^{n-1}\\sigma_i^2\\left( \\frac{\\partial \\beta_j}{\\partial y_i}\\right)^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "resulting in" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\sigma^2(\\beta_j) = \\left(\\sum_{k=0}^{p-1}h_{jk}\\sum_{i=0}^{n-1}a_{ik}\\right)\\left(\\sum_{l=0}^{p-1}h_{jl}\\sum_{m=0}^{n-1}a_{ml}\\right) = h_{jj}!\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The $\\chi^2$ function\n", + "The first step here is to approximate the function $y$ with a first-order polynomial, that is we write" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "y=y(x) \\rightarrow y(x_i) \\approx \\beta_0+\\beta_1 x_i.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By computing the derivatives of $\\chi^2$ with respect to $\\beta_0$ and $\\beta_1$ show that these are given by" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\partial \\chi^2(\\boldsymbol{\\beta})}{\\partial \\beta_0} = -2\\left[ \\frac{1}{n}\\sum_{i=0}^{n-1}\\left(\\frac{y_i-\\beta_0-\\beta_1x_{i}}{\\sigma_i^2}\\right)\\right]=0,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\partial \\chi^2(\\boldsymbol{\\beta})}{\\partial \\beta_1} = -\\frac{2}{n}\\left[ \\sum_{i=0}^{n-1}x_i\\left(\\frac{y_i-\\beta_0-\\beta_1x_{i}}{\\sigma_i^2}\\right)\\right]=0.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The $\\chi^2$ function\n", + "\n", + "For a linear fit (a first-order polynomial) we don't need to invert a matrix!! \n", + "Defining" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\gamma = \\sum_{i=0}^{n-1}\\frac{1}{\\sigma_i^2},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\gamma_x = \\sum_{i=0}^{n-1}\\frac{x_{i}}{\\sigma_i^2},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\gamma_y = \\sum_{i=0}^{n-1}\\left(\\frac{y_i}{\\sigma_i^2}\\right),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\gamma_{xx} = \\sum_{i=0}^{n-1}\\frac{x_ix_{i}}{\\sigma_i^2},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\gamma_{xy} = \\sum_{i=0}^{n-1}\\frac{y_ix_{i}}{\\sigma_i^2},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we obtain" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\beta_0 = \\frac{\\gamma_{xx}\\gamma_y-\\gamma_x\\gamma_y}{\\gamma\\gamma_{xx}-\\gamma_x^2},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\beta_1 = \\frac{\\gamma_{xy}\\gamma-\\gamma_x\\gamma_y}{\\gamma\\gamma_{xx}-\\gamma_x^2}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This approach (different linear and non-linear regression) suffers\n", + "often from both being underdetermined and overdetermined in the\n", + "unknown coefficients $\\beta_i$. A better approach is to use the\n", + "Singular Value Decomposition (SVD) method discussed below. Or using\n", + "Lasso and Ridge regression. See below.\n", + "\n", + "\n", + "\n", + "\n", + "## Fitting an Equation of State for Dense Nuclear Matter\n", + "\n", + "Before we continue, let us introduce yet another example. We are going to fit the\n", + "nuclear equation of state using results from many-body calculations.\n", + "The equation of state we have made available here, as function of\n", + "density, has been derived using modern nucleon-nucleon potentials with\n", + "[the addition of three-body\n", + "forces](https://www.sciencedirect.com/science/article/pii/S0370157399001106). This\n", + "time the file is presented as a standard **csv** file.\n", + "\n", + "The beginning of the Python code here is similar to what you have seen\n", + "before, with the same initializations and declarations. We use also\n", + "**pandas** again, rather extensively in order to organize our data.\n", + "\n", + "The difference now is that we use **Scikit-Learn's** regression tools\n", + "instead of our own matrix inversion implementation. Furthermore, we\n", + "sneak in **Ridge** regression (to be discussed below) which includes a\n", + "hyperparameter $\\lambda$, also to be explained below.\n", + "\n", + "## The code" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean squared error: 12.36\n", + "Variance score: 1.00\n", + "Mean absolute error: 2.83\n", + "[ 0. 618.32047562 -861.13519106 1404.91549644] -11.057088709963637\n", + "Mean squared error: 197.93\n", + "Variance score: 1.00\n", + "Mean absolute error: 11.69\n", + "[ 0. 28.18220995 282.79902342 842.30879705] 12.946893955206974\n" + ] + }, + { + "data": { + "image/png": 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    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/regression_117_1.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Common imports\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.pyplot as plt\n", + "import sklearn.linear_model as skl\n", + "from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error\n", + "\n", + "# Where to save the figures and data files\n", + "PROJECT_ROOT_DIR = \"Results\"\n", + "FIGURE_ID = \"Results/FigureFiles\"\n", + "DATA_ID = \"DataFiles/\"\n", + "\n", + "if not os.path.exists(PROJECT_ROOT_DIR):\n", + " os.mkdir(PROJECT_ROOT_DIR)\n", + "\n", + "if not os.path.exists(FIGURE_ID):\n", + " os.makedirs(FIGURE_ID)\n", + "\n", + "if not os.path.exists(DATA_ID):\n", + " os.makedirs(DATA_ID)\n", + "\n", + "def image_path(fig_id):\n", + " return os.path.join(FIGURE_ID, fig_id)\n", + "\n", + "def data_path(dat_id):\n", + " return os.path.join(DATA_ID, dat_id)\n", + "\n", + "def save_fig(fig_id):\n", + " plt.savefig(image_path(fig_id) + \".png\", format='png')\n", + "\n", + "infile = open(data_path(\"EoS.csv\"),'r')\n", + "\n", + "# Read the EoS data as csv file and organize the data into two arrays with density and energies\n", + "EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n", + "EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n", + "EoS = EoS.dropna()\n", + "Energies = EoS['Energy']\n", + "Density = EoS['Density']\n", + "# The design matrix now as function of various polytrops\n", + "X = np.zeros((len(Density),4))\n", + "X[:,3] = Density**(4.0/3.0)\n", + "X[:,2] = Density\n", + "X[:,1] = Density**(2.0/3.0)\n", + "X[:,0] = 1\n", + "\n", + "# We use now Scikit-Learn's linear regressor and ridge regressor\n", + "# OLS part\n", + "clf = skl.LinearRegression().fit(X, Energies)\n", + "ytilde = clf.predict(X)\n", + "EoS['Eols'] = ytilde\n", + "# The mean squared error \n", + "print(\"Mean squared error: %.2f\" % mean_squared_error(Energies, ytilde))\n", + "# Explained variance score: 1 is perfect prediction \n", + "print('Variance score: %.2f' % r2_score(Energies, ytilde))\n", + "# Mean absolute error \n", + "print('Mean absolute error: %.2f' % mean_absolute_error(Energies, ytilde))\n", + "print(clf.coef_, clf.intercept_)\n", + "\n", + "# The Ridge regression with a hyperparameter lambda = 0.1\n", + "_lambda = 0.1\n", + "clf_ridge = skl.Ridge(alpha=_lambda).fit(X, Energies)\n", + "yridge = clf_ridge.predict(X)\n", + "EoS['Eridge'] = yridge\n", + "# The mean squared error \n", + "print(\"Mean squared error: %.2f\" % mean_squared_error(Energies, yridge))\n", + "# Explained variance score: 1 is perfect prediction \n", + "print('Variance score: %.2f' % r2_score(Energies, yridge))\n", + "# Mean absolute error \n", + "print('Mean absolute error: %.2f' % mean_absolute_error(Energies, yridge))\n", + "print(clf_ridge.coef_, clf_ridge.intercept_)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel(r'$\\rho[\\mathrm{fm}^{-3}]$')\n", + "ax.set_ylabel(r'Energy per particle')\n", + "ax.plot(EoS['Density'], EoS['Energy'], alpha=0.7, lw=2,\n", + " label='Theoretical data')\n", + "ax.plot(EoS['Density'], EoS['Eols'], alpha=0.7, lw=2, c='m',\n", + " label='OLS')\n", + "ax.plot(EoS['Density'], EoS['Eridge'], alpha=0.7, lw=2, c='g',\n", + " label='Ridge $\\lambda = 0.1$')\n", + "ax.legend()\n", + "save_fig(\"EoSfitting\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above simple polynomial in density $\\rho$ gives an excellent fit\n", + "to the data. \n", + "\n", + "We note also that there is a small deviation between the\n", + "standard OLS and the Ridge regression at higher densities. We discuss this in more detail\n", + "below.\n", + "\n", + "\n", + "## Splitting our Data in Training and Test data\n", + "\n", + "It is normal in essentially all Machine Learning studies to split the\n", + "data in a training set and a test set (sometimes also an additional\n", + "validation set). **Scikit-Learn** has an own function for this. There\n", + "is no explicit recipe for how much data should be included as training\n", + "data and say test data. An accepted rule of thumb is to use\n", + "approximately $2/3$ to $4/5$ of the data as training data. We will\n", + "postpone a discussion of this splitting to the end of these notes and\n", + "our discussion of the so-called **bias-variance** tradeoff. Here we\n", + "limit ourselves to repeat the above equation of state fitting example\n", + "but now splitting the data into a training set and a test set." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Training R2\n", + "0.9999959552801078\n", + "Training MSE\n", + "1.399604246278012\n", + "Test R2\n", + "0.9998709070860495\n", + "Test MSE\n", + "108.66034829156496\n" + ] + } + ], + "source": [ + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.model_selection import train_test_split\n", + "# Where to save the figures and data files\n", + "PROJECT_ROOT_DIR = \"Results\"\n", + "FIGURE_ID = \"Results/FigureFiles\"\n", + "DATA_ID = \"DataFiles/\"\n", + "\n", + "if not os.path.exists(PROJECT_ROOT_DIR):\n", + " os.mkdir(PROJECT_ROOT_DIR)\n", + "\n", + "if not os.path.exists(FIGURE_ID):\n", + " os.makedirs(FIGURE_ID)\n", + "\n", + "if not os.path.exists(DATA_ID):\n", + " os.makedirs(DATA_ID)\n", + "\n", + "def image_path(fig_id):\n", + " return os.path.join(FIGURE_ID, fig_id)\n", + "\n", + "def data_path(dat_id):\n", + " return os.path.join(DATA_ID, dat_id)\n", + "\n", + "def save_fig(fig_id):\n", + " plt.savefig(image_path(fig_id) + \".png\", format='png')\n", + "\n", + "def R2(y_data, y_model):\n", + " return 1 - np.sum((y_data - y_model) ** 2) / np.sum((y_data - np.mean(y_data)) ** 2)\n", + "def MSE(y_data,y_model):\n", + " n = np.size(y_model)\n", + " return np.sum((y_data-y_model)**2)/n\n", + "\n", + "infile = open(data_path(\"EoS.csv\"),'r')\n", + "\n", + "# Read the EoS data as csv file and organized into two arrays with density and energies\n", + "EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n", + "EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n", + "EoS = EoS.dropna()\n", + "Energies = EoS['Energy']\n", + "Density = EoS['Density']\n", + "# The design matrix now as function of various polytrops\n", + "X = np.zeros((len(Density),5))\n", + "X[:,0] = 1\n", + "X[:,1] = Density**(2.0/3.0)\n", + "X[:,2] = Density\n", + "X[:,3] = Density**(4.0/3.0)\n", + "X[:,4] = Density**(5.0/3.0)\n", + "# We split the data in test and training data\n", + "X_train, X_test, y_train, y_test = train_test_split(X, Energies, test_size=0.2)\n", + "# matrix inversion to find beta\n", + "beta = np.linalg.inv(X_train.T.dot(X_train)).dot(X_train.T).dot(y_train)\n", + "# and then make the prediction\n", + "ytilde = X_train @ beta\n", + "print(\"Training R2\")\n", + "print(R2(y_train,ytilde))\n", + "print(\"Training MSE\")\n", + "print(MSE(y_train,ytilde))\n", + "ypredict = X_test @ beta\n", + "print(\"Test R2\")\n", + "print(R2(y_test,ypredict))\n", + "print(\"Test MSE\")\n", + "print(MSE(y_test,ypredict))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## The Boston housing data example\n", + "\n", + "The Boston housing \n", + "data set was originally a part of UCI Machine Learning Repository\n", + "and has been removed now. The data set is now included in **Scikit-Learn**'s \n", + "library. There are 506 samples and 13 feature (predictor) variables\n", + "in this data set. The objective is to predict the value of prices of\n", + "the house using the features (predictors) listed here.\n", + "\n", + "The features/predictors are\n", + "1. CRIM: Per capita crime rate by town\n", + "\n", + "2. ZN: Proportion of residential land zoned for lots over 25000 square feet\n", + "\n", + "3. INDUS: Proportion of non-retail business acres per town\n", + "\n", + "4. CHAS: Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n", + "\n", + "5. NOX: Nitric oxide concentration (parts per 10 million)\n", + "\n", + "6. RM: Average number of rooms per dwelling\n", + "\n", + "7. AGE: Proportion of owner-occupied units built prior to 1940\n", + "\n", + "8. DIS: Weighted distances to five Boston employment centers\n", + "\n", + "9. RAD: Index of accessibility to radial highways\n", + "\n", + "10. TAX: Full-value property tax rate per USD10000\n", + "\n", + "11. B: $1000(Bk - 0.63)^2$, where $Bk$ is the proportion of [people of African American descent] by town\n", + "\n", + "12. LSTAT: Percentage of lower status of the population\n", + "\n", + "13. MEDV: Median value of owner-occupied homes in USD 1000s\n", + "\n", + "## Housing data, the code\n", + "We start by importing the libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt \n", + "\n", + "import pandas as pd \n", + "import seaborn as sns" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and load the Boston Housing DataSet from **Scikit-Learn**" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename'])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.datasets import load_boston\n", + "\n", + "boston_dataset = load_boston()\n", + "\n", + "# boston_dataset is a dictionary\n", + "# let's check what it contains\n", + "boston_dataset.keys()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then we invoke Pandas" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "boston = pd.DataFrame(boston_dataset.data, columns=boston_dataset.feature_names)\n", + "boston.head()\n", + "boston['MEDV'] = boston_dataset.target" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and preprocess the data" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "CRIM 0\n", + "ZN 0\n", + "INDUS 0\n", + "CHAS 0\n", + "NOX 0\n", + "RM 0\n", + "AGE 0\n", + "DIS 0\n", + "RAD 0\n", + "TAX 0\n", + "PTRATIO 0\n", + "B 0\n", + "LSTAT 0\n", + "MEDV 0\n", + "dtype: int64" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# check for missing values in all the columns\n", + "boston.isnull().sum()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can then visualize the data" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/regression_129_0.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# set the size of the figure\n", + "sns.set(rc={'figure.figsize':(11.7,8.27)})\n", + "\n", + "# plot a histogram showing the distribution of the target values\n", + "sns.distplot(boston['MEDV'], bins=30)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is now useful to look at the correlation matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/regression_131_1.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# compute the pair wise correlation for all columns \n", + "correlation_matrix = boston.corr().round(2)\n", + "# use the heatmap function from seaborn to plot the correlation matrix\n", + "# annot = True to print the values inside the square\n", + "sns.heatmap(data=correlation_matrix, annot=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From the above coorelation plot we can see that **MEDV** is strongly correlated to **LSTAT** and **RM**. We see also that **RAD** and **TAX** are stronly correlated, but we don't include this in our features together to avoid multi-colinearity" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/regression_133_0.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(20, 5))\n", + "\n", + "features = ['LSTAT', 'RM']\n", + "target = boston['MEDV']\n", + "\n", + "for i, col in enumerate(features):\n", + " plt.subplot(1, len(features) , i+1)\n", + " x = boston[col]\n", + " y = target\n", + " plt.scatter(x, y, marker='o')\n", + " plt.title(col)\n", + " plt.xlabel(col)\n", + " plt.ylabel('MEDV')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we start training our model" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "X = pd.DataFrame(np.c_[boston['LSTAT'], boston['RM']], columns = ['LSTAT','RM'])\n", + "Y = boston['MEDV']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We split the data into training and test sets" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(404, 2)\n", + "(102, 2)\n", + "(404,)\n", + "(102,)\n" + ] + } + ], + "source": [ + "from sklearn.model_selection import train_test_split\n", + "\n", + "# splits the training and test data set in 80% : 20%\n", + "# assign random_state to any value.This ensures consistency.\n", + "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.2, random_state=5)\n", + "print(X_train.shape)\n", + "print(X_test.shape)\n", + "print(Y_train.shape)\n", + "print(Y_test.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then we use the linear regression functionality from **Scikit-Learn**" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The model performance for training set\n", + "--------------------------------------\n", + "RMSE is 5.6371293350711955\n", + "R2 score is 0.6300745149331701\n", + "\n", + "\n", + "The model performance for testing set\n", + "--------------------------------------\n", + "RMSE is 5.137400784702912\n", + "R2 score is 0.6628996975186952\n" + ] + } + ], + "source": [ + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.metrics import mean_squared_error, r2_score\n", + "\n", + "lin_model = LinearRegression()\n", + "lin_model.fit(X_train, Y_train)\n", + "\n", + "# model evaluation for training set\n", + "\n", + "y_train_predict = lin_model.predict(X_train)\n", + "rmse = (np.sqrt(mean_squared_error(Y_train, y_train_predict)))\n", + "r2 = r2_score(Y_train, y_train_predict)\n", + "\n", + "print(\"The model performance for training set\")\n", + "print(\"--------------------------------------\")\n", + "print('RMSE is {}'.format(rmse))\n", + "print('R2 score is {}'.format(r2))\n", + "print(\"\\n\")\n", + "\n", + "# model evaluation for testing set\n", + "\n", + "y_test_predict = lin_model.predict(X_test)\n", + "# root mean square error of the model\n", + "rmse = (np.sqrt(mean_squared_error(Y_test, y_test_predict)))\n", + "\n", + "# r-squared score of the model\n", + "r2 = r2_score(Y_test, y_test_predict)\n", + "\n", + "print(\"The model performance for testing set\")\n", + "print(\"--------------------------------------\")\n", + "print('RMSE is {}'.format(rmse))\n", + "print('R2 score is {}'.format(r2))" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/regression_140_0.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# plotting the y_test vs y_pred\n", + "# ideally should have been a straight line\n", + "plt.scatter(Y_test, y_test_predict)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reducing the number of degrees of freedom, overarching view\n", + "\n", + "Many Machine Learning problems involve thousands or even millions of\n", + "features for each training instance. Not only does this make training\n", + "extremely slow, it can also make it much harder to find a good\n", + "solution, as we will see. This problem is often referred to as the\n", + "curse of dimensionality. Fortunately, in real-world problems, it is\n", + "often possible to reduce the number of features considerably, turning\n", + "an intractable problem into a tractable one.\n", + "\n", + "Later we will discuss some of the most popular dimensionality reduction\n", + "techniques: the principal component analysis (PCA), Kernel PCA, and\n", + "Locally Linear Embedding (LLE). \n", + "\n", + "\n", + "Principal component analysis and its various variants deal with the\n", + "problem of fitting a low-dimensional [affine\n", + "subspace](https://en.wikipedia.org/wiki/Affine_space) to a set of of\n", + "data points in a high-dimensional space. With its family of methods it\n", + "is one of the most used tools in data modeling, compression and\n", + "visualization.\n", + "\n", + "\n", + "\n", + "\n", + "## Preprocessing our data\n", + "\n", + "Before we proceed however, we will discuss how to preprocess our\n", + "data. Till now and in connection with our previous examples we have\n", + "not met so many cases where we are too sensitive to the scaling of our\n", + "data. Normally the data may need a rescaling and/or may be sensitive\n", + "to extreme values. Scaling the data renders our inputs much more\n", + "suitable for the algorithms we want to employ.\n", + "\n", + "**Scikit-Learn** has several functions which allow us to rescale the\n", + "data, normally resulting in much better results in terms of various\n", + "accuracy scores. The **StandardScaler** function in **Scikit-Learn**\n", + "ensures that for each feature/predictor we study the mean value is\n", + "zero and the variance is one (every column in the design/feature\n", + "matrix). This scaling has the drawback that it does not ensure that\n", + "we have a particular maximum or minimum in our data set. Another\n", + "function included in **Scikit-Learn** is the **MinMaxScaler** which\n", + "ensures that all features are exactly between $0$ and $1$. The\n", + "\n", + "## More preprocessing\n", + "\n", + "\n", + "The **Normalizer** scales each data\n", + "point such that the feature vector has a euclidean length of one. In other words, it\n", + "projects a data point on the circle (or sphere in the case of higher dimensions) with a\n", + "radius of 1. This means every data point is scaled by a different number (by the\n", + "inverse of it’s length).\n", + "This normalization is often used when only the direction (or angle) of the data matters,\n", + "not the length of the feature vector.\n", + "\n", + "The **RobustScaler** works similarly to the StandardScaler in that it\n", + "ensures statistical properties for each feature that guarantee that\n", + "they are on the same scale. However, the RobustScaler uses the median\n", + "and quartiles, instead of mean and variance. This makes the\n", + "RobustScaler ignore data points that are very different from the rest\n", + "(like measurement errors). These odd data points are also called\n", + "outliers, and might often lead to trouble for other scaling\n", + "techniques.\n", + "\n", + "\n", + "\n", + "## Simple preprocessing examples, Franke function and regression" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MSE before scaling: 0.00\n", + "R2 score before scaling 0.99\n", + "Feature min values before scaling:\n", + " [1.00000000e+00 3.41860739e-03 3.03733002e-03 1.16868765e-05\n", + " 1.03834388e-05 9.22537365e-06 3.99528422e-08 3.54969007e-08\n", + " 3.15379305e-08 2.80205043e-08 1.36583081e-10 1.21349967e-10\n", + " 1.07815802e-10 9.57911031e-11 8.51075190e-11 4.66923931e-13\n", + " 4.14847893e-13 3.68579898e-13 3.27472173e-13 2.90949193e-13\n", + " 2.58499622e-13]\n", + "Feature max values before scaling:\n", + " [1. 0.99885903 0.99923003 0.99771937 0.99808994 0.99846064\n", + " 0.99658101 0.99695115 0.99732143 0.99769185 0.99544394 0.99581367\n", + " 0.99618353 0.99655352 0.99692366 0.99430818 0.99467748 0.99504691\n", + " 0.99541649 0.9957862 0.99615605]\n", + "Feature min values after scaling:\n", + " [ 0. -1.7254643 -1.67770844 -1.10618517 -1.1025354 -1.09809372\n", + " -0.86168855 -0.86697524 -0.87176225 -0.87600208 -0.72427577 -0.73199173\n", + " -0.7395003 -0.74676012 -0.75372886 -0.63410995 -0.64215466 -0.65016915\n", + " -0.65812548 -0.66599361 -0.67374146]\n", + "Feature max values after scaling:\n", + " [0. 1.83073388 1.70897028 2.39821909 2.29644339 2.19375534\n", + " 2.86764938 2.77826937 2.68697805 2.59393592 3.27571709 3.19719242\n", + " 3.11653264 3.03378065 2.94899889 3.64172054 3.57247381 3.50118655\n", + " 3.42784008 3.35242656 3.27495059]\n", + "MSE after scaling: 0.00\n", + "R2 score for scaled data: 0.99\n" + ] + } + ], + "source": [ + "# Common imports\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "import sklearn.linear_model as skl\n", + "from sklearn.metrics import mean_squared_error\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.preprocessing import MinMaxScaler, StandardScaler, Normalizer\n", + "\n", + "# Where to save the figures and data files\n", + "PROJECT_ROOT_DIR = \"Results\"\n", + "FIGURE_ID = \"Results/FigureFiles\"\n", + "DATA_ID = \"DataFiles/\"\n", + "\n", + "if not os.path.exists(PROJECT_ROOT_DIR):\n", + " os.mkdir(PROJECT_ROOT_DIR)\n", + "\n", + "if not os.path.exists(FIGURE_ID):\n", + " os.makedirs(FIGURE_ID)\n", + "\n", + "if not os.path.exists(DATA_ID):\n", + " os.makedirs(DATA_ID)\n", + "\n", + "def image_path(fig_id):\n", + " return os.path.join(FIGURE_ID, fig_id)\n", + "\n", + "def data_path(dat_id):\n", + " return os.path.join(DATA_ID, dat_id)\n", + "\n", + "def save_fig(fig_id):\n", + " plt.savefig(image_path(fig_id) + \".png\", format='png')\n", + "\n", + "\n", + "def FrankeFunction(x,y):\n", + "\tterm1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2))\n", + "\tterm2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1))\n", + "\tterm3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2))\n", + "\tterm4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2)\n", + "\treturn term1 + term2 + term3 + term4\n", + "\n", + "\n", + "def create_X(x, y, n ):\n", + "\tif len(x.shape) > 1:\n", + "\t\tx = np.ravel(x)\n", + "\t\ty = np.ravel(y)\n", + "\n", + "\tN = len(x)\n", + "\tl = int((n+1)*(n+2)/2)\t\t# Number of elements in beta\n", + "\tX = np.ones((N,l))\n", + "\n", + "\tfor i in range(1,n+1):\n", + "\t\tq = int((i)*(i+1)/2)\n", + "\t\tfor k in range(i+1):\n", + "\t\t\tX[:,q+k] = (x**(i-k))*(y**k)\n", + "\n", + "\treturn X\n", + "\n", + "\n", + "# Making meshgrid of datapoints and compute Franke's function\n", + "n = 5\n", + "N = 1000\n", + "x = np.sort(np.random.uniform(0, 1, N))\n", + "y = np.sort(np.random.uniform(0, 1, N))\n", + "z = FrankeFunction(x, y)\n", + "X = create_X(x, y, n=n) \n", + "# split in training and test data\n", + "X_train, X_test, y_train, y_test = train_test_split(X,z,test_size=0.2)\n", + "\n", + "\n", + "clf = skl.LinearRegression().fit(X_train, y_train)\n", + "\n", + "# The mean squared error and R2 score\n", + "print(\"MSE before scaling: {:.2f}\".format(mean_squared_error(clf.predict(X_test), y_test)))\n", + "print(\"R2 score before scaling {:.2f}\".format(clf.score(X_test,y_test)))\n", + "\n", + "scaler = StandardScaler()\n", + "scaler.fit(X_train)\n", + "X_train_scaled = scaler.transform(X_train)\n", + "X_test_scaled = scaler.transform(X_test)\n", + "\n", + "print(\"Feature min values before scaling:\\n {}\".format(X_train.min(axis=0)))\n", + "print(\"Feature max values before scaling:\\n {}\".format(X_train.max(axis=0)))\n", + "\n", + "print(\"Feature min values after scaling:\\n {}\".format(X_train_scaled.min(axis=0)))\n", + "print(\"Feature max values after scaling:\\n {}\".format(X_train_scaled.max(axis=0)))\n", + "\n", + "clf = skl.LinearRegression().fit(X_train_scaled, y_train)\n", + "\n", + "\n", + "print(\"MSE after scaling: {:.2f}\".format(mean_squared_error(clf.predict(X_test_scaled), y_test)))\n", + "print(\"R2 score for scaled data: {:.2f}\".format(clf.score(X_test_scaled,y_test)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The singular value decomposition\n", + "\n", + "\n", + "The examples we have looked at so far are cases where we normally can\n", + "invert the matrix $\\boldsymbol{X}^T\\boldsymbol{X}$. Using a polynomial expansion as we\n", + "did both for the masses and the fitting of the equation of state,\n", + "leads to row vectors of the design matrix which are essentially\n", + "orthogonal due to the polynomial character of our model. Obtaining the inverse of the design matrix is then often done via a so-called LU, QR or Cholesky decomposition. \n", + "\n", + "\n", + "\n", + "This may\n", + "however not the be case in general and a standard matrix inversion\n", + "algorithm based on say LU, QR or Cholesky decomposition may lead to singularities. We will see examples of this below.\n", + "\n", + "There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions. \n", + "\n", + "This is given by the **Singular Value Decomposition** algorithm, perhaps\n", + "the most powerful linear algebra algorithm. Let us look at a\n", + "different example where we may have problems with the standard matrix\n", + "inversion algorithm. Thereafter we dive into the math of the SVD.\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## Linear Regression Problems\n", + "\n", + "One of the typical problems we encounter with linear regression, in particular \n", + "when the matrix $\\boldsymbol{X}$ (our so-called design matrix) is high-dimensional, \n", + "are problems with near singular or singular matrices. The column vectors of $\\boldsymbol{X}$ \n", + "may be linearly dependent, normally referred to as super-collinearity. \n", + "This means that the matrix may be rank deficient and it is basically impossible to \n", + "to model the data using linear regression. As an example, consider the matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*}\n", + "\\mathbf{X} & = \\left[\n", + "\\begin{array}{rrr}\n", + "1 & -1 & 2\n", + "\\\\\n", + "1 & 0 & 1\n", + "\\\\\n", + "1 & 2 & -1\n", + "\\\\\n", + "1 & 1 & 0\n", + "\\end{array} \\right]\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The columns of $\\boldsymbol{X}$ are linearly dependent. We see this easily since the \n", + "the first column is the row-wise sum of the other two columns. The rank (more correct,\n", + "the column rank) of a matrix is the dimension of the space spanned by the\n", + "column vectors. Hence, the rank of $\\mathbf{X}$ is equal to the number\n", + "of linearly independent columns. In this particular case the matrix has rank 2.\n", + "\n", + "Super-collinearity of an $(n \\times p)$-dimensional design matrix $\\mathbf{X}$ implies\n", + "that the inverse of the matrix $\\boldsymbol{X}^T\\boldsymbol{X}$ (the matrix we need to invert to solve the linear regression equations) is non-invertible. If we have a square matrix that does not have an inverse, we say this matrix singular. The example here demonstrates this" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*}\n", + "\\boldsymbol{X} & = \\left[\n", + "\\begin{array}{rr}\n", + "1 & -1\n", + "\\\\\n", + "1 & -1\n", + "\\end{array} \\right].\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see easily that $\\mbox{det}(\\boldsymbol{X}) = x_{11} x_{22} - x_{12} x_{21} = 1 \\times (-1) - 1 \\times (-1) = 0$. Hence, $\\mathbf{X}$ is singular and its inverse is undefined.\n", + "This is equivalent to saying that the matrix $\\boldsymbol{X}$ has at least an eigenvalue which is zero.\n", + "\n", + "\n", + "## Fixing the singularity\n", + "\n", + "If our design matrix $\\boldsymbol{X}$ which enters the linear regression problem" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + "\\boldsymbol{\\beta} = (\\boldsymbol{X}^{T} \\boldsymbol{X})^{-1} \\boldsymbol{X}^{T} \\boldsymbol{y},\n", + "\\label{_auto1} \\tag{1}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "has linearly dependent column vectors, we will not be able to compute the inverse\n", + "of $\\boldsymbol{X}^T\\boldsymbol{X}$ and we cannot find the parameters (estimators) $\\beta_i$. \n", + "The estimators are only well-defined if $(\\boldsymbol{X}^{T}\\boldsymbol{X})^{-1}$ exits. \n", + "This is more likely to happen when the matrix $\\boldsymbol{X}$ is high-dimensional. In this case it is likely to encounter a situation where \n", + "the regression parameters $\\beta_i$ cannot be estimated.\n", + "\n", + "A cheap *ad hoc* approach is simply to add a small diagonal component to the matrix to invert, that is we change" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}^{T} \\boldsymbol{X} \\rightarrow \\boldsymbol{X}^{T} \\boldsymbol{X}+\\lambda \\boldsymbol{I},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $\\boldsymbol{I}$ is the identity matrix. When we discuss **Ridge** regression this is actually what we end up evaluating. The parameter $\\lambda$ is called a hyperparameter. More about this later. \n", + "\n", + "\n", + "\n", + "## Basic math of the SVD\n", + "\n", + "\n", + "From standard linear algebra we know that a square matrix $\\boldsymbol{X}$ can be diagonalized if and only it is \n", + "a so-called [normal matrix](https://en.wikipedia.org/wiki/Normal_matrix), that is if $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times n}$\n", + "we have $\\boldsymbol{X}\\boldsymbol{X}^T=\\boldsymbol{X}^T\\boldsymbol{X}$ or if $\\boldsymbol{X}\\in {\\mathbb{C}}^{n\\times n}$ we have $\\boldsymbol{X}\\boldsymbol{X}^{\\dagger}=\\boldsymbol{X}^{\\dagger}\\boldsymbol{X}$.\n", + "The matrix has then a set of eigenpairs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "(\\lambda_1,\\boldsymbol{u}_1),\\dots, (\\lambda_n,\\boldsymbol{u}_n),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and the eigenvalues are given by the diagonal matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\Sigma}=\\mathrm{Diag}(\\lambda_1, \\dots,\\lambda_n).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The matrix $\\boldsymbol{X}$ can be written in terms of an orthogonal/unitary transformation $\\boldsymbol{U}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X} = \\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "with $\\boldsymbol{U}\\boldsymbol{U}^T=\\boldsymbol{I}$ or $\\boldsymbol{U}\\boldsymbol{U}^{\\dagger}=\\boldsymbol{I}$.\n", + "\n", + "Not all square matrices are diagonalizable. A matrix like the one discussed above" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X} = \\begin{bmatrix} \n", + "1& -1 \\\\\n", + "1& -1\\\\\n", + "\\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "is not diagonalizable, it is a so-called [defective matrix](https://en.wikipedia.org/wiki/Defective_matrix). It is easy to see that the condition\n", + "$\\boldsymbol{X}\\boldsymbol{X}^T=\\boldsymbol{X}^T\\boldsymbol{X}$ is not fulfilled. \n", + "\n", + "\n", + "## The SVD, a Fantastic Algorithm\n", + "\n", + "\n", + "However, and this is the strength of the SVD algorithm, any general\n", + "matrix $\\boldsymbol{X}$ can be decomposed in terms of a diagonal matrix and\n", + "two orthogonal/unitary matrices. The [Singular Value Decompostion\n", + "(SVD) theorem](https://en.wikipedia.org/wiki/Singular_value_decomposition)\n", + "states that a general $m\\times n$ matrix $\\boldsymbol{X}$ can be written in\n", + "terms of a diagonal matrix $\\boldsymbol{\\Sigma}$ of dimensionality $m\\times n$\n", + "and two orthognal matrices $\\boldsymbol{U}$ and $\\boldsymbol{V}$, where the first has\n", + "dimensionality $m \\times m$ and the last dimensionality $n\\times n$.\n", + "We have then" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X} = \\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As an example, the above defective matrix can be decomposed as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X} = \\frac{1}{\\sqrt{2}}\\begin{bmatrix} 1& 1 \\\\ 1& -1\\\\ \\end{bmatrix} \\begin{bmatrix} 2& 0 \\\\ 0& 0\\\\ \\end{bmatrix} \\frac{1}{\\sqrt{2}}\\begin{bmatrix} 1& -1 \\\\ 1& 1\\\\ \\end{bmatrix}=\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "with eigenvalues $\\sigma_1=2$ and $\\sigma_2=0$. \n", + "The SVD exits always! \n", + "\n", + "The SVD\n", + "decomposition (singular values) gives eigenvalues \n", + "$\\sigma_i\\geq\\sigma_{i+1}$ for all $i$ and for dimensions larger than $i=p$, the\n", + "eigenvalues (singular values) are zero.\n", + "\n", + "In the general case, where our design matrix $\\boldsymbol{X}$ has dimension\n", + "$n\\times p$, the matrix is thus decomposed into an $n\\times n$\n", + "orthogonal matrix $\\boldsymbol{U}$, a $p\\times p$ orthogonal matrix $\\boldsymbol{V}$\n", + "and a diagonal matrix $\\boldsymbol{\\Sigma}$ with $r=\\mathrm{min}(n,p)$\n", + "singular values $\\sigma_i\\geq 0$ on the main diagonal and zeros filling\n", + "the rest of the matrix. There are at most $p$ singular values\n", + "assuming that $n > p$. In our regression examples for the nuclear\n", + "masses and the equation of state this is indeed the case, while for\n", + "the Ising model we have $p > n$. These are often cases that lead to\n", + "near singular or singular matrices.\n", + "\n", + "The columns of $\\boldsymbol{U}$ are called the left singular vectors while the columns of $\\boldsymbol{V}$ are the right singular vectors.\n", + "\n", + "## Economy-size SVD\n", + "\n", + "If we assume that $n > p$, then our matrix $\\boldsymbol{U}$ has dimension $n\n", + "\\times n$. The last $n-p$ columns of $\\boldsymbol{U}$ become however\n", + "irrelevant in our calculations since they are multiplied with the\n", + "zeros in $\\boldsymbol{\\Sigma}$.\n", + "\n", + "The economy-size decomposition removes extra rows or columns of zeros\n", + "from the diagonal matrix of singular values, $\\boldsymbol{\\Sigma}$, along with the columns\n", + "in either $\\boldsymbol{U}$ or $\\boldsymbol{V}$ that multiply those zeros in the expression. \n", + "Removing these zeros and columns can improve execution time\n", + "and reduce storage requirements without compromising the accuracy of\n", + "the decomposition.\n", + "\n", + "If $n > p$, we keep only the first $p$ columns of $\\boldsymbol{U}$ and $\\boldsymbol{\\Sigma}$ has dimension $p\\times p$. \n", + "If $p > n$, then only the first $n$ columns of $\\boldsymbol{V}$ are computed and $\\boldsymbol{\\Sigma}$ has dimension $n\\times n$.\n", + "The $n=p$ case is obvious, we retain the full SVD. \n", + "In general the economy-size SVD leads to less FLOPS and still conserving the desired accuracy.\n", + "\n", + "## Codes for the SVD" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1. -1. 2.]\n", + " [ 1. 0. 1.]\n", + " [ 1. 2. -1.]\n", + " [ 1. 1. 0.]]\n", + "[[ 4. 2. 2.]\n", + " [ 2. 6. -4.]\n", + " [ 2. -4. 6.]]\n", + "[[-9.57425734e-17 8.16496581e-01 -5.77350269e-01]\n", + " [-7.07106781e-01 4.08248290e-01 5.77350269e-01]\n", + " [ 7.07106781e-01 4.08248290e-01 5.77350269e-01]]\n", + "[1.00000000e+01 6.00000000e+00 9.10898112e-32]\n", + "[[ 3.33066907e-17 -7.07106781e-01 7.07106781e-01]\n", + " [ 8.16496581e-01 4.08248290e-01 4.08248290e-01]\n", + " [ 5.77350269e-01 -5.77350269e-01 -5.77350269e-01]]\n", + "[[-3.65939208e+30 3.65939208e+30 3.65939208e+30]\n", + " [ 3.65939208e+30 -3.65939208e+30 -3.65939208e+30]\n", + " [ 3.65939208e+30 -3.65939208e+30 -3.65939208e+30]]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "# SVD inversion\n", + "def SVDinv(A):\n", + " ''' Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD).\n", + " SVD is numerically more stable than the inversion algorithms provided by\n", + " numpy and scipy.linalg at the cost of being slower.\n", + " '''\n", + " U, s, VT = np.linalg.svd(A)\n", + "# print('test U')\n", + "# print( (np.transpose(U) @ U - U @np.transpose(U)))\n", + "# print('test VT')\n", + "# print( (np.transpose(VT) @ VT - VT @np.transpose(VT)))\n", + " print(U)\n", + " print(s)\n", + " print(VT)\n", + "\n", + " D = np.zeros((len(U),len(VT)))\n", + " for i in range(0,len(VT)):\n", + " D[i,i]=s[i]\n", + " UT = np.transpose(U); V = np.transpose(VT); invD = np.linalg.inv(D)\n", + " return np.matmul(V,np.matmul(invD,UT))\n", + "\n", + "\n", + "X = np.array([ [1.0, -1.0, 2.0], [1.0, 0.0, 1.0], [1.0, 2.0, -1.0], [1.0, 1.0, 0.0] ])\n", + "print(X)\n", + "A = np.transpose(X) @ X\n", + "print(A)\n", + "# Brute force inversion of super-collinear matrix\n", + "#B = np.linalg.inv(A)\n", + "#print(B)\n", + "C = SVDinv(A)\n", + "print(C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The matrix $\\boldsymbol{X}$ has columns that are linearly dependent. The first\n", + "column is the row-wise sum of the other two columns. The rank of a\n", + "matrix (the column rank) is the dimension of space spanned by the\n", + "column vectors. The rank of the matrix is the number of linearly\n", + "independent columns, in this case just $2$. We see this from the\n", + "singular values when running the above code. Running the standard\n", + "inversion algorithm for matrix inversion with $\\boldsymbol{X}^T\\boldsymbol{X}$ results\n", + "in the program terminating due to a singular matrix.\n", + "\n", + "\n", + "\n", + "## Mathematical Properties\n", + "\n", + "There are several interesting mathematical properties which will be\n", + "relevant when we are going to discuss the differences between say\n", + "ordinary least squares (OLS) and **Ridge** regression.\n", + "\n", + "We have from OLS that the parameters of the linear approximation are given by" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\tilde{y}} = \\boldsymbol{X}\\boldsymbol{\\beta} = \\boldsymbol{X}\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The matrix to invert can be rewritten in terms of our SVD decomposition as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}^T\\boldsymbol{X} = \\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{U}^T\\boldsymbol{U}\\boldsymbol{\\Sigma}\\boldsymbol{V}^T.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the orthogonality properties of $\\boldsymbol{U}$ we have" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}^T\\boldsymbol{X} = \\boldsymbol{V}\\boldsymbol{\\Sigma}^T\\boldsymbol{\\Sigma}\\boldsymbol{V}^T = \\boldsymbol{V}\\boldsymbol{D}\\boldsymbol{V}^T,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "with $\\boldsymbol{D}$ being a diagonal matrix with values along the diagonal given by the singular values squared. \n", + "\n", + "This means that" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "(\\boldsymbol{X}^T\\boldsymbol{X})\\boldsymbol{V} = \\boldsymbol{V}\\boldsymbol{D},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "that is the eigenvectors of $(\\boldsymbol{X}^T\\boldsymbol{X})$ are given by the columns of the right singular matrix of $\\boldsymbol{X}$ and the eigenvalues are the squared singular values. It is easy to show (show this) that" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "(\\boldsymbol{X}\\boldsymbol{X}^T)\\boldsymbol{U} = \\boldsymbol{U}\\boldsymbol{D},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "that is, the eigenvectors of $(\\boldsymbol{X}\\boldsymbol{X})^T$ are the columns of the left singular matrix and the eigenvalues are the same. \n", + "\n", + "Going back to our OLS equation we have" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}\\boldsymbol{\\beta} = \\boldsymbol{X}\\left(\\boldsymbol{V}\\boldsymbol{D}\\boldsymbol{V}^T \\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}=\\boldsymbol{U\\Sigma V^T}\\left(\\boldsymbol{V}\\boldsymbol{D}\\boldsymbol{V}^T \\right)^{-1}(\\boldsymbol{U\\Sigma V^T})^T\\boldsymbol{y}=\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will come back to this expression when we discuss Ridge regression. \n", + "\n", + "\n", + "## Ridge and LASSO Regression\n", + "\n", + "Let us remind ourselves about the expression for the standard Mean Squared Error (MSE) which we used to define our cost function and the equations for the ordinary least squares (OLS) method, that is \n", + "our optimization problem is" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in {\\mathbb{R}}^{p}}}\\frac{1}{n}\\left\\{\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right)\\right\\}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "or we can state it as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n", + "{\\mathbb{R}}^{p}}}\\frac{1}{n}\\sum_{i=0}^{n-1}\\left(y_i-\\tilde{y}_i\\right)^2=\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where we have used the definition of a norm-2 vector, that is" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\vert\\vert \\boldsymbol{x}\\vert\\vert_2 = \\sqrt{\\sum_i x_i^2}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By minimizing the above equation with respect to the parameters\n", + "$\\boldsymbol{\\beta}$ we could then obtain an analytical expression for the\n", + "parameters $\\boldsymbol{\\beta}$. We can add a regularization parameter $\\lambda$ by\n", + "defining a new cost function to be optimized, that is" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n", + "{\\mathbb{R}}^{p}}}\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2+\\lambda\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_2^2\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which leads to the Ridge regression minimization problem where we\n", + "require that $\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_2^2\\le t$, where $t$ is\n", + "a finite number larger than zero. By defining" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "C(\\boldsymbol{X},\\boldsymbol{\\beta})=\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2+\\lambda\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_1,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we have a new optimization equation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "{\\displaystyle \\min_{\\boldsymbol{\\beta}\\in\n", + "{\\mathbb{R}}^{p}}}\\frac{1}{n}\\vert\\vert \\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\vert\\vert_2^2+\\lambda\\vert\\vert \\boldsymbol{\\beta}\\vert\\vert_1\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which leads to Lasso regression. Lasso stands for least absolute shrinkage and selection operator. \n", + "\n", + "Here we have defined the norm-1 as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\vert\\vert \\boldsymbol{x}\\vert\\vert_1 = \\sum_i \\vert x_i\\vert.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More on Ridge Regression\n", + "\n", + "Using the matrix-vector expression for Ridge regression," + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "C(\\boldsymbol{X},\\boldsymbol{\\beta})=\\frac{1}{n}\\left\\{(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})^T(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\right\\}+\\lambda\\boldsymbol{\\beta}^T\\boldsymbol{\\beta},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "by taking the derivatives with respect to $\\boldsymbol{\\beta}$ we obtain then\n", + "a slightly modified matrix inversion problem which for finite values\n", + "of $\\lambda$ does not suffer from singularity problems. We obtain" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\beta}^{\\mathrm{Ridge}} = \\left(\\boldsymbol{X}^T\\boldsymbol{X}+\\lambda\\boldsymbol{I}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "with $\\boldsymbol{I}$ being a $p\\times p$ identity matrix with the constraint that" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\sum_{i=0}^{p-1} \\beta_i^2 \\leq t,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "with $t$ a finite positive number. \n", + "\n", + "We see that Ridge regression is nothing but the standard\n", + "OLS with a modified diagonal term added to $\\boldsymbol{X}^T\\boldsymbol{X}$. The\n", + "consequences, in particular for our discussion of the bias-variance tradeoff \n", + "are rather interesting.\n", + "\n", + "Furthermore, if we use the result above in terms of the SVD decomposition (our analysis was done for the OLS method), we had" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "(\\boldsymbol{X}\\boldsymbol{X}^T)\\boldsymbol{U} = \\boldsymbol{U}\\boldsymbol{D}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can analyse the OLS solutions in terms of the eigenvectors (the columns) of the right singular value matrix $\\boldsymbol{U}$ as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}\\boldsymbol{\\beta} = \\boldsymbol{X}\\left(\\boldsymbol{V}\\boldsymbol{D}\\boldsymbol{V}^T \\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}=\\boldsymbol{U\\Sigma V^T}\\left(\\boldsymbol{V}\\boldsymbol{D}\\boldsymbol{V}^T \\right)^{-1}(\\boldsymbol{U\\Sigma V^T})^T\\boldsymbol{y}=\\boldsymbol{U}\\boldsymbol{U}^T\\boldsymbol{y}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For Ridge regression this becomes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}\\boldsymbol{\\beta}^{\\mathrm{Ridge}} = \\boldsymbol{U\\Sigma V^T}\\left(\\boldsymbol{V}\\boldsymbol{D}\\boldsymbol{V}^T+\\lambda\\boldsymbol{I} \\right)^{-1}(\\boldsymbol{U\\Sigma V^T})^T\\boldsymbol{y}=\\sum_{j=0}^{p-1}\\boldsymbol{u}_j\\boldsymbol{u}_j^T\\frac{\\sigma_j^2}{\\sigma_j^2+\\lambda}\\boldsymbol{y},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "with the vectors $\\boldsymbol{u}_j$ being the columns of $\\boldsymbol{U}$. \n", + "\n", + "## Interpreting the Ridge results\n", + "\n", + "Since $\\lambda \\geq 0$, it means that compared to OLS, we have" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\frac{\\sigma_j^2}{\\sigma_j^2+\\lambda} \\leq 1.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ridge regression finds the coordinates of $\\boldsymbol{y}$ with respect to the\n", + "orthonormal basis $\\boldsymbol{U}$, it then shrinks the coordinates by\n", + "$\\frac{\\sigma_j^2}{\\sigma_j^2+\\lambda}$. Recall that the SVD has\n", + "eigenvalues ordered in a descending way, that is $\\sigma_i \\geq\n", + "\\sigma_{i+1}$.\n", + "\n", + "For small eigenvalues $\\sigma_i$ it means that their contributions become less important, a fact which can be used to reduce the number of degrees of freedom.\n", + "Actually, calculating the variance of $\\boldsymbol{X}\\boldsymbol{v}_j$ shows that this quantity is equal to $\\sigma_j^2/n$.\n", + "With a parameter $\\lambda$ we can thus shrink the role of specific parameters. \n", + "\n", + "\n", + "## More interpretations\n", + "\n", + "For the sake of simplicity, let us assume that the design matrix is orthonormal, that is" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}^T\\boldsymbol{X}=(\\boldsymbol{X}^T\\boldsymbol{X})^{-1} =\\boldsymbol{I}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this case the standard OLS results in" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\beta}^{\\mathrm{OLS}} = \\boldsymbol{X}^T\\boldsymbol{y}=\\sum_{i=0}^{p-1}\\boldsymbol{u}_j\\boldsymbol{u}_j^T\\boldsymbol{y},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\beta}^{\\mathrm{Ridge}} = \\left(\\boldsymbol{I}+\\lambda\\boldsymbol{I}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}=\\left(1+\\lambda\\right)^{-1}\\boldsymbol{\\beta}^{\\mathrm{OLS}},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "that is the Ridge estimator scales the OLS estimator by the inverse of a factor $1+\\lambda$, and\n", + "the Ridge estimator converges to zero when the hyperparameter goes to\n", + "infinity.\n", + "\n", + "We will come back to more interpreations after we have gone through some of the statistical analysis part. \n", + "\n", + "For more discussions of Ridge and Lasso regression, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended.\n", + "Similarly, [Mehta et al's article](https://arxiv.org/abs/1803.08823) is also recommended.\n", + "\n", + "\n", + "\n", + "## A better understanding of regularization\n", + "\n", + "The parameter $\\lambda$ that we have introduced in the Ridge (and\n", + "Lasso as well) regression is often called a regularization parameter\n", + "or shrinkage parameter. It is common to call it a hyperparameter. What does it mean mathemtically?\n", + "\n", + "Here we will first look at how to analyze the difference between the\n", + "standard OLS equations and the Ridge expressions in terms of a linear\n", + "algebra analysis using the SVD algorithm. Thereafter, we will link\n", + "(see the material on the bias-variance tradeoff below) these\n", + "observation to the statisical analysis of the results. In particular\n", + "we consider how the variance of the parameters $\\boldsymbol{\\beta}$ is\n", + "affected by changing the parameter $\\lambda$.\n", + "\n", + "## Decomposing the OLS and Ridge expressions\n", + "\n", + "We have our design matrix\n", + " $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$. With the SVD we decompose it as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X} = \\boldsymbol{U\\Sigma V^T},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "with $\\boldsymbol{U}\\in {\\mathbb{R}}^{n\\times n}$, $\\boldsymbol{\\Sigma}\\in {\\mathbb{R}}^{n\\times p}$\n", + "and $\\boldsymbol{V}\\in {\\mathbb{R}}^{p\\times p}$.\n", + "\n", + "The matrices $\\boldsymbol{U}$ and $\\boldsymbol{V}$ are unitary/orthonormal matrices, that is in case the matrices are real we have $\\boldsymbol{U}^T\\boldsymbol{U}=\\boldsymbol{U}\\boldsymbol{U}^T=\\boldsymbol{I}$ and $\\boldsymbol{V}^T\\boldsymbol{V}=\\boldsymbol{V}\\boldsymbol{V}^T=\\boldsymbol{I}$.\n", + "\n", + "\n", + "\n", + "## Introducing the Covariance and Correlation functions\n", + "\n", + "Before we discuss the link between for example Ridge regression and the singular value decomposition, we need to remind ourselves about\n", + "the definition of the covariance and the correlation function. These are quantities \n", + "\n", + "Suppose we have defined two vectors\n", + "$\\hat{x}$ and $\\hat{y}$ with $n$ elements each. The covariance matrix $\\boldsymbol{C}$ is defined as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{C}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{x}] & \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n", + " \\mathrm{cov}[\\boldsymbol{y},\\boldsymbol{x}] & \\mathrm{cov}[\\boldsymbol{y},\\boldsymbol{y}] \\\\\n", + " \\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where for example" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] =\\frac{1}{n} \\sum_{i=0}^{n-1}(x_i- \\overline{x})(y_i- \\overline{y}).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With this definition and recalling that the variance is defined as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathrm{var}[\\boldsymbol{x}]=\\frac{1}{n} \\sum_{i=0}^{n-1}(x_i- \\overline{x})^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we can rewrite the covariance matrix as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{C}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} \\mathrm{var}[\\boldsymbol{x}] & \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n", + " \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] & \\mathrm{var}[\\boldsymbol{y}] \\\\\n", + " \\end{bmatrix}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The covariance takes values between zero and infinity and may thus\n", + "lead to problems with loss of numerical precision for particularly\n", + "large values. It is common to scale the covariance matrix by\n", + "introducing instead the correlation matrix defined via the so-called\n", + "correlation function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}]=\\frac{\\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}]}{\\sqrt{\\mathrm{var}[\\boldsymbol{x}] \\mathrm{var}[\\boldsymbol{y}]}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The correlation function is then given by values $\\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}]\n", + "\\in [-1,1]$. This avoids eventual problems with too large values. We\n", + "can then define the correlation matrix for the two vectors $\\boldsymbol{x}$\n", + "and $\\boldsymbol{y}$ as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{K}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} 1 & \\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n", + " \\mathrm{corr}[\\boldsymbol{y},\\boldsymbol{x}] & 1 \\\\\n", + " \\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the above example this is the function we constructed using **pandas**.\n", + "\n", + "## Correlation Function and Design/Feature Matrix\n", + "\n", + "In our derivation of the various regression algorithms like **Ordinary Least Squares** or **Ridge regression**\n", + "we defined the design/feature matrix $\\boldsymbol{X}$ as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}=\\begin{bmatrix}\n", + "x_{0,0} & x_{0,1} & x_{0,2}& \\dots & \\dots x_{0,p-1}\\\\\n", + "x_{1,0} & x_{1,1} & x_{1,2}& \\dots & \\dots x_{1,p-1}\\\\\n", + "x_{2,0} & x_{2,1} & x_{2,2}& \\dots & \\dots x_{2,p-1}\\\\\n", + "\\dots & \\dots & \\dots & \\dots \\dots & \\dots \\\\\n", + "x_{n-2,0} & x_{n-2,1} & x_{n-2,2}& \\dots & \\dots x_{n-2,p-1}\\\\\n", + "x_{n-1,0} & x_{n-1,1} & x_{n-1,2}& \\dots & \\dots x_{n-1,p-1}\\\\\n", + "\\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "with $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$, with the predictors/features $p$ refering to the column numbers and the\n", + "entries $n$ being the row elements.\n", + "We can rewrite the design/feature matrix in terms of its column vectors as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}=\\begin{bmatrix} \\boldsymbol{x}_0 & \\boldsymbol{x}_1 & \\boldsymbol{x}_2 & \\dots & \\dots & \\boldsymbol{x}_{p-1}\\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "with a given vector" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{x}_i^T = \\begin{bmatrix}x_{0,i} & x_{1,i} & x_{2,i}& \\dots & \\dots x_{n-1,i}\\end{bmatrix}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With these definitions, we can now rewrite our $2\\times 2$\n", + "correaltion/covariance matrix in terms of a moe general design/feature\n", + "matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$. This leads to a $p\\times p$\n", + "covariance matrix for the vectors $\\boldsymbol{x}_i$ with $i=0,1,\\dots,p-1$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{C}[\\boldsymbol{x}] = \\begin{bmatrix}\n", + "\\mathrm{var}[\\boldsymbol{x}_0] & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_{p-1}]\\\\\n", + "\\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_0] & \\mathrm{var}[\\boldsymbol{x}_1] & \\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_{p-1}]\\\\\n", + "\\mathrm{cov}[\\boldsymbol{x}_2,\\boldsymbol{x}_0] & \\mathrm{cov}[\\boldsymbol{x}_2,\\boldsymbol{x}_1] & \\mathrm{var}[\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{cov}[\\boldsymbol{x}_2,\\boldsymbol{x}_{p-1}]\\\\\n", + "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n", + "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n", + "\\mathrm{cov}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_0] & \\mathrm{cov}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_1] & \\mathrm{cov}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_{2}] & \\dots & \\dots & \\mathrm{var}[\\boldsymbol{x}_{p-1}]\\\\\n", + "\\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and the correlation matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{K}[\\boldsymbol{x}] = \\begin{bmatrix}\n", + "1 & \\mathrm{corr}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] & \\mathrm{corr}[\\boldsymbol{x}_0,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{corr}[\\boldsymbol{x}_0,\\boldsymbol{x}_{p-1}]\\\\\n", + "\\mathrm{corr}[\\boldsymbol{x}_1,\\boldsymbol{x}_0] & 1 & \\mathrm{corr}[\\boldsymbol{x}_1,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{corr}[\\boldsymbol{x}_1,\\boldsymbol{x}_{p-1}]\\\\\n", + "\\mathrm{corr}[\\boldsymbol{x}_2,\\boldsymbol{x}_0] & \\mathrm{corr}[\\boldsymbol{x}_2,\\boldsymbol{x}_1] & 1 & \\dots & \\dots & \\mathrm{corr}[\\boldsymbol{x}_2,\\boldsymbol{x}_{p-1}]\\\\\n", + "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n", + "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n", + "\\mathrm{corr}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_0] & \\mathrm{corr}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_1] & \\mathrm{corr}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_{2}] & \\dots & \\dots & 1\\\\\n", + "\\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Covariance Matrix Examples\n", + "\n", + "\n", + "The Numpy function **np.cov** calculates the covariance elements using\n", + "the factor $1/(n-1)$ instead of $1/n$ since it assumes we do not have\n", + "the exact mean values. The following simple function uses the\n", + "**np.vstack** function which takes each vector of dimension $1\\times n$\n", + "and produces a $2\\times n$ matrix $\\boldsymbol{W}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{W} = \\begin{bmatrix} x_0 & y_0 \\\\\n", + " x_1 & y_1 \\\\\n", + " x_2 & y_2\\\\\n", + " \\dots & \\dots \\\\\n", + " x_{n-2} & y_{n-2}\\\\\n", + " x_{n-1} & y_{n-1} & \n", + " \\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which in turn is converted into into the $2\\times 2$ covariance matrix\n", + "$\\boldsymbol{C}$ via the Numpy function **np.cov()**. We note that we can also calculate\n", + "the mean value of each set of samples $\\boldsymbol{x}$ etc using the Numpy\n", + "function **np.mean(x)**. We can also extract the eigenvalues of the\n", + "covariance matrix through the **np.linalg.eig()** function." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.04140991370132292\n", + "4.133094065754784\n", + "[[0.83862682 2.46540728]\n", + " [2.46540728 8.112507 ]]\n" + ] + } + ], + "source": [ + "# Importing various packages\n", + "import numpy as np\n", + "n = 100\n", + "x = np.random.normal(size=n)\n", + "print(np.mean(x))\n", + "y = 4+3*x+np.random.normal(size=n)\n", + "print(np.mean(y))\n", + "W = np.vstack((x, y))\n", + "C = np.cov(W)\n", + "print(C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Correlation Matrix\n", + "\n", + "The previous example can be converted into the correlation matrix by\n", + "simply scaling the matrix elements with the variances. We should also\n", + "subtract the mean values for each column. This leads to the following\n", + "code which sets up the correlations matrix for the previous example in\n", + "a more brute force way. Here we scale the mean values for each column of the design matrix, calculate the relevant mean values and variances and then finally set up the $2\\times 2$ correlation matrix (since we have only two vectors)." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.07656990655277283\n", + "1.8665678444491798\n", + "[[1. 0.69108461]\n", + " [0.69108461 1. ]]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "n = 100\n", + "# define two vectors \n", + "x = np.random.random(size=n)\n", + "y = 4+3*x+np.random.normal(size=n)\n", + "#scaling the x and y vectors \n", + "x = x - np.mean(x)\n", + "y = y - np.mean(y)\n", + "variance_x = np.sum(x@x)/n\n", + "variance_y = np.sum(y@y)/n\n", + "print(variance_x)\n", + "print(variance_y)\n", + "cov_xy = np.sum(x@y)/n\n", + "cov_xx = np.sum(x@x)/n\n", + "cov_yy = np.sum(y@y)/n\n", + "C = np.zeros((2,2))\n", + "C[0,0]= cov_xx/variance_x\n", + "C[1,1]= cov_yy/variance_y\n", + "C[0,1]= cov_xy/np.sqrt(variance_y*variance_x)\n", + "C[1,0]= C[0,1]\n", + "print(C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that the matrix elements along the diagonal are one as they\n", + "should be and that the matrix is symmetric. Furthermore, diagonalizing\n", + "this matrix we easily see that it is a positive definite matrix.\n", + "\n", + "The above procedure with **numpy** can be made more compact if we use **pandas**.\n", + "\n", + "## Correlation Matrix with Pandas\n", + "\n", + "We whow here how we can set up the correlation matrix using **pandas**, as done in this simple code" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-0.64776602 -0.79292513]\n", + " [ 1.68156561 4.88768237]\n", + " [-1.08504058 -3.69264564]\n", + " [ 1.2289263 3.27086518]\n", + " [ 0.53948725 0.9271575 ]\n", + " [-1.49466842 -4.88750576]\n", + " [-0.61503889 -1.84939235]\n", + " [ 0.49561415 1.88023243]\n", + " [-0.07610463 -0.68642246]\n", + " [-0.02697476 0.94295385]]\n", + " 0 1\n", + "0 -0.647766 -0.792925\n", + "1 1.681566 4.887682\n", + "2 -1.085041 -3.692646\n", + "3 1.228926 3.270865\n", + "4 0.539487 0.927158\n", + "5 -1.494668 -4.887506\n", + "6 -0.615039 -1.849392\n", + "7 0.495614 1.880232\n", + "8 -0.076105 -0.686422\n", + "9 -0.026975 0.942954\n", + " 0 1\n", + "0 1.000000 0.976998\n", + "1 0.976998 1.000000\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "n = 10\n", + "x = np.random.normal(size=n)\n", + "x = x - np.mean(x)\n", + "y = 4+3*x+np.random.normal(size=n)\n", + "y = y - np.mean(y)\n", + "X = (np.vstack((x, y))).T\n", + "print(X)\n", + "Xpd = pd.DataFrame(X)\n", + "print(Xpd)\n", + "correlation_matrix = Xpd.corr()\n", + "print(correlation_matrix)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We expand this model to the Franke function discussed above.\n", + "\n", + "## Correlation Matrix with Pandas and the Franke function" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0 1 2 3 4 5 6 7 \\\n", + "0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 \n", + "1 0.0 0.078592 0.080857 0.080360 0.081589 0.082766 0.072541 0.073589 \n", + "2 0.0 0.080857 0.084290 0.081925 0.083646 0.085326 0.073569 0.074907 \n", + "3 0.0 0.080360 0.081925 0.086912 0.088010 0.089049 0.081480 0.082496 \n", + "4 0.0 0.081589 0.083646 0.088010 0.089395 0.090727 0.082323 0.083538 \n", + "5 0.0 0.082766 0.085326 0.089049 0.090727 0.092363 0.083106 0.084525 \n", + "6 0.0 0.072541 0.073569 0.081480 0.082323 0.083106 0.078559 0.079374 \n", + "7 0.0 0.073589 0.074907 0.082496 0.083538 0.084525 0.079374 0.080338 \n", + "8 0.0 0.074700 0.076320 0.083569 0.084817 0.086017 0.080230 0.081349 \n", + "9 0.0 0.075881 0.077815 0.084701 0.086164 0.087586 0.081130 0.082412 \n", + "10 0.0 0.064487 0.065152 0.074449 0.075044 0.075578 0.073336 0.073934 \n", + "11 0.0 0.065356 0.066219 0.075303 0.076047 0.076733 0.074023 0.074738 \n", + "12 0.0 0.066293 0.067363 0.076224 0.077122 0.077967 0.074765 0.075601 \n", + "13 0.0 0.067302 0.068589 0.077214 0.078273 0.079283 0.075564 0.076525 \n", + "14 0.0 0.068386 0.069900 0.078277 0.079503 0.080687 0.076421 0.077514 \n", + "\n", + " 8 9 10 11 12 13 14 \n", + "0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 \n", + "1 0.074700 0.075881 0.064487 0.065356 0.066293 0.067302 0.068386 \n", + "2 0.076320 0.077815 0.065152 0.066219 0.067363 0.068589 0.069900 \n", + "3 0.083569 0.084701 0.074449 0.075303 0.076224 0.077214 0.078277 \n", + "4 0.084817 0.086164 0.075044 0.076047 0.077122 0.078273 0.079503 \n", + "5 0.086017 0.087586 0.075578 0.076733 0.077967 0.079283 0.080687 \n", + "6 0.080230 0.081130 0.073336 0.074023 0.074765 0.075564 0.076421 \n", + "7 0.081349 0.082412 0.073934 0.074738 0.075601 0.076525 0.077514 \n", + "8 0.082522 0.083753 0.074560 0.075485 0.076474 0.077530 0.078656 \n", + "9 0.083753 0.085160 0.075217 0.076268 0.077388 0.078581 0.079851 \n", + "10 0.074560 0.075217 0.069627 0.070134 0.070683 0.071275 0.071913 \n", + "11 0.075485 0.076268 0.070134 0.070733 0.071378 0.072072 0.072814 \n", + "12 0.076474 0.077388 0.070683 0.071378 0.072124 0.072922 0.073775 \n", + "13 0.077530 0.078581 0.071275 0.072072 0.072922 0.073830 0.074797 \n", + "14 0.078656 0.079851 0.071913 0.072814 0.073775 0.074797 0.075884 \n" + ] + } + ], + "source": [ + "# Common imports\n", + "import numpy as np\n", + "import pandas as pd\n", + "\n", + "\n", + "def FrankeFunction(x,y):\n", + "\tterm1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2))\n", + "\tterm2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1))\n", + "\tterm3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2))\n", + "\tterm4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2)\n", + "\treturn term1 + term2 + term3 + term4\n", + "\n", + "\n", + "def create_X(x, y, n ):\n", + "\tif len(x.shape) > 1:\n", + "\t\tx = np.ravel(x)\n", + "\t\ty = np.ravel(y)\n", + "\n", + "\tN = len(x)\n", + "\tl = int((n+1)*(n+2)/2)\t\t# Number of elements in beta\n", + "\tX = np.ones((N,l))\n", + "\n", + "\tfor i in range(1,n+1):\n", + "\t\tq = int((i)*(i+1)/2)\n", + "\t\tfor k in range(i+1):\n", + "\t\t\tX[:,q+k] = (x**(i-k))*(y**k)\n", + "\n", + "\treturn X\n", + "\n", + "\n", + "# Making meshgrid of datapoints and compute Franke's function\n", + "n = 4\n", + "N = 100\n", + "x = np.sort(np.random.uniform(0, 1, N))\n", + "y = np.sort(np.random.uniform(0, 1, N))\n", + "z = FrankeFunction(x, y)\n", + "X = create_X(x, y, n=n) \n", + "\n", + "Xpd = pd.DataFrame(X)\n", + "# subtract the mean values and set up the covariance matrix\n", + "Xpd = Xpd - Xpd.mean()\n", + "covariance_matrix = Xpd.cov()\n", + "print(covariance_matrix)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We note here that the covariance is zero for the first rows and\n", + "columns since all matrix elements in the design matrix were set to one\n", + "(we are fitting the function in terms of a polynomial of degree $n$).\n", + "\n", + "This means that the variance for these elements will be zero and will\n", + "cause problems when we set up the correlation matrix. We can simply\n", + "drop these elements and construct a correlation\n", + "matrix without these elements. \n", + "\n", + "\n", + "## Rewriting the Covariance and/or Correlation Matrix\n", + "\n", + "We can rewrite the covariance matrix in a more compact form in terms of the design/feature matrix $\\boldsymbol{X}$ as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{C}[\\boldsymbol{x}] = \\frac{1}{n}\\boldsymbol{X}^T\\boldsymbol{X}= \\mathbb{E}[\\boldsymbol{X}^T\\boldsymbol{X}].\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To see this let us simply look at a design matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{2\\times 2}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}=\\begin{bmatrix}\n", + "x_{00} & x_{01}\\\\\n", + "x_{10} & x_{11}\\\\\n", + "\\end{bmatrix}=\\begin{bmatrix}\n", + "\\boldsymbol{x}_{0} & \\boldsymbol{x}_{1}\\\\\n", + "\\end{bmatrix}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we then compute the expectation value" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathbb{E}[\\boldsymbol{X}^T\\boldsymbol{X}] = \\frac{1}{n}\\boldsymbol{X}^T\\boldsymbol{X}=\\begin{bmatrix}\n", + "x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\\\\n", + "x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\\\\n", + "\\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which is just" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{C}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] = \\boldsymbol{C}[\\boldsymbol{x}]=\\begin{bmatrix} \\mathrm{var}[\\boldsymbol{x}_0] & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] \\\\\n", + " \\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_0] & \\mathrm{var}[\\boldsymbol{x}_1] \\\\\n", + " \\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where we wrote $$\\boldsymbol{C}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] = \\boldsymbol{C}[\\boldsymbol{x}]$$ to indicate that this the covariance of the vectors $\\boldsymbol{x}$ of the design/feature matrix $\\boldsymbol{X}$.\n", + "\n", + "It is easy to generalize this to a matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$.\n", + "\n", + "\n", + "## Linking with SVD\n", + "\n", + "See lecture september 11. More text to be added here soon.\n", + "\n", + "\n", + "\n", + "\n", + "## Where are we going?\n", + "\n", + "Before we proceed, we need to rethink what we have been doing. In our\n", + "eager to fit the data, we have omitted several important elements in\n", + "our regression analysis. In what follows we will\n", + "1. look at statistical properties, including a discussion of mean values, variance and the so-called bias-variance tradeoff\n", + "\n", + "2. introduce resampling techniques like cross-validation, bootstrapping and jackknife and more\n", + "\n", + "This will allow us to link the standard linear algebra methods we have discussed above to a statistical interpretation of the methods. \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## Resampling methods\n", + "Resampling methods are an indispensable tool in modern\n", + "statistics. They involve repeatedly drawing samples from a training\n", + "set and refitting a model of interest on each sample in order to\n", + "obtain additional information about the fitted model. For example, in\n", + "order to estimate the variability of a linear regression fit, we can\n", + "repeatedly draw different samples from the training data, fit a linear\n", + "regression to each new sample, and then examine the extent to which\n", + "the resulting fits differ. Such an approach may allow us to obtain\n", + "information that would not be available from fitting the model only\n", + "once using the original training sample.\n", + "\n", + "Two resampling methods are often used in Machine Learning analyses,\n", + "1. The **bootstrap method**\n", + "\n", + "2. and **Cross-Validation**\n", + "\n", + "In addition there are several other methods such as the Jackknife and the Blocking methods. We will discuss in particular\n", + "cross-validation and the bootstrap method.\n", + "\n", + "\n", + "\n", + "\n", + "## Resampling approaches can be computationally expensive\n", + "\n", + "Resampling approaches can be computationally expensive, because they\n", + "involve fitting the same statistical method multiple times using\n", + "different subsets of the training data. However, due to recent\n", + "advances in computing power, the computational requirements of\n", + "resampling methods generally are not prohibitive. In this chapter, we\n", + "discuss two of the most commonly used resampling methods,\n", + "cross-validation and the bootstrap. Both methods are important tools\n", + "in the practical application of many statistical learning\n", + "procedures. For example, cross-validation can be used to estimate the\n", + "test error associated with a given statistical learning method in\n", + "order to evaluate its performance, or to select the appropriate level\n", + "of flexibility. The process of evaluating a model’s performance is\n", + "known as model assessment, whereas the process of selecting the proper\n", + "level of flexibility for a model is known as model selection. The\n", + "bootstrap is widely used.\n", + "\n", + "\n", + "\n", + "## Why resampling methods ?\n", + "**Statistical analysis.**\n", + "\n", + "\n", + "* Our simulations can be treated as *computer experiments*. This is particularly the case for Monte Carlo methods\n", + "\n", + "* The results can be analysed with the same statistical tools as we would use analysing experimental data.\n", + "\n", + "* As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors.\n", + "\n", + " \n", + "\n", + "## Statistical analysis\n", + "\n", + "* As in other experiments, many numerical experiments have two classes of errors:\n", + "\n", + " * Statistical errors\n", + "\n", + " * Systematical errors\n", + "\n", + "\n", + "* Statistical errors can be estimated using standard tools from statistics\n", + "\n", + "* Systematical errors are method specific and must be treated differently from case to case.\n", + "\n", + " \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## Linking the regression analysis with a statistical interpretation\n", + "\n", + "\n", + "The\n", + "advantage of doing linear regression is that we actually end up with\n", + "analytical expressions for several statistical quantities. \n", + "Standard least squares and Ridge regression allow us to\n", + "derive quantities like the variance and other expectation values in a\n", + "rather straightforward way.\n", + "\n", + "\n", + "It is assumed that $\\varepsilon_i\n", + "\\sim \\mathcal{N}(0, \\sigma^2)$ and the $\\varepsilon_{i}$ are\n", + "independent, i.e.:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*} \n", + "\\mbox{Cov}(\\varepsilon_{i_1},\n", + "\\varepsilon_{i_2}) & = \\left\\{ \\begin{array}{lcc} \\sigma^2 & \\mbox{if}\n", + "& i_1 = i_2, \\\\ 0 & \\mbox{if} & i_1 \\not= i_2. \\end{array} \\right.\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The randomness of $\\varepsilon_i$ implies that\n", + "$\\mathbf{y}_i$ is also a random variable. In particular,\n", + "$\\mathbf{y}_i$ is normally distributed, because $\\varepsilon_i \\sim\n", + "\\mathcal{N}(0, \\sigma^2)$ and $\\mathbf{X}_{i,\\ast} \\, \\boldsymbol{\\beta}$ is a\n", + "non-random scalar. To specify the parameters of the distribution of\n", + "$\\mathbf{y}_i$ we need to calculate its first two moments. \n", + "\n", + "Recall that $\\boldsymbol{X}$ is a matrix of dimensionality $n\\times p$. The\n", + "notation above $\\mathbf{X}_{i,\\ast}$ means that we are looking at the\n", + "row number $i$ and perform a sum over all values $p$.\n", + "\n", + "\n", + "## Assumptions made\n", + "\n", + "The assumption we have made here can be summarized as (and this is going to be useful when we discuss the bias-variance trade off)\n", + "that there exists a function $f(\\boldsymbol{x})$ and a normal distributed error $\\boldsymbol{\\varepsilon}\\sim \\mathcal{N}(0, \\sigma^2)$\n", + "which describe our data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{y} = f(\\boldsymbol{x})+\\boldsymbol{\\varepsilon}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We approximate this function with our model from the solution of the linear regression equations, that is our\n", + "function $f$ is approximated by $\\boldsymbol{\\tilde{y}}$ where we want to minimize $(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2$, our MSE, with" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\tilde{y}} = \\boldsymbol{X}\\boldsymbol{\\beta}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Expectation value and variance\n", + "\n", + "We can calculate the expectation value of $\\boldsymbol{y}$ for a given element $i$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*} \n", + "\\mathbb{E}(y_i) & =\n", + "\\mathbb{E}(\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}) + \\mathbb{E}(\\varepsilon_i)\n", + "\\, \\, \\, = \\, \\, \\, \\mathbf{X}_{i, \\ast} \\, \\beta, \n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "while\n", + "its variance is" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*} \\mbox{Var}(y_i) & = \\mathbb{E} \\{ [y_i\n", + "- \\mathbb{E}(y_i)]^2 \\} \\, \\, \\, = \\, \\, \\, \\mathbb{E} ( y_i^2 ) -\n", + "[\\mathbb{E}(y_i)]^2 \\\\ & = \\mathbb{E} [ ( \\mathbf{X}_{i, \\ast} \\,\n", + "\\beta + \\varepsilon_i )^2] - ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 \\\\ &\n", + "= \\mathbb{E} [ ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 + 2 \\varepsilon_i\n", + "\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta} + \\varepsilon_i^2 ] - ( \\mathbf{X}_{i,\n", + "\\ast} \\, \\beta)^2 \\\\ & = ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 + 2\n", + "\\mathbb{E}(\\varepsilon_i) \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta} +\n", + "\\mathbb{E}(\\varepsilon_i^2 ) - ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 \n", + "\\\\ & = \\mathbb{E}(\\varepsilon_i^2 ) \\, \\, \\, = \\, \\, \\,\n", + "\\mbox{Var}(\\varepsilon_i) \\, \\, \\, = \\, \\, \\, \\sigma^2. \n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Hence, $y_i \\sim \\mathcal{N}( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}, \\sigma^2)$, that is $\\boldsymbol{y}$ follows a normal distribution with \n", + "mean value $\\boldsymbol{X}\\boldsymbol{\\beta}$ and variance $\\sigma^2$ (not be confused with the singular values of the SVD). \n", + "\n", + "## Expectation value and variance for $\\boldsymbol{\\beta}$\n", + "\n", + "With the OLS expressions for the parameters $\\boldsymbol{\\beta}$ we can evaluate the expectation value" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathbb{E}(\\boldsymbol{\\beta}) = \\mathbb{E}[ (\\mathbf{X}^{\\top} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbb{E}[ \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\mathbf{X}^{T}\\mathbf{X}\\boldsymbol{\\beta}=\\boldsymbol{\\beta}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This means that the estimator of the regression parameters is unbiased.\n", + "\n", + "We can also calculate the variance\n", + "\n", + "The variance of $\\boldsymbol{\\beta}$ is" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{eqnarray*}\n", + "\\mbox{Var}(\\boldsymbol{\\beta}) & = & \\mathbb{E} \\{ [\\boldsymbol{\\beta} - \\mathbb{E}(\\boldsymbol{\\beta})] [\\boldsymbol{\\beta} - \\mathbb{E}(\\boldsymbol{\\beta})]^{T} \\}\n", + "\\\\\n", + "& = & \\mathbb{E} \\{ [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} - \\boldsymbol{\\beta}] \\, [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} - \\boldsymbol{\\beta}]^{T} \\}\n", + "\\\\\n", + "% & = & \\mathbb{E} \\{ [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y}] \\, [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y}]^{T} \\} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n", + "% \\\\\n", + "% & = & \\mathbb{E} \\{ (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} \\, \\mathbf{Y}^{T} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n", + "% \\\\\n", + "& = & (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\, \\mathbb{E} \\{ \\mathbf{Y} \\, \\mathbf{Y}^{T} \\} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n", + "\\\\\n", + "& = & (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\, \\{ \\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} \\, \\mathbf{X}^{T} + \\sigma^2 \\} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n", + "% \\\\\n", + "% & = & (\\mathbf{X}^T \\mathbf{X})^{-1} \\, \\mathbf{X}^T \\, \\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^T \\, \\mathbf{X}^T \\, \\mathbf{X} \\, (\\mathbf{X}^T % \\mathbf{X})^{-1}\n", + "% \\\\\n", + "% & & + \\, \\, \\sigma^2 \\, (\\mathbf{X}^T \\mathbf{X})^{-1} \\, \\mathbf{X}^T \\, \\mathbf{X} \\, (\\mathbf{X}^T \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\boldsymbol{\\beta}^T\n", + "\\\\\n", + "& = & \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} + \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n", + "\\, \\, \\, = \\, \\, \\, \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1},\n", + "\\end{eqnarray*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where we have used that $\\mathbb{E} (\\mathbf{Y} \\mathbf{Y}^{T}) =\n", + "\\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} \\, \\mathbf{X}^{T} +\n", + "\\sigma^2 \\, \\mathbf{I}_{nn}$. From $\\mbox{Var}(\\boldsymbol{\\beta}) = \\sigma^2\n", + "\\, (\\mathbf{X}^{T} \\mathbf{X})^{-1}$, one obtains an estimate of the\n", + "variance of the estimate of the $j$-th regression coefficient:\n", + "$\\boldsymbol{\\sigma}^2 (\\boldsymbol{\\beta}_j ) = \\boldsymbol{\\sigma}^2 \\sqrt{\n", + "[(\\mathbf{X}^{T} \\mathbf{X})^{-1}]_{jj} }$. This may be used to\n", + "construct a confidence interval for the estimates.\n", + "\n", + "\n", + "In a similar way, we can obtain analytical expressions for say the\n", + "expectation values of the parameters $\\boldsymbol{\\beta}$ and their variance\n", + "when we employ Ridge regression, allowing us again to define a confidence interval. \n", + "\n", + "It is rather straightforward to show that" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big]=(\\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I}_{pp})^{-1} (\\mathbf{X}^{\\top} \\mathbf{X})\\boldsymbol{\\beta}^{\\mathrm{OLS}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see clearly that \n", + "$\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big] \\not= \\boldsymbol{\\beta}^{\\mathrm{OLS}}$ for any $\\lambda > 0$. We say then that the ridge estimator is biased.\n", + "\n", + "We can also compute the variance as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mbox{Var}[\\boldsymbol{\\beta}^{\\mathrm{Ridge}}]=\\sigma^2[ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1} \\mathbf{X}^{T} \\mathbf{X} \\{ [ \\mathbf{X}^{\\top} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and it is easy to see that if the parameter $\\lambda$ goes to infinity then the variance of Ridge parameters $\\boldsymbol{\\beta}$ goes to zero. \n", + "\n", + "With this, we can compute the difference" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mbox{Var}[\\boldsymbol{\\beta}^{\\mathrm{OLS}}]-\\mbox{Var}(\\boldsymbol{\\beta}^{\\mathrm{Ridge}})=\\sigma^2 [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}[ 2\\lambda\\mathbf{I} + \\lambda^2 (\\mathbf{X}^{T} \\mathbf{X})^{-1} ] \\{ [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The difference is non-negative definite since each component of the\n", + "matrix product is non-negative definite. \n", + "This means the variance we obtain with the standard OLS will always for $\\lambda > 0$ be larger than the variance of $\\boldsymbol{\\beta}$ obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below. \n", + "\n", + "\n", + "## Resampling methods\n", + "\n", + "With all these analytical equations for both the OLS and Ridge\n", + "regression, we will now outline how to assess a given model. This will\n", + "lead us to a discussion of the so-called bias-variance tradeoff (see\n", + "below) and so-called resampling methods.\n", + "\n", + "One of the quantities we have discussed as a way to measure errors is\n", + "the mean-squared error (MSE), mainly used for fitting of continuous\n", + "functions. Another choice is the absolute error.\n", + "\n", + "In the discussions below we will focus on the MSE and in particular since we will split the data into test and training data,\n", + "we discuss the\n", + "1. prediction error or simply the **test error** $\\mathrm{Err_{Test}}$, where we have a fixed training set and the test error is the MSE arising from the data reserved for testing. We discuss also the \n", + "\n", + "2. training error $\\mathrm{Err_{Train}}$, which is the average loss over the training data.\n", + "\n", + "As our model becomes more and more complex, more of the training data tends to used. The training may thence adapt to more complicated structures in the data. This may lead to a decrease in the bias (see below for code example) and a slight increase of the variance for the test error.\n", + "For a certain level of complexity the test error will reach minimum, before starting to increase again. The\n", + "training error reaches a saturation.\n", + "\n", + "\n", + "\n", + "\n", + "## Resampling methods: Jackknife and Bootstrap\n", + "\n", + "Two famous\n", + "resampling methods are the **independent bootstrap** and **the jackknife**. \n", + "\n", + "The jackknife is a special case of the independent bootstrap. Still, the jackknife was made\n", + "popular prior to the independent bootstrap. And as the popularity of\n", + "the independent bootstrap soared, new variants, such as **the dependent bootstrap**.\n", + "\n", + "The Jackknife and independent bootstrap work for\n", + "independent, identically distributed random variables.\n", + "If these conditions are not\n", + "satisfied, the methods will fail. Yet, it should be said that if the data are\n", + "independent, identically distributed, and we only want to estimate the\n", + "variance of $\\overline{X}$ (which often is the case), then there is no\n", + "need for bootstrapping. \n", + "\n", + "## Resampling methods: Jackknife\n", + "\n", + "The Jackknife works by making many replicas of the estimator $\\widehat{\\theta}$. \n", + "The jackknife is a resampling method where we systematically leave out one observation from the vector of observed values $\\boldsymbol{x} = (x_1,x_2,\\cdots,X_n)$. \n", + "Let $\\boldsymbol{x}_i$ denote the vector" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{x}_i = (x_1,x_2,\\cdots,x_{i-1},x_{i+1},\\cdots,x_n),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which equals the vector $\\boldsymbol{x}$ with the exception that observation\n", + "number $i$ is left out. Using this notation, define\n", + "$\\widehat{\\theta}_i$ to be the estimator\n", + "$\\widehat{\\theta}$ computed using $\\vec{X}_i$. \n", + "\n", + "\n", + "## Jackknife code example" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Runtime: 0.402381 sec\n", + "Jackknife Statistics :\n", + "original bias std. error\n", + " 99.8665 99.8565 0.150694\n" + ] + } + ], + "source": [ + "from numpy import *\n", + "from numpy.random import randint, randn\n", + "from time import time\n", + "\n", + "def jackknife(data, stat):\n", + " n = len(data);t = zeros(n); inds = arange(n); t0 = time()\n", + " ## 'jackknifing' by leaving out an observation for each i \n", + " for i in range(n):\n", + " t[i] = stat(delete(data,i) )\n", + "\n", + " # analysis \n", + " print(\"Runtime: %g sec\" % (time()-t0)); print(\"Jackknife Statistics :\")\n", + " print(\"original bias std. error\")\n", + " print(\"%8g %14g %15g\" % (stat(data),(n-1)*mean(t)/n, (n*var(t))**.5))\n", + "\n", + " return t\n", + "\n", + "\n", + "# Returns mean of data samples \n", + "def stat(data):\n", + " return mean(data)\n", + "\n", + "\n", + "mu, sigma = 100, 15\n", + "datapoints = 10000\n", + "x = mu + sigma*random.randn(datapoints)\n", + "# jackknife returns the data sample \n", + "t = jackknife(x, stat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Resampling methods: Bootstrap\n", + "Bootstrapping is a nonparametric approach to statistical inference\n", + "that substitutes computation for more traditional distributional\n", + "assumptions and asymptotic results. Bootstrapping offers a number of\n", + "advantages: \n", + "1. The bootstrap is quite general, although there are some cases in which it fails. \n", + "\n", + "2. Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small. \n", + "\n", + "3. It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically. \n", + "\n", + "4. It is relatively simple to apply the bootstrap to complex data-collection plans (such as stratified and clustered samples).\n", + "\n", + "\n", + "\n", + "\n", + "## Resampling methods: Bootstrap background\n", + "\n", + "Since $\\widehat{\\theta} = \\widehat{\\theta}(\\boldsymbol{X})$ is a function of random variables,\n", + "$\\widehat{\\theta}$ itself must be a random variable. Thus it has\n", + "a pdf, call this function $p(\\boldsymbol{t})$. The aim of the bootstrap is to\n", + "estimate $p(\\boldsymbol{t})$ by the relative frequency of\n", + "$\\widehat{\\theta}$. You can think of this as using a histogram\n", + "in the place of $p(\\boldsymbol{t})$. If the relative frequency closely\n", + "resembles $p(\\vec{t})$, then using numerics, it is straight forward to\n", + "estimate all the interesting parameters of $p(\\boldsymbol{t})$ using point\n", + "estimators. \n", + "\n", + "\n", + "## Resampling methods: More Bootstrap background\n", + "\n", + "In the case that $\\widehat{\\theta}$ has\n", + "more than one component, and the components are independent, we use the\n", + "same estimator on each component separately. If the probability\n", + "density function of $X_i$, $p(x)$, had been known, then it would have\n", + "been straight forward to do this by: \n", + "1. Drawing lots of numbers from $p(x)$, suppose we call one such set of numbers $(X_1^*, X_2^*, \\cdots, X_n^*)$. \n", + "\n", + "2. Then using these numbers, we could compute a replica of $\\widehat{\\theta}$ called $\\widehat{\\theta}^*$. \n", + "\n", + "By repeated use of (1) and (2), many\n", + "estimates of $\\widehat{\\theta}$ could have been obtained. The\n", + "idea is to use the relative frequency of $\\widehat{\\theta}^*$\n", + "(think of a histogram) as an estimate of $p(\\boldsymbol{t})$.\n", + "\n", + "## Resampling methods: Bootstrap approach\n", + "\n", + "But\n", + "unless there is enough information available about the process that\n", + "generated $X_1,X_2,\\cdots,X_n$, $p(x)$ is in general\n", + "unknown. Therefore, [Efron in 1979](https://projecteuclid.org/euclid.aos/1176344552) asked the\n", + "question: What if we replace $p(x)$ by the relative frequency\n", + "of the observation $X_i$; if we draw observations in accordance with\n", + "the relative frequency of the observations, will we obtain the same\n", + "result in some asymptotic sense? The answer is yes.\n", + "\n", + "\n", + "Instead of generating the histogram for the relative\n", + "frequency of the observation $X_i$, just draw the values\n", + "$(X_1^*,X_2^*,\\cdots,X_n^*)$ with replacement from the vector\n", + "$\\boldsymbol{X}$. \n", + "\n", + "## Resampling methods: Bootstrap steps\n", + "\n", + "The independent bootstrap works like this: \n", + "\n", + "1. Draw with replacement $n$ numbers for the observed variables $\\boldsymbol{x} = (x_1,x_2,\\cdots,x_n)$. \n", + "\n", + "2. Define a vector $\\boldsymbol{x}^*$ containing the values which were drawn from $\\boldsymbol{x}$. \n", + "\n", + "3. Using the vector $\\boldsymbol{x}^*$ compute $\\widehat{\\theta}^*$ by evaluating $\\widehat \\theta$ under the observations $\\boldsymbol{x}^*$. \n", + "\n", + "4. Repeat this process $k$ times. \n", + "\n", + "When you are done, you can draw a histogram of the relative frequency\n", + "of $\\widehat \\theta^*$. This is your estimate of the probability\n", + "distribution $p(t)$. Using this probability distribution you can\n", + "estimate any statistics thereof. In principle you never draw the\n", + "histogram of the relative frequency of $\\widehat{\\theta}^*$. Instead\n", + "you use the estimators corresponding to the statistic of interest. For\n", + "example, if you are interested in estimating the variance of $\\widehat\n", + "\\theta$, apply the etsimator $\\widehat \\sigma^2$ to the values\n", + "$\\widehat \\theta ^*$.\n", + "\n", + "\n", + "## Code example for the Bootstrap method\n", + "\n", + "The following code starts with a Gaussian distribution with mean value\n", + "$\\mu =100$ and variance $\\sigma=15$. We use this to generate the data\n", + "used in the bootstrap analysis. The bootstrap analysis returns a data\n", + "set after a given number of bootstrap operations (as many as we have\n", + "data points). This data set consists of estimated mean values for each\n", + "bootstrap operation. The histogram generated by the bootstrap method\n", + "shows that the distribution for these mean values is also a Gaussian,\n", + "centered around the mean value $\\mu=100$ but with standard deviation\n", + "$\\sigma/\\sqrt{n}$, where $n$ is the number of bootstrap samples (in\n", + "this case the same as the number of original data points). The value\n", + "of the standard deviation is what we expect from the central limit\n", + "theorem." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Runtime: 2.03903 sec\n", + "Bootstrap Statistics :\n", + "original bias std. error\n", + " 100.101 14.9209 100.102 0.149138\n" + ] + }, + { + "ename": "AttributeError", + "evalue": "'Rectangle' object has no property 'normed'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 29\u001b[0m \u001b[0mt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbootstrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstat\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mret\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/artist.py\u001b[0m in \u001b[0;36m_update_property\u001b[0;34m(self, k, v)\u001b[0m\n\u001b[1;32m 999\u001b[0m \u001b[0mfunc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'set_'\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1000\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcallable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1001\u001b[0;31m raise AttributeError('{!r} object has no property {!r}'\n\u001b[0m\u001b[1;32m 1002\u001b[0m .format(type(self).__name__, k))\n\u001b[1;32m 1003\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mAttributeError\u001b[0m: 'Rectangle' object has no property 'normed'" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/regression_278_2.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "from numpy import *\n", + "from numpy.random import randint, randn\n", + "from time import time\n", + "import matplotlib.mlab as mlab\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Returns mean of bootstrap samples \n", + "def stat(data):\n", + " return mean(data)\n", + "\n", + "# Bootstrap algorithm\n", + "def bootstrap(data, statistic, R):\n", + " t = zeros(R); n = len(data); inds = arange(n); t0 = time()\n", + " # non-parametric bootstrap \n", + " for i in range(R):\n", + " t[i] = statistic(data[randint(0,n,n)])\n", + "\n", + " # analysis \n", + " print(\"Runtime: %g sec\" % (time()-t0)); print(\"Bootstrap Statistics :\")\n", + " print(\"original bias std. error\")\n", + " print(\"%8g %8g %14g %15g\" % (statistic(data), std(data),mean(t),std(t)))\n", + " return t\n", + "\n", + "\n", + "mu, sigma = 100, 15\n", + "datapoints = 10000\n", + "x = mu + sigma*random.randn(datapoints)\n", + "# bootstrap returns the data sample \n", + "t = bootstrap(x, stat, datapoints)\n", + "# the histogram of the bootstrapped data \n", + "n, binsboot, patches = plt.hist(t, 50, normed=1, facecolor='red', alpha=0.75)\n", + "\n", + "# add a 'best fit' line \n", + "y = mlab.normpdf( binsboot, mean(t), std(t))\n", + "lt = plt.plot(binsboot, y, 'r--', linewidth=1)\n", + "plt.xlabel('Smarts')\n", + "plt.ylabel('Probability')\n", + "plt.axis([99.5, 100.6, 0, 3.0])\n", + "plt.grid(True)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Various steps in cross-validation\n", + "\n", + "When the repetitive splitting of the data set is done randomly,\n", + "samples may accidently end up in a fast majority of the splits in\n", + "either training or test set. Such samples may have an unbalanced\n", + "influence on either model building or prediction evaluation. To avoid\n", + "this $k$-fold cross-validation structures the data splitting. The\n", + "samples are divided into $k$ more or less equally sized exhaustive and\n", + "mutually exclusive subsets. In turn (at each split) one of these\n", + "subsets plays the role of the test set while the union of the\n", + "remaining subsets constitutes the training set. Such a splitting\n", + "warrants a balanced representation of each sample in both training and\n", + "test set over the splits. Still the division into the $k$ subsets\n", + "involves a degree of randomness. This may be fully excluded when\n", + "choosing $k=n$. This particular case is referred to as leave-one-out\n", + "cross-validation (LOOCV). \n", + "\n", + "\n", + "## How to set up the cross-validation for Ridge and/or Lasso\n", + "\n", + "* Define a range of interest for the penalty parameter.\n", + "\n", + "* Divide the data set into training and test set comprising samples $\\{1, \\ldots, n\\} \\setminus i$ and $\\{ i \\}$, respectively.\n", + "\n", + "* Fit the linear regression model by means of ridge estimation for each $\\lambda$ in the grid using the training set, and the corresponding estimate of the error variance $\\boldsymbol{\\sigma}_{-i}^2(\\lambda)$, as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*}\n", + "\\boldsymbol{\\beta}_{-i}(\\lambda) & = ( \\boldsymbol{X}_{-i, \\ast}^{T}\n", + "\\boldsymbol{X}_{-i, \\ast} + \\lambda \\boldsymbol{I}_{pp})^{-1}\n", + "\\boldsymbol{X}_{-i, \\ast}^{T} \\boldsymbol{y}_{-i}\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Evaluate the prediction performance of these models on the test set by $\\log\\{L[y_i, \\boldsymbol{X}_{i, \\ast}; \\boldsymbol{\\beta}_{-i}(\\lambda), \\boldsymbol{\\sigma}_{-i}^2(\\lambda)]\\}$. Or, by the prediction error $|y_i - \\boldsymbol{X}_{i, \\ast} \\boldsymbol{\\beta}_{-i}(\\lambda)|$, the relative error, the error squared or the R2 score function.\n", + "\n", + "* Repeat the first three steps such that each sample plays the role of the test set once.\n", + "\n", + "* Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*}\n", + "\\frac{1}{n} \\sum_{i = 1}^n \\log\\{L[y_i, \\mathbf{X}_{i, \\ast}; \\boldsymbol{\\beta}_{-i}(\\lambda), \\boldsymbol{\\sigma}_{-i}^2(\\lambda)]\\}.\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Cross-validation in brief\n", + "\n", + "For the various values of $k$\n", + "\n", + "1. shuffle the dataset randomly.\n", + "\n", + "2. Split the dataset into $k$ groups.\n", + "\n", + "3. For each unique group:\n", + "\n", + "a. Decide which group to use as set for test data\n", + "\n", + "b. Take the remaining groups as a training data set\n", + "\n", + "c. Fit a model on the training set and evaluate it on the test set\n", + "\n", + "d. Retain the evaluation score and discard the model\n", + "\n", + "\n", + "5. Summarize the model using the sample of model evaluation scores\n", + "\n", + "## Code Example for Cross-validation and $k$-fold Cross-validation\n", + "\n", + "The code here uses Ridge regression with cross-validation (CV) resampling and $k$-fold CV in order to fit a specific polynomial." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.model_selection import KFold\n", + "from sklearn.linear_model import Ridge\n", + "from sklearn.model_selection import cross_val_score\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "\n", + "# A seed just to ensure that the random numbers are the same for every run.\n", + "# Useful for eventual debugging.\n", + "np.random.seed(3155)\n", + "\n", + "# Generate the data.\n", + "nsamples = 100\n", + "x = np.random.randn(nsamples)\n", + "y = 3*x**2 + np.random.randn(nsamples)\n", + "\n", + "## Cross-validation on Ridge regression using KFold only\n", + "\n", + "# Decide degree on polynomial to fit\n", + "poly = PolynomialFeatures(degree = 6)\n", + "\n", + "# Decide which values of lambda to use\n", + "nlambdas = 500\n", + "lambdas = np.logspace(-3, 5, nlambdas)\n", + "\n", + "# Initialize a KFold instance\n", + "k = 5\n", + "kfold = KFold(n_splits = k)\n", + "\n", + "# Perform the cross-validation to estimate MSE\n", + "scores_KFold = np.zeros((nlambdas, k))\n", + "\n", + "i = 0\n", + "for lmb in lambdas:\n", + " ridge = Ridge(alpha = lmb)\n", + " j = 0\n", + " for train_inds, test_inds in kfold.split(x):\n", + " xtrain = x[train_inds]\n", + " ytrain = y[train_inds]\n", + "\n", + " xtest = x[test_inds]\n", + " ytest = y[test_inds]\n", + "\n", + " Xtrain = poly.fit_transform(xtrain[:, np.newaxis])\n", + " ridge.fit(Xtrain, ytrain[:, np.newaxis])\n", + "\n", + " Xtest = poly.fit_transform(xtest[:, np.newaxis])\n", + " ypred = ridge.predict(Xtest)\n", + "\n", + " scores_KFold[i,j] = np.sum((ypred - ytest[:, np.newaxis])**2)/np.size(ypred)\n", + "\n", + " j += 1\n", + " i += 1\n", + "\n", + "\n", + "estimated_mse_KFold = np.mean(scores_KFold, axis = 1)\n", + "\n", + "## Cross-validation using cross_val_score from sklearn along with KFold\n", + "\n", + "# kfold is an instance initialized above as:\n", + "# kfold = KFold(n_splits = k)\n", + "\n", + "estimated_mse_sklearn = np.zeros(nlambdas)\n", + "i = 0\n", + "for lmb in lambdas:\n", + " ridge = Ridge(alpha = lmb)\n", + "\n", + " X = poly.fit_transform(x[:, np.newaxis])\n", + " estimated_mse_folds = cross_val_score(ridge, X, y[:, np.newaxis], scoring='neg_mean_squared_error', cv=kfold)\n", + "\n", + " # cross_val_score return an array containing the estimated negative mse for every fold.\n", + " # we have to the the mean of every array in order to get an estimate of the mse of the model\n", + " estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds)\n", + "\n", + " i += 1\n", + "\n", + "## Plot and compare the slightly different ways to perform cross-validation\n", + "\n", + "plt.figure()\n", + "\n", + "plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score')\n", + "plt.plot(np.log10(lambdas), estimated_mse_KFold, 'r--', label = 'KFold')\n", + "\n", + "plt.xlabel('log10(lambda)')\n", + "plt.ylabel('mse')\n", + "\n", + "plt.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The bias-variance tradeoff\n", + "\n", + "\n", + "We will discuss the bias-variance tradeoff in the context of\n", + "continuous predictions such as regression. However, many of the\n", + "intuitions and ideas discussed here also carry over to classification\n", + "tasks. Consider a dataset $\\mathcal{L}$ consisting of the data\n", + "$\\mathbf{X}_\\mathcal{L}=\\{(y_j, \\boldsymbol{x}_j), j=0\\ldots n-1\\}$. \n", + "\n", + "Let us assume that the true data is generated from a noisy model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $\\epsilon$ is normally distributed with mean zero and standard deviation $\\sigma^2$.\n", + "\n", + "In our derivation of the ordinary least squares method we defined then\n", + "an approximation to the function $f$ in terms of the parameters\n", + "$\\boldsymbol{\\beta}$ and the design matrix $\\boldsymbol{X}$ which embody our model,\n", + "that is $\\boldsymbol{\\tilde{y}}=\\boldsymbol{X}\\boldsymbol{\\beta}$. \n", + "\n", + "Thereafter we found the parameters $\\boldsymbol{\\beta}$ by optimizing the means squared error via the so-called cost function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "C(\\boldsymbol{X},\\boldsymbol{\\beta}) =\\frac{1}{n}\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2=\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right].\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can rewrite this as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\frac{1}{n}\\sum_i(f_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\sigma^2.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The three terms represent the square of the bias of the learning\n", + "method, which can be thought of as the error caused by the simplifying\n", + "assumptions built into the method. The second term represents the\n", + "variance of the chosen model and finally the last terms is variance of\n", + "the error $\\boldsymbol{\\epsilon}$.\n", + "\n", + "To derive this equation, we need to recall that the variance of $\\boldsymbol{y}$ and $\\boldsymbol{\\epsilon}$ are both equal to $\\sigma^2$. The mean value of $\\boldsymbol{\\epsilon}$ is by definition equal to zero. Furthermore, the function $f$ is not a stochastics variable, idem for $\\boldsymbol{\\tilde{y}}$.\n", + "We use a more compact notation in terms of the expectation value" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}})^2\\right],\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and adding and subtracting $\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]$ we get" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}}+\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right],\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which, using the abovementioned expectation values can be rewritten as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right]+\\mathrm{Var}\\left[\\boldsymbol{\\tilde{y}}\\right]+\\sigma^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "that is the rewriting in terms of the so-called bias, the variance of the model $\\boldsymbol{\\tilde{y}}$ and the variance of $\\boldsymbol{\\epsilon}$.\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## Example code for Bias-Variance tradeoff" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.pipeline import make_pipeline\n", + "from sklearn.utils import resample\n", + "\n", + "np.random.seed(2018)\n", + "\n", + "n = 500\n", + "n_boostraps = 100\n", + "degree = 18 # A quite high value, just to show.\n", + "noise = 0.1\n", + "\n", + "# Make data set.\n", + "x = np.linspace(-1, 3, n).reshape(-1, 1)\n", + "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2) + np.random.normal(0, 0.1, x.shape)\n", + "\n", + "# Hold out some test data that is never used in training.\n", + "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n", + "\n", + "# Combine x transformation and model into one operation.\n", + "# Not neccesary, but convenient.\n", + "model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n", + "\n", + "# The following (m x n_bootstraps) matrix holds the column vectors y_pred\n", + "# for each bootstrap iteration.\n", + "y_pred = np.empty((y_test.shape[0], n_boostraps))\n", + "for i in range(n_boostraps):\n", + " x_, y_ = resample(x_train, y_train)\n", + "\n", + " # Evaluate the new model on the same test data each time.\n", + " y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n", + "\n", + "# Note: Expectations and variances taken w.r.t. different training\n", + "# data sets, hence the axis=1. Subsequent means are taken across the test data\n", + "# set in order to obtain a total value, but before this we have error/bias/variance\n", + "# calculated per data point in the test set.\n", + "# Note 2: The use of keepdims=True is important in the calculation of bias as this \n", + "# maintains the column vector form. Dropping this yields very unexpected results.\n", + "error = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n", + "bias = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n", + "variance = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n", + "print('Error:', error)\n", + "print('Bias^2:', bias)\n", + "print('Var:', variance)\n", + "print('{} >= {} + {} = {}'.format(error, bias, variance, bias+variance))\n", + "\n", + "plt.plot(x[::5, :], y[::5, :], label='f(x)')\n", + "plt.scatter(x_test, y_test, label='Data points')\n", + "plt.scatter(x_test, np.mean(y_pred, axis=1), label='Pred')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Understanding what happens" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Polynomial degree: 0\n", + "Error: 0.2937910450030775\n", + "Bias^2: 0.2929212799917661\n", + "Var: 0.0008697650113114119\n", + "0.2937910450030775 >= 0.2929212799917661 + 0.0008697650113114119 = 0.2937910450030775\n", + "Polynomial degree: 1\n", + "Error: 0.06894146856540674\n", + "Bias^2: 0.06832043024896824\n", + "Var: 0.0006210383164384989\n", + "0.06894146856540674 >= 0.06832043024896824 + 0.0006210383164384989 = 0.06894146856540674\n", + "Polynomial degree: 2\n", + "Error: 0.06106765054837855\n", + "Bias^2: 0.060547654220995305\n", + "Var: 0.0005199963273832372\n", + "0.06106765054837855 >= 0.060547654220995305 + 0.0005199963273832372 = 0.061067650548378545\n", + "Polynomial degree: 3\n", + "Error: 0.03346202229536659\n", + "Bias^2: 0.0331409564680546\n", + "Var: 0.00032106582731199456\n", + "0.03346202229536659 >= 0.0331409564680546 + 0.00032106582731199456 = 0.03346202229536659\n", + "Polynomial degree: 4\n", + "Error: 0.0335277871704832\n", + "Bias^2: 0.03311607538577367\n", + "Var: 0.0004117117847095335\n", + "0.0335277871704832 >= 0.03311607538577367 + 0.0004117117847095335 = 0.03352778717048321\n", + "Polynomial degree: 5\n", + "Error: 0.025517151530854786\n", + "Bias^2: 0.024968890209256463\n", + "Var: 0.0005482613215983259\n", + "0.025517151530854786 >= 0.024968890209256463 + 0.0005482613215983259 = 0.02551715153085479\n", + "Polynomial degree: 6\n", + "Error: 0.01994607606842793\n", + "Bias^2: 0.019502076889868637\n", + "Var: 0.00044399917855929527\n", + "0.01994607606842793 >= 0.019502076889868637 + 0.00044399917855929527 = 0.019946076068427934\n", + "Polynomial degree: 7\n", + "Error: 0.018695928655417676\n", + "Bias^2: 0.01797984009000237\n", + "Var: 0.0007160885654153078\n", + "0.018695928655417676 >= 0.01797984009000237 + 0.0007160885654153078 = 0.01869592865541768\n", + "Polynomial degree: 8\n", + "Error: 0.010736105188369479\n", + "Bias^2: 0.010376602508045063\n", + "Var: 0.00035950268032441344\n", + "0.010736105188369479 >= 0.010376602508045063 + 0.00035950268032441344 = 0.010736105188369477\n", + "Polynomial degree: 9\n", + "Error: 0.01101329065273084\n", + "Bias^2: 0.010539027867197629\n", + "Var: 0.0004742627855332104\n", + "0.01101329065273084 >= 0.010539027867197629 + 0.0004742627855332104 = 0.01101329065273084\n", + "Polynomial degree: 10\n", + "Error: 0.010972468815261078\n", + "Bias^2: 0.010593565969983903\n", + "Var: 0.00037890284527716995\n", + "0.010972468815261078 >= 0.010593565969983903 + 0.00037890284527716995 = 0.010972468815261073\n", + "Polynomial degree: 11\n", + "Error: 0.01084055593776807\n", + "Bias^2: 0.010348475861989281\n", + "Var: 0.0004920800757787882\n", + "0.01084055593776807 >= 0.010348475861989281 + 0.0004920800757787882 = 0.01084055593776807\n", + "Polynomial degree: 12\n", + "Error: 0.010192472149429362\n", + "Bias^2: 0.009610568640072627\n", + "Var: 0.0005819035093567355\n", + "0.010192472149429362 >= 0.009610568640072627 + 0.0005819035093567355 = 0.010192472149429362\n", + "Polynomial degree: 13\n", + "Error: 0.010312285920590011\n", + "Bias^2: 0.009802534263801815\n", + "Var: 0.0005097516567881938\n", + "0.010312285920590011 >= 0.009802534263801815 + 0.0005097516567881938 = 0.01031228592059001\n", + "Polynomial degree: 14\n", + "Error: 0.010722455299595876\n", + "Bias^2: 0.01008891676024437\n", + "Var: 0.0006335385393515036\n", + "0.010722455299595876 >= 0.01008891676024437 + 0.0006335385393515036 = 0.010722455299595875\n", + "Polynomial degree: 15\n", + "Error: 0.011155437503231998\n", + "Bias^2: 0.010311761228670724\n", + "Var: 0.0008436762745612778\n", + "0.011155437503231998 >= 0.010311761228670724 + 0.0008436762745612778 = 0.011155437503232002\n", + "Polynomial degree: 16\n", + "Error: 0.011028026782676708\n", + "Bias^2: 0.010223572382311492\n", + "Var: 0.0008044544003652116\n", + "0.011028026782676708 >= 0.010223572382311492 + 0.0008044544003652116 = 0.011028026782676703\n", + "Polynomial degree: 17\n", + "Error: 0.011628743129658555\n", + "Bias^2: 0.010533948734129592\n", + "Var: 0.001094794395528961\n", + "0.011628743129658555 >= 0.010533948734129592 + 0.001094794395528961 = 0.011628743129658553\n", + "Polynomial degree: 18\n", + "Error: 0.014371682171531027\n", + "Bias^2: 0.010922362242870073\n", + "Var: 0.0034493199286609573\n", + "0.014371682171531027 >= 0.010922362242870073 + 0.0034493199286609573 = 0.01437168217153103\n", + "Polynomial degree: 19\n", + "Error: 0.026986306199342624\n", + "Bias^2: 0.01214176442858653\n", + "Var: 0.014844541770756087\n", + "0.026986306199342624 >= 0.01214176442858653 + 0.014844541770756087 = 0.026986306199342617\n", + "Polynomial degree: 20\n", + "Error: 0.012249244024160728\n", + "Bias^2: 0.01006785246285396\n", + "Var: 0.002181391561306766\n", + "0.012249244024160728 >= 0.01006785246285396 + 0.002181391561306766 = 0.012249244024160727\n", + "Polynomial degree: 21\n", + "Error: 0.014973172820830053\n", + "Bias^2: 0.010154371176360328\n", + "Var: 0.00481880164446972\n", + "0.014973172820830053 >= 0.010154371176360328 + 0.00481880164446972 = 0.014973172820830048\n", + "Polynomial degree: 22\n", + "Error: 0.014186606932681737\n", + "Bias^2: 0.009594131981212376\n", + "Var: 0.0045924749514693625\n", + "0.014186606932681737 >= 0.009594131981212376 + 0.0045924749514693625 = 0.014186606932681738\n", + "Polynomial degree: 23\n", + "Error: 0.025574552577788824\n", + "Bias^2: 0.009477519033249752\n", + "Var: 0.016097033544539077\n", + "0.025574552577788824 >= 0.009477519033249752 + 0.016097033544539077 = 0.02557455257778883\n", + "Polynomial degree: 24\n", + "Error: 0.03147298632679604\n", + "Bias^2: 0.009565267585507206\n", + "Var: 0.021907718741288846\n", + "0.03147298632679604 >= 0.009565267585507206 + 0.021907718741288846 = 0.03147298632679605\n", + "Polynomial degree: 25\n", + "Error: 0.03929027799369515\n", + "Bias^2: 0.009776269005896726\n", + "Var: 0.029514008987798424\n", + "0.03929027799369515 >= 0.009776269005896726 + 0.029514008987798424 = 0.03929027799369515\n", + "Polynomial degree: 26\n", + "Error: 0.15813256009613183\n", + "Bias^2: 0.013239726753028333\n", + "Var: 0.14489283334310352\n", + "0.15813256009613183 >= 0.013239726753028333 + 0.14489283334310352 = 0.15813256009613186\n", + "Polynomial degree: 27\n", + "Error: 0.1360840943498259\n", + "Bias^2: 0.01326608592145169\n", + "Var: 0.12281800842837416\n", + "0.1360840943498259 >= 0.01326608592145169 + 0.12281800842837416 = 0.13608409434982585\n", + "Polynomial degree: 28\n", + "Error: 0.7210723692205014\n", + "Bias^2: 0.04436186918146108\n", + "Var: 0.6767105000390408\n", + "0.7210723692205014 >= 0.04436186918146108 + 0.6767105000390408 = 0.7210723692205019\n", + "Polynomial degree: 29\n", + "Error: 0.48454430745837984\n", + "Bias^2: 0.011809368338879722\n", + "Var: 0.4727349391195001\n", + "0.48454430745837984 >= 0.011809368338879722 + 0.4727349391195001 = 0.48454430745837984\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/regression_300_1.png" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.pipeline import make_pipeline\n", + "from sklearn.utils import resample\n", + "\n", + "np.random.seed(2018)\n", + "\n", + "n = 400\n", + "n_boostraps = 100\n", + "maxdegree = 30\n", + "\n", + "\n", + "# Make data set.\n", + "x = np.linspace(-3, 3, n).reshape(-1, 1)\n", + "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n", + "error = np.zeros(maxdegree)\n", + "bias = np.zeros(maxdegree)\n", + "variance = np.zeros(maxdegree)\n", + "polydegree = np.zeros(maxdegree)\n", + "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n", + "\n", + "for degree in range(maxdegree):\n", + " model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n", + " y_pred = np.empty((y_test.shape[0], n_boostraps))\n", + " for i in range(n_boostraps):\n", + " x_, y_ = resample(x_train, y_train)\n", + " y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n", + "\n", + " polydegree[degree] = degree\n", + " error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n", + " bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n", + " variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n", + " print('Polynomial degree:', degree)\n", + " print('Error:', error[degree])\n", + " print('Bias^2:', bias[degree])\n", + " print('Var:', variance[degree])\n", + " print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n", + "\n", + "plt.plot(polydegree, error, label='Error')\n", + "plt.plot(polydegree, bias, label='bias')\n", + "plt.plot(polydegree, variance, label='Variance')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Summing up\n", + "\n", + "\n", + "\n", + "\n", + "The bias-variance tradeoff summarizes the fundamental tension in\n", + "machine learning, particularly supervised learning, between the\n", + "complexity of a model and the amount of training data needed to train\n", + "it. Since data is often limited, in practice it is often useful to\n", + "use a less-complex model with higher bias, that is a model whose asymptotic\n", + "performance is worse than another model because it is easier to\n", + "train and less sensitive to sampling noise arising from having a\n", + "finite-sized training dataset (smaller variance). \n", + "\n", + "\n", + "\n", + "The above equations tell us that in\n", + "order to minimize the expected test error, we need to select a\n", + "statistical learning method that simultaneously achieves low variance\n", + "and low bias. Note that variance is inherently a nonnegative quantity,\n", + "and squared bias is also nonnegative. Hence, we see that the expected\n", + "test MSE can never lie below $Var(\\epsilon)$, the irreducible error.\n", + "\n", + "\n", + "What do we mean by the variance and bias of a statistical learning\n", + "method? The variance refers to the amount by which our model would change if we\n", + "estimated it using a different training data set. Since the training\n", + "data are used to fit the statistical learning method, different\n", + "training data sets will result in a different estimate. But ideally the\n", + "estimate for our model should not vary too much between training\n", + "sets. However, if a method has high variance then small changes in\n", + "the training data can result in large changes in the model. In general, more\n", + "flexible statistical methods have higher variance.\n", + "\n", + "\n", + "You may also find this recent [article](https://www.pnas.org/content/116/32/15849) of interest.\n", + "\n", + "## Another Example from Scikit-Learn's Repository" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + "============================\n", + "Underfitting vs. Overfitting\n", + "============================\n", + "\n", + "This example demonstrates the problems of underfitting and overfitting and\n", + "how we can use linear regression with polynomial features to approximate\n", + "nonlinear functions. The plot shows the function that we want to approximate,\n", + "which is a part of the cosine function. In addition, the samples from the\n", + "real function and the approximations of different models are displayed. The\n", + "models have polynomial features of different degrees. We can see that a\n", + "linear function (polynomial with degree 1) is not sufficient to fit the\n", + "training samples. This is called **underfitting**. A polynomial of degree 4\n", + "approximates the true function almost perfectly. However, for higher degrees\n", + "the model will **overfit** the training data, i.e. it learns the noise of the\n", + "training data.\n", + "We evaluate quantitatively **overfitting** / **underfitting** by using\n", + "cross-validation. We calculate the mean squared error (MSE) on the validation\n", + "set, the higher, the less likely the model generalizes correctly from the\n", + "training data.\n", + "\"\"\"\n", + "\n", + "print(__doc__)\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.pipeline import Pipeline\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.model_selection import cross_val_score\n", + "\n", + "\n", + "def true_fun(X):\n", + " return np.cos(1.5 * np.pi * X)\n", + "\n", + "np.random.seed(0)\n", + "\n", + "n_samples = 30\n", + "degrees = [1, 4, 15]\n", + "\n", + "X = np.sort(np.random.rand(n_samples))\n", + "y = true_fun(X) + np.random.randn(n_samples) * 0.1\n", + "\n", + "plt.figure(figsize=(14, 5))\n", + "for i in range(len(degrees)):\n", + " ax = plt.subplot(1, len(degrees), i + 1)\n", + " plt.setp(ax, xticks=(), yticks=())\n", + "\n", + " polynomial_features = PolynomialFeatures(degree=degrees[i],\n", + " include_bias=False)\n", + " linear_regression = LinearRegression()\n", + " pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n", + " (\"linear_regression\", linear_regression)])\n", + " pipeline.fit(X[:, np.newaxis], y)\n", + "\n", + " # Evaluate the models using crossvalidation\n", + " scores = cross_val_score(pipeline, X[:, np.newaxis], y,\n", + " scoring=\"neg_mean_squared_error\", cv=10)\n", + "\n", + " X_test = np.linspace(0, 1, 100)\n", + " plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n", + " plt.plot(X_test, true_fun(X_test), label=\"True function\")\n", + " plt.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n", + " plt.xlabel(\"x\")\n", + " plt.ylabel(\"y\")\n", + " plt.xlim((0, 1))\n", + " plt.ylim((-2, 2))\n", + " plt.legend(loc=\"best\")\n", + " plt.title(\"Degree {}\\nMSE = {:.2e}(+/- {:.2e})\".format(\n", + " degrees[i], -scores.mean(), scores.std()))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More examples on bootstrap and cross-validation and errors" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Common imports\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.utils import resample\n", + "from sklearn.metrics import mean_squared_error\n", + "# Where to save the figures and data files\n", + "PROJECT_ROOT_DIR = \"Results\"\n", + "FIGURE_ID = \"Results/FigureFiles\"\n", + "DATA_ID = \"DataFiles/\"\n", + "\n", + "if not os.path.exists(PROJECT_ROOT_DIR):\n", + " os.mkdir(PROJECT_ROOT_DIR)\n", + "\n", + "if not os.path.exists(FIGURE_ID):\n", + " os.makedirs(FIGURE_ID)\n", + "\n", + "if not os.path.exists(DATA_ID):\n", + " os.makedirs(DATA_ID)\n", + "\n", + "def image_path(fig_id):\n", + " return os.path.join(FIGURE_ID, fig_id)\n", + "\n", + "def data_path(dat_id):\n", + " return os.path.join(DATA_ID, dat_id)\n", + "\n", + "def save_fig(fig_id):\n", + " plt.savefig(image_path(fig_id) + \".png\", format='png')\n", + "\n", + "infile = open(data_path(\"EoS.csv\"),'r')\n", + "\n", + "# Read the EoS data as csv file and organize the data into two arrays with density and energies\n", + "EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n", + "EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n", + "EoS = EoS.dropna()\n", + "Energies = EoS['Energy']\n", + "Density = EoS['Density']\n", + "# The design matrix now as function of various polytrops\n", + "\n", + "Maxpolydegree = 30\n", + "X = np.zeros((len(Density),Maxpolydegree))\n", + "X[:,0] = 1.0\n", + "testerror = np.zeros(Maxpolydegree)\n", + "trainingerror = np.zeros(Maxpolydegree)\n", + "polynomial = np.zeros(Maxpolydegree)\n", + "\n", + "trials = 100\n", + "for polydegree in range(1, Maxpolydegree):\n", + " polynomial[polydegree] = polydegree\n", + " for degree in range(polydegree):\n", + " X[:,degree] = Density**(degree/3.0)\n", + "\n", + "# loop over trials in order to estimate the expectation value of the MSE\n", + " testerror[polydegree] = 0.0\n", + " trainingerror[polydegree] = 0.0\n", + " for samples in range(trials):\n", + " x_train, x_test, y_train, y_test = train_test_split(X, Energies, test_size=0.2)\n", + " model = LinearRegression(fit_intercept=True).fit(x_train, y_train)\n", + " ypred = model.predict(x_train)\n", + " ytilde = model.predict(x_test)\n", + " testerror[polydegree] += mean_squared_error(y_test, ytilde)\n", + " trainingerror[polydegree] += mean_squared_error(y_train, ypred) \n", + "\n", + " testerror[polydegree] /= trials\n", + " trainingerror[polydegree] /= trials\n", + " print(\"Degree of polynomial: %3d\"% polynomial[polydegree])\n", + " print(\"Mean squared error on training data: %.8f\" % trainingerror[polydegree])\n", + " print(\"Mean squared error on test data: %.8f\" % testerror[polydegree])\n", + "\n", + "plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n", + "plt.plot(polynomial, np.log10(testerror), label='Test Error')\n", + "plt.xlabel('Polynomial degree')\n", + "plt.ylabel('log10[MSE]')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## The same example but now with cross-validation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Common imports\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", + "from sklearn.metrics import mean_squared_error\n", + "from sklearn.model_selection import KFold\n", + "from sklearn.model_selection import cross_val_score\n", + "\n", + "\n", + "# Where to save the figures and data files\n", + "PROJECT_ROOT_DIR = \"Results\"\n", + "FIGURE_ID = \"Results/FigureFiles\"\n", + "DATA_ID = \"DataFiles/\"\n", + "\n", + "if not os.path.exists(PROJECT_ROOT_DIR):\n", + " os.mkdir(PROJECT_ROOT_DIR)\n", + "\n", + "if not os.path.exists(FIGURE_ID):\n", + " os.makedirs(FIGURE_ID)\n", + "\n", + "if not os.path.exists(DATA_ID):\n", + " os.makedirs(DATA_ID)\n", + "\n", + "def image_path(fig_id):\n", + " return os.path.join(FIGURE_ID, fig_id)\n", + "\n", + "def data_path(dat_id):\n", + " return os.path.join(DATA_ID, dat_id)\n", + "\n", + "def save_fig(fig_id):\n", + " plt.savefig(image_path(fig_id) + \".png\", format='png')\n", + "\n", + "infile = open(data_path(\"EoS.csv\"),'r')\n", + "\n", + "# Read the EoS data as csv file and organize the data into two arrays with density and energies\n", + "EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n", + "EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n", + "EoS = EoS.dropna()\n", + "Energies = EoS['Energy']\n", + "Density = EoS['Density']\n", + "# The design matrix now as function of various polytrops\n", + "\n", + "Maxpolydegree = 30\n", + "X = np.zeros((len(Density),Maxpolydegree))\n", + "X[:,0] = 1.0\n", + "estimated_mse_sklearn = np.zeros(Maxpolydegree)\n", + "polynomial = np.zeros(Maxpolydegree)\n", + "k =5\n", + "kfold = KFold(n_splits = k)\n", + "\n", + "for polydegree in range(1, Maxpolydegree):\n", + " polynomial[polydegree] = polydegree\n", + " for degree in range(polydegree):\n", + " X[:,degree] = Density**(degree/3.0)\n", + " OLS = LinearRegression()\n", + "# loop over trials in order to estimate the expectation value of the MSE\n", + " estimated_mse_folds = cross_val_score(OLS, X, Energies, scoring='neg_mean_squared_error', cv=kfold)\n", + "#[:, np.newaxis]\n", + " estimated_mse_sklearn[polydegree] = np.mean(-estimated_mse_folds)\n", + "\n", + "plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n", + "plt.xlabel('Polynomial degree')\n", + "plt.ylabel('log10[MSE]')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Cross-validation with Ridge" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.model_selection import KFold\n", + "from sklearn.linear_model import Ridge\n", + "from sklearn.model_selection import cross_val_score\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "\n", + "# A seed just to ensure that the random numbers are the same for every run.\n", + "np.random.seed(3155)\n", + "# Generate the data.\n", + "n = 100\n", + "x = np.linspace(-3, 3, n).reshape(-1, 1)\n", + "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n", + "# Decide degree on polynomial to fit\n", + "poly = PolynomialFeatures(degree = 10)\n", + "\n", + "# Decide which values of lambda to use\n", + "nlambdas = 500\n", + "lambdas = np.logspace(-3, 5, nlambdas)\n", + "# Initialize a KFold instance\n", + "k = 5\n", + "kfold = KFold(n_splits = k)\n", + "estimated_mse_sklearn = np.zeros(nlambdas)\n", + "i = 0\n", + "for lmb in lambdas:\n", + " ridge = Ridge(alpha = lmb)\n", + " estimated_mse_folds = cross_val_score(ridge, x, y, scoring='neg_mean_squared_error', cv=kfold)\n", + " estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds)\n", + " i += 1\n", + "plt.figure()\n", + "plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score')\n", + "plt.xlabel('log10(lambda)')\n", + "plt.ylabel('MSE')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Ising model\n", + "\n", + "The one-dimensional Ising model with nearest neighbor interaction, no\n", + "external field and a constant coupling constant $J$ is given by" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " H = -J \\sum_{k}^L s_k s_{k + 1},\n", + "\\label{_auto2} \\tag{2}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $s_i \\in \\{-1, 1\\}$ and $s_{N + 1} = s_1$. The number of spins\n", + "in the system is determined by $L$. For the one-dimensional system\n", + "there is no phase transition.\n", + "\n", + "We will look at a system of $L = 40$ spins with a coupling constant of\n", + "$J = 1$. To get enough training data we will generate 10000 states\n", + "with their respective energies." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", + "import seaborn as sns\n", + "import scipy.linalg as scl\n", + "from sklearn.model_selection import train_test_split\n", + "import tqdm\n", + "sns.set(color_codes=True)\n", + "cmap_args=dict(vmin=-1., vmax=1., cmap='seismic')\n", + "\n", + "L = 40\n", + "n = int(1e4)\n", + "\n", + "spins = np.random.choice([-1, 1], size=(n, L))\n", + "J = 1.0\n", + "\n", + "energies = np.zeros(n)\n", + "\n", + "for i in range(n):\n", + " energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we use ordinary least squares\n", + "regression to predict the energy for the nearest neighbor\n", + "one-dimensional Ising model on a ring, i.e., the endpoints wrap\n", + "around. We will use linear regression to fit a value for\n", + "the coupling constant to achieve this.\n", + "\n", + "## Reformulating the problem to suit regression\n", + "\n", + "A more general form for the one-dimensional Ising model is" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " H = - \\sum_j^L \\sum_k^L s_j s_k J_{jk}.\n", + "\\label{_auto3} \\tag{3}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we allow for interactions beyond the nearest neighbors and a state dependent\n", + "coupling constant. This latter expression can be formulated as\n", + "a matrix-product" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " \\boldsymbol{H} = \\boldsymbol{X} J,\n", + "\\label{_auto4} \\tag{4}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $X_{jk} = s_j s_k$ and $J$ is a matrix which consists of the\n", + "elements $-J_{jk}$. This form of writing the energy fits perfectly\n", + "with the form utilized in linear regression, that is" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " \\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon},\n", + "\\label{_auto5} \\tag{5}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We split the data in training and test data as discussed in the previous example" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "X = np.zeros((n, L ** 2))\n", + "for i in range(n):\n", + " X[i] = np.outer(spins[i], spins[i]).ravel()\n", + "y = energies\n", + "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Linear regression\n", + "\n", + "In the ordinary least squares method we choose the cost function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " C(\\boldsymbol{X}, \\boldsymbol{\\beta})= \\frac{1}{n}\\left\\{(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})\\right\\}.\n", + "\\label{_auto6} \\tag{6}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then find the extremal point of $C$ by taking the derivative with respect to $\\boldsymbol{\\beta}$ as discussed above.\n", + "This yields the expression for $\\boldsymbol{\\beta}$ to be" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\beta} = \\frac{\\boldsymbol{X}^T \\boldsymbol{y}}{\\boldsymbol{X}^T \\boldsymbol{X}},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which immediately imposes some requirements on $\\boldsymbol{X}$ as there must exist\n", + "an inverse of $\\boldsymbol{X}^T \\boldsymbol{X}$. If the expression we are modeling contains an\n", + "intercept, i.e., a constant term, we must make sure that the\n", + "first column of $\\boldsymbol{X}$ consists of $1$. We do this here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "X_train_own = np.concatenate(\n", + " (np.ones(len(X_train))[:, np.newaxis], X_train),\n", + " axis=1\n", + ")\n", + "X_test_own = np.concatenate(\n", + " (np.ones(len(X_test))[:, np.newaxis], X_test),\n", + " axis=1\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def ols_inv(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n", + " return scl.inv(x.T @ x) @ (x.T @ y)\n", + "beta = ols_inv(X_train_own, y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Singular Value decomposition\n", + "\n", + "Doing the inversion directly turns out to be a bad idea since the matrix\n", + "$\\boldsymbol{X}^T\\boldsymbol{X}$ is singular. An alternative approach is to use the **singular\n", + "value decomposition**. Using the definition of the Moore-Penrose\n", + "pseudoinverse we can write the equation for $\\boldsymbol{\\beta}$ as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{\\beta} = \\boldsymbol{X}^{+}\\boldsymbol{y},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where the pseudoinverse of $\\boldsymbol{X}$ is given by" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\boldsymbol{X}^{+} = \\frac{\\boldsymbol{X}^T}{\\boldsymbol{X}^T\\boldsymbol{X}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using singular value decomposition we can decompose the matrix $\\boldsymbol{X} = \\boldsymbol{U}\\boldsymbol{\\Sigma} \\boldsymbol{V}^T$,\n", + "where $\\boldsymbol{U}$ and $\\boldsymbol{V}$ are orthogonal(unitary) matrices and $\\boldsymbol{\\Sigma}$ contains the singular values (more details below).\n", + "where $X^{+} = V\\Sigma^{+} U^T$. This reduces the equation for\n", + "$\\omega$ to" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " \\boldsymbol{\\beta} = \\boldsymbol{V}\\boldsymbol{\\Sigma}^{+} \\boldsymbol{U}^T \\boldsymbol{y}.\n", + "\\label{_auto7} \\tag{7}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that solving this equation by actually doing the pseudoinverse\n", + "(which is what we will do) is not a good idea as this operation scales\n", + "as $\\mathcal{O}(n^3)$, where $n$ is the number of elements in a\n", + "general matrix. Instead, doing $QR$-factorization and solving the\n", + "linear system as an equation would reduce this down to\n", + "$\\mathcal{O}(n^2)$ operations." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def ols_svd(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n", + " u, s, v = scl.svd(x)\n", + " return v.T @ scl.pinv(scl.diagsvd(s, u.shape[0], v.shape[0])) @ u.T @ y" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "beta = ols_svd(X_train_own,y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When extracting the $J$-matrix we need to make sure that we remove the intercept, as is done here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "J = beta[1:].reshape(L, L)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A way of looking at the coefficients in $J$ is to plot the matrices as images." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = plt.figure(figsize=(20, 14))\n", + "im = plt.imshow(J, **cmap_args)\n", + "plt.title(\"OLS\", fontsize=18)\n", + "plt.xticks(fontsize=18)\n", + "plt.yticks(fontsize=18)\n", + "cb = fig.colorbar(im)\n", + "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is interesting to note that OLS\n", + "considers both $J_{j, j + 1} = -0.5$ and $J_{j, j - 1} = -0.5$ as\n", + "valid matrix elements for $J$.\n", + "In our discussion below on hyperparameters and Ridge and Lasso regression we will see that\n", + "this problem can be removed, partly and only with Lasso regression. \n", + "\n", + "In this case our matrix inversion was actually possible. The obvious question now is what is the mathematics behind the SVD?\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## The one-dimensional Ising model\n", + "\n", + "Let us bring back the Ising model again, but now with an additional\n", + "focus on Ridge and Lasso regression as well. We repeat some of the\n", + "basic parts of the Ising model and the setup of the training and test\n", + "data. The one-dimensional Ising model with nearest neighbor\n", + "interaction, no external field and a constant coupling constant $J$ is\n", + "given by" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " H = -J \\sum_{k}^L s_k s_{k + 1},\n", + "\\label{_auto8} \\tag{8}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $s_i \\in \\{-1, 1\\}$ and $s_{N + 1} = s_1$. The number of spins in the system is determined by $L$. For the one-dimensional system there is no phase transition.\n", + "\n", + "We will look at a system of $L = 40$ spins with a coupling constant of $J = 1$. To get enough training data we will generate 10000 states with their respective energies." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", + "import seaborn as sns\n", + "import scipy.linalg as scl\n", + "from sklearn.model_selection import train_test_split\n", + "import sklearn.linear_model as skl\n", + "import tqdm\n", + "sns.set(color_codes=True)\n", + "cmap_args=dict(vmin=-1., vmax=1., cmap='seismic')\n", + "\n", + "L = 40\n", + "n = int(1e4)\n", + "\n", + "spins = np.random.choice([-1, 1], size=(n, L))\n", + "J = 1.0\n", + "\n", + "energies = np.zeros(n)\n", + "\n", + "for i in range(n):\n", + " energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A more general form for the one-dimensional Ising model is" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " H = - \\sum_j^L \\sum_k^L s_j s_k J_{jk}.\n", + "\\label{_auto9} \\tag{9}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we allow for interactions beyond the nearest neighbors and a more\n", + "adaptive coupling matrix. This latter expression can be formulated as\n", + "a matrix-product on the form" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " H = X J,\n", + "\\label{_auto10} \\tag{10}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $X_{jk} = s_j s_k$ and $J$ is the matrix consisting of the\n", + "elements $-J_{jk}$. This form of writing the energy fits perfectly\n", + "with the form utilized in linear regression, viz." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " \\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon}.\n", + "\\label{_auto11} \\tag{11}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We organize the data as we did above" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "X = np.zeros((n, L ** 2))\n", + "for i in range(n):\n", + " X[i] = np.outer(spins[i], spins[i]).ravel()\n", + "y = energies\n", + "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.96)\n", + "\n", + "X_train_own = np.concatenate(\n", + " (np.ones(len(X_train))[:, np.newaxis], X_train),\n", + " axis=1\n", + ")\n", + "\n", + "X_test_own = np.concatenate(\n", + " (np.ones(len(X_test))[:, np.newaxis], X_test),\n", + " axis=1\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will do all fitting with **Scikit-Learn**," + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "clf = skl.LinearRegression().fit(X_train, y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When extracting the $J$-matrix we make sure to remove the intercept" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "J_sk = clf.coef_.reshape(L, L)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And then we plot the results" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = plt.figure(figsize=(20, 14))\n", + "im = plt.imshow(J_sk, **cmap_args)\n", + "plt.title(\"LinearRegression from Scikit-learn\", fontsize=18)\n", + "plt.xticks(fontsize=18)\n", + "plt.yticks(fontsize=18)\n", + "cb = fig.colorbar(im)\n", + "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The results perfectly with our previous discussion where we used our own code.\n", + "\n", + "## Ridge regression\n", + "\n", + "Having explored the ordinary least squares we move on to ridge\n", + "regression. In ridge regression we include a **regularizer**. This\n", + "involves a new cost function which leads to a new estimate for the\n", + "weights $\\boldsymbol{\\beta}$. This results in a penalized regression problem. The\n", + "cost function is given by" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1\n", + "3\n", + "6\n", + " \n", + "<\n", + "<\n", + "<\n", + "!\n", + "!\n", + "M\n", + "A\n", + "T\n", + "H\n", + "_\n", + "B\n", + "L\n", + "O\n", + "C\n", + "K" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "_lambda = 0.1\n", + "clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train)\n", + "J_ridge_sk = clf_ridge.coef_.reshape(L, L)\n", + "fig = plt.figure(figsize=(20, 14))\n", + "im = plt.imshow(J_ridge_sk, **cmap_args)\n", + "plt.title(\"Ridge from Scikit-learn\", fontsize=18)\n", + "plt.xticks(fontsize=18)\n", + "plt.yticks(fontsize=18)\n", + "cb = fig.colorbar(im)\n", + "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## LASSO regression\n", + "\n", + "In the **Least Absolute Shrinkage and Selection Operator** (LASSO)-method we get a third cost function." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " C(\\boldsymbol{X}, \\boldsymbol{\\beta}; \\lambda) = (\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y}) + \\lambda \\sqrt{\\boldsymbol{\\beta}^T\\boldsymbol{\\beta}}.\n", + "\\label{_auto13} \\tag{13}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finding the extremal point of this cost function is not so straight-forward as in least squares and ridge. We will therefore rely solely on the function ``Lasso`` from **Scikit-Learn**." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n", + "J_lasso_sk = clf_lasso.coef_.reshape(L, L)\n", + "fig = plt.figure(figsize=(20, 14))\n", + "im = plt.imshow(J_lasso_sk, **cmap_args)\n", + "plt.title(\"Lasso from Scikit-learn\", fontsize=18)\n", + "plt.xticks(fontsize=18)\n", + "plt.yticks(fontsize=18)\n", + "cb = fig.colorbar(im)\n", + "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is quite striking how LASSO breaks the symmetry of the coupling\n", + "constant as opposed to ridge and OLS. We get a sparse solution with\n", + "$J_{j, j + 1} = -1$.\n", + "\n", + "\n", + "\n", + "## Performance as function of the regularization parameter\n", + "\n", + "We see how the different models perform for a different set of values for $\\lambda$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "lambdas = np.logspace(-4, 5, 10)\n", + "\n", + "train_errors = {\n", + " \"ols_sk\": np.zeros(lambdas.size),\n", + " \"ridge_sk\": np.zeros(lambdas.size),\n", + " \"lasso_sk\": np.zeros(lambdas.size)\n", + "}\n", + "\n", + "test_errors = {\n", + " \"ols_sk\": np.zeros(lambdas.size),\n", + " \"ridge_sk\": np.zeros(lambdas.size),\n", + " \"lasso_sk\": np.zeros(lambdas.size)\n", + "}\n", + "\n", + "plot_counter = 1\n", + "\n", + "fig = plt.figure(figsize=(32, 54))\n", + "\n", + "for i, _lambda in enumerate(tqdm.tqdm(lambdas)):\n", + " for key, method in zip(\n", + " [\"ols_sk\", \"ridge_sk\", \"lasso_sk\"],\n", + " [skl.LinearRegression(), skl.Ridge(alpha=_lambda), skl.Lasso(alpha=_lambda)]\n", + " ):\n", + " method = method.fit(X_train, y_train)\n", + "\n", + " train_errors[key][i] = method.score(X_train, y_train)\n", + " test_errors[key][i] = method.score(X_test, y_test)\n", + "\n", + " omega = method.coef_.reshape(L, L)\n", + "\n", + " plt.subplot(10, 5, plot_counter)\n", + " plt.imshow(omega, **cmap_args)\n", + " plt.title(r\"%s, $\\lambda = %.4f$\" % (key, _lambda))\n", + " plot_counter += 1\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that LASSO reaches a good solution for low\n", + "values of $\\lambda$, but will \"wither\" when we increase $\\lambda$ too\n", + "much. Ridge is more stable over a larger range of values for\n", + "$\\lambda$, but eventually also fades away.\n", + "\n", + "## Finding the optimal value of $\\lambda$\n", + "\n", + "To determine which value of $\\lambda$ is best we plot the accuracy of\n", + "the models when predicting the training and the testing set. We expect\n", + "the accuracy of the training set to be quite good, but if the accuracy\n", + "of the testing set is much lower this tells us that we might be\n", + "subject to an overfit model. The ideal scenario is an accuracy on the\n", + "testing set that is close to the accuracy of the training set." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = plt.figure(figsize=(20, 14))\n", + "\n", + "colors = {\n", + " \"ols_sk\": \"r\",\n", + " \"ridge_sk\": \"y\",\n", + " \"lasso_sk\": \"c\"\n", + "}\n", + "\n", + "for key in train_errors:\n", + " plt.semilogx(\n", + " lambdas,\n", + " train_errors[key],\n", + " colors[key],\n", + " label=\"Train {0}\".format(key),\n", + " linewidth=4.0\n", + " )\n", + "\n", + "for key in test_errors:\n", + " plt.semilogx(\n", + " lambdas,\n", + " test_errors[key],\n", + " colors[key] + \"--\",\n", + " label=\"Test {0}\".format(key),\n", + " linewidth=4.0\n", + " )\n", + "plt.legend(loc=\"best\", fontsize=18)\n", + "plt.xlabel(r\"$\\lambda$\", fontsize=18)\n", + "plt.ylabel(r\"$R^2$\", fontsize=18)\n", + "plt.tick_params(labelsize=18)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From the above figure we can see that LASSO with $\\lambda = 10^{-2}$\n", + "achieves a very good accuracy on the test set. This by far surpasses the\n", + "other models for all values of $\\lambda$." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} \ No newline at end of file diff --git a/doc/src/LectureNotes/_build/jupyter_execute/regression.py b/doc/src/LectureNotes/_build/jupyter_execute/regression.py new file mode 100644 index 000000000..4d4ddde7c --- /dev/null +++ b/doc/src/LectureNotes/_build/jupyter_execute/regression.py @@ -0,0 +1,3681 @@ + +# Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis + + +**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University + +Date: **Sep 11, 2020** + +Copyright 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license + + + + + + +## Why Linear Regression (aka Ordinary Least Squares and family) + +Fitting a continuous function with linear parameterization in terms of the parameters $\boldsymbol{\beta}$. +* Method of choice for fitting a continuous function! + +* Gives an excellent introduction to central Machine Learning features with **understandable pedagogical** links to other methods like **Neural Networks**, **Support Vector Machines** etc + +* Analytical expression for the fitting parameters $\boldsymbol{\beta}$ + +* Analytical expressions for statistical propertiers like mean values, variances, confidence intervals and more + +* Analytical relation with probabilistic interpretations + +* Easy to introduce basic concepts like bias-variance tradeoff, cross-validation, resampling and regularization techniques and many other ML topics + +* Easy to code! And links well with classification problems and logistic regression and neural networks + +* Allows for **easy** hands-on understanding of gradient descent methods + +* and many more features + +For more discussions of Ridge and Lasso regression, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended. +Similarly, [Mehta et al's article](https://arxiv.org/abs/1803.08823) is also recommended. + + +## Regression analysis, overarching aims + +Regression modeling deals with the description of the sampling distribution of a given random variable $y$ and how it varies as function of another variable or a set of such variables $\boldsymbol{x} =[x_0, x_1,\dots, x_{n-1}]^T$. +The first variable is called the **dependent**, the **outcome** or the **response** variable while the set of variables $\boldsymbol{x}$ is called the independent variable, or the predictor variable or the explanatory variable. + +A regression model aims at finding a likelihood function $p(\boldsymbol{y}\vert \boldsymbol{x})$, that is the conditional distribution for $\boldsymbol{y}$ with a given $\boldsymbol{x}$. The estimation of $p(\boldsymbol{y}\vert \boldsymbol{x})$ is made using a data set with +* $n$ cases $i = 0, 1, 2, \dots, n-1$ + +* Response (target, dependent or outcome) variable $y_i$ with $i = 0, 1, 2, \dots, n-1$ + +* $p$ so-called explanatory (independent or predictor) variables $\boldsymbol{x}_i=[x_{i0}, x_{i1}, \dots, x_{ip-1}]$ with $i = 0, 1, 2, \dots, n-1$ and explanatory variables running from $0$ to $p-1$. See below for more explicit examples. + + The goal of the regression analysis is to extract/exploit relationship between $\boldsymbol{y}$ and $\boldsymbol{x}$ in or to infer causal dependencies, approximations to the likelihood functions, functional relationships and to make predictions, making fits and many other things. + + + +## Regression analysis, overarching aims II + + +Consider an experiment in which $p$ characteristics of $n$ samples are +measured. The data from this experiment, for various explanatory variables $p$ are normally represented by a matrix +$\mathbf{X}$. + +The matrix $\mathbf{X}$ is called the *design +matrix*. Additional information of the samples is available in the +form of $\boldsymbol{y}$ (also as above). The variable $\boldsymbol{y}$ is +generally referred to as the *response variable*. The aim of +regression analysis is to explain $\boldsymbol{y}$ in terms of +$\boldsymbol{X}$ through a functional relationship like $y_i = +f(\mathbf{X}_{i,\ast})$. When no prior knowledge on the form of +$f(\cdot)$ is available, it is common to assume a linear relationship +between $\boldsymbol{X}$ and $\boldsymbol{y}$. This assumption gives rise to +the *linear regression model* where $\boldsymbol{\beta} = [\beta_0, \ldots, +\beta_{p-1}]^{T}$ are the *regression parameters*. + +Linear regression gives us a set of analytical equations for the parameters $\beta_j$. + + + + + +## Examples +In order to understand the relation among the predictors $p$, the set of data $n$ and the target (outcome, output etc) $\boldsymbol{y}$, +consider the model we discussed for describing nuclear binding energies. + +There we assumed that we could parametrize the data using a polynomial approximation based on the liquid drop model. +Assuming + +$$ +BE(A) = a_0+a_1A+a_2A^{2/3}+a_3A^{-1/3}+a_4A^{-1}, +$$ + +we have five predictors, that is the intercept, the $A$ dependent term, the $A^{2/3}$ term and the $A^{-1/3}$ and $A^{-1}$ terms. +This gives $p=0,1,2,3,4$. Furthermore we have $n$ entries for each predictor. It means that our design matrix is a +$p\times n$ matrix $\boldsymbol{X}$. + +Here the predictors are based on a model we have made. A popular data set which is widely encountered in ML applications is the +so-called [credit card default data from Taiwan](https://www.sciencedirect.com/science/article/pii/S0957417407006719?via%3Dihub). The data set contains data on $n=30000$ credit card holders with predictors like gender, marital status, age, profession, education, etc. In total there are $24$ such predictors or attributes leading to a design matrix of dimensionality $24 \times 30000$. This is however a classification problem and we will come back to it when we discuss Logistic Regression. + + + + + + + +## General linear models +Before we proceed let us study a case from linear algebra where we aim at fitting a set of data $\boldsymbol{y}=[y_0,y_1,\dots,y_{n-1}]$. We could think of these data as a result of an experiment or a complicated numerical experiment. These data are functions of a series of variables $\boldsymbol{x}=[x_0,x_1,\dots,x_{n-1}]$, that is $y_i = y(x_i)$ with $i=0,1,2,\dots,n-1$. The variables $x_i$ could represent physical quantities like time, temperature, position etc. We assume that $y(x)$ is a smooth function. + +Since obtaining these data points may not be trivial, we want to use these data to fit a function which can allow us to make predictions for values of $y$ which are not in the present set. The perhaps simplest approach is to assume we can parametrize our function in terms of a polynomial of degree $n-1$ with $n$ points, that is + +$$ +y=y(x) \rightarrow y(x_i)=\tilde{y}_i+\epsilon_i=\sum_{j=0}^{n-1} \beta_j x_i^j+\epsilon_i, +$$ + +where $\epsilon_i$ is the error in our approximation. + + + + +## Rewriting the fitting procedure as a linear algebra problem +For every set of values $y_i,x_i$ we have thus the corresponding set of equations + +$$ +\begin{align*} +y_0&=\beta_0+\beta_1x_0^1+\beta_2x_0^2+\dots+\beta_{n-1}x_0^{n-1}+\epsilon_0\\ +y_1&=\beta_0+\beta_1x_1^1+\beta_2x_1^2+\dots+\beta_{n-1}x_1^{n-1}+\epsilon_1\\ +y_2&=\beta_0+\beta_1x_2^1+\beta_2x_2^2+\dots+\beta_{n-1}x_2^{n-1}+\epsilon_2\\ +\dots & \dots \\ +y_{n-1}&=\beta_0+\beta_1x_{n-1}^1+\beta_2x_{n-1}^2+\dots+\beta_{n-1}x_{n-1}^{n-1}+\epsilon_{n-1}.\\ +\end{align*} +$$ + +## Rewriting the fitting procedure as a linear algebra problem, more details +Defining the vectors + +$$ +\boldsymbol{y} = [y_0,y_1, y_2,\dots, y_{n-1}]^T, +$$ + +and + +$$ +\boldsymbol{\beta} = [\beta_0,\beta_1, \beta_2,\dots, \beta_{n-1}]^T, +$$ + +and + +$$ +\boldsymbol{\epsilon} = [\epsilon_0,\epsilon_1, \epsilon_2,\dots, \epsilon_{n-1}]^T, +$$ + +and the design matrix + +$$ +\boldsymbol{X}= +\begin{bmatrix} +1& x_{0}^1 &x_{0}^2& \dots & \dots &x_{0}^{n-1}\\ +1& x_{1}^1 &x_{1}^2& \dots & \dots &x_{1}^{n-1}\\ +1& x_{2}^1 &x_{2}^2& \dots & \dots &x_{2}^{n-1}\\ +\dots& \dots &\dots& \dots & \dots &\dots\\ +1& x_{n-1}^1 &x_{n-1}^2& \dots & \dots &x_{n-1}^{n-1}\\ +\end{bmatrix} +$$ + +we can rewrite our equations as + +$$ +\boldsymbol{y} = \boldsymbol{X}\boldsymbol{\beta}+\boldsymbol{\epsilon}. +$$ + +The above design matrix is called a [Vandermonde matrix](https://en.wikipedia.org/wiki/Vandermonde_matrix). + + + + +## Generalizing the fitting procedure as a linear algebra problem + +We are obviously not limited to the above polynomial expansions. We +could replace the various powers of $x$ with elements of Fourier +series or instead of $x_i^j$ we could have $\cos{(j x_i)}$ or $\sin{(j +x_i)}$, or time series or other orthogonal functions. For every set +of values $y_i,x_i$ we can then generalize the equations to + +$$ +\begin{align*} +y_0&=\beta_0x_{00}+\beta_1x_{01}+\beta_2x_{02}+\dots+\beta_{n-1}x_{0n-1}+\epsilon_0\\ +y_1&=\beta_0x_{10}+\beta_1x_{11}+\beta_2x_{12}+\dots+\beta_{n-1}x_{1n-1}+\epsilon_1\\ +y_2&=\beta_0x_{20}+\beta_1x_{21}+\beta_2x_{22}+\dots+\beta_{n-1}x_{2n-1}+\epsilon_2\\ +\dots & \dots \\ +y_{i}&=\beta_0x_{i0}+\beta_1x_{i1}+\beta_2x_{i2}+\dots+\beta_{n-1}x_{in-1}+\epsilon_i\\ +\dots & \dots \\ +y_{n-1}&=\beta_0x_{n-1,0}+\beta_1x_{n-1,2}+\beta_2x_{n-1,2}+\dots+\beta_{n-1}x_{n-1,n-1}+\epsilon_{n-1}.\\ +\end{align*} +$$ + +**Note that we have $p=n$ here. The matrix is symmetric. This is generally not the case!** + + + + +## Generalizing the fitting procedure as a linear algebra problem +We redefine in turn the matrix $\boldsymbol{X}$ as + +$$ +\boldsymbol{X}= +\begin{bmatrix} +x_{00}& x_{01} &x_{02}& \dots & \dots &x_{0,n-1}\\ +x_{10}& x_{11} &x_{12}& \dots & \dots &x_{1,n-1}\\ +x_{20}& x_{21} &x_{22}& \dots & \dots &x_{2,n-1}\\ +\dots& \dots &\dots& \dots & \dots &\dots\\ +x_{n-1,0}& x_{n-1,1} &x_{n-1,2}& \dots & \dots &x_{n-1,n-1}\\ +\end{bmatrix} +$$ + +and without loss of generality we rewrite again our equations as + +$$ +\boldsymbol{y} = \boldsymbol{X}\boldsymbol{\beta}+\boldsymbol{\epsilon}. +$$ + +The left-hand side of this equation is kwown. Our error vector $\boldsymbol{\epsilon}$ and the parameter vector $\boldsymbol{\beta}$ are our unknow quantities. How can we obtain the optimal set of $\beta_i$ values? + + + + +## Optimizing our parameters +We have defined the matrix $\boldsymbol{X}$ via the equations + +$$ +\begin{align*} +y_0&=\beta_0x_{00}+\beta_1x_{01}+\beta_2x_{02}+\dots+\beta_{n-1}x_{0n-1}+\epsilon_0\\ +y_1&=\beta_0x_{10}+\beta_1x_{11}+\beta_2x_{12}+\dots+\beta_{n-1}x_{1n-1}+\epsilon_1\\ +y_2&=\beta_0x_{20}+\beta_1x_{21}+\beta_2x_{22}+\dots+\beta_{n-1}x_{2n-1}+\epsilon_1\\ +\dots & \dots \\ +y_{i}&=\beta_0x_{i0}+\beta_1x_{i1}+\beta_2x_{i2}+\dots+\beta_{n-1}x_{in-1}+\epsilon_1\\ +\dots & \dots \\ +y_{n-1}&=\beta_0x_{n-1,0}+\beta_1x_{n-1,2}+\beta_2x_{n-1,2}+\dots+\beta_{n-1}x_{n-1,n-1}+\epsilon_{n-1}.\\ +\end{align*} +$$ + +As we noted above, we stayed with a system with the design matrix + $\boldsymbol{X}\in {\mathbb{R}}^{n\times n}$, that is we have $p=n$. For reasons to come later (algorithmic arguments) we will hereafter define +our matrix as $\boldsymbol{X}\in {\mathbb{R}}^{n\times p}$, with the predictors refering to the column numbers and the entries $n$ being the row elements. + + + + +## Our model for the nuclear binding energies + +In our [introductory notes](https://compphysics.github.io/MachineLearning/doc/pub/How2ReadData/html/How2ReadData.html) we looked at the so-called [liquid drop model](https://en.wikipedia.org/wiki/Semi-empirical_mass_formula). Let us remind ourselves about what we did by looking at the code. + +We restate the parts of the code we are most interested in. + +%matplotlib inline + +# Common imports +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +from IPython.display import display +import os + +# Where to save the figures and data files +PROJECT_ROOT_DIR = "Results" +FIGURE_ID = "Results/FigureFiles" +DATA_ID = "DataFiles/" + +if not os.path.exists(PROJECT_ROOT_DIR): + os.mkdir(PROJECT_ROOT_DIR) + +if not os.path.exists(FIGURE_ID): + os.makedirs(FIGURE_ID) + +if not os.path.exists(DATA_ID): + os.makedirs(DATA_ID) + +def image_path(fig_id): + return os.path.join(FIGURE_ID, fig_id) + +def data_path(dat_id): + return os.path.join(DATA_ID, dat_id) + +def save_fig(fig_id): + plt.savefig(image_path(fig_id) + ".png", format='png') + +infile = open(data_path("MassEval2016.dat"),'r') + + +# Read the experimental data with Pandas +Masses = pd.read_fwf(infile, usecols=(2,3,4,6,11), + names=('N', 'Z', 'A', 'Element', 'Ebinding'), + widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1), + header=39, + index_col=False) + +# Extrapolated values are indicated by '#' in place of the decimal place, so +# the Ebinding column won't be numeric. Coerce to float and drop these entries. +Masses['Ebinding'] = pd.to_numeric(Masses['Ebinding'], errors='coerce') +Masses = Masses.dropna() +# Convert from keV to MeV. +Masses['Ebinding'] /= 1000 + +# Group the DataFrame by nucleon number, A. +Masses = Masses.groupby('A') +# Find the rows of the grouped DataFrame with the maximum binding energy. +Masses = Masses.apply(lambda t: t[t.Ebinding==t.Ebinding.max()]) +A = Masses['A'] +Z = Masses['Z'] +N = Masses['N'] +Element = Masses['Element'] +Energies = Masses['Ebinding'] + +# Now we set up the design matrix X +X = np.zeros((len(A),5)) +X[:,0] = 1 +X[:,1] = A +X[:,2] = A**(2.0/3.0) +X[:,3] = A**(-1.0/3.0) +X[:,4] = A**(-1.0) +# Then nice printout using pandas +DesignMatrix = pd.DataFrame(X) +DesignMatrix.index = A +DesignMatrix.columns = ['1', 'A', 'A^(2/3)', 'A^(-1/3)', '1/A'] +display(DesignMatrix) + +With $\boldsymbol{\beta}\in {\mathbb{R}}^{p\times 1}$, it means that we will hereafter write our equations for the approximation as + +$$ +\boldsymbol{\tilde{y}}= \boldsymbol{X}\boldsymbol{\beta}, +$$ + +throughout these lectures. + + +## Optimizing our parameters, more details +With the above we use the design matrix to define the approximation $\boldsymbol{\tilde{y}}$ via the unknown quantity $\boldsymbol{\beta}$ as + +$$ +\boldsymbol{\tilde{y}}= \boldsymbol{X}\boldsymbol{\beta}, +$$ + +and in order to find the optimal parameters $\beta_i$ instead of solving the above linear algebra problem, we define a function which gives a measure of the spread between the values $y_i$ (which represent hopefully the exact values) and the parameterized values $\tilde{y}_i$, namely + +$$ +C(\boldsymbol{\beta})=\frac{1}{n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{\tilde{y}}\right)^T\left(\boldsymbol{y}-\boldsymbol{\tilde{y}}\right)\right\}, +$$ + +or using the matrix $\boldsymbol{X}$ and in a more compact matrix-vector notation as + +$$ +C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}. +$$ + +This function is one possible way to define the so-called cost function. + + + +It is also common to define +the function $C$ as + +$$ +C(\boldsymbol{\beta})=\frac{1}{2n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2, +$$ + +since when taking the first derivative with respect to the unknown parameters $\beta$, the factor of $2$ cancels out. + + + + +## Interpretations and optimizing our parameters + +The function + +$$ +C(\boldsymbol{\beta})=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}, +$$ + +can be linked to the variance of the quantity $y_i$ if we interpret the latter as the mean value. +When linking (see the discussion below) with the maximum likelihood approach below, we will indeed interpret $y_i$ as a mean value + +$$ +y_{i}=\langle y_i \rangle = \beta_0x_{i,0}+\beta_1x_{i,1}+\beta_2x_{i,2}+\dots+\beta_{n-1}x_{i,n-1}+\epsilon_i, +$$ + +where $\langle y_i \rangle$ is the mean value. Keep in mind also that +till now we have treated $y_i$ as the exact value. Normally, the +response (dependent or outcome) variable $y_i$ the outcome of a +numerical experiment or another type of experiment and is thus only an +approximation to the true value. It is then always accompanied by an +error estimate, often limited to a statistical error estimate given by +the standard deviation discussed earlier. In the discussion here we +will treat $y_i$ as our exact value for the response variable. + +In order to find the parameters $\beta_i$ we will then minimize the spread of $C(\boldsymbol{\beta})$, that is we are going to solve the problem + +$$ +{\displaystyle \min_{\boldsymbol{\beta}\in +{\mathbb{R}}^{p}}}\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}. +$$ + +In practical terms it means we will require + +$$ +\frac{\partial C(\boldsymbol{\beta})}{\partial \beta_j} = \frac{\partial }{\partial \beta_j}\left[ \frac{1}{n}\sum_{i=0}^{n-1}\left(y_i-\beta_0x_{i,0}-\beta_1x_{i,1}-\beta_2x_{i,2}-\dots-\beta_{n-1}x_{i,n-1}\right)^2\right]=0, +$$ + +which results in + +$$ +\frac{\partial C(\boldsymbol{\beta})}{\partial \beta_j} = -\frac{2}{n}\left[ \sum_{i=0}^{n-1}x_{ij}\left(y_i-\beta_0x_{i,0}-\beta_1x_{i,1}-\beta_2x_{i,2}-\dots-\beta_{n-1}x_{i,n-1}\right)\right]=0, +$$ + +or in a matrix-vector form as + +$$ +\frac{\partial C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}} = 0 = \boldsymbol{X}^T\left( \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right). +$$ + +## Interpretations and optimizing our parameters +We can rewrite + +$$ +\frac{\partial C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}} = 0 = \boldsymbol{X}^T\left( \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right), +$$ + +as + +$$ +\boldsymbol{X}^T\boldsymbol{y} = \boldsymbol{X}^T\boldsymbol{X}\boldsymbol{\beta}, +$$ + +and if the matrix $\boldsymbol{X}^T\boldsymbol{X}$ is invertible we have the solution + +$$ +\boldsymbol{\beta} =\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}. +$$ + +We note also that since our design matrix is defined as $\boldsymbol{X}\in +{\mathbb{R}}^{n\times p}$, the product $\boldsymbol{X}^T\boldsymbol{X} \in +{\mathbb{R}}^{p\times p}$. In the above case we have that $p \ll n$, +in our case $p=5$ meaning that we end up with inverting a small +$5\times 5$ matrix. This is a rather common situation, in many cases we end up with low-dimensional +matrices to invert. The methods discussed here and for many other +supervised learning algorithms like classification with logistic +regression or support vector machines, exhibit dimensionalities which +allow for the usage of direct linear algebra methods such as **LU** decomposition or **Singular Value Decomposition** (SVD) for finding the inverse of the matrix +$\boldsymbol{X}^T\boldsymbol{X}$. + + + +**Small question**: Do you think the example we have at hand here (the nuclear binding energies) can lead to problems in inverting the matrix $\boldsymbol{X}^T\boldsymbol{X}$? What kind of problems can we expect? + + + +## Some useful matrix and vector expressions + +The following matrix and vector relation will be useful here and for the rest of the course. Vectors are always written as boldfaced lower case letters and +matrices as upper case boldfaced letters. + +2 +6 + +< +< +< +! +! +M +A +T +H +_ +B +L +O +C +K + +2 +7 + +< +< +< +! +! +M +A +T +H +_ +B +L +O +C +K + +2 +8 + +< +< +< +! +! +M +A +T +H +_ +B +L +O +C +K + +$$ +\frac{\partial \log{\vert\boldsymbol{A}\vert}}{\partial \boldsymbol{A}} = (\boldsymbol{A}^{-1})^T. +$$ + +## Interpretations and optimizing our parameters +The residuals $\boldsymbol{\epsilon}$ are in turn given by + +$$ +\boldsymbol{\epsilon} = \boldsymbol{y}-\boldsymbol{\tilde{y}} = \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}, +$$ + +and with + +$$ +\boldsymbol{X}^T\left( \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)= 0, +$$ + +we have + +$$ +\boldsymbol{X}^T\boldsymbol{\epsilon}=\boldsymbol{X}^T\left( \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)= 0, +$$ + +meaning that the solution for $\boldsymbol{\beta}$ is the one which minimizes the residuals. Later we will link this with the maximum likelihood approach. + + + + +Let us now return to our nuclear binding energies and simply code the above equations. + +## Own code for Ordinary Least Squares + +It is rather straightforward to implement the matrix inversion and obtain the parameters $\boldsymbol{\beta}$. After having defined the matrix $\boldsymbol{X}$ we simply need to +write + +# matrix inversion to find beta +beta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Energies) +# and then make the prediction +ytilde = X @ beta + +Alternatively, you can use the least squares functionality in **Numpy** as + +fit = np.linalg.lstsq(X, Energies, rcond =None)[0] +ytildenp = np.dot(fit,X.T) + +And finally we plot our fit with and compare with data + +Masses['Eapprox'] = ytilde +# Generate a plot comparing the experimental with the fitted values values. +fig, ax = plt.subplots() +ax.set_xlabel(r'$A = N + Z$') +ax.set_ylabel(r'$E_\mathrm{bind}\,/\mathrm{MeV}$') +ax.plot(Masses['A'], Masses['Ebinding'], alpha=0.7, lw=2, + label='Ame2016') +ax.plot(Masses['A'], Masses['Eapprox'], alpha=0.7, lw=2, c='m', + label='Fit') +ax.legend() +save_fig("Masses2016OLS") +plt.show() + +## Adding error analysis and training set up + +We can easily test our fit by computing the $R2$ score that we discussed in connection with the functionality of **Scikit-Learn** in the introductory slides. +Since we are not using **Scikit-Learn** here we can define our own $R2$ function as + +def R2(y_data, y_model): + return 1 - np.sum((y_data - y_model) ** 2) / np.sum((y_data - np.mean(y_data)) ** 2) + +and we would be using it as + +print(R2(Energies,ytilde)) + +We can easily add our **MSE** score as + +def MSE(y_data,y_model): + n = np.size(y_model) + return np.sum((y_data-y_model)**2)/n + +print(MSE(Energies,ytilde)) + +and finally the relative error as + +def RelativeError(y_data,y_model): + return abs((y_data-y_model)/y_data) +print(RelativeError(Energies, ytilde)) + +## The $\chi^2$ function + +Normally, the response (dependent or outcome) variable $y_i$ is the +outcome of a numerical experiment or another type of experiment and is +thus only an approximation to the true value. It is then always +accompanied by an error estimate, often limited to a statistical error +estimate given by the standard deviation discussed earlier. In the +discussion here we will treat $y_i$ as our exact value for the +response variable. + +Introducing the standard deviation $\sigma_i$ for each measurement +$y_i$, we define now the $\chi^2$ function (omitting the $1/n$ term) +as + +$$ +\chi^2(\boldsymbol{\beta})=\frac{1}{n}\sum_{i=0}^{n-1}\frac{\left(y_i-\tilde{y}_i\right)^2}{\sigma_i^2}=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{\tilde{y}}\right)^T\frac{1}{\boldsymbol{\Sigma^2}}\left(\boldsymbol{y}-\boldsymbol{\tilde{y}}\right)\right\}, +$$ + +where the matrix $\boldsymbol{\Sigma}$ is a diagonal matrix with $\sigma_i$ as matrix elements. + + + +## The $\chi^2$ function + +In order to find the parameters $\beta_i$ we will then minimize the spread of $\chi^2(\boldsymbol{\beta})$ by requiring + +$$ +\frac{\partial \chi^2(\boldsymbol{\beta})}{\partial \beta_j} = \frac{\partial }{\partial \beta_j}\left[ \frac{1}{n}\sum_{i=0}^{n-1}\left(\frac{y_i-\beta_0x_{i,0}-\beta_1x_{i,1}-\beta_2x_{i,2}-\dots-\beta_{n-1}x_{i,n-1}}{\sigma_i}\right)^2\right]=0, +$$ + +which results in + +$$ +\frac{\partial \chi^2(\boldsymbol{\beta})}{\partial \beta_j} = -\frac{2}{n}\left[ \sum_{i=0}^{n-1}\frac{x_{ij}}{\sigma_i}\left(\frac{y_i-\beta_0x_{i,0}-\beta_1x_{i,1}-\beta_2x_{i,2}-\dots-\beta_{n-1}x_{i,n-1}}{\sigma_i}\right)\right]=0, +$$ + +or in a matrix-vector form as + +$$ +\frac{\partial \chi^2(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}} = 0 = \boldsymbol{A}^T\left( \boldsymbol{b}-\boldsymbol{A}\boldsymbol{\beta}\right). +$$ + +where we have defined the matrix $\boldsymbol{A} =\boldsymbol{X}/\boldsymbol{\Sigma}$ with matrix elements $a_{ij} = x_{ij}/\sigma_i$ and the vector $\boldsymbol{b}$ with elements $b_i = y_i/\sigma_i$. + + + +## The $\chi^2$ function + +We can rewrite + +$$ +\frac{\partial \chi^2(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}} = 0 = \boldsymbol{A}^T\left( \boldsymbol{b}-\boldsymbol{A}\boldsymbol{\beta}\right), +$$ + +as + +$$ +\boldsymbol{A}^T\boldsymbol{b} = \boldsymbol{A}^T\boldsymbol{A}\boldsymbol{\beta}, +$$ + +and if the matrix $\boldsymbol{A}^T\boldsymbol{A}$ is invertible we have the solution + +$$ +\boldsymbol{\beta} =\left(\boldsymbol{A}^T\boldsymbol{A}\right)^{-1}\boldsymbol{A}^T\boldsymbol{b}. +$$ + +## The $\chi^2$ function + +If we then introduce the matrix + +$$ +\boldsymbol{H} = \left(\boldsymbol{A}^T\boldsymbol{A}\right)^{-1}, +$$ + +we have then the following expression for the parameters $\beta_j$ (the matrix elements of $\boldsymbol{H}$ are $h_{ij}$) + +$$ +\beta_j = \sum_{k=0}^{p-1}h_{jk}\sum_{i=0}^{n-1}\frac{y_i}{\sigma_i}\frac{x_{ik}}{\sigma_i} = \sum_{k=0}^{p-1}h_{jk}\sum_{i=0}^{n-1}b_ia_{ik} +$$ + +We state without proof the expression for the uncertainty in the parameters $\beta_j$ as (we leave this as an exercise) + +$$ +\sigma^2(\beta_j) = \sum_{i=0}^{n-1}\sigma_i^2\left( \frac{\partial \beta_j}{\partial y_i}\right)^2, +$$ + +resulting in + +$$ +\sigma^2(\beta_j) = \left(\sum_{k=0}^{p-1}h_{jk}\sum_{i=0}^{n-1}a_{ik}\right)\left(\sum_{l=0}^{p-1}h_{jl}\sum_{m=0}^{n-1}a_{ml}\right) = h_{jj}! +$$ + +## The $\chi^2$ function +The first step here is to approximate the function $y$ with a first-order polynomial, that is we write + +$$ +y=y(x) \rightarrow y(x_i) \approx \beta_0+\beta_1 x_i. +$$ + +By computing the derivatives of $\chi^2$ with respect to $\beta_0$ and $\beta_1$ show that these are given by + +$$ +\frac{\partial \chi^2(\boldsymbol{\beta})}{\partial \beta_0} = -2\left[ \frac{1}{n}\sum_{i=0}^{n-1}\left(\frac{y_i-\beta_0-\beta_1x_{i}}{\sigma_i^2}\right)\right]=0, +$$ + +and + +$$ +\frac{\partial \chi^2(\boldsymbol{\beta})}{\partial \beta_1} = -\frac{2}{n}\left[ \sum_{i=0}^{n-1}x_i\left(\frac{y_i-\beta_0-\beta_1x_{i}}{\sigma_i^2}\right)\right]=0. +$$ + +## The $\chi^2$ function + +For a linear fit (a first-order polynomial) we don't need to invert a matrix!! +Defining + +$$ +\gamma = \sum_{i=0}^{n-1}\frac{1}{\sigma_i^2}, +$$ + +$$ +\gamma_x = \sum_{i=0}^{n-1}\frac{x_{i}}{\sigma_i^2}, +$$ + +$$ +\gamma_y = \sum_{i=0}^{n-1}\left(\frac{y_i}{\sigma_i^2}\right), +$$ + +$$ +\gamma_{xx} = \sum_{i=0}^{n-1}\frac{x_ix_{i}}{\sigma_i^2}, +$$ + +$$ +\gamma_{xy} = \sum_{i=0}^{n-1}\frac{y_ix_{i}}{\sigma_i^2}, +$$ + +we obtain + +$$ +\beta_0 = \frac{\gamma_{xx}\gamma_y-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2}, +$$ + +$$ +\beta_1 = \frac{\gamma_{xy}\gamma-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2}. +$$ + +This approach (different linear and non-linear regression) suffers +often from both being underdetermined and overdetermined in the +unknown coefficients $\beta_i$. A better approach is to use the +Singular Value Decomposition (SVD) method discussed below. Or using +Lasso and Ridge regression. See below. + + + + +## Fitting an Equation of State for Dense Nuclear Matter + +Before we continue, let us introduce yet another example. We are going to fit the +nuclear equation of state using results from many-body calculations. +The equation of state we have made available here, as function of +density, has been derived using modern nucleon-nucleon potentials with +[the addition of three-body +forces](https://www.sciencedirect.com/science/article/pii/S0370157399001106). This +time the file is presented as a standard **csv** file. + +The beginning of the Python code here is similar to what you have seen +before, with the same initializations and declarations. We use also +**pandas** again, rather extensively in order to organize our data. + +The difference now is that we use **Scikit-Learn's** regression tools +instead of our own matrix inversion implementation. Furthermore, we +sneak in **Ridge** regression (to be discussed below) which includes a +hyperparameter $\lambda$, also to be explained below. + +## The code + +# Common imports +import os +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +import matplotlib.pyplot as plt +import sklearn.linear_model as skl +from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error + +# Where to save the figures and data files +PROJECT_ROOT_DIR = "Results" +FIGURE_ID = "Results/FigureFiles" +DATA_ID = "DataFiles/" + +if not os.path.exists(PROJECT_ROOT_DIR): + os.mkdir(PROJECT_ROOT_DIR) + +if not os.path.exists(FIGURE_ID): + os.makedirs(FIGURE_ID) + +if not os.path.exists(DATA_ID): + os.makedirs(DATA_ID) + +def image_path(fig_id): + return os.path.join(FIGURE_ID, fig_id) + +def data_path(dat_id): + return os.path.join(DATA_ID, dat_id) + +def save_fig(fig_id): + plt.savefig(image_path(fig_id) + ".png", format='png') + +infile = open(data_path("EoS.csv"),'r') + +# Read the EoS data as csv file and organize the data into two arrays with density and energies +EoS = pd.read_csv(infile, names=('Density', 'Energy')) +EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce') +EoS = EoS.dropna() +Energies = EoS['Energy'] +Density = EoS['Density'] +# The design matrix now as function of various polytrops +X = np.zeros((len(Density),4)) +X[:,3] = Density**(4.0/3.0) +X[:,2] = Density +X[:,1] = Density**(2.0/3.0) +X[:,0] = 1 + +# We use now Scikit-Learn's linear regressor and ridge regressor +# OLS part +clf = skl.LinearRegression().fit(X, Energies) +ytilde = clf.predict(X) +EoS['Eols'] = ytilde +# The mean squared error +print("Mean squared error: %.2f" % mean_squared_error(Energies, ytilde)) +# Explained variance score: 1 is perfect prediction +print('Variance score: %.2f' % r2_score(Energies, ytilde)) +# Mean absolute error +print('Mean absolute error: %.2f' % mean_absolute_error(Energies, ytilde)) +print(clf.coef_, clf.intercept_) + +# The Ridge regression with a hyperparameter lambda = 0.1 +_lambda = 0.1 +clf_ridge = skl.Ridge(alpha=_lambda).fit(X, Energies) +yridge = clf_ridge.predict(X) +EoS['Eridge'] = yridge +# The mean squared error +print("Mean squared error: %.2f" % mean_squared_error(Energies, yridge)) +# Explained variance score: 1 is perfect prediction +print('Variance score: %.2f' % r2_score(Energies, yridge)) +# Mean absolute error +print('Mean absolute error: %.2f' % mean_absolute_error(Energies, yridge)) +print(clf_ridge.coef_, clf_ridge.intercept_) + +fig, ax = plt.subplots() +ax.set_xlabel(r'$\rho[\mathrm{fm}^{-3}]$') +ax.set_ylabel(r'Energy per particle') +ax.plot(EoS['Density'], EoS['Energy'], alpha=0.7, lw=2, + label='Theoretical data') +ax.plot(EoS['Density'], EoS['Eols'], alpha=0.7, lw=2, c='m', + label='OLS') +ax.plot(EoS['Density'], EoS['Eridge'], alpha=0.7, lw=2, c='g', + label='Ridge $\lambda = 0.1$') +ax.legend() +save_fig("EoSfitting") +plt.show() + +The above simple polynomial in density $\rho$ gives an excellent fit +to the data. + +We note also that there is a small deviation between the +standard OLS and the Ridge regression at higher densities. We discuss this in more detail +below. + + +## Splitting our Data in Training and Test data + +It is normal in essentially all Machine Learning studies to split the +data in a training set and a test set (sometimes also an additional +validation set). **Scikit-Learn** has an own function for this. There +is no explicit recipe for how much data should be included as training +data and say test data. An accepted rule of thumb is to use +approximately $2/3$ to $4/5$ of the data as training data. We will +postpone a discussion of this splitting to the end of these notes and +our discussion of the so-called **bias-variance** tradeoff. Here we +limit ourselves to repeat the above equation of state fitting example +but now splitting the data into a training set and a test set. + +import os +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +from sklearn.model_selection import train_test_split +# Where to save the figures and data files +PROJECT_ROOT_DIR = "Results" +FIGURE_ID = "Results/FigureFiles" +DATA_ID = "DataFiles/" + +if not os.path.exists(PROJECT_ROOT_DIR): + os.mkdir(PROJECT_ROOT_DIR) + +if not os.path.exists(FIGURE_ID): + os.makedirs(FIGURE_ID) + +if not os.path.exists(DATA_ID): + os.makedirs(DATA_ID) + +def image_path(fig_id): + return os.path.join(FIGURE_ID, fig_id) + +def data_path(dat_id): + return os.path.join(DATA_ID, dat_id) + +def save_fig(fig_id): + plt.savefig(image_path(fig_id) + ".png", format='png') + +def R2(y_data, y_model): + return 1 - np.sum((y_data - y_model) ** 2) / np.sum((y_data - np.mean(y_data)) ** 2) +def MSE(y_data,y_model): + n = np.size(y_model) + return np.sum((y_data-y_model)**2)/n + +infile = open(data_path("EoS.csv"),'r') + +# Read the EoS data as csv file and organized into two arrays with density and energies +EoS = pd.read_csv(infile, names=('Density', 'Energy')) +EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce') +EoS = EoS.dropna() +Energies = EoS['Energy'] +Density = EoS['Density'] +# The design matrix now as function of various polytrops +X = np.zeros((len(Density),5)) +X[:,0] = 1 +X[:,1] = Density**(2.0/3.0) +X[:,2] = Density +X[:,3] = Density**(4.0/3.0) +X[:,4] = Density**(5.0/3.0) +# We split the data in test and training data +X_train, X_test, y_train, y_test = train_test_split(X, Energies, test_size=0.2) +# matrix inversion to find beta +beta = np.linalg.inv(X_train.T.dot(X_train)).dot(X_train.T).dot(y_train) +# and then make the prediction +ytilde = X_train @ beta +print("Training R2") +print(R2(y_train,ytilde)) +print("Training MSE") +print(MSE(y_train,ytilde)) +ypredict = X_test @ beta +print("Test R2") +print(R2(y_test,ypredict)) +print("Test MSE") +print(MSE(y_test,ypredict)) + + +## The Boston housing data example + +The Boston housing +data set was originally a part of UCI Machine Learning Repository +and has been removed now. The data set is now included in **Scikit-Learn**'s +library. There are 506 samples and 13 feature (predictor) variables +in this data set. The objective is to predict the value of prices of +the house using the features (predictors) listed here. + +The features/predictors are +1. CRIM: Per capita crime rate by town + +2. ZN: Proportion of residential land zoned for lots over 25000 square feet + +3. INDUS: Proportion of non-retail business acres per town + +4. CHAS: Charles River dummy variable (= 1 if tract bounds river; 0 otherwise) + +5. NOX: Nitric oxide concentration (parts per 10 million) + +6. RM: Average number of rooms per dwelling + +7. AGE: Proportion of owner-occupied units built prior to 1940 + +8. DIS: Weighted distances to five Boston employment centers + +9. RAD: Index of accessibility to radial highways + +10. TAX: Full-value property tax rate per USD10000 + +11. B: $1000(Bk - 0.63)^2$, where $Bk$ is the proportion of [people of African American descent] by town + +12. LSTAT: Percentage of lower status of the population + +13. MEDV: Median value of owner-occupied homes in USD 1000s + +## Housing data, the code +We start by importing the libraries + +import numpy as np +import matplotlib.pyplot as plt + +import pandas as pd +import seaborn as sns + +and load the Boston Housing DataSet from **Scikit-Learn** + +from sklearn.datasets import load_boston + +boston_dataset = load_boston() + +# boston_dataset is a dictionary +# let's check what it contains +boston_dataset.keys() + +Then we invoke Pandas + +boston = pd.DataFrame(boston_dataset.data, columns=boston_dataset.feature_names) +boston.head() +boston['MEDV'] = boston_dataset.target + +and preprocess the data + +# check for missing values in all the columns +boston.isnull().sum() + +We can then visualize the data + +# set the size of the figure +sns.set(rc={'figure.figsize':(11.7,8.27)}) + +# plot a histogram showing the distribution of the target values +sns.distplot(boston['MEDV'], bins=30) +plt.show() + +It is now useful to look at the correlation matrix + +# compute the pair wise correlation for all columns +correlation_matrix = boston.corr().round(2) +# use the heatmap function from seaborn to plot the correlation matrix +# annot = True to print the values inside the square +sns.heatmap(data=correlation_matrix, annot=True) + +From the above coorelation plot we can see that **MEDV** is strongly correlated to **LSTAT** and **RM**. We see also that **RAD** and **TAX** are stronly correlated, but we don't include this in our features together to avoid multi-colinearity + +plt.figure(figsize=(20, 5)) + +features = ['LSTAT', 'RM'] +target = boston['MEDV'] + +for i, col in enumerate(features): + plt.subplot(1, len(features) , i+1) + x = boston[col] + y = target + plt.scatter(x, y, marker='o') + plt.title(col) + plt.xlabel(col) + plt.ylabel('MEDV') + +Now we start training our model + +X = pd.DataFrame(np.c_[boston['LSTAT'], boston['RM']], columns = ['LSTAT','RM']) +Y = boston['MEDV'] + +We split the data into training and test sets + +from sklearn.model_selection import train_test_split + +# splits the training and test data set in 80% : 20% +# assign random_state to any value.This ensures consistency. +X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.2, random_state=5) +print(X_train.shape) +print(X_test.shape) +print(Y_train.shape) +print(Y_test.shape) + +Then we use the linear regression functionality from **Scikit-Learn** + +from sklearn.linear_model import LinearRegression +from sklearn.metrics import mean_squared_error, r2_score + +lin_model = LinearRegression() +lin_model.fit(X_train, Y_train) + +# model evaluation for training set + +y_train_predict = lin_model.predict(X_train) +rmse = (np.sqrt(mean_squared_error(Y_train, y_train_predict))) +r2 = r2_score(Y_train, y_train_predict) + +print("The model performance for training set") +print("--------------------------------------") +print('RMSE is {}'.format(rmse)) +print('R2 score is {}'.format(r2)) +print("\n") + +# model evaluation for testing set + +y_test_predict = lin_model.predict(X_test) +# root mean square error of the model +rmse = (np.sqrt(mean_squared_error(Y_test, y_test_predict))) + +# r-squared score of the model +r2 = r2_score(Y_test, y_test_predict) + +print("The model performance for testing set") +print("--------------------------------------") +print('RMSE is {}'.format(rmse)) +print('R2 score is {}'.format(r2)) + +# plotting the y_test vs y_pred +# ideally should have been a straight line +plt.scatter(Y_test, y_test_predict) +plt.show() + +## Reducing the number of degrees of freedom, overarching view + +Many Machine Learning problems involve thousands or even millions of +features for each training instance. Not only does this make training +extremely slow, it can also make it much harder to find a good +solution, as we will see. This problem is often referred to as the +curse of dimensionality. Fortunately, in real-world problems, it is +often possible to reduce the number of features considerably, turning +an intractable problem into a tractable one. + +Later we will discuss some of the most popular dimensionality reduction +techniques: the principal component analysis (PCA), Kernel PCA, and +Locally Linear Embedding (LLE). + + +Principal component analysis and its various variants deal with the +problem of fitting a low-dimensional [affine +subspace](https://en.wikipedia.org/wiki/Affine_space) to a set of of +data points in a high-dimensional space. With its family of methods it +is one of the most used tools in data modeling, compression and +visualization. + + + + +## Preprocessing our data + +Before we proceed however, we will discuss how to preprocess our +data. Till now and in connection with our previous examples we have +not met so many cases where we are too sensitive to the scaling of our +data. Normally the data may need a rescaling and/or may be sensitive +to extreme values. Scaling the data renders our inputs much more +suitable for the algorithms we want to employ. + +**Scikit-Learn** has several functions which allow us to rescale the +data, normally resulting in much better results in terms of various +accuracy scores. The **StandardScaler** function in **Scikit-Learn** +ensures that for each feature/predictor we study the mean value is +zero and the variance is one (every column in the design/feature +matrix). This scaling has the drawback that it does not ensure that +we have a particular maximum or minimum in our data set. Another +function included in **Scikit-Learn** is the **MinMaxScaler** which +ensures that all features are exactly between $0$ and $1$. The + +## More preprocessing + + +The **Normalizer** scales each data +point such that the feature vector has a euclidean length of one. In other words, it +projects a data point on the circle (or sphere in the case of higher dimensions) with a +radius of 1. This means every data point is scaled by a different number (by the +inverse of it’s length). +This normalization is often used when only the direction (or angle) of the data matters, +not the length of the feature vector. + +The **RobustScaler** works similarly to the StandardScaler in that it +ensures statistical properties for each feature that guarantee that +they are on the same scale. However, the RobustScaler uses the median +and quartiles, instead of mean and variance. This makes the +RobustScaler ignore data points that are very different from the rest +(like measurement errors). These odd data points are also called +outliers, and might often lead to trouble for other scaling +techniques. + + + +## Simple preprocessing examples, Franke function and regression + +# Common imports +import os +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +import sklearn.linear_model as skl +from sklearn.metrics import mean_squared_error +from sklearn.model_selection import train_test_split +from sklearn.preprocessing import MinMaxScaler, StandardScaler, Normalizer + +# Where to save the figures and data files +PROJECT_ROOT_DIR = "Results" +FIGURE_ID = "Results/FigureFiles" +DATA_ID = "DataFiles/" + +if not os.path.exists(PROJECT_ROOT_DIR): + os.mkdir(PROJECT_ROOT_DIR) + +if not os.path.exists(FIGURE_ID): + os.makedirs(FIGURE_ID) + +if not os.path.exists(DATA_ID): + os.makedirs(DATA_ID) + +def image_path(fig_id): + return os.path.join(FIGURE_ID, fig_id) + +def data_path(dat_id): + return os.path.join(DATA_ID, dat_id) + +def save_fig(fig_id): + plt.savefig(image_path(fig_id) + ".png", format='png') + + +def FrankeFunction(x,y): + term1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2)) + term2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1)) + term3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2)) + term4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2) + return term1 + term2 + term3 + term4 + + +def create_X(x, y, n ): + if len(x.shape) > 1: + x = np.ravel(x) + y = np.ravel(y) + + N = len(x) + l = int((n+1)*(n+2)/2) # Number of elements in beta + X = np.ones((N,l)) + + for i in range(1,n+1): + q = int((i)*(i+1)/2) + for k in range(i+1): + X[:,q+k] = (x**(i-k))*(y**k) + + return X + + +# Making meshgrid of datapoints and compute Franke's function +n = 5 +N = 1000 +x = np.sort(np.random.uniform(0, 1, N)) +y = np.sort(np.random.uniform(0, 1, N)) +z = FrankeFunction(x, y) +X = create_X(x, y, n=n) +# split in training and test data +X_train, X_test, y_train, y_test = train_test_split(X,z,test_size=0.2) + + +clf = skl.LinearRegression().fit(X_train, y_train) + +# The mean squared error and R2 score +print("MSE before scaling: {:.2f}".format(mean_squared_error(clf.predict(X_test), y_test))) +print("R2 score before scaling {:.2f}".format(clf.score(X_test,y_test))) + +scaler = StandardScaler() +scaler.fit(X_train) +X_train_scaled = scaler.transform(X_train) +X_test_scaled = scaler.transform(X_test) + +print("Feature min values before scaling:\n {}".format(X_train.min(axis=0))) +print("Feature max values before scaling:\n {}".format(X_train.max(axis=0))) + +print("Feature min values after scaling:\n {}".format(X_train_scaled.min(axis=0))) +print("Feature max values after scaling:\n {}".format(X_train_scaled.max(axis=0))) + +clf = skl.LinearRegression().fit(X_train_scaled, y_train) + + +print("MSE after scaling: {:.2f}".format(mean_squared_error(clf.predict(X_test_scaled), y_test))) +print("R2 score for scaled data: {:.2f}".format(clf.score(X_test_scaled,y_test))) + +## The singular value decomposition + + +The examples we have looked at so far are cases where we normally can +invert the matrix $\boldsymbol{X}^T\boldsymbol{X}$. Using a polynomial expansion as we +did both for the masses and the fitting of the equation of state, +leads to row vectors of the design matrix which are essentially +orthogonal due to the polynomial character of our model. Obtaining the inverse of the design matrix is then often done via a so-called LU, QR or Cholesky decomposition. + + + +This may +however not the be case in general and a standard matrix inversion +algorithm based on say LU, QR or Cholesky decomposition may lead to singularities. We will see examples of this below. + +There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions. + +This is given by the **Singular Value Decomposition** algorithm, perhaps +the most powerful linear algebra algorithm. Let us look at a +different example where we may have problems with the standard matrix +inversion algorithm. Thereafter we dive into the math of the SVD. + + + + + +## Linear Regression Problems + +One of the typical problems we encounter with linear regression, in particular +when the matrix $\boldsymbol{X}$ (our so-called design matrix) is high-dimensional, +are problems with near singular or singular matrices. The column vectors of $\boldsymbol{X}$ +may be linearly dependent, normally referred to as super-collinearity. +This means that the matrix may be rank deficient and it is basically impossible to +to model the data using linear regression. As an example, consider the matrix + +$$ +\begin{align*} +\mathbf{X} & = \left[ +\begin{array}{rrr} +1 & -1 & 2 +\\ +1 & 0 & 1 +\\ +1 & 2 & -1 +\\ +1 & 1 & 0 +\end{array} \right] +\end{align*} +$$ + +The columns of $\boldsymbol{X}$ are linearly dependent. We see this easily since the +the first column is the row-wise sum of the other two columns. The rank (more correct, +the column rank) of a matrix is the dimension of the space spanned by the +column vectors. Hence, the rank of $\mathbf{X}$ is equal to the number +of linearly independent columns. In this particular case the matrix has rank 2. + +Super-collinearity of an $(n \times p)$-dimensional design matrix $\mathbf{X}$ implies +that the inverse of the matrix $\boldsymbol{X}^T\boldsymbol{X}$ (the matrix we need to invert to solve the linear regression equations) is non-invertible. If we have a square matrix that does not have an inverse, we say this matrix singular. The example here demonstrates this + +$$ +\begin{align*} +\boldsymbol{X} & = \left[ +\begin{array}{rr} +1 & -1 +\\ +1 & -1 +\end{array} \right]. +\end{align*} +$$ + +We see easily that $\mbox{det}(\boldsymbol{X}) = x_{11} x_{22} - x_{12} x_{21} = 1 \times (-1) - 1 \times (-1) = 0$. Hence, $\mathbf{X}$ is singular and its inverse is undefined. +This is equivalent to saying that the matrix $\boldsymbol{X}$ has at least an eigenvalue which is zero. + + +## Fixing the singularity + +If our design matrix $\boldsymbol{X}$ which enters the linear regression problem + + +
    + +$$ +\begin{equation} +\boldsymbol{\beta} = (\boldsymbol{X}^{T} \boldsymbol{X})^{-1} \boldsymbol{X}^{T} \boldsymbol{y}, +\label{_auto1} \tag{1} +\end{equation} +$$ + +has linearly dependent column vectors, we will not be able to compute the inverse +of $\boldsymbol{X}^T\boldsymbol{X}$ and we cannot find the parameters (estimators) $\beta_i$. +The estimators are only well-defined if $(\boldsymbol{X}^{T}\boldsymbol{X})^{-1}$ exits. +This is more likely to happen when the matrix $\boldsymbol{X}$ is high-dimensional. In this case it is likely to encounter a situation where +the regression parameters $\beta_i$ cannot be estimated. + +A cheap *ad hoc* approach is simply to add a small diagonal component to the matrix to invert, that is we change + +$$ +\boldsymbol{X}^{T} \boldsymbol{X} \rightarrow \boldsymbol{X}^{T} \boldsymbol{X}+\lambda \boldsymbol{I}, +$$ + +where $\boldsymbol{I}$ is the identity matrix. When we discuss **Ridge** regression this is actually what we end up evaluating. The parameter $\lambda$ is called a hyperparameter. More about this later. + + + +## Basic math of the SVD + + +From standard linear algebra we know that a square matrix $\boldsymbol{X}$ can be diagonalized if and only it is +a so-called [normal matrix](https://en.wikipedia.org/wiki/Normal_matrix), that is if $\boldsymbol{X}\in {\mathbb{R}}^{n\times n}$ +we have $\boldsymbol{X}\boldsymbol{X}^T=\boldsymbol{X}^T\boldsymbol{X}$ or if $\boldsymbol{X}\in {\mathbb{C}}^{n\times n}$ we have $\boldsymbol{X}\boldsymbol{X}^{\dagger}=\boldsymbol{X}^{\dagger}\boldsymbol{X}$. +The matrix has then a set of eigenpairs + +$$ +(\lambda_1,\boldsymbol{u}_1),\dots, (\lambda_n,\boldsymbol{u}_n), +$$ + +and the eigenvalues are given by the diagonal matrix + +$$ +\boldsymbol{\Sigma}=\mathrm{Diag}(\lambda_1, \dots,\lambda_n). +$$ + +The matrix $\boldsymbol{X}$ can be written in terms of an orthogonal/unitary transformation $\boldsymbol{U}$ + +$$ +\boldsymbol{X} = \boldsymbol{U}\boldsymbol{\Sigma}\boldsymbol{V}^T, +$$ + +with $\boldsymbol{U}\boldsymbol{U}^T=\boldsymbol{I}$ or $\boldsymbol{U}\boldsymbol{U}^{\dagger}=\boldsymbol{I}$. + +Not all square matrices are diagonalizable. A matrix like the one discussed above + +$$ +\boldsymbol{X} = \begin{bmatrix} +1& -1 \\ +1& -1\\ +\end{bmatrix} +$$ + +is not diagonalizable, it is a so-called [defective matrix](https://en.wikipedia.org/wiki/Defective_matrix). It is easy to see that the condition +$\boldsymbol{X}\boldsymbol{X}^T=\boldsymbol{X}^T\boldsymbol{X}$ is not fulfilled. + + +## The SVD, a Fantastic Algorithm + + +However, and this is the strength of the SVD algorithm, any general +matrix $\boldsymbol{X}$ can be decomposed in terms of a diagonal matrix and +two orthogonal/unitary matrices. The [Singular Value Decompostion +(SVD) theorem](https://en.wikipedia.org/wiki/Singular_value_decomposition) +states that a general $m\times n$ matrix $\boldsymbol{X}$ can be written in +terms of a diagonal matrix $\boldsymbol{\Sigma}$ of dimensionality $m\times n$ +and two orthognal matrices $\boldsymbol{U}$ and $\boldsymbol{V}$, where the first has +dimensionality $m \times m$ and the last dimensionality $n\times n$. +We have then + +$$ +\boldsymbol{X} = \boldsymbol{U}\boldsymbol{\Sigma}\boldsymbol{V}^T +$$ + +As an example, the above defective matrix can be decomposed as + +$$ +\boldsymbol{X} = \frac{1}{\sqrt{2}}\begin{bmatrix} 1& 1 \\ 1& -1\\ \end{bmatrix} \begin{bmatrix} 2& 0 \\ 0& 0\\ \end{bmatrix} \frac{1}{\sqrt{2}}\begin{bmatrix} 1& -1 \\ 1& 1\\ \end{bmatrix}=\boldsymbol{U}\boldsymbol{\Sigma}\boldsymbol{V}^T, +$$ + +with eigenvalues $\sigma_1=2$ and $\sigma_2=0$. +The SVD exits always! + +The SVD +decomposition (singular values) gives eigenvalues +$\sigma_i\geq\sigma_{i+1}$ for all $i$ and for dimensions larger than $i=p$, the +eigenvalues (singular values) are zero. + +In the general case, where our design matrix $\boldsymbol{X}$ has dimension +$n\times p$, the matrix is thus decomposed into an $n\times n$ +orthogonal matrix $\boldsymbol{U}$, a $p\times p$ orthogonal matrix $\boldsymbol{V}$ +and a diagonal matrix $\boldsymbol{\Sigma}$ with $r=\mathrm{min}(n,p)$ +singular values $\sigma_i\geq 0$ on the main diagonal and zeros filling +the rest of the matrix. There are at most $p$ singular values +assuming that $n > p$. In our regression examples for the nuclear +masses and the equation of state this is indeed the case, while for +the Ising model we have $p > n$. These are often cases that lead to +near singular or singular matrices. + +The columns of $\boldsymbol{U}$ are called the left singular vectors while the columns of $\boldsymbol{V}$ are the right singular vectors. + +## Economy-size SVD + +If we assume that $n > p$, then our matrix $\boldsymbol{U}$ has dimension $n +\times n$. The last $n-p$ columns of $\boldsymbol{U}$ become however +irrelevant in our calculations since they are multiplied with the +zeros in $\boldsymbol{\Sigma}$. + +The economy-size decomposition removes extra rows or columns of zeros +from the diagonal matrix of singular values, $\boldsymbol{\Sigma}$, along with the columns +in either $\boldsymbol{U}$ or $\boldsymbol{V}$ that multiply those zeros in the expression. +Removing these zeros and columns can improve execution time +and reduce storage requirements without compromising the accuracy of +the decomposition. + +If $n > p$, we keep only the first $p$ columns of $\boldsymbol{U}$ and $\boldsymbol{\Sigma}$ has dimension $p\times p$. +If $p > n$, then only the first $n$ columns of $\boldsymbol{V}$ are computed and $\boldsymbol{\Sigma}$ has dimension $n\times n$. +The $n=p$ case is obvious, we retain the full SVD. +In general the economy-size SVD leads to less FLOPS and still conserving the desired accuracy. + +## Codes for the SVD + +import numpy as np +# SVD inversion +def SVDinv(A): + ''' Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD). + SVD is numerically more stable than the inversion algorithms provided by + numpy and scipy.linalg at the cost of being slower. + ''' + U, s, VT = np.linalg.svd(A) +# print('test U') +# print( (np.transpose(U) @ U - U @np.transpose(U))) +# print('test VT') +# print( (np.transpose(VT) @ VT - VT @np.transpose(VT))) + print(U) + print(s) + print(VT) + + D = np.zeros((len(U),len(VT))) + for i in range(0,len(VT)): + D[i,i]=s[i] + UT = np.transpose(U); V = np.transpose(VT); invD = np.linalg.inv(D) + return np.matmul(V,np.matmul(invD,UT)) + + +X = np.array([ [1.0, -1.0, 2.0], [1.0, 0.0, 1.0], [1.0, 2.0, -1.0], [1.0, 1.0, 0.0] ]) +print(X) +A = np.transpose(X) @ X +print(A) +# Brute force inversion of super-collinear matrix +#B = np.linalg.inv(A) +#print(B) +C = SVDinv(A) +print(C) + +The matrix $\boldsymbol{X}$ has columns that are linearly dependent. The first +column is the row-wise sum of the other two columns. The rank of a +matrix (the column rank) is the dimension of space spanned by the +column vectors. The rank of the matrix is the number of linearly +independent columns, in this case just $2$. We see this from the +singular values when running the above code. Running the standard +inversion algorithm for matrix inversion with $\boldsymbol{X}^T\boldsymbol{X}$ results +in the program terminating due to a singular matrix. + + + +## Mathematical Properties + +There are several interesting mathematical properties which will be +relevant when we are going to discuss the differences between say +ordinary least squares (OLS) and **Ridge** regression. + +We have from OLS that the parameters of the linear approximation are given by + +$$ +\boldsymbol{\tilde{y}} = \boldsymbol{X}\boldsymbol{\beta} = \boldsymbol{X}\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}. +$$ + +The matrix to invert can be rewritten in terms of our SVD decomposition as + +$$ +\boldsymbol{X}^T\boldsymbol{X} = \boldsymbol{V}\boldsymbol{\Sigma}^T\boldsymbol{U}^T\boldsymbol{U}\boldsymbol{\Sigma}\boldsymbol{V}^T. +$$ + +Using the orthogonality properties of $\boldsymbol{U}$ we have + +$$ +\boldsymbol{X}^T\boldsymbol{X} = \boldsymbol{V}\boldsymbol{\Sigma}^T\boldsymbol{\Sigma}\boldsymbol{V}^T = \boldsymbol{V}\boldsymbol{D}\boldsymbol{V}^T, +$$ + +with $\boldsymbol{D}$ being a diagonal matrix with values along the diagonal given by the singular values squared. + +This means that + +$$ +(\boldsymbol{X}^T\boldsymbol{X})\boldsymbol{V} = \boldsymbol{V}\boldsymbol{D}, +$$ + +that is the eigenvectors of $(\boldsymbol{X}^T\boldsymbol{X})$ are given by the columns of the right singular matrix of $\boldsymbol{X}$ and the eigenvalues are the squared singular values. It is easy to show (show this) that + +$$ +(\boldsymbol{X}\boldsymbol{X}^T)\boldsymbol{U} = \boldsymbol{U}\boldsymbol{D}, +$$ + +that is, the eigenvectors of $(\boldsymbol{X}\boldsymbol{X})^T$ are the columns of the left singular matrix and the eigenvalues are the same. + +Going back to our OLS equation we have + +$$ +\boldsymbol{X}\boldsymbol{\beta} = \boldsymbol{X}\left(\boldsymbol{V}\boldsymbol{D}\boldsymbol{V}^T \right)^{-1}\boldsymbol{X}^T\boldsymbol{y}=\boldsymbol{U\Sigma V^T}\left(\boldsymbol{V}\boldsymbol{D}\boldsymbol{V}^T \right)^{-1}(\boldsymbol{U\Sigma V^T})^T\boldsymbol{y}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y}. +$$ + +We will come back to this expression when we discuss Ridge regression. + + +## Ridge and LASSO Regression + +Let us remind ourselves about the expression for the standard Mean Squared Error (MSE) which we used to define our cost function and the equations for the ordinary least squares (OLS) method, that is +our optimization problem is + +$$ +{\displaystyle \min_{\boldsymbol{\beta}\in {\mathbb{R}}^{p}}}\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)\right\}. +$$ + +or we can state it as + +$$ +{\displaystyle \min_{\boldsymbol{\beta}\in +{\mathbb{R}}^{p}}}\frac{1}{n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2=\frac{1}{n}\vert\vert \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\vert\vert_2^2, +$$ + +where we have used the definition of a norm-2 vector, that is + +$$ +\vert\vert \boldsymbol{x}\vert\vert_2 = \sqrt{\sum_i x_i^2}. +$$ + +By minimizing the above equation with respect to the parameters +$\boldsymbol{\beta}$ we could then obtain an analytical expression for the +parameters $\boldsymbol{\beta}$. We can add a regularization parameter $\lambda$ by +defining a new cost function to be optimized, that is + +$$ +{\displaystyle \min_{\boldsymbol{\beta}\in +{\mathbb{R}}^{p}}}\frac{1}{n}\vert\vert \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\vert\vert_2^2+\lambda\vert\vert \boldsymbol{\beta}\vert\vert_2^2 +$$ + +which leads to the Ridge regression minimization problem where we +require that $\vert\vert \boldsymbol{\beta}\vert\vert_2^2\le t$, where $t$ is +a finite number larger than zero. By defining + +$$ +C(\boldsymbol{X},\boldsymbol{\beta})=\frac{1}{n}\vert\vert \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\vert\vert_2^2+\lambda\vert\vert \boldsymbol{\beta}\vert\vert_1, +$$ + +we have a new optimization equation + +$$ +{\displaystyle \min_{\boldsymbol{\beta}\in +{\mathbb{R}}^{p}}}\frac{1}{n}\vert\vert \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\vert\vert_2^2+\lambda\vert\vert \boldsymbol{\beta}\vert\vert_1 +$$ + +which leads to Lasso regression. Lasso stands for least absolute shrinkage and selection operator. + +Here we have defined the norm-1 as + +$$ +\vert\vert \boldsymbol{x}\vert\vert_1 = \sum_i \vert x_i\vert. +$$ + +## More on Ridge Regression + +Using the matrix-vector expression for Ridge regression, + +$$ +C(\boldsymbol{X},\boldsymbol{\beta})=\frac{1}{n}\left\{(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})^T(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\right\}+\lambda\boldsymbol{\beta}^T\boldsymbol{\beta}, +$$ + +by taking the derivatives with respect to $\boldsymbol{\beta}$ we obtain then +a slightly modified matrix inversion problem which for finite values +of $\lambda$ does not suffer from singularity problems. We obtain + +$$ +\boldsymbol{\beta}^{\mathrm{Ridge}} = \left(\boldsymbol{X}^T\boldsymbol{X}+\lambda\boldsymbol{I}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}, +$$ + +with $\boldsymbol{I}$ being a $p\times p$ identity matrix with the constraint that + +$$ +\sum_{i=0}^{p-1} \beta_i^2 \leq t, +$$ + +with $t$ a finite positive number. + +We see that Ridge regression is nothing but the standard +OLS with a modified diagonal term added to $\boldsymbol{X}^T\boldsymbol{X}$. The +consequences, in particular for our discussion of the bias-variance tradeoff +are rather interesting. + +Furthermore, if we use the result above in terms of the SVD decomposition (our analysis was done for the OLS method), we had + +$$ +(\boldsymbol{X}\boldsymbol{X}^T)\boldsymbol{U} = \boldsymbol{U}\boldsymbol{D}. +$$ + +We can analyse the OLS solutions in terms of the eigenvectors (the columns) of the right singular value matrix $\boldsymbol{U}$ as + +$$ +\boldsymbol{X}\boldsymbol{\beta} = \boldsymbol{X}\left(\boldsymbol{V}\boldsymbol{D}\boldsymbol{V}^T \right)^{-1}\boldsymbol{X}^T\boldsymbol{y}=\boldsymbol{U\Sigma V^T}\left(\boldsymbol{V}\boldsymbol{D}\boldsymbol{V}^T \right)^{-1}(\boldsymbol{U\Sigma V^T})^T\boldsymbol{y}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y} +$$ + +For Ridge regression this becomes + +$$ +\boldsymbol{X}\boldsymbol{\beta}^{\mathrm{Ridge}} = \boldsymbol{U\Sigma V^T}\left(\boldsymbol{V}\boldsymbol{D}\boldsymbol{V}^T+\lambda\boldsymbol{I} \right)^{-1}(\boldsymbol{U\Sigma V^T})^T\boldsymbol{y}=\sum_{j=0}^{p-1}\boldsymbol{u}_j\boldsymbol{u}_j^T\frac{\sigma_j^2}{\sigma_j^2+\lambda}\boldsymbol{y}, +$$ + +with the vectors $\boldsymbol{u}_j$ being the columns of $\boldsymbol{U}$. + +## Interpreting the Ridge results + +Since $\lambda \geq 0$, it means that compared to OLS, we have + +$$ +\frac{\sigma_j^2}{\sigma_j^2+\lambda} \leq 1. +$$ + +Ridge regression finds the coordinates of $\boldsymbol{y}$ with respect to the +orthonormal basis $\boldsymbol{U}$, it then shrinks the coordinates by +$\frac{\sigma_j^2}{\sigma_j^2+\lambda}$. Recall that the SVD has +eigenvalues ordered in a descending way, that is $\sigma_i \geq +\sigma_{i+1}$. + +For small eigenvalues $\sigma_i$ it means that their contributions become less important, a fact which can be used to reduce the number of degrees of freedom. +Actually, calculating the variance of $\boldsymbol{X}\boldsymbol{v}_j$ shows that this quantity is equal to $\sigma_j^2/n$. +With a parameter $\lambda$ we can thus shrink the role of specific parameters. + + +## More interpretations + +For the sake of simplicity, let us assume that the design matrix is orthonormal, that is + +$$ +\boldsymbol{X}^T\boldsymbol{X}=(\boldsymbol{X}^T\boldsymbol{X})^{-1} =\boldsymbol{I}. +$$ + +In this case the standard OLS results in + +$$ +\boldsymbol{\beta}^{\mathrm{OLS}} = \boldsymbol{X}^T\boldsymbol{y}=\sum_{i=0}^{p-1}\boldsymbol{u}_j\boldsymbol{u}_j^T\boldsymbol{y}, +$$ + +and + +$$ +\boldsymbol{\beta}^{\mathrm{Ridge}} = \left(\boldsymbol{I}+\lambda\boldsymbol{I}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}=\left(1+\lambda\right)^{-1}\boldsymbol{\beta}^{\mathrm{OLS}}, +$$ + +that is the Ridge estimator scales the OLS estimator by the inverse of a factor $1+\lambda$, and +the Ridge estimator converges to zero when the hyperparameter goes to +infinity. + +We will come back to more interpreations after we have gone through some of the statistical analysis part. + +For more discussions of Ridge and Lasso regression, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended. +Similarly, [Mehta et al's article](https://arxiv.org/abs/1803.08823) is also recommended. + + + +## A better understanding of regularization + +The parameter $\lambda$ that we have introduced in the Ridge (and +Lasso as well) regression is often called a regularization parameter +or shrinkage parameter. It is common to call it a hyperparameter. What does it mean mathemtically? + +Here we will first look at how to analyze the difference between the +standard OLS equations and the Ridge expressions in terms of a linear +algebra analysis using the SVD algorithm. Thereafter, we will link +(see the material on the bias-variance tradeoff below) these +observation to the statisical analysis of the results. In particular +we consider how the variance of the parameters $\boldsymbol{\beta}$ is +affected by changing the parameter $\lambda$. + +## Decomposing the OLS and Ridge expressions + +We have our design matrix + $\boldsymbol{X}\in {\mathbb{R}}^{n\times p}$. With the SVD we decompose it as + +$$ +\boldsymbol{X} = \boldsymbol{U\Sigma V^T}, +$$ + +with $\boldsymbol{U}\in {\mathbb{R}}^{n\times n}$, $\boldsymbol{\Sigma}\in {\mathbb{R}}^{n\times p}$ +and $\boldsymbol{V}\in {\mathbb{R}}^{p\times p}$. + +The matrices $\boldsymbol{U}$ and $\boldsymbol{V}$ are unitary/orthonormal matrices, that is in case the matrices are real we have $\boldsymbol{U}^T\boldsymbol{U}=\boldsymbol{U}\boldsymbol{U}^T=\boldsymbol{I}$ and $\boldsymbol{V}^T\boldsymbol{V}=\boldsymbol{V}\boldsymbol{V}^T=\boldsymbol{I}$. + + + +## Introducing the Covariance and Correlation functions + +Before we discuss the link between for example Ridge regression and the singular value decomposition, we need to remind ourselves about +the definition of the covariance and the correlation function. These are quantities + +Suppose we have defined two vectors +$\hat{x}$ and $\hat{y}$ with $n$ elements each. The covariance matrix $\boldsymbol{C}$ is defined as + +$$ +\boldsymbol{C}[\boldsymbol{x},\boldsymbol{y}] = \begin{bmatrix} \mathrm{cov}[\boldsymbol{x},\boldsymbol{x}] & \mathrm{cov}[\boldsymbol{x},\boldsymbol{y}] \\ + \mathrm{cov}[\boldsymbol{y},\boldsymbol{x}] & \mathrm{cov}[\boldsymbol{y},\boldsymbol{y}] \\ + \end{bmatrix}, +$$ + +where for example + +$$ +\mathrm{cov}[\boldsymbol{x},\boldsymbol{y}] =\frac{1}{n} \sum_{i=0}^{n-1}(x_i- \overline{x})(y_i- \overline{y}). +$$ + +With this definition and recalling that the variance is defined as + +$$ +\mathrm{var}[\boldsymbol{x}]=\frac{1}{n} \sum_{i=0}^{n-1}(x_i- \overline{x})^2, +$$ + +we can rewrite the covariance matrix as + +$$ +\boldsymbol{C}[\boldsymbol{x},\boldsymbol{y}] = \begin{bmatrix} \mathrm{var}[\boldsymbol{x}] & \mathrm{cov}[\boldsymbol{x},\boldsymbol{y}] \\ + \mathrm{cov}[\boldsymbol{x},\boldsymbol{y}] & \mathrm{var}[\boldsymbol{y}] \\ + \end{bmatrix}. +$$ + +The covariance takes values between zero and infinity and may thus +lead to problems with loss of numerical precision for particularly +large values. It is common to scale the covariance matrix by +introducing instead the correlation matrix defined via the so-called +correlation function + +$$ +\mathrm{corr}[\boldsymbol{x},\boldsymbol{y}]=\frac{\mathrm{cov}[\boldsymbol{x},\boldsymbol{y}]}{\sqrt{\mathrm{var}[\boldsymbol{x}] \mathrm{var}[\boldsymbol{y}]}}. +$$ + +The correlation function is then given by values $\mathrm{corr}[\boldsymbol{x},\boldsymbol{y}] +\in [-1,1]$. This avoids eventual problems with too large values. We +can then define the correlation matrix for the two vectors $\boldsymbol{x}$ +and $\boldsymbol{y}$ as + +$$ +\boldsymbol{K}[\boldsymbol{x},\boldsymbol{y}] = \begin{bmatrix} 1 & \mathrm{corr}[\boldsymbol{x},\boldsymbol{y}] \\ + \mathrm{corr}[\boldsymbol{y},\boldsymbol{x}] & 1 \\ + \end{bmatrix}, +$$ + +In the above example this is the function we constructed using **pandas**. + +## Correlation Function and Design/Feature Matrix + +In our derivation of the various regression algorithms like **Ordinary Least Squares** or **Ridge regression** +we defined the design/feature matrix $\boldsymbol{X}$ as + +$$ +\boldsymbol{X}=\begin{bmatrix} +x_{0,0} & x_{0,1} & x_{0,2}& \dots & \dots x_{0,p-1}\\ +x_{1,0} & x_{1,1} & x_{1,2}& \dots & \dots x_{1,p-1}\\ +x_{2,0} & x_{2,1} & x_{2,2}& \dots & \dots x_{2,p-1}\\ +\dots & \dots & \dots & \dots \dots & \dots \\ +x_{n-2,0} & x_{n-2,1} & x_{n-2,2}& \dots & \dots x_{n-2,p-1}\\ +x_{n-1,0} & x_{n-1,1} & x_{n-1,2}& \dots & \dots x_{n-1,p-1}\\ +\end{bmatrix}, +$$ + +with $\boldsymbol{X}\in {\mathbb{R}}^{n\times p}$, with the predictors/features $p$ refering to the column numbers and the +entries $n$ being the row elements. +We can rewrite the design/feature matrix in terms of its column vectors as + +$$ +\boldsymbol{X}=\begin{bmatrix} \boldsymbol{x}_0 & \boldsymbol{x}_1 & \boldsymbol{x}_2 & \dots & \dots & \boldsymbol{x}_{p-1}\end{bmatrix}, +$$ + +with a given vector + +$$ +\boldsymbol{x}_i^T = \begin{bmatrix}x_{0,i} & x_{1,i} & x_{2,i}& \dots & \dots x_{n-1,i}\end{bmatrix}. +$$ + +With these definitions, we can now rewrite our $2\times 2$ +correaltion/covariance matrix in terms of a moe general design/feature +matrix $\boldsymbol{X}\in {\mathbb{R}}^{n\times p}$. This leads to a $p\times p$ +covariance matrix for the vectors $\boldsymbol{x}_i$ with $i=0,1,\dots,p-1$ + +$$ +\boldsymbol{C}[\boldsymbol{x}] = \begin{bmatrix} +\mathrm{var}[\boldsymbol{x}_0] & \mathrm{cov}[\boldsymbol{x}_0,\boldsymbol{x}_1] & \mathrm{cov}[\boldsymbol{x}_0,\boldsymbol{x}_2] & \dots & \dots & \mathrm{cov}[\boldsymbol{x}_0,\boldsymbol{x}_{p-1}]\\ +\mathrm{cov}[\boldsymbol{x}_1,\boldsymbol{x}_0] & \mathrm{var}[\boldsymbol{x}_1] & \mathrm{cov}[\boldsymbol{x}_1,\boldsymbol{x}_2] & \dots & \dots & \mathrm{cov}[\boldsymbol{x}_1,\boldsymbol{x}_{p-1}]\\ +\mathrm{cov}[\boldsymbol{x}_2,\boldsymbol{x}_0] & \mathrm{cov}[\boldsymbol{x}_2,\boldsymbol{x}_1] & \mathrm{var}[\boldsymbol{x}_2] & \dots & \dots & \mathrm{cov}[\boldsymbol{x}_2,\boldsymbol{x}_{p-1}]\\ +\dots & \dots & \dots & \dots & \dots & \dots \\ +\dots & \dots & \dots & \dots & \dots & \dots \\ +\mathrm{cov}[\boldsymbol{x}_{p-1},\boldsymbol{x}_0] & \mathrm{cov}[\boldsymbol{x}_{p-1},\boldsymbol{x}_1] & \mathrm{cov}[\boldsymbol{x}_{p-1},\boldsymbol{x}_{2}] & \dots & \dots & \mathrm{var}[\boldsymbol{x}_{p-1}]\\ +\end{bmatrix}, +$$ + +and the correlation matrix + +$$ +\boldsymbol{K}[\boldsymbol{x}] = \begin{bmatrix} +1 & \mathrm{corr}[\boldsymbol{x}_0,\boldsymbol{x}_1] & \mathrm{corr}[\boldsymbol{x}_0,\boldsymbol{x}_2] & \dots & \dots & \mathrm{corr}[\boldsymbol{x}_0,\boldsymbol{x}_{p-1}]\\ +\mathrm{corr}[\boldsymbol{x}_1,\boldsymbol{x}_0] & 1 & \mathrm{corr}[\boldsymbol{x}_1,\boldsymbol{x}_2] & \dots & \dots & \mathrm{corr}[\boldsymbol{x}_1,\boldsymbol{x}_{p-1}]\\ +\mathrm{corr}[\boldsymbol{x}_2,\boldsymbol{x}_0] & \mathrm{corr}[\boldsymbol{x}_2,\boldsymbol{x}_1] & 1 & \dots & \dots & \mathrm{corr}[\boldsymbol{x}_2,\boldsymbol{x}_{p-1}]\\ +\dots & \dots & \dots & \dots & \dots & \dots \\ +\dots & \dots & \dots & \dots & \dots & \dots \\ +\mathrm{corr}[\boldsymbol{x}_{p-1},\boldsymbol{x}_0] & \mathrm{corr}[\boldsymbol{x}_{p-1},\boldsymbol{x}_1] & \mathrm{corr}[\boldsymbol{x}_{p-1},\boldsymbol{x}_{2}] & \dots & \dots & 1\\ +\end{bmatrix}, +$$ + +## Covariance Matrix Examples + + +The Numpy function **np.cov** calculates the covariance elements using +the factor $1/(n-1)$ instead of $1/n$ since it assumes we do not have +the exact mean values. The following simple function uses the +**np.vstack** function which takes each vector of dimension $1\times n$ +and produces a $2\times n$ matrix $\boldsymbol{W}$ + +$$ +\boldsymbol{W} = \begin{bmatrix} x_0 & y_0 \\ + x_1 & y_1 \\ + x_2 & y_2\\ + \dots & \dots \\ + x_{n-2} & y_{n-2}\\ + x_{n-1} & y_{n-1} & + \end{bmatrix}, +$$ + +which in turn is converted into into the $2\times 2$ covariance matrix +$\boldsymbol{C}$ via the Numpy function **np.cov()**. We note that we can also calculate +the mean value of each set of samples $\boldsymbol{x}$ etc using the Numpy +function **np.mean(x)**. We can also extract the eigenvalues of the +covariance matrix through the **np.linalg.eig()** function. + +# Importing various packages +import numpy as np +n = 100 +x = np.random.normal(size=n) +print(np.mean(x)) +y = 4+3*x+np.random.normal(size=n) +print(np.mean(y)) +W = np.vstack((x, y)) +C = np.cov(W) +print(C) + +## Correlation Matrix + +The previous example can be converted into the correlation matrix by +simply scaling the matrix elements with the variances. We should also +subtract the mean values for each column. This leads to the following +code which sets up the correlations matrix for the previous example in +a more brute force way. Here we scale the mean values for each column of the design matrix, calculate the relevant mean values and variances and then finally set up the $2\times 2$ correlation matrix (since we have only two vectors). + +import numpy as np +n = 100 +# define two vectors +x = np.random.random(size=n) +y = 4+3*x+np.random.normal(size=n) +#scaling the x and y vectors +x = x - np.mean(x) +y = y - np.mean(y) +variance_x = np.sum(x@x)/n +variance_y = np.sum(y@y)/n +print(variance_x) +print(variance_y) +cov_xy = np.sum(x@y)/n +cov_xx = np.sum(x@x)/n +cov_yy = np.sum(y@y)/n +C = np.zeros((2,2)) +C[0,0]= cov_xx/variance_x +C[1,1]= cov_yy/variance_y +C[0,1]= cov_xy/np.sqrt(variance_y*variance_x) +C[1,0]= C[0,1] +print(C) + +We see that the matrix elements along the diagonal are one as they +should be and that the matrix is symmetric. Furthermore, diagonalizing +this matrix we easily see that it is a positive definite matrix. + +The above procedure with **numpy** can be made more compact if we use **pandas**. + +## Correlation Matrix with Pandas + +We whow here how we can set up the correlation matrix using **pandas**, as done in this simple code + +import numpy as np +import pandas as pd +n = 10 +x = np.random.normal(size=n) +x = x - np.mean(x) +y = 4+3*x+np.random.normal(size=n) +y = y - np.mean(y) +X = (np.vstack((x, y))).T +print(X) +Xpd = pd.DataFrame(X) +print(Xpd) +correlation_matrix = Xpd.corr() +print(correlation_matrix) + +We expand this model to the Franke function discussed above. + +## Correlation Matrix with Pandas and the Franke function + +# Common imports +import numpy as np +import pandas as pd + + +def FrankeFunction(x,y): + term1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2)) + term2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1)) + term3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2)) + term4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2) + return term1 + term2 + term3 + term4 + + +def create_X(x, y, n ): + if len(x.shape) > 1: + x = np.ravel(x) + y = np.ravel(y) + + N = len(x) + l = int((n+1)*(n+2)/2) # Number of elements in beta + X = np.ones((N,l)) + + for i in range(1,n+1): + q = int((i)*(i+1)/2) + for k in range(i+1): + X[:,q+k] = (x**(i-k))*(y**k) + + return X + + +# Making meshgrid of datapoints and compute Franke's function +n = 4 +N = 100 +x = np.sort(np.random.uniform(0, 1, N)) +y = np.sort(np.random.uniform(0, 1, N)) +z = FrankeFunction(x, y) +X = create_X(x, y, n=n) + +Xpd = pd.DataFrame(X) +# subtract the mean values and set up the covariance matrix +Xpd = Xpd - Xpd.mean() +covariance_matrix = Xpd.cov() +print(covariance_matrix) + +We note here that the covariance is zero for the first rows and +columns since all matrix elements in the design matrix were set to one +(we are fitting the function in terms of a polynomial of degree $n$). + +This means that the variance for these elements will be zero and will +cause problems when we set up the correlation matrix. We can simply +drop these elements and construct a correlation +matrix without these elements. + + +## Rewriting the Covariance and/or Correlation Matrix + +We can rewrite the covariance matrix in a more compact form in terms of the design/feature matrix $\boldsymbol{X}$ as + +$$ +\boldsymbol{C}[\boldsymbol{x}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}= \mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}]. +$$ + +To see this let us simply look at a design matrix $\boldsymbol{X}\in {\mathbb{R}}^{2\times 2}$ + +$$ +\boldsymbol{X}=\begin{bmatrix} +x_{00} & x_{01}\\ +x_{10} & x_{11}\\ +\end{bmatrix}=\begin{bmatrix} +\boldsymbol{x}_{0} & \boldsymbol{x}_{1}\\ +\end{bmatrix}. +$$ + +If we then compute the expectation value + +$$ +\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\begin{bmatrix} +x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\ +x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\ +\end{bmatrix}, +$$ + +which is just + +$$ +\boldsymbol{C}[\boldsymbol{x}_0,\boldsymbol{x}_1] = \boldsymbol{C}[\boldsymbol{x}]=\begin{bmatrix} \mathrm{var}[\boldsymbol{x}_0] & \mathrm{cov}[\boldsymbol{x}_0,\boldsymbol{x}_1] \\ + \mathrm{cov}[\boldsymbol{x}_1,\boldsymbol{x}_0] & \mathrm{var}[\boldsymbol{x}_1] \\ + \end{bmatrix}, +$$ + +where we wrote $$\boldsymbol{C}[\boldsymbol{x}_0,\boldsymbol{x}_1] = \boldsymbol{C}[\boldsymbol{x}]$$ to indicate that this the covariance of the vectors $\boldsymbol{x}$ of the design/feature matrix $\boldsymbol{X}$. + +It is easy to generalize this to a matrix $\boldsymbol{X}\in {\mathbb{R}}^{n\times p}$. + + +## Linking with SVD + +See lecture september 11. More text to be added here soon. + + + + +## Where are we going? + +Before we proceed, we need to rethink what we have been doing. In our +eager to fit the data, we have omitted several important elements in +our regression analysis. In what follows we will +1. look at statistical properties, including a discussion of mean values, variance and the so-called bias-variance tradeoff + +2. introduce resampling techniques like cross-validation, bootstrapping and jackknife and more + +This will allow us to link the standard linear algebra methods we have discussed above to a statistical interpretation of the methods. + + + + + +## Resampling methods +Resampling methods are an indispensable tool in modern +statistics. They involve repeatedly drawing samples from a training +set and refitting a model of interest on each sample in order to +obtain additional information about the fitted model. For example, in +order to estimate the variability of a linear regression fit, we can +repeatedly draw different samples from the training data, fit a linear +regression to each new sample, and then examine the extent to which +the resulting fits differ. Such an approach may allow us to obtain +information that would not be available from fitting the model only +once using the original training sample. + +Two resampling methods are often used in Machine Learning analyses, +1. The **bootstrap method** + +2. and **Cross-Validation** + +In addition there are several other methods such as the Jackknife and the Blocking methods. We will discuss in particular +cross-validation and the bootstrap method. + + + + +## Resampling approaches can be computationally expensive + +Resampling approaches can be computationally expensive, because they +involve fitting the same statistical method multiple times using +different subsets of the training data. However, due to recent +advances in computing power, the computational requirements of +resampling methods generally are not prohibitive. In this chapter, we +discuss two of the most commonly used resampling methods, +cross-validation and the bootstrap. Both methods are important tools +in the practical application of many statistical learning +procedures. For example, cross-validation can be used to estimate the +test error associated with a given statistical learning method in +order to evaluate its performance, or to select the appropriate level +of flexibility. The process of evaluating a model’s performance is +known as model assessment, whereas the process of selecting the proper +level of flexibility for a model is known as model selection. The +bootstrap is widely used. + + + +## Why resampling methods ? +**Statistical analysis.** + + +* Our simulations can be treated as *computer experiments*. This is particularly the case for Monte Carlo methods + +* The results can be analysed with the same statistical tools as we would use analysing experimental data. + +* As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors. + + + +## Statistical analysis + +* As in other experiments, many numerical experiments have two classes of errors: + + * Statistical errors + + * Systematical errors + + +* Statistical errors can be estimated using standard tools from statistics + +* Systematical errors are method specific and must be treated differently from case to case. + + + + + + + +## Linking the regression analysis with a statistical interpretation + + +The +advantage of doing linear regression is that we actually end up with +analytical expressions for several statistical quantities. +Standard least squares and Ridge regression allow us to +derive quantities like the variance and other expectation values in a +rather straightforward way. + + +It is assumed that $\varepsilon_i +\sim \mathcal{N}(0, \sigma^2)$ and the $\varepsilon_{i}$ are +independent, i.e.: + +$$ +\begin{align*} +\mbox{Cov}(\varepsilon_{i_1}, +\varepsilon_{i_2}) & = \left\{ \begin{array}{lcc} \sigma^2 & \mbox{if} +& i_1 = i_2, \\ 0 & \mbox{if} & i_1 \not= i_2. \end{array} \right. +\end{align*} +$$ + +The randomness of $\varepsilon_i$ implies that +$\mathbf{y}_i$ is also a random variable. In particular, +$\mathbf{y}_i$ is normally distributed, because $\varepsilon_i \sim +\mathcal{N}(0, \sigma^2)$ and $\mathbf{X}_{i,\ast} \, \boldsymbol{\beta}$ is a +non-random scalar. To specify the parameters of the distribution of +$\mathbf{y}_i$ we need to calculate its first two moments. + +Recall that $\boldsymbol{X}$ is a matrix of dimensionality $n\times p$. The +notation above $\mathbf{X}_{i,\ast}$ means that we are looking at the +row number $i$ and perform a sum over all values $p$. + + +## Assumptions made + +The assumption we have made here can be summarized as (and this is going to be useful when we discuss the bias-variance trade off) +that there exists a function $f(\boldsymbol{x})$ and a normal distributed error $\boldsymbol{\varepsilon}\sim \mathcal{N}(0, \sigma^2)$ +which describe our data + +$$ +\boldsymbol{y} = f(\boldsymbol{x})+\boldsymbol{\varepsilon} +$$ + +We approximate this function with our model from the solution of the linear regression equations, that is our +function $f$ is approximated by $\boldsymbol{\tilde{y}}$ where we want to minimize $(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2$, our MSE, with + +$$ +\boldsymbol{\tilde{y}} = \boldsymbol{X}\boldsymbol{\beta}. +$$ + +## Expectation value and variance + +We can calculate the expectation value of $\boldsymbol{y}$ for a given element $i$ + +$$ +\begin{align*} +\mathbb{E}(y_i) & = +\mathbb{E}(\mathbf{X}_{i, \ast} \, \boldsymbol{\beta}) + \mathbb{E}(\varepsilon_i) +\, \, \, = \, \, \, \mathbf{X}_{i, \ast} \, \beta, +\end{align*} +$$ + +while +its variance is + +$$ +\begin{align*} \mbox{Var}(y_i) & = \mathbb{E} \{ [y_i +- \mathbb{E}(y_i)]^2 \} \, \, \, = \, \, \, \mathbb{E} ( y_i^2 ) - +[\mathbb{E}(y_i)]^2 \\ & = \mathbb{E} [ ( \mathbf{X}_{i, \ast} \, +\beta + \varepsilon_i )^2] - ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 \\ & += \mathbb{E} [ ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 + 2 \varepsilon_i +\mathbf{X}_{i, \ast} \, \boldsymbol{\beta} + \varepsilon_i^2 ] - ( \mathbf{X}_{i, +\ast} \, \beta)^2 \\ & = ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 + 2 +\mathbb{E}(\varepsilon_i) \mathbf{X}_{i, \ast} \, \boldsymbol{\beta} + +\mathbb{E}(\varepsilon_i^2 ) - ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 +\\ & = \mathbb{E}(\varepsilon_i^2 ) \, \, \, = \, \, \, +\mbox{Var}(\varepsilon_i) \, \, \, = \, \, \, \sigma^2. +\end{align*} +$$ + +Hence, $y_i \sim \mathcal{N}( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta}, \sigma^2)$, that is $\boldsymbol{y}$ follows a normal distribution with +mean value $\boldsymbol{X}\boldsymbol{\beta}$ and variance $\sigma^2$ (not be confused with the singular values of the SVD). + +## Expectation value and variance for $\boldsymbol{\beta}$ + +With the OLS expressions for the parameters $\boldsymbol{\beta}$ we can evaluate the expectation value + +$$ +\mathbb{E}(\boldsymbol{\beta}) = \mathbb{E}[ (\mathbf{X}^{\top} \mathbf{X})^{-1}\mathbf{X}^{T} \mathbf{Y}]=(\mathbf{X}^{T} \mathbf{X})^{-1}\mathbf{X}^{T} \mathbb{E}[ \mathbf{Y}]=(\mathbf{X}^{T} \mathbf{X})^{-1} \mathbf{X}^{T}\mathbf{X}\boldsymbol{\beta}=\boldsymbol{\beta}. +$$ + +This means that the estimator of the regression parameters is unbiased. + +We can also calculate the variance + +The variance of $\boldsymbol{\beta}$ is + +$$ +\begin{eqnarray*} +\mbox{Var}(\boldsymbol{\beta}) & = & \mathbb{E} \{ [\boldsymbol{\beta} - \mathbb{E}(\boldsymbol{\beta})] [\boldsymbol{\beta} - \mathbb{E}(\boldsymbol{\beta})]^{T} \} +\\ +& = & \mathbb{E} \{ [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y} - \boldsymbol{\beta}] \, [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y} - \boldsymbol{\beta}]^{T} \} +\\ +% & = & \mathbb{E} \{ [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y}] \, [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y}]^{T} \} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} +% \\ +% & = & \mathbb{E} \{ (\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y} \, \mathbf{Y}^{T} \, \mathbf{X} \, (\mathbf{X}^{T} \mathbf{X})^{-1} \} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} +% \\ +& = & (\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \, \mathbb{E} \{ \mathbf{Y} \, \mathbf{Y}^{T} \} \, \mathbf{X} \, (\mathbf{X}^{T} \mathbf{X})^{-1} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} +\\ +& = & (\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \, \{ \mathbf{X} \, \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} \, \mathbf{X}^{T} + \sigma^2 \} \, \mathbf{X} \, (\mathbf{X}^{T} \mathbf{X})^{-1} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} +% \\ +% & = & (\mathbf{X}^T \mathbf{X})^{-1} \, \mathbf{X}^T \, \mathbf{X} \, \boldsymbol{\beta} \, \boldsymbol{\beta}^T \, \mathbf{X}^T \, \mathbf{X} \, (\mathbf{X}^T % \mathbf{X})^{-1} +% \\ +% & & + \, \, \sigma^2 \, (\mathbf{X}^T \mathbf{X})^{-1} \, \mathbf{X}^T \, \mathbf{X} \, (\mathbf{X}^T \mathbf{X})^{-1} - \boldsymbol{\beta} \boldsymbol{\beta}^T +\\ +& = & \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} + \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} +\, \, \, = \, \, \, \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1}, +\end{eqnarray*} +$$ + +where we have used that $\mathbb{E} (\mathbf{Y} \mathbf{Y}^{T}) = +\mathbf{X} \, \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} \, \mathbf{X}^{T} + +\sigma^2 \, \mathbf{I}_{nn}$. From $\mbox{Var}(\boldsymbol{\beta}) = \sigma^2 +\, (\mathbf{X}^{T} \mathbf{X})^{-1}$, one obtains an estimate of the +variance of the estimate of the $j$-th regression coefficient: +$\boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 \sqrt{ +[(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} }$. This may be used to +construct a confidence interval for the estimates. + + +In a similar way, we can obtain analytical expressions for say the +expectation values of the parameters $\boldsymbol{\beta}$ and their variance +when we employ Ridge regression, allowing us again to define a confidence interval. + +It is rather straightforward to show that + +$$ +\mathbb{E} \big[ \boldsymbol{\beta}^{\mathrm{Ridge}} \big]=(\mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I}_{pp})^{-1} (\mathbf{X}^{\top} \mathbf{X})\boldsymbol{\beta}^{\mathrm{OLS}}. +$$ + +We see clearly that +$\mathbb{E} \big[ \boldsymbol{\beta}^{\mathrm{Ridge}} \big] \not= \boldsymbol{\beta}^{\mathrm{OLS}}$ for any $\lambda > 0$. We say then that the ridge estimator is biased. + +We can also compute the variance as + +$$ +\mbox{Var}[\boldsymbol{\beta}^{\mathrm{Ridge}}]=\sigma^2[ \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1} \mathbf{X}^{T} \mathbf{X} \{ [ \mathbf{X}^{\top} \mathbf{X} + \lambda \mathbf{I} ]^{-1}\}^{T}, +$$ + +and it is easy to see that if the parameter $\lambda$ goes to infinity then the variance of Ridge parameters $\boldsymbol{\beta}$ goes to zero. + +With this, we can compute the difference + +$$ +\mbox{Var}[\boldsymbol{\beta}^{\mathrm{OLS}}]-\mbox{Var}(\boldsymbol{\beta}^{\mathrm{Ridge}})=\sigma^2 [ \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1}[ 2\lambda\mathbf{I} + \lambda^2 (\mathbf{X}^{T} \mathbf{X})^{-1} ] \{ [ \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1}\}^{T}. +$$ + +The difference is non-negative definite since each component of the +matrix product is non-negative definite. +This means the variance we obtain with the standard OLS will always for $\lambda > 0$ be larger than the variance of $\boldsymbol{\beta}$ obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below. + + +## Resampling methods + +With all these analytical equations for both the OLS and Ridge +regression, we will now outline how to assess a given model. This will +lead us to a discussion of the so-called bias-variance tradeoff (see +below) and so-called resampling methods. + +One of the quantities we have discussed as a way to measure errors is +the mean-squared error (MSE), mainly used for fitting of continuous +functions. Another choice is the absolute error. + +In the discussions below we will focus on the MSE and in particular since we will split the data into test and training data, +we discuss the +1. prediction error or simply the **test error** $\mathrm{Err_{Test}}$, where we have a fixed training set and the test error is the MSE arising from the data reserved for testing. We discuss also the + +2. training error $\mathrm{Err_{Train}}$, which is the average loss over the training data. + +As our model becomes more and more complex, more of the training data tends to used. The training may thence adapt to more complicated structures in the data. This may lead to a decrease in the bias (see below for code example) and a slight increase of the variance for the test error. +For a certain level of complexity the test error will reach minimum, before starting to increase again. The +training error reaches a saturation. + + + + +## Resampling methods: Jackknife and Bootstrap + +Two famous +resampling methods are the **independent bootstrap** and **the jackknife**. + +The jackknife is a special case of the independent bootstrap. Still, the jackknife was made +popular prior to the independent bootstrap. And as the popularity of +the independent bootstrap soared, new variants, such as **the dependent bootstrap**. + +The Jackknife and independent bootstrap work for +independent, identically distributed random variables. +If these conditions are not +satisfied, the methods will fail. Yet, it should be said that if the data are +independent, identically distributed, and we only want to estimate the +variance of $\overline{X}$ (which often is the case), then there is no +need for bootstrapping. + +## Resampling methods: Jackknife + +The Jackknife works by making many replicas of the estimator $\widehat{\theta}$. +The jackknife is a resampling method where we systematically leave out one observation from the vector of observed values $\boldsymbol{x} = (x_1,x_2,\cdots,X_n)$. +Let $\boldsymbol{x}_i$ denote the vector + +$$ +\boldsymbol{x}_i = (x_1,x_2,\cdots,x_{i-1},x_{i+1},\cdots,x_n), +$$ + +which equals the vector $\boldsymbol{x}$ with the exception that observation +number $i$ is left out. Using this notation, define +$\widehat{\theta}_i$ to be the estimator +$\widehat{\theta}$ computed using $\vec{X}_i$. + + +## Jackknife code example + +from numpy import * +from numpy.random import randint, randn +from time import time + +def jackknife(data, stat): + n = len(data);t = zeros(n); inds = arange(n); t0 = time() + ## 'jackknifing' by leaving out an observation for each i + for i in range(n): + t[i] = stat(delete(data,i) ) + + # analysis + print("Runtime: %g sec" % (time()-t0)); print("Jackknife Statistics :") + print("original bias std. error") + print("%8g %14g %15g" % (stat(data),(n-1)*mean(t)/n, (n*var(t))**.5)) + + return t + + +# Returns mean of data samples +def stat(data): + return mean(data) + + +mu, sigma = 100, 15 +datapoints = 10000 +x = mu + sigma*random.randn(datapoints) +# jackknife returns the data sample +t = jackknife(x, stat) + +## Resampling methods: Bootstrap +Bootstrapping is a nonparametric approach to statistical inference +that substitutes computation for more traditional distributional +assumptions and asymptotic results. Bootstrapping offers a number of +advantages: +1. The bootstrap is quite general, although there are some cases in which it fails. + +2. Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small. + +3. It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically. + +4. It is relatively simple to apply the bootstrap to complex data-collection plans (such as stratified and clustered samples). + + + + +## Resampling methods: Bootstrap background + +Since $\widehat{\theta} = \widehat{\theta}(\boldsymbol{X})$ is a function of random variables, +$\widehat{\theta}$ itself must be a random variable. Thus it has +a pdf, call this function $p(\boldsymbol{t})$. The aim of the bootstrap is to +estimate $p(\boldsymbol{t})$ by the relative frequency of +$\widehat{\theta}$. You can think of this as using a histogram +in the place of $p(\boldsymbol{t})$. If the relative frequency closely +resembles $p(\vec{t})$, then using numerics, it is straight forward to +estimate all the interesting parameters of $p(\boldsymbol{t})$ using point +estimators. + + +## Resampling methods: More Bootstrap background + +In the case that $\widehat{\theta}$ has +more than one component, and the components are independent, we use the +same estimator on each component separately. If the probability +density function of $X_i$, $p(x)$, had been known, then it would have +been straight forward to do this by: +1. Drawing lots of numbers from $p(x)$, suppose we call one such set of numbers $(X_1^*, X_2^*, \cdots, X_n^*)$. + +2. Then using these numbers, we could compute a replica of $\widehat{\theta}$ called $\widehat{\theta}^*$. + +By repeated use of (1) and (2), many +estimates of $\widehat{\theta}$ could have been obtained. The +idea is to use the relative frequency of $\widehat{\theta}^*$ +(think of a histogram) as an estimate of $p(\boldsymbol{t})$. + +## Resampling methods: Bootstrap approach + +But +unless there is enough information available about the process that +generated $X_1,X_2,\cdots,X_n$, $p(x)$ is in general +unknown. Therefore, [Efron in 1979](https://projecteuclid.org/euclid.aos/1176344552) asked the +question: What if we replace $p(x)$ by the relative frequency +of the observation $X_i$; if we draw observations in accordance with +the relative frequency of the observations, will we obtain the same +result in some asymptotic sense? The answer is yes. + + +Instead of generating the histogram for the relative +frequency of the observation $X_i$, just draw the values +$(X_1^*,X_2^*,\cdots,X_n^*)$ with replacement from the vector +$\boldsymbol{X}$. + +## Resampling methods: Bootstrap steps + +The independent bootstrap works like this: + +1. Draw with replacement $n$ numbers for the observed variables $\boldsymbol{x} = (x_1,x_2,\cdots,x_n)$. + +2. Define a vector $\boldsymbol{x}^*$ containing the values which were drawn from $\boldsymbol{x}$. + +3. Using the vector $\boldsymbol{x}^*$ compute $\widehat{\theta}^*$ by evaluating $\widehat \theta$ under the observations $\boldsymbol{x}^*$. + +4. Repeat this process $k$ times. + +When you are done, you can draw a histogram of the relative frequency +of $\widehat \theta^*$. This is your estimate of the probability +distribution $p(t)$. Using this probability distribution you can +estimate any statistics thereof. In principle you never draw the +histogram of the relative frequency of $\widehat{\theta}^*$. Instead +you use the estimators corresponding to the statistic of interest. For +example, if you are interested in estimating the variance of $\widehat +\theta$, apply the etsimator $\widehat \sigma^2$ to the values +$\widehat \theta ^*$. + + +## Code example for the Bootstrap method + +The following code starts with a Gaussian distribution with mean value +$\mu =100$ and variance $\sigma=15$. We use this to generate the data +used in the bootstrap analysis. The bootstrap analysis returns a data +set after a given number of bootstrap operations (as many as we have +data points). This data set consists of estimated mean values for each +bootstrap operation. The histogram generated by the bootstrap method +shows that the distribution for these mean values is also a Gaussian, +centered around the mean value $\mu=100$ but with standard deviation +$\sigma/\sqrt{n}$, where $n$ is the number of bootstrap samples (in +this case the same as the number of original data points). The value +of the standard deviation is what we expect from the central limit +theorem. + +from numpy import * +from numpy.random import randint, randn +from time import time +import matplotlib.mlab as mlab +import matplotlib.pyplot as plt + +# Returns mean of bootstrap samples +def stat(data): + return mean(data) + +# Bootstrap algorithm +def bootstrap(data, statistic, R): + t = zeros(R); n = len(data); inds = arange(n); t0 = time() + # non-parametric bootstrap + for i in range(R): + t[i] = statistic(data[randint(0,n,n)]) + + # analysis + print("Runtime: %g sec" % (time()-t0)); print("Bootstrap Statistics :") + print("original bias std. error") + print("%8g %8g %14g %15g" % (statistic(data), std(data),mean(t),std(t))) + return t + + +mu, sigma = 100, 15 +datapoints = 10000 +x = mu + sigma*random.randn(datapoints) +# bootstrap returns the data sample +t = bootstrap(x, stat, datapoints) +# the histogram of the bootstrapped data +n, binsboot, patches = plt.hist(t, 50, normed=1, facecolor='red', alpha=0.75) + +# add a 'best fit' line +y = mlab.normpdf( binsboot, mean(t), std(t)) +lt = plt.plot(binsboot, y, 'r--', linewidth=1) +plt.xlabel('Smarts') +plt.ylabel('Probability') +plt.axis([99.5, 100.6, 0, 3.0]) +plt.grid(True) + +plt.show() + + +## Various steps in cross-validation + +When the repetitive splitting of the data set is done randomly, +samples may accidently end up in a fast majority of the splits in +either training or test set. Such samples may have an unbalanced +influence on either model building or prediction evaluation. To avoid +this $k$-fold cross-validation structures the data splitting. The +samples are divided into $k$ more or less equally sized exhaustive and +mutually exclusive subsets. In turn (at each split) one of these +subsets plays the role of the test set while the union of the +remaining subsets constitutes the training set. Such a splitting +warrants a balanced representation of each sample in both training and +test set over the splits. Still the division into the $k$ subsets +involves a degree of randomness. This may be fully excluded when +choosing $k=n$. This particular case is referred to as leave-one-out +cross-validation (LOOCV). + + +## How to set up the cross-validation for Ridge and/or Lasso + +* Define a range of interest for the penalty parameter. + +* Divide the data set into training and test set comprising samples $\{1, \ldots, n\} \setminus i$ and $\{ i \}$, respectively. + +* Fit the linear regression model by means of ridge estimation for each $\lambda$ in the grid using the training set, and the corresponding estimate of the error variance $\boldsymbol{\sigma}_{-i}^2(\lambda)$, as + +$$ +\begin{align*} +\boldsymbol{\beta}_{-i}(\lambda) & = ( \boldsymbol{X}_{-i, \ast}^{T} +\boldsymbol{X}_{-i, \ast} + \lambda \boldsymbol{I}_{pp})^{-1} +\boldsymbol{X}_{-i, \ast}^{T} \boldsymbol{y}_{-i} +\end{align*} +$$ + +* Evaluate the prediction performance of these models on the test set by $\log\{L[y_i, \boldsymbol{X}_{i, \ast}; \boldsymbol{\beta}_{-i}(\lambda), \boldsymbol{\sigma}_{-i}^2(\lambda)]\}$. Or, by the prediction error $|y_i - \boldsymbol{X}_{i, \ast} \boldsymbol{\beta}_{-i}(\lambda)|$, the relative error, the error squared or the R2 score function. + +* Repeat the first three steps such that each sample plays the role of the test set once. + +* Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as + +$$ +\begin{align*} +\frac{1}{n} \sum_{i = 1}^n \log\{L[y_i, \mathbf{X}_{i, \ast}; \boldsymbol{\beta}_{-i}(\lambda), \boldsymbol{\sigma}_{-i}^2(\lambda)]\}. +\end{align*} +$$ + +## Cross-validation in brief + +For the various values of $k$ + +1. shuffle the dataset randomly. + +2. Split the dataset into $k$ groups. + +3. For each unique group: + +a. Decide which group to use as set for test data + +b. Take the remaining groups as a training data set + +c. Fit a model on the training set and evaluate it on the test set + +d. Retain the evaluation score and discard the model + + +5. Summarize the model using the sample of model evaluation scores + +## Code Example for Cross-validation and $k$-fold Cross-validation + +The code here uses Ridge regression with cross-validation (CV) resampling and $k$-fold CV in order to fit a specific polynomial. + +import numpy as np +import matplotlib.pyplot as plt +from sklearn.model_selection import KFold +from sklearn.linear_model import Ridge +from sklearn.model_selection import cross_val_score +from sklearn.preprocessing import PolynomialFeatures + +# A seed just to ensure that the random numbers are the same for every run. +# Useful for eventual debugging. +np.random.seed(3155) + +# Generate the data. +nsamples = 100 +x = np.random.randn(nsamples) +y = 3*x**2 + np.random.randn(nsamples) + +## Cross-validation on Ridge regression using KFold only + +# Decide degree on polynomial to fit +poly = PolynomialFeatures(degree = 6) + +# Decide which values of lambda to use +nlambdas = 500 +lambdas = np.logspace(-3, 5, nlambdas) + +# Initialize a KFold instance +k = 5 +kfold = KFold(n_splits = k) + +# Perform the cross-validation to estimate MSE +scores_KFold = np.zeros((nlambdas, k)) + +i = 0 +for lmb in lambdas: + ridge = Ridge(alpha = lmb) + j = 0 + for train_inds, test_inds in kfold.split(x): + xtrain = x[train_inds] + ytrain = y[train_inds] + + xtest = x[test_inds] + ytest = y[test_inds] + + Xtrain = poly.fit_transform(xtrain[:, np.newaxis]) + ridge.fit(Xtrain, ytrain[:, np.newaxis]) + + Xtest = poly.fit_transform(xtest[:, np.newaxis]) + ypred = ridge.predict(Xtest) + + scores_KFold[i,j] = np.sum((ypred - ytest[:, np.newaxis])**2)/np.size(ypred) + + j += 1 + i += 1 + + +estimated_mse_KFold = np.mean(scores_KFold, axis = 1) + +## Cross-validation using cross_val_score from sklearn along with KFold + +# kfold is an instance initialized above as: +# kfold = KFold(n_splits = k) + +estimated_mse_sklearn = np.zeros(nlambdas) +i = 0 +for lmb in lambdas: + ridge = Ridge(alpha = lmb) + + X = poly.fit_transform(x[:, np.newaxis]) + estimated_mse_folds = cross_val_score(ridge, X, y[:, np.newaxis], scoring='neg_mean_squared_error', cv=kfold) + + # cross_val_score return an array containing the estimated negative mse for every fold. + # we have to the the mean of every array in order to get an estimate of the mse of the model + estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds) + + i += 1 + +## Plot and compare the slightly different ways to perform cross-validation + +plt.figure() + +plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score') +plt.plot(np.log10(lambdas), estimated_mse_KFold, 'r--', label = 'KFold') + +plt.xlabel('log10(lambda)') +plt.ylabel('mse') + +plt.legend() + +plt.show() + +## The bias-variance tradeoff + + +We will discuss the bias-variance tradeoff in the context of +continuous predictions such as regression. However, many of the +intuitions and ideas discussed here also carry over to classification +tasks. Consider a dataset $\mathcal{L}$ consisting of the data +$\mathbf{X}_\mathcal{L}=\{(y_j, \boldsymbol{x}_j), j=0\ldots n-1\}$. + +Let us assume that the true data is generated from a noisy model + +$$ +\boldsymbol{y}=f(\boldsymbol{x}) + \boldsymbol{\epsilon} +$$ + +where $\epsilon$ is normally distributed with mean zero and standard deviation $\sigma^2$. + +In our derivation of the ordinary least squares method we defined then +an approximation to the function $f$ in terms of the parameters +$\boldsymbol{\beta}$ and the design matrix $\boldsymbol{X}$ which embody our model, +that is $\boldsymbol{\tilde{y}}=\boldsymbol{X}\boldsymbol{\beta}$. + +Thereafter we found the parameters $\boldsymbol{\beta}$ by optimizing the means squared error via the so-called cost function + +$$ +C(\boldsymbol{X},\boldsymbol{\beta}) =\frac{1}{n}\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2=\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]. +$$ + +We can rewrite this as + +$$ +\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\frac{1}{n}\sum_i(f_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2+\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2+\sigma^2. +$$ + +The three terms represent the square of the bias of the learning +method, which can be thought of as the error caused by the simplifying +assumptions built into the method. The second term represents the +variance of the chosen model and finally the last terms is variance of +the error $\boldsymbol{\epsilon}$. + +To derive this equation, we need to recall that the variance of $\boldsymbol{y}$ and $\boldsymbol{\epsilon}$ are both equal to $\sigma^2$. The mean value of $\boldsymbol{\epsilon}$ is by definition equal to zero. Furthermore, the function $f$ is not a stochastics variable, idem for $\boldsymbol{\tilde{y}}$. +We use a more compact notation in terms of the expectation value + +$$ +\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathbb{E}\left[(\boldsymbol{f}+\boldsymbol{\epsilon}-\boldsymbol{\tilde{y}})^2\right], +$$ + +and adding and subtracting $\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]$ we get + +$$ +\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathbb{E}\left[(\boldsymbol{f}+\boldsymbol{\epsilon}-\boldsymbol{\tilde{y}}+\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2\right], +$$ + +which, using the abovementioned expectation values can be rewritten as + +$$ +\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathbb{E}\left[(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2\right]+\mathrm{Var}\left[\boldsymbol{\tilde{y}}\right]+\sigma^2, +$$ + +that is the rewriting in terms of the so-called bias, the variance of the model $\boldsymbol{\tilde{y}}$ and the variance of $\boldsymbol{\epsilon}$. + + + + + +## Example code for Bias-Variance tradeoff + +import matplotlib.pyplot as plt +import numpy as np +from sklearn.linear_model import LinearRegression, Ridge, Lasso +from sklearn.preprocessing import PolynomialFeatures +from sklearn.model_selection import train_test_split +from sklearn.pipeline import make_pipeline +from sklearn.utils import resample + +np.random.seed(2018) + +n = 500 +n_boostraps = 100 +degree = 18 # A quite high value, just to show. +noise = 0.1 + +# Make data set. +x = np.linspace(-1, 3, n).reshape(-1, 1) +y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2) + np.random.normal(0, 0.1, x.shape) + +# Hold out some test data that is never used in training. +x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2) + +# Combine x transformation and model into one operation. +# Not neccesary, but convenient. +model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False)) + +# The following (m x n_bootstraps) matrix holds the column vectors y_pred +# for each bootstrap iteration. +y_pred = np.empty((y_test.shape[0], n_boostraps)) +for i in range(n_boostraps): + x_, y_ = resample(x_train, y_train) + + # Evaluate the new model on the same test data each time. + y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel() + +# Note: Expectations and variances taken w.r.t. different training +# data sets, hence the axis=1. Subsequent means are taken across the test data +# set in order to obtain a total value, but before this we have error/bias/variance +# calculated per data point in the test set. +# Note 2: The use of keepdims=True is important in the calculation of bias as this +# maintains the column vector form. Dropping this yields very unexpected results. +error = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) ) +bias = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 ) +variance = np.mean( np.var(y_pred, axis=1, keepdims=True) ) +print('Error:', error) +print('Bias^2:', bias) +print('Var:', variance) +print('{} >= {} + {} = {}'.format(error, bias, variance, bias+variance)) + +plt.plot(x[::5, :], y[::5, :], label='f(x)') +plt.scatter(x_test, y_test, label='Data points') +plt.scatter(x_test, np.mean(y_pred, axis=1), label='Pred') +plt.legend() +plt.show() + +## Understanding what happens + +import matplotlib.pyplot as plt +import numpy as np +from sklearn.linear_model import LinearRegression, Ridge, Lasso +from sklearn.preprocessing import PolynomialFeatures +from sklearn.model_selection import train_test_split +from sklearn.pipeline import make_pipeline +from sklearn.utils import resample + +np.random.seed(2018) + +n = 400 +n_boostraps = 100 +maxdegree = 30 + + +# Make data set. +x = np.linspace(-3, 3, n).reshape(-1, 1) +y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape) +error = np.zeros(maxdegree) +bias = np.zeros(maxdegree) +variance = np.zeros(maxdegree) +polydegree = np.zeros(maxdegree) +x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2) + +for degree in range(maxdegree): + model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False)) + y_pred = np.empty((y_test.shape[0], n_boostraps)) + for i in range(n_boostraps): + x_, y_ = resample(x_train, y_train) + y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel() + + polydegree[degree] = degree + error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) ) + bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 ) + variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) ) + print('Polynomial degree:', degree) + print('Error:', error[degree]) + print('Bias^2:', bias[degree]) + print('Var:', variance[degree]) + print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree])) + +plt.plot(polydegree, error, label='Error') +plt.plot(polydegree, bias, label='bias') +plt.plot(polydegree, variance, label='Variance') +plt.legend() +plt.show() + + +## Summing up + + + + +The bias-variance tradeoff summarizes the fundamental tension in +machine learning, particularly supervised learning, between the +complexity of a model and the amount of training data needed to train +it. Since data is often limited, in practice it is often useful to +use a less-complex model with higher bias, that is a model whose asymptotic +performance is worse than another model because it is easier to +train and less sensitive to sampling noise arising from having a +finite-sized training dataset (smaller variance). + + + +The above equations tell us that in +order to minimize the expected test error, we need to select a +statistical learning method that simultaneously achieves low variance +and low bias. Note that variance is inherently a nonnegative quantity, +and squared bias is also nonnegative. Hence, we see that the expected +test MSE can never lie below $Var(\epsilon)$, the irreducible error. + + +What do we mean by the variance and bias of a statistical learning +method? The variance refers to the amount by which our model would change if we +estimated it using a different training data set. Since the training +data are used to fit the statistical learning method, different +training data sets will result in a different estimate. But ideally the +estimate for our model should not vary too much between training +sets. However, if a method has high variance then small changes in +the training data can result in large changes in the model. In general, more +flexible statistical methods have higher variance. + + +You may also find this recent [article](https://www.pnas.org/content/116/32/15849) of interest. + +## Another Example from Scikit-Learn's Repository + +""" +============================ +Underfitting vs. Overfitting +============================ + +This example demonstrates the problems of underfitting and overfitting and +how we can use linear regression with polynomial features to approximate +nonlinear functions. The plot shows the function that we want to approximate, +which is a part of the cosine function. In addition, the samples from the +real function and the approximations of different models are displayed. The +models have polynomial features of different degrees. We can see that a +linear function (polynomial with degree 1) is not sufficient to fit the +training samples. This is called **underfitting**. A polynomial of degree 4 +approximates the true function almost perfectly. However, for higher degrees +the model will **overfit** the training data, i.e. it learns the noise of the +training data. +We evaluate quantitatively **overfitting** / **underfitting** by using +cross-validation. We calculate the mean squared error (MSE) on the validation +set, the higher, the less likely the model generalizes correctly from the +training data. +""" + +print(__doc__) + +import numpy as np +import matplotlib.pyplot as plt +from sklearn.pipeline import Pipeline +from sklearn.preprocessing import PolynomialFeatures +from sklearn.linear_model import LinearRegression +from sklearn.model_selection import cross_val_score + + +def true_fun(X): + return np.cos(1.5 * np.pi * X) + +np.random.seed(0) + +n_samples = 30 +degrees = [1, 4, 15] + +X = np.sort(np.random.rand(n_samples)) +y = true_fun(X) + np.random.randn(n_samples) * 0.1 + +plt.figure(figsize=(14, 5)) +for i in range(len(degrees)): + ax = plt.subplot(1, len(degrees), i + 1) + plt.setp(ax, xticks=(), yticks=()) + + polynomial_features = PolynomialFeatures(degree=degrees[i], + include_bias=False) + linear_regression = LinearRegression() + pipeline = Pipeline([("polynomial_features", polynomial_features), + ("linear_regression", linear_regression)]) + pipeline.fit(X[:, np.newaxis], y) + + # Evaluate the models using crossvalidation + scores = cross_val_score(pipeline, X[:, np.newaxis], y, + scoring="neg_mean_squared_error", cv=10) + + X_test = np.linspace(0, 1, 100) + plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label="Model") + plt.plot(X_test, true_fun(X_test), label="True function") + plt.scatter(X, y, edgecolor='b', s=20, label="Samples") + plt.xlabel("x") + plt.ylabel("y") + plt.xlim((0, 1)) + plt.ylim((-2, 2)) + plt.legend(loc="best") + plt.title("Degree {}\nMSE = {:.2e}(+/- {:.2e})".format( + degrees[i], -scores.mean(), scores.std())) +plt.show() + +## More examples on bootstrap and cross-validation and errors + +# Common imports +import os +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +from sklearn.linear_model import LinearRegression, Ridge, Lasso +from sklearn.model_selection import train_test_split +from sklearn.utils import resample +from sklearn.metrics import mean_squared_error +# Where to save the figures and data files +PROJECT_ROOT_DIR = "Results" +FIGURE_ID = "Results/FigureFiles" +DATA_ID = "DataFiles/" + +if not os.path.exists(PROJECT_ROOT_DIR): + os.mkdir(PROJECT_ROOT_DIR) + +if not os.path.exists(FIGURE_ID): + os.makedirs(FIGURE_ID) + +if not os.path.exists(DATA_ID): + os.makedirs(DATA_ID) + +def image_path(fig_id): + return os.path.join(FIGURE_ID, fig_id) + +def data_path(dat_id): + return os.path.join(DATA_ID, dat_id) + +def save_fig(fig_id): + plt.savefig(image_path(fig_id) + ".png", format='png') + +infile = open(data_path("EoS.csv"),'r') + +# Read the EoS data as csv file and organize the data into two arrays with density and energies +EoS = pd.read_csv(infile, names=('Density', 'Energy')) +EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce') +EoS = EoS.dropna() +Energies = EoS['Energy'] +Density = EoS['Density'] +# The design matrix now as function of various polytrops + +Maxpolydegree = 30 +X = np.zeros((len(Density),Maxpolydegree)) +X[:,0] = 1.0 +testerror = np.zeros(Maxpolydegree) +trainingerror = np.zeros(Maxpolydegree) +polynomial = np.zeros(Maxpolydegree) + +trials = 100 +for polydegree in range(1, Maxpolydegree): + polynomial[polydegree] = polydegree + for degree in range(polydegree): + X[:,degree] = Density**(degree/3.0) + +# loop over trials in order to estimate the expectation value of the MSE + testerror[polydegree] = 0.0 + trainingerror[polydegree] = 0.0 + for samples in range(trials): + x_train, x_test, y_train, y_test = train_test_split(X, Energies, test_size=0.2) + model = LinearRegression(fit_intercept=True).fit(x_train, y_train) + ypred = model.predict(x_train) + ytilde = model.predict(x_test) + testerror[polydegree] += mean_squared_error(y_test, ytilde) + trainingerror[polydegree] += mean_squared_error(y_train, ypred) + + testerror[polydegree] /= trials + trainingerror[polydegree] /= trials + print("Degree of polynomial: %3d"% polynomial[polydegree]) + print("Mean squared error on training data: %.8f" % trainingerror[polydegree]) + print("Mean squared error on test data: %.8f" % testerror[polydegree]) + +plt.plot(polynomial, np.log10(trainingerror), label='Training Error') +plt.plot(polynomial, np.log10(testerror), label='Test Error') +plt.xlabel('Polynomial degree') +plt.ylabel('log10[MSE]') +plt.legend() +plt.show() + + +## The same example but now with cross-validation + +# Common imports +import os +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +from sklearn.linear_model import LinearRegression, Ridge, Lasso +from sklearn.metrics import mean_squared_error +from sklearn.model_selection import KFold +from sklearn.model_selection import cross_val_score + + +# Where to save the figures and data files +PROJECT_ROOT_DIR = "Results" +FIGURE_ID = "Results/FigureFiles" +DATA_ID = "DataFiles/" + +if not os.path.exists(PROJECT_ROOT_DIR): + os.mkdir(PROJECT_ROOT_DIR) + +if not os.path.exists(FIGURE_ID): + os.makedirs(FIGURE_ID) + +if not os.path.exists(DATA_ID): + os.makedirs(DATA_ID) + +def image_path(fig_id): + return os.path.join(FIGURE_ID, fig_id) + +def data_path(dat_id): + return os.path.join(DATA_ID, dat_id) + +def save_fig(fig_id): + plt.savefig(image_path(fig_id) + ".png", format='png') + +infile = open(data_path("EoS.csv"),'r') + +# Read the EoS data as csv file and organize the data into two arrays with density and energies +EoS = pd.read_csv(infile, names=('Density', 'Energy')) +EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce') +EoS = EoS.dropna() +Energies = EoS['Energy'] +Density = EoS['Density'] +# The design matrix now as function of various polytrops + +Maxpolydegree = 30 +X = np.zeros((len(Density),Maxpolydegree)) +X[:,0] = 1.0 +estimated_mse_sklearn = np.zeros(Maxpolydegree) +polynomial = np.zeros(Maxpolydegree) +k =5 +kfold = KFold(n_splits = k) + +for polydegree in range(1, Maxpolydegree): + polynomial[polydegree] = polydegree + for degree in range(polydegree): + X[:,degree] = Density**(degree/3.0) + OLS = LinearRegression() +# loop over trials in order to estimate the expectation value of the MSE + estimated_mse_folds = cross_val_score(OLS, X, Energies, scoring='neg_mean_squared_error', cv=kfold) +#[:, np.newaxis] + estimated_mse_sklearn[polydegree] = np.mean(-estimated_mse_folds) + +plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error') +plt.xlabel('Polynomial degree') +plt.ylabel('log10[MSE]') +plt.legend() +plt.show() + +## Cross-validation with Ridge + +import numpy as np +import matplotlib.pyplot as plt +from sklearn.model_selection import KFold +from sklearn.linear_model import Ridge +from sklearn.model_selection import cross_val_score +from sklearn.preprocessing import PolynomialFeatures + +# A seed just to ensure that the random numbers are the same for every run. +np.random.seed(3155) +# Generate the data. +n = 100 +x = np.linspace(-3, 3, n).reshape(-1, 1) +y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape) +# Decide degree on polynomial to fit +poly = PolynomialFeatures(degree = 10) + +# Decide which values of lambda to use +nlambdas = 500 +lambdas = np.logspace(-3, 5, nlambdas) +# Initialize a KFold instance +k = 5 +kfold = KFold(n_splits = k) +estimated_mse_sklearn = np.zeros(nlambdas) +i = 0 +for lmb in lambdas: + ridge = Ridge(alpha = lmb) + estimated_mse_folds = cross_val_score(ridge, x, y, scoring='neg_mean_squared_error', cv=kfold) + estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds) + i += 1 +plt.figure() +plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score') +plt.xlabel('log10(lambda)') +plt.ylabel('MSE') +plt.legend() +plt.show() + +## The Ising model + +The one-dimensional Ising model with nearest neighbor interaction, no +external field and a constant coupling constant $J$ is given by + + +
    + +$$ +\begin{equation} + H = -J \sum_{k}^L s_k s_{k + 1}, +\label{_auto2} \tag{2} +\end{equation} +$$ + +where $s_i \in \{-1, 1\}$ and $s_{N + 1} = s_1$. The number of spins +in the system is determined by $L$. For the one-dimensional system +there is no phase transition. + +We will look at a system of $L = 40$ spins with a coupling constant of +$J = 1$. To get enough training data we will generate 10000 states +with their respective energies. + +import numpy as np +import matplotlib.pyplot as plt +from mpl_toolkits.axes_grid1 import make_axes_locatable +import seaborn as sns +import scipy.linalg as scl +from sklearn.model_selection import train_test_split +import tqdm +sns.set(color_codes=True) +cmap_args=dict(vmin=-1., vmax=1., cmap='seismic') + +L = 40 +n = int(1e4) + +spins = np.random.choice([-1, 1], size=(n, L)) +J = 1.0 + +energies = np.zeros(n) + +for i in range(n): + energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1)) + +Here we use ordinary least squares +regression to predict the energy for the nearest neighbor +one-dimensional Ising model on a ring, i.e., the endpoints wrap +around. We will use linear regression to fit a value for +the coupling constant to achieve this. + +## Reformulating the problem to suit regression + +A more general form for the one-dimensional Ising model is + + +
    + +$$ +\begin{equation} + H = - \sum_j^L \sum_k^L s_j s_k J_{jk}. +\label{_auto3} \tag{3} +\end{equation} +$$ + +Here we allow for interactions beyond the nearest neighbors and a state dependent +coupling constant. This latter expression can be formulated as +a matrix-product + + +
    + +$$ +\begin{equation} + \boldsymbol{H} = \boldsymbol{X} J, +\label{_auto4} \tag{4} +\end{equation} +$$ + +where $X_{jk} = s_j s_k$ and $J$ is a matrix which consists of the +elements $-J_{jk}$. This form of writing the energy fits perfectly +with the form utilized in linear regression, that is + + +
    + +$$ +\begin{equation} + \boldsymbol{y} = \boldsymbol{X}\boldsymbol{\beta} + \boldsymbol{\epsilon}, +\label{_auto5} \tag{5} +\end{equation} +$$ + +We split the data in training and test data as discussed in the previous example + +X = np.zeros((n, L ** 2)) +for i in range(n): + X[i] = np.outer(spins[i], spins[i]).ravel() +y = energies +X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2) + +## Linear regression + +In the ordinary least squares method we choose the cost function + + +
    + +$$ +\begin{equation} + C(\boldsymbol{X}, \boldsymbol{\beta})= \frac{1}{n}\left\{(\boldsymbol{X}\boldsymbol{\beta} - \boldsymbol{y})^T(\boldsymbol{X}\boldsymbol{\beta} - \boldsymbol{y})\right\}. +\label{_auto6} \tag{6} +\end{equation} +$$ + +We then find the extremal point of $C$ by taking the derivative with respect to $\boldsymbol{\beta}$ as discussed above. +This yields the expression for $\boldsymbol{\beta}$ to be + +$$ +\boldsymbol{\beta} = \frac{\boldsymbol{X}^T \boldsymbol{y}}{\boldsymbol{X}^T \boldsymbol{X}}, +$$ + +which immediately imposes some requirements on $\boldsymbol{X}$ as there must exist +an inverse of $\boldsymbol{X}^T \boldsymbol{X}$. If the expression we are modeling contains an +intercept, i.e., a constant term, we must make sure that the +first column of $\boldsymbol{X}$ consists of $1$. We do this here + +X_train_own = np.concatenate( + (np.ones(len(X_train))[:, np.newaxis], X_train), + axis=1 +) +X_test_own = np.concatenate( + (np.ones(len(X_test))[:, np.newaxis], X_test), + axis=1 +) + +def ols_inv(x: np.ndarray, y: np.ndarray) -> np.ndarray: + return scl.inv(x.T @ x) @ (x.T @ y) +beta = ols_inv(X_train_own, y_train) + +## Singular Value decomposition + +Doing the inversion directly turns out to be a bad idea since the matrix +$\boldsymbol{X}^T\boldsymbol{X}$ is singular. An alternative approach is to use the **singular +value decomposition**. Using the definition of the Moore-Penrose +pseudoinverse we can write the equation for $\boldsymbol{\beta}$ as + +$$ +\boldsymbol{\beta} = \boldsymbol{X}^{+}\boldsymbol{y}, +$$ + +where the pseudoinverse of $\boldsymbol{X}$ is given by + +$$ +\boldsymbol{X}^{+} = \frac{\boldsymbol{X}^T}{\boldsymbol{X}^T\boldsymbol{X}}. +$$ + +Using singular value decomposition we can decompose the matrix $\boldsymbol{X} = \boldsymbol{U}\boldsymbol{\Sigma} \boldsymbol{V}^T$, +where $\boldsymbol{U}$ and $\boldsymbol{V}$ are orthogonal(unitary) matrices and $\boldsymbol{\Sigma}$ contains the singular values (more details below). +where $X^{+} = V\Sigma^{+} U^T$. This reduces the equation for +$\omega$ to + + +
    + +$$ +\begin{equation} + \boldsymbol{\beta} = \boldsymbol{V}\boldsymbol{\Sigma}^{+} \boldsymbol{U}^T \boldsymbol{y}. +\label{_auto7} \tag{7} +\end{equation} +$$ + +Note that solving this equation by actually doing the pseudoinverse +(which is what we will do) is not a good idea as this operation scales +as $\mathcal{O}(n^3)$, where $n$ is the number of elements in a +general matrix. Instead, doing $QR$-factorization and solving the +linear system as an equation would reduce this down to +$\mathcal{O}(n^2)$ operations. + +def ols_svd(x: np.ndarray, y: np.ndarray) -> np.ndarray: + u, s, v = scl.svd(x) + return v.T @ scl.pinv(scl.diagsvd(s, u.shape[0], v.shape[0])) @ u.T @ y + +beta = ols_svd(X_train_own,y_train) + +When extracting the $J$-matrix we need to make sure that we remove the intercept, as is done here + +J = beta[1:].reshape(L, L) + +A way of looking at the coefficients in $J$ is to plot the matrices as images. + +fig = plt.figure(figsize=(20, 14)) +im = plt.imshow(J, **cmap_args) +plt.title("OLS", fontsize=18) +plt.xticks(fontsize=18) +plt.yticks(fontsize=18) +cb = fig.colorbar(im) +cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18) +plt.show() + +It is interesting to note that OLS +considers both $J_{j, j + 1} = -0.5$ and $J_{j, j - 1} = -0.5$ as +valid matrix elements for $J$. +In our discussion below on hyperparameters and Ridge and Lasso regression we will see that +this problem can be removed, partly and only with Lasso regression. + +In this case our matrix inversion was actually possible. The obvious question now is what is the mathematics behind the SVD? + + + + + +## The one-dimensional Ising model + +Let us bring back the Ising model again, but now with an additional +focus on Ridge and Lasso regression as well. We repeat some of the +basic parts of the Ising model and the setup of the training and test +data. The one-dimensional Ising model with nearest neighbor +interaction, no external field and a constant coupling constant $J$ is +given by + + +
    + +$$ +\begin{equation} + H = -J \sum_{k}^L s_k s_{k + 1}, +\label{_auto8} \tag{8} +\end{equation} +$$ + +where $s_i \in \{-1, 1\}$ and $s_{N + 1} = s_1$. The number of spins in the system is determined by $L$. For the one-dimensional system there is no phase transition. + +We will look at a system of $L = 40$ spins with a coupling constant of $J = 1$. To get enough training data we will generate 10000 states with their respective energies. + +import numpy as np +import matplotlib.pyplot as plt +from mpl_toolkits.axes_grid1 import make_axes_locatable +import seaborn as sns +import scipy.linalg as scl +from sklearn.model_selection import train_test_split +import sklearn.linear_model as skl +import tqdm +sns.set(color_codes=True) +cmap_args=dict(vmin=-1., vmax=1., cmap='seismic') + +L = 40 +n = int(1e4) + +spins = np.random.choice([-1, 1], size=(n, L)) +J = 1.0 + +energies = np.zeros(n) + +for i in range(n): + energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1)) + +A more general form for the one-dimensional Ising model is + + +
    + +$$ +\begin{equation} + H = - \sum_j^L \sum_k^L s_j s_k J_{jk}. +\label{_auto9} \tag{9} +\end{equation} +$$ + +Here we allow for interactions beyond the nearest neighbors and a more +adaptive coupling matrix. This latter expression can be formulated as +a matrix-product on the form + + +
    + +$$ +\begin{equation} + H = X J, +\label{_auto10} \tag{10} +\end{equation} +$$ + +where $X_{jk} = s_j s_k$ and $J$ is the matrix consisting of the +elements $-J_{jk}$. This form of writing the energy fits perfectly +with the form utilized in linear regression, viz. + + +
    + +$$ +\begin{equation} + \boldsymbol{y} = \boldsymbol{X}\boldsymbol{\beta} + \boldsymbol{\epsilon}. +\label{_auto11} \tag{11} +\end{equation} +$$ + +We organize the data as we did above + +X = np.zeros((n, L ** 2)) +for i in range(n): + X[i] = np.outer(spins[i], spins[i]).ravel() +y = energies +X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.96) + +X_train_own = np.concatenate( + (np.ones(len(X_train))[:, np.newaxis], X_train), + axis=1 +) + +X_test_own = np.concatenate( + (np.ones(len(X_test))[:, np.newaxis], X_test), + axis=1 +) + +We will do all fitting with **Scikit-Learn**, + +clf = skl.LinearRegression().fit(X_train, y_train) + +When extracting the $J$-matrix we make sure to remove the intercept + +J_sk = clf.coef_.reshape(L, L) + +And then we plot the results + +fig = plt.figure(figsize=(20, 14)) +im = plt.imshow(J_sk, **cmap_args) +plt.title("LinearRegression from Scikit-learn", fontsize=18) +plt.xticks(fontsize=18) +plt.yticks(fontsize=18) +cb = fig.colorbar(im) +cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18) +plt.show() + +The results perfectly with our previous discussion where we used our own code. + +## Ridge regression + +Having explored the ordinary least squares we move on to ridge +regression. In ridge regression we include a **regularizer**. This +involves a new cost function which leads to a new estimate for the +weights $\boldsymbol{\beta}$. This results in a penalized regression problem. The +cost function is given by + +1 +3 +6 + +< +< +< +! +! +M +A +T +H +_ +B +L +O +C +K + +_lambda = 0.1 +clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train) +J_ridge_sk = clf_ridge.coef_.reshape(L, L) +fig = plt.figure(figsize=(20, 14)) +im = plt.imshow(J_ridge_sk, **cmap_args) +plt.title("Ridge from Scikit-learn", fontsize=18) +plt.xticks(fontsize=18) +plt.yticks(fontsize=18) +cb = fig.colorbar(im) +cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18) + +plt.show() + +## LASSO regression + +In the **Least Absolute Shrinkage and Selection Operator** (LASSO)-method we get a third cost function. + + +
    + +$$ +\begin{equation} + C(\boldsymbol{X}, \boldsymbol{\beta}; \lambda) = (\boldsymbol{X}\boldsymbol{\beta} - \boldsymbol{y})^T(\boldsymbol{X}\boldsymbol{\beta} - \boldsymbol{y}) + \lambda \sqrt{\boldsymbol{\beta}^T\boldsymbol{\beta}}. +\label{_auto13} \tag{13} +\end{equation} +$$ + +Finding the extremal point of this cost function is not so straight-forward as in least squares and ridge. We will therefore rely solely on the function ``Lasso`` from **Scikit-Learn**. + +clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train) +J_lasso_sk = clf_lasso.coef_.reshape(L, L) +fig = plt.figure(figsize=(20, 14)) +im = plt.imshow(J_lasso_sk, **cmap_args) +plt.title("Lasso from Scikit-learn", fontsize=18) +plt.xticks(fontsize=18) +plt.yticks(fontsize=18) +cb = fig.colorbar(im) +cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18) + +plt.show() + +It is quite striking how LASSO breaks the symmetry of the coupling +constant as opposed to ridge and OLS. We get a sparse solution with +$J_{j, j + 1} = -1$. + + + +## Performance as function of the regularization parameter + +We see how the different models perform for a different set of values for $\lambda$. + +lambdas = np.logspace(-4, 5, 10) + +train_errors = { + "ols_sk": np.zeros(lambdas.size), + "ridge_sk": np.zeros(lambdas.size), + "lasso_sk": np.zeros(lambdas.size) +} + +test_errors = { + "ols_sk": np.zeros(lambdas.size), + "ridge_sk": np.zeros(lambdas.size), + "lasso_sk": np.zeros(lambdas.size) +} + +plot_counter = 1 + +fig = plt.figure(figsize=(32, 54)) + +for i, _lambda in enumerate(tqdm.tqdm(lambdas)): + for key, method in zip( + ["ols_sk", "ridge_sk", "lasso_sk"], + [skl.LinearRegression(), skl.Ridge(alpha=_lambda), skl.Lasso(alpha=_lambda)] + ): + method = method.fit(X_train, y_train) + + train_errors[key][i] = method.score(X_train, y_train) + test_errors[key][i] = method.score(X_test, y_test) + + omega = method.coef_.reshape(L, L) + + plt.subplot(10, 5, plot_counter) + plt.imshow(omega, **cmap_args) + plt.title(r"%s, $\lambda = %.4f$" % (key, _lambda)) + plot_counter += 1 + +plt.show() + +We see that LASSO reaches a good solution for low +values of $\lambda$, but will "wither" when we increase $\lambda$ too +much. Ridge is more stable over a larger range of values for +$\lambda$, but eventually also fades away. + +## Finding the optimal value of $\lambda$ + +To determine which value of $\lambda$ is best we plot the accuracy of +the models when predicting the training and the testing set. We expect +the accuracy of the training set to be quite good, but if the accuracy +of the testing set is much lower this tells us that we might be +subject to an overfit model. The ideal scenario is an accuracy on the +testing set that is close to the accuracy of the training set. + +fig = plt.figure(figsize=(20, 14)) + +colors = { + "ols_sk": "r", + "ridge_sk": "y", + "lasso_sk": "c" +} + +for key in train_errors: + plt.semilogx( + lambdas, + train_errors[key], + colors[key], + label="Train {0}".format(key), + linewidth=4.0 + ) + +for key in test_errors: + plt.semilogx( + lambdas, + test_errors[key], + colors[key] + "--", + label="Test {0}".format(key), + linewidth=4.0 + ) +plt.legend(loc="best", fontsize=18) +plt.xlabel(r"$\lambda$", fontsize=18) +plt.ylabel(r"$R^2$", fontsize=18) +plt.tick_params(labelsize=18) +plt.show() + +From the above figure we can see that LASSO with $\lambda = 10^{-2}$ +achieves a very good accuracy on the test set. 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74, in wrapped + return just_run(coro(*args, **kwargs)) + File "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/nbclient/util.py", line 53, in just_run + return loop.run_until_complete(coro) + File "/Users/hjensen/opt/anaconda3/lib/python3.8/asyncio/base_events.py", line 616, in run_until_complete + return future.result() + File "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/nbclient/client.py", line 535, in async_execute + await self.async_execute_cell( + File "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/nbclient/client.py", line 827, in async_execute_cell + self._check_raise_for_error(cell, exec_reply) + File "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/nbclient/client.py", line 735, in _check_raise_for_error + raise CellExecutionError.from_cell_and_msg(cell, exec_reply['content']) +nbclient.exceptions.CellExecutionError: An error occurred while executing the following cell: +------------------ +# Common imports +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +import sklearn.linear_model as skl +from sklearn.model_selection import train_test_split +from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error +import os + +# Where to save the figures and data files +PROJECT_ROOT_DIR = "Results" +FIGURE_ID = "Results/FigureFiles" +DATA_ID = "DataFiles/" + +if not os.path.exists(PROJECT_ROOT_DIR): + os.mkdir(PROJECT_ROOT_DIR) + +if not os.path.exists(FIGURE_ID): + os.makedirs(FIGURE_ID) + +if not os.path.exists(DATA_ID): + os.makedirs(DATA_ID) + +def image_path(fig_id): + return os.path.join(FIGURE_ID, fig_id) + +def data_path(dat_id): + return os.path.join(DATA_ID, dat_id) + +def save_fig(fig_id): + plt.savefig(image_path(fig_id) + ".png", format='png') + +infile = open(data_path("MassEval2016.dat"),'r') +------------------ + +--------------------------------------------------------------------------- +FileNotFoundError Traceback (most recent call last) + in  + 31 plt.savefig(image_path(fig_id) + ".png", format='png') + 32  +---> 33 infile = open(data_path("MassEval2016.dat"),'r') + +FileNotFoundError: [Errno 2] No such file or directory: 'DataFiles/MassEval2016.dat' +FileNotFoundError: [Errno 2] No such file or directory: 'DataFiles/MassEval2016.dat' + diff --git a/doc/src/LectureNotes/_build/latex/reports/regression.log b/doc/src/LectureNotes/_build/latex/reports/regression.log new file mode 100644 index 000000000..2d6f09692 --- /dev/null +++ b/doc/src/LectureNotes/_build/latex/reports/regression.log @@ -0,0 +1,116 @@ +Traceback (most recent call last): + File "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/jupyter_cache/executors/utils.py", line 51, in single_nb_execution + executenb( + File "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/nbclient/client.py", line 1082, in execute + return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute() + File "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/nbclient/util.py", line 74, in wrapped + return just_run(coro(*args, **kwargs)) + File "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/nbclient/util.py", line 53, in just_run + return loop.run_until_complete(coro) + File "/Users/hjensen/opt/anaconda3/lib/python3.8/asyncio/base_events.py", line 616, in run_until_complete + return future.result() + File "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/nbclient/client.py", line 535, in async_execute + await self.async_execute_cell( + File "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/nbclient/client.py", line 827, in async_execute_cell + self._check_raise_for_error(cell, exec_reply) + File "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/nbclient/client.py", line 735, in _check_raise_for_error + raise CellExecutionError.from_cell_and_msg(cell, exec_reply['content']) +nbclient.exceptions.CellExecutionError: An error occurred while executing the following cell: +------------------ +from numpy import * +from numpy.random import randint, randn +from time import time +import matplotlib.mlab as mlab +import matplotlib.pyplot as plt + +# Returns mean of bootstrap samples +def stat(data): + return mean(data) + +# Bootstrap algorithm +def bootstrap(data, statistic, R): + t = zeros(R); n = len(data); inds = arange(n); t0 = time() + # non-parametric bootstrap + for i in range(R): + t[i] = statistic(data[randint(0,n,n)]) + + # analysis + print("Runtime: %g sec" % (time()-t0)); print("Bootstrap Statistics :") + print("original bias std. error") + print("%8g %8g %14g %15g" % (statistic(data), std(data),mean(t),std(t))) + return t + + +mu, sigma = 100, 15 +datapoints = 10000 +x = mu + sigma*random.randn(datapoints) +# bootstrap returns the data sample +t = bootstrap(x, stat, datapoints) +# the histogram of the bootstrapped data +n, binsboot, patches = plt.hist(t, 50, normed=1, facecolor='red', alpha=0.75) + +# add a 'best fit' line +y = mlab.normpdf( binsboot, mean(t), std(t)) +lt = plt.plot(binsboot, y, 'r--', linewidth=1) +plt.xlabel('Smarts') +plt.ylabel('Probability') +plt.axis([99.5, 100.6, 0, 3.0]) +plt.grid(True) + +plt.show() +------------------ + +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) + in  + 29 t = bootstrap(x, stat, datapoints) + 30 # the histogram of the bootstrapped data +---> 31 n, binsboot, patches = plt.hist(t, 50, normed=1, facecolor='red', alpha=0.75) + 32  + 33 # add a 'best fit' line + +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/pyplot.py in hist(x, bins, range, density, weights, cumulative, bottom, histtype, align, orientation, rwidth, log, color, label, stacked, data, **kwargs) + 2603 orientation='vertical', rwidth=None, log=False, color=None, + 2604 label=None, stacked=False, *, data=None, **kwargs): +-> 2605 return gca().hist( + 2606 x, bins=bins, range=range, density=density, weights=weights, + 2607 cumulative=cumulative, bottom=bottom, histtype=histtype, + +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/__init__.py in inner(ax, data, *args, **kwargs) + 1563 def inner(ax, *args, data=None, **kwargs): + 1564 if data is None: +-> 1565 return func(ax, *map(sanitize_sequence, args), **kwargs) + 1566  + 1567 bound = new_sig.bind(ax, *args, **kwargs) + +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/axes/_axes.py in hist(self, x, bins, range, density, weights, cumulative, bottom, histtype, align, orientation, rwidth, log, color, label, stacked, **kwargs) + 6817 if patch: + 6818 p = patch[0] +-> 6819 p.update(kwargs) + 6820 if lbl is not None: + 6821 p.set_label(lbl) + +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/artist.py in update(self, props) + 1004  + 1005 with cbook._setattr_cm(self, eventson=False): +-> 1006 ret = [_update_property(self, k, v) for k, v in props.items()] + 1007  + 1008 if len(ret): + +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/artist.py in (.0) + 1004  + 1005 with cbook._setattr_cm(self, eventson=False): +-> 1006 ret = [_update_property(self, k, v) for k, v in props.items()] + 1007  + 1008 if len(ret): + +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/artist.py in _update_property(self, k, v) + 999 func = getattr(self, 'set_' + k, None) + 1000 if not callable(func): +-> 1001 raise AttributeError('{!r} object has no property {!r}' + 1002 .format(type(self).__name__, k)) + 1003 return func(v) + +AttributeError: 'Rectangle' object has no property 'normed' +AttributeError: 'Rectangle' object has no property 'normed' + diff --git a/doc/src/LectureNotes/_toc.yml b/doc/src/LectureNotes/_toc.yml index 6a57c9727..6b339ecb6 100644 --- a/doc/src/LectureNotes/_toc.yml +++ b/doc/src/LectureNotes/_toc.yml @@ -1,4 +1,4 @@ -- file: introduction.ipynb +- file: intro.md - part: Getting started #includes also linear algebra chapters: - file: gettingstarted.ipynb diff --git a/doc/src/LectureNotes/introduction.md b/doc/src/LectureNotes/introduction.md new file mode 100644 index 000000000..5d5627872 --- /dev/null +++ b/doc/src/LectureNotes/introduction.md @@ -0,0 +1,339 @@ + +# Introduction to Applied Data Analysis and Machine Learning + + +**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University + +Date: **Nov 19, 2019** + +Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license + + + + + +## Introduction + +During the last two decades there has been a swift and amazing +development of Machine Learning techniques and algorithms that impact +many areas in not only Science and Technology but also the Humanities, +Social Sciences, Medicine, Law, indeed, almost all possible +disciplines. The applications are incredibly many, from self-driving +cars to solving high-dimensional differential equations or complicated +quantum mechanical many-body problems. Machine Learning is perceived +by many as one of the main disruptive techniques nowadays. + +Statistics, Data science and Machine Learning form important +fields of research in modern science. They describe how to learn and +make predictions from data, as well as allowing us to extract +important correlations about physical process and the underlying laws +of motion in large data sets. The latter, big data sets, appear +frequently in essentially all disciplines, from the traditional +Science, Technology, Mathematics and Engineering fields to Life +Science, Law, education research, the Humanities and the Social +Sciences. + +It has become more +and more common to see research projects on big data in for example +the Social Sciences where extracting patterns from complicated survey +data is one of many research directions. Having a solid grasp of data +analysis and machine learning is thus becoming central to scientific +computing in many fields, and competences and skills within the fields +of machine learning and scientific computing are nowadays strongly +requested by many potential employers. The latter cannot be +overstated, familiarity with machine learning has almost become a +prerequisite for many of the most exciting employment opportunities, +whether they are in bioinformatics, life science, physics or finance, +in the private or the public sector. This author has had several +students or met students who have been hired recently based on their +skills and competences in scientific computing and data science, often +with marginal knowledge of machine learning. + +Machine learning is a subfield of computer science, and is closely +related to computational statistics. It evolved from the study of +pattern recognition in artificial intelligence (AI) research, and has +made contributions to AI tasks like computer vision, natural language +processing and speech recognition. Many of the methods we will study are also +strongly rooted in basic mathematics and physics research. + +Ideally, machine learning represents the science of giving computers +the ability to learn without being explicitly programmed. The idea is +that there exist generic algorithms which can be used to find patterns +in a broad class of data sets without having to write code +specifically for each problem. The algorithm will build its own logic +based on the data. You should however always keep in mind that +machines and algorithms are to a large extent developed by humans. The +insights and knowledge we have about a specific system, play a central +role when we develop a specific machine learning algorithm. + +Machine learning is an extremely rich field, in spite of its young +age. The increases we have seen during the last three decades in +computational capabilities have been followed by developments of +methods and techniques for analyzing and handling large date sets, +relying heavily on statistics, computer science and mathematics. The +field is rather new and developing rapidly. Popular software packages +written in Python for machine learning like +[Scikit-learn](http://scikit-learn.org/stable/), +[Tensorflow](https://www.tensorflow.org/), +[PyTorch](http://pytorch.org/) and [Keras](https://keras.io/), all +freely available at their respective GitHub sites, encompass +communities of developers in the thousands or more. And the number of +code developers and contributors keeps increasing. Not all the +algorithms and methods can be given a rigorous mathematical +justification, opening up thereby large rooms for experimenting and +trial and error and thereby exciting new developments. However, a +solid command of linear algebra, multivariate theory, probability +theory, statistical data analysis, understanding errors and Monte +Carlo methods are central elements in a proper understanding of many +of algorithms and methods we will discuss. + + + +## Learning outcomes + +These sets of lectures aim at giving you an overview of central aspects of +statistical data analysis as well as some of the central algorithms +used in machine learning. We will introduce a variety of central +algorithms and methods essential for studies of data analysis and +machine learning. + +Hands-on projects and experimenting with data and algorithms plays a central role in +these lectures, and our hope is, through the various +projects and exercises, to expose you to fundamental +research problems in these fields, with the aim to reproduce state of +the art scientific results. You will learn to develop and +structure codes for studying these systems, get acquainted with +computing facilities and learn to handle large scientific projects. A +good scientific and ethical conduct is emphasized throughout the +course. More specifically, you will + +1. Learn about basic data analysis, Bayesian statistics, Monte Carlo methods, data optimization and machine learning; + +2. Be capable of extending the acquired knowledge to other systems and cases; + +3. Have an understanding of central algorithms used in data analysis and machine learning; + +4. Gain knowledge of central aspects of Monte Carlo methods, Markov chains, Gibbs samplers and their possible applications, from numerical integration to simulation of stock markets; + +5. Understand methods for regression and classification; + +6. Learn about neural network, genetic algorithms and Boltzmann machines; + +7. Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++, in addition to a basic knowledge of linear algebra (typically taught during the first one or two years of undergraduate studies). + +There are several topics we will cover here, spanning from +statistical data analysis and its basic concepts such as expectation +values, variance, covariance, correlation functions and errors, via +well-known probability distribution functions like the uniform +distribution, the binomial distribution, the Poisson distribution and +simple and multivariate normal distributions to central elements of +Bayesian statistics and modeling. We will also remind the reader about +central elements from linear algebra and standard methods based on +linear algebra used to optimize (minimize) functions (the family of gradient descent methods) +and the Singular-value decomposition and +least square methods for parameterizing data. + +We will also cover Monte Carlo methods, Markov chains, well-known +algorithms for sampling stochastic events like the Metropolis-Hastings +and Gibbs sampling methods. An important aspect of all our +calculations is a proper estimation of errors. Here we will also +discuss famous resampling techniques like the blocking, the bootstrapping +and the jackknife methods and the infamous bias-variance tradeoff. + +The second part of the material covers several algorithms used in +machine learning. + + + + + + +## Types of Machine Learning + + +The approaches to machine learning are many, but are often split into +two main categories. In *supervised learning* we know the answer to a +problem, and let the computer deduce the logic behind it. On the other +hand, *unsupervised learning* is a method for finding patterns and +relationship in data sets without any prior knowledge of the system. +Some authours also operate with a third category, namely +*reinforcement learning*. This is a paradigm of learning inspired by +behavioral psychology, where learning is achieved by trial-and-error, +solely from rewards and punishment. + +Another way to categorize machine learning tasks is to consider the +desired output of a system. Some of the most common tasks are: + + * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning. + + * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values. + + * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning. + +The methods we cover have three main topics in common, irrespective of +whether we deal with supervised or unsupervised learning. The first +ingredient is normally our data set (which can be subdivided into +training and test data), the second item is a model which is normally +a function of some parameters. The model reflects our knowledge of +the system (or lack thereof). As an example, if we know that our data +show a behavior similar to what would be predicted by a polynomial, +fitting our data to a polynomial of some degree would then determin +our model. + +The last ingredient is a so-called **cost** +function which allows us to present an estimate on how good our model +is in reproducing the data it is supposed to train. + +Here we will build our machine learning approach on elements of the +statistical foundation discussed above, with elements from data +analysis, stochastic processes etc. We will discuss the following +machine learning algorithms + +1. Linear regression and its variants + +2. Decision tree algorithms, from single trees to random forests + +3. Bayesian statistics and regression + +4. Support vector machines and finally various variants of + +5. Artifical neural networks and deep learning, including convolutional neural networks and Bayesian neural networks + +6. Networks for unsupervised learning using for example reduced Boltzmann machines. + +## Choice of programming language + +Python plays nowadays a central role in the development of machine +learning techniques and tools for data analysis. In particular, seen +the wealth of machine learning and data analysis libraries written in +Python, easy to use libraries with immediate visualization(and not the +least impressive galleries of existing examples), the popularity of the +Jupyter notebook framework with the possibility to run **R** codes or +compiled programs written in C++, and much more made our choice of +programming language for this series of lectures easy. However, +since the focus here is not only on using existing Python libraries such +as **Scikit-Learn** or **Tensorflow**, but also on developing your own +algorithms and codes, we will as far as possible present many of these +algorithms either as a Python codes or C++ or Fortran (or other languages) codes. + +The reason we also focus on compiled languages like C++ (or +Fortran), is that Python is still notoriously slow when we do not +utilize highly streamlined computational libraries like +[Lapack](http://www.netlib.org/lapack/) or other numerical libraries +written in compiled languages (many of these libraries are written in +Fortran). Although a project like [Numba](https://numba.pydata.org/) +holds great promise for speeding up the unrolling of lengthy loops, C++ +and Fortran are presently still the performance winners. Numba gives +you potentially the power to speed up your applications with high +performance functions written directly in Python. In particular, +array-oriented and math-heavy Python code can achieve similar +performance to C, C++ and Fortran. However, even with these speed-ups, +for codes involving heavy Markov Chain Monte Carlo analyses and +optimizations of cost functions, C++/C or Fortran codes tend to +outperform Python codes. + +Presently thus, the community tends to let +code written in C++/C or Fortran do the heavy duty numerical +number crunching and leave the post-analysis of the data to the above +mentioned Python modules or software packages. However, with the developments taking place in for example the Python community, and seen +the changes during the last decade, the above situation may change swiftly in the not too distant future. + +Many of the examples we discuss in this series of lectures come with +existing data files or provide code examples which produce the data to +be analyzed. Most of the applications we will discuss deal with +small data sets (less than a terabyte of information) and can easily +be analyzed and tested on standard off the shelf laptops you find in general +stores. + +## Data handling, machine learning and ethical aspects + +In most of the cases we will study, we will either generate the data +to analyze ourselves (both for supervised learning and unsupervised +learning) or we will recur again and again to data present in say +**Scikit-Learn** or **Tensorflow**. Many of the examples we end up +dealing with are from a privacy and data protection point of view, +rather inoccuous and boring results of numerical +calculations. However, this does not hinder us from developing a sound +ethical attitude to the data we use, how we analyze the data and how +we handle the data. + +The most immediate and simplest possible ethical aspects deal with our +approach to the scientific process. Nowadays, with version control +software like [Git](https://git-scm.com/) and various online +repositories like [Github](https://github.com/), +[Gitlab](https://about.gitlab.com/) etc, we can easily make our codes +and data sets we have used, freely and easily accessible to a wider +community. This helps us almost automagically in making our science +reproducible. The large open-source development communities involved +in say [Scikit-Learn](http://scikit-learn.org/stable/), +[Tensorflow](https://www.tensorflow.org/), +[PyTorch](http://pytorch.org/) and [Keras](https://keras.io/), are +all excellent examples of this. The codes can be tested and improved +upon continuosly, helping thereby our scientific community at large in +developing data analysis and machine learning tools. It is much +easier today to gain traction and acceptance for making your science +reproducible. From a societal stand, this is an important element +since many of the developers are employees of large public institutions like +universities and research labs. Our fellow taxpayers do deserve to get +something back for their bucks. + +However, this more mechanical aspect of the ethics of science (in +particular the reproducibility of scientific results) is something +which is obvious and everybody should do so as part of the dialectics of +science. The fact that many scientists are not willing to share their codes or +data is detrimental to the scientific discourse. + +Before we proceed, we should add a disclaimer. Even though +we may dream of computers developing some kind of higher learning +capabilities, at the end (even if the artificial intelligence +community keeps touting our ears full of fancy futuristic avenues), it is we, yes you reading these lines, +who end up constructing and instructing, via various algorithms, the +machine learning approaches. Self-driving cars for example, rely on sofisticated +programs which take into account all possible situations a car can +encounter. In addition, extensive usage of training data from GPS +information, maps etc, are typically fed into the software for +self-driving cars. Adding to this various sensors and cameras that +feed information to the programs, there are zillions of ethical issues +which arise from this. + +For self-driving cars, where basically many of the standard machine +learning algorithms discussed here enter into the codes, at a certain +stage we have to make choices. Yes, we , the lads and lasses who wrote +a program for a specific brand of a self-driving car. As an example, +all carmakers have as their utmost priority the security of the +driver and the accompanying passengers. A famous European carmaker, which is +one of the leaders in the market of self-driving cars, had **if** +statements of the following type: suppose there are two obstacles in +front of you and you cannot avoid to collide with one of them. One of +the obstacles is a monstertruck while the other one is a kindergarten +class trying to cross the road. The self-driving car algo would then +opt for the hitting the small folks instead of the monstertruck, since +the likelihood of surving a collision with our future citizens, is +much higher. + +This leads to serious ethical aspects. Why should we opt for such an +option? Who decides and who is entitled to make such choices? Keep in +mind that many of the algorithms you will encounter in this series of +lectures or hear about later, are indeed based on simple programming +instructions. And you are very likely to be one of the people who may +end up writing such a code. Thus, developing a sound ethical attitude +to what we do, an approach well beyond the simple mechanistic one of +making our science available and reproducible, is much needed. The +example of the self-driving cars is just one of infinitely many cases +where we have to make choices. When you analyze data on economic +inequalities, who guarantees that you are not weighting some data in a +particular way, perhaps because you dearly want a specific conclusion +which may support your political views? Or what about the recent +claims that a famous IT company like Apple has a sexist bias on the +their recently [launched credit card](https://qz.com/1748321/the-role-of-goldman-sachs-algorithms-in-the-apple-credit-card-scandal/)? + +We do not have the answers here, nor will we venture into a deeper +discussions of these aspects, but we want you think over these topics +in a more overarching way. A statistical data analysis with its dry +numbers and graphs meant to guide the eye, does not necessarily +reflect the truth, whatever that is. As a scientist, and after a +university education, you are supposedly a better citizen, with an +improved critical view and understanding of the scientific method, and +perhaps some deeper understanding of the ethics of science at +large. Use these insights. Be a critical citizen. You owe it to our +society. diff --git a/doc/src/NeuralNet/ode.py~ b/doc/src/NeuralNet/ode.py~ new file mode 100644 index 000000000..351a6b69d --- /dev/null +++ b/doc/src/NeuralNet/ode.py~ @@ -0,0 +1,123 @@ +import tensorflow.compat.v1 as tf +tf.disable_v2_behavior() +#tf.reset_default_graph() + +# import necessary packages +import numpy as np +import matplotlib.pyplot as plt +from sklearn import datasets + + +# ensure the same random numbers appear every time +np.random.seed(0) + +plt.rcParams['figure.figsize'] = (12,12) + + +# download MNIST dataset +digits = datasets.load_digits() + +# define inputs and labels +inputs = digits.images +labels = digits.target + +print("inputs = (n_inputs, pixel_width, pixel_height) = " + str(inputs.shape)) +print("labels = (n_inputs) = " + str(labels.shape)) + + +# flatten the image +# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64 +n_inputs = len(inputs) +inputs = inputs.reshape(n_inputs, -1) +print("X = (n_inputs, n_features) = " + str(inputs.shape)) + + +# choose some random images to display +indices = np.arange(n_inputs) +random_indices = np.random.choice(indices, size=5) + +for i, image in enumerate(digits.images[random_indices]): + plt.subplot(1, 5, i+1) + plt.axis('off') + plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest') + plt.title("Label: %d" % digits.target[random_indices[i]]) +plt.show() + +from keras.utils import to_categorical +from sklearn.model_selection import train_test_split + +# one-hot representation of labels +labels = to_categorical(labels) + +# split into train and test data +train_size = 0.8 +test_size = 1 - train_size +X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size, + test_size=test_size) + +epochs = 100 +batch_size = 100 +n_neurons_layer1 = 100 +n_neurons_layer2 = 50 +n_categories = 10 +eta_vals = np.logspace(-5, 1, 7) +lmbd_vals = np.logspace(-5, 1, 7) +from keras.models import Sequential +from keras.layers import Dense +from keras.regularizers import l2 +from keras.optimizers import SGD + +def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd): + model = Sequential() + model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=l2(lmbd))) + model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=l2(lmbd))) + model.add(Dense(n_categories, activation='softmax')) + + sgd = SGD(lr=eta) + model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy']) + + return model + +DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object) + +for i, eta in enumerate(eta_vals): + for j, lmbd in enumerate(lmbd_vals): + DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,eta=eta, lmbd=lmbd) + DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0) + scores = DNN.evaluate(X_test, Y_test) + + DNN_keras[i][j] = DNN + + print("Learning rate = ", eta) + print("Lambda = ", lmbd) + print("Test accuracy: %.3f" % scores[1]) + print() + +import seaborn as sns + +sns.set() + +train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals))) +test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals))) + +for i in range(len(eta_vals)): + for j in range(len(lmbd_vals)): + DNN = DNN_keras[i][j] + + train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[1] + test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[1] + + +fig, ax = plt.subplots(figsize = (10, 10)) +sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis") +ax.set_title("Training Accuracy") +ax.set_ylabel("$\eta$") +ax.set_xlabel("$\lambda$") +plt.show() + +fig, ax = plt.subplots(figsize = (10, 10)) +sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis") +ax.set_title("Test Accuracy") +ax.set_ylabel("$\eta$") +ax.set_xlabel("$\lambda$") +plt.show() diff --git a/doc/src/Regression/Bootstrap.py b/doc/src/Regression/Bootstrap.py new file mode 100644 index 000000000..6bc514447 --- /dev/null +++ b/doc/src/Regression/Bootstrap.py @@ -0,0 +1,42 @@ +from numpy import * +from numpy.random import randint, randn +from time import time +import matplotlib.mlab as mlab +import matplotlib.pyplot as plt + +# Returns mean of bootstrap samples +def stat(data): + return mean(data) + +# Bootstrap algorithm +def bootstrap(data, statistic, R): + t = zeros(R); n = len(data); inds = arange(n); t0 = time() + # non-parametric bootstrap + for i in range(R): + t[i] = statistic(data[randint(0,n,n)]) + + # analysis + print("Runtime: %g sec" % (time()-t0)); print("Bootstrap Statistics :") + print("original bias std. error") + print("%8g %8g %14g %15g" % (statistic(data), std(data),mean(t),std(t))) + return t + + +mu, sigma = 100, 15 +datapoints = 10000 +x = mu + sigma*random.randn(datapoints) +# bootstrap returns the data sample +t = bootstrap(x, stat, datapoints) +# the histogram of the bootstrapped data +n, binsboot, patches = plt.hist(t, 50, facecolor='red', alpha=0.75) + +# add a 'best fit' line +#y = mlab.normpdf( binsboot, mean(t), std(t)) +#lt = plt.plot(binsboot, y, 'r--', linewidth=1) +plt.xlabel('Smarts') +plt.ylabel('Probability') +plt.axis([95, 105, 0, 10.0]) +plt.grid(True) + +plt.show() +

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\n", + "image/png": 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Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", + "\n", + "Date: **Dec 25, 2019**\n", + "\n", + "Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## Introduction\n", + "\n", + "Our emphasis throughout this series of lectures \n", + "is on understanding the mathematical aspects of\n", + "different algorithms used in the fields of data analysis and machine learning. \n", + "\n", + "However, where possible we will emphasize the\n", + "importance of using available software. We start thus with a hands-on\n", + "and top-down approach to machine learning. The aim is thus to start with\n", + "relevant data or data we have produced \n", + "and use these to introduce statistical data analysis\n", + "concepts and machine learning algorithms before we delve into the\n", + "algorithms themselves. The examples we will use in the beginning, start with simple\n", + "polynomials with random noise added. We will use the Python\n", + "software package [Scikit-Learn](http://scikit-learn.org/stable/) and\n", + "introduce various machine learning algorithms to make fits of\n", + "the data and predictions. We move thereafter to more interesting\n", + "cases such as data from say experiments (below we will look at experimental nuclear binding energies as an example).\n", + "These are examples where we can easily set up the data and\n", + "then use machine learning algorithms included in for example\n", + "**Scikit-Learn**. \n", + "\n", + "These examples will serve us the purpose of getting\n", + "started. Furthermore, they allow us to catch more than two birds with\n", + "a stone. They will allow us to bring in some programming specific\n", + "topics and tools as well as showing the power of various Python \n", + "libraries for machine learning and statistical data analysis. \n", + "\n", + "Here, we will mainly focus on two\n", + "specific Python packages for Machine Learning, Scikit-Learn and\n", + "Tensorflow (see below for links etc). Moreover, the examples we\n", + "introduce will serve as inputs to many of our discussions later, as\n", + "well as allowing you to set up models and produce your own data and\n", + "get started with programming.\n", + "\n", + "\n", + "\n", + "## What is Machine Learning?\n", + "\n", + "Statistics, data science and machine learning form important fields of\n", + "research in modern science. They describe how to learn and make\n", + "predictions from data, as well as allowing us to extract important\n", + "correlations about physical process and the underlying laws of motion\n", + "in large data sets. The latter, big data sets, appear frequently in\n", + "essentially all disciplines, from the traditional Science, Technology,\n", + "Mathematics and Engineering fields to Life Science, Law, education\n", + "research, the Humanities and the Social Sciences. \n", + "\n", + "It has become more\n", + "and more common to see research projects on big data in for example\n", + "the Social Sciences where extracting patterns from complicated survey\n", + "data is one of many research directions. Having a solid grasp of data\n", + "analysis and machine learning is thus becoming central to scientific\n", + "computing in many fields, and competences and skills within the fields\n", + "of machine learning and scientific computing are nowadays strongly\n", + "requested by many potential employers. The latter cannot be\n", + "overstated, familiarity with machine learning has almost become a\n", + "prerequisite for many of the most exciting employment opportunities,\n", + "whether they are in bioinformatics, life science, physics or finance,\n", + "in the private or the public sector. This author has had several\n", + "students or met students who have been hired recently based on their\n", + "skills and competences in scientific computing and data science, often\n", + "with marginal knowledge of machine learning.\n", + "\n", + "Machine learning is a subfield of computer science, and is closely\n", + "related to computational statistics. It evolved from the study of\n", + "pattern recognition in artificial intelligence (AI) research, and has\n", + "made contributions to AI tasks like computer vision, natural language\n", + "processing and speech recognition. Many of the methods we will study are also \n", + "strongly rooted in basic mathematics and physics research. \n", + "\n", + "Ideally, machine learning represents the science of giving computers\n", + "the ability to learn without being explicitly programmed. The idea is\n", + "that there exist generic algorithms which can be used to find patterns\n", + "in a broad class of data sets without having to write code\n", + "specifically for each problem. The algorithm will build its own logic\n", + "based on the data. You should however always keep in mind that\n", + "machines and algorithms are to a large extent developed by humans. The\n", + "insights and knowledge we have about a specific system, play a central\n", + "role when we develop a specific machine learning algorithm. \n", + "\n", + "Machine learning is an extremely rich field, in spite of its young\n", + "age. The increases we have seen during the last three decades in\n", + "computational capabilities have been followed by developments of\n", + "methods and techniques for analyzing and handling large date sets,\n", + "relying heavily on statistics, computer science and mathematics. The\n", + "field is rather new and developing rapidly. Popular software packages\n", + "written in Python for machine learning like\n", + "[Scikit-learn](http://scikit-learn.org/stable/),\n", + "[Tensorflow](https://www.tensorflow.org/),\n", + "[PyTorch](http://pytorch.org/) and [Keras](https://keras.io/), all\n", + "freely available at their respective GitHub sites, encompass\n", + "communities of developers in the thousands or more. And the number of\n", + "code developers and contributors keeps increasing. Not all the\n", + "algorithms and methods can be given a rigorous mathematical\n", + "justification, opening up thereby large rooms for experimenting and\n", + "trial and error and thereby exciting new developments. However, a\n", + "solid command of linear algebra, multivariate theory, probability\n", + "theory, statistical data analysis, understanding errors and Monte\n", + "Carlo methods are central elements in a proper understanding of many\n", + "of algorithms and methods we will discuss.\n", + "\n", + "\n", + "\n", + "## Types of Machine Learning\n", + "\n", + "\n", + "The approaches to machine learning are many, but are often split into\n", + "two main categories. In *supervised learning* we know the answer to a\n", + "problem, and let the computer deduce the logic behind it. On the other\n", + "hand, *unsupervised learning* is a method for finding patterns and\n", + "relationship in data sets without any prior knowledge of the system.\n", + "Some authours also operate with a third category, namely\n", + "*reinforcement learning*. This is a paradigm of learning inspired by\n", + "behavioral psychology, where learning is achieved by trial-and-error,\n", + "solely from rewards and punishment.\n", + "\n", + "Another way to categorize machine learning tasks is to consider the\n", + "desired output of a system. Some of the most common tasks are:\n", + "\n", + " * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.\n", + "\n", + " * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.\n", + "\n", + " * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.\n", + "\n", + "The methods we cover have three main topics in common, irrespective of\n", + "whether we deal with supervised or unsupervised learning. The first\n", + "ingredient is normally our data set (which can be subdivided into\n", + "training and test data), the second item is a model which is normally a\n", + "function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model. \n", + "\n", + "The last ingredient is a so-called **cost**\n", + "function which allows us to present an estimate on how good our model\n", + "is in reproducing the data it is supposed to train. \n", + "At the heart of basically all ML algorithms there are so-called minimization algorithms, often we end up with various variants of **gradient** methods.\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## Software and needed installations\n", + "\n", + "We will make extensive use of Python as programming language and its\n", + "myriad of available libraries. You will find\n", + "Jupyter notebooks invaluable in your work. You can run **R**\n", + "codes in the Jupyter/IPython notebooks, with the immediate benefit of\n", + "visualizing your data. You can also use compiled languages like C++,\n", + "Rust, Julia, Fortran etc if you prefer. The focus in these lectures will be\n", + "on Python.\n", + "\n", + "\n", + "If you have Python installed (we strongly recommend Python3) and you feel\n", + "pretty familiar with installing different packages, we recommend that\n", + "you install the following Python packages via **pip** as \n", + "\n", + "1. pip install numpy scipy matplotlib ipython scikit-learn mglearn sympy pandas pillow \n", + "\n", + "For Python3, replace **pip** with **pip3**.\n", + "\n", + "For OSX users we recommend, after having installed Xcode, to\n", + "install **brew**. Brew allows for a seamless installation of additional\n", + "software via for example \n", + "\n", + "1. brew install python3\n", + "\n", + "For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,\n", + "you can use **pip** as well and simply install Python as \n", + "\n", + "1. sudo apt-get install python3 (or python for pyhton2.7)\n", + "\n", + "etc etc. \n", + "\n", + "\n", + "\n", + "## Python installers\n", + "\n", + "If you don't want to perform these operations separately and venture\n", + "into the hassle of exploring how to set up dependencies and paths, we\n", + "recommend two widely used distrubutions which set up all relevant\n", + "dependencies for Python, namely \n", + "\n", + "* [Anaconda](https://docs.anaconda.com/), \n", + "\n", + "which is an open source\n", + "distribution of the Python and R programming languages for large-scale\n", + "data processing, predictive analytics, and scientific computing, that\n", + "aims to simplify package management and deployment. Package versions\n", + "are managed by the package management system **conda**. \n", + "\n", + "* [Enthought canopy](https://www.enthought.com/product/canopy/) \n", + "\n", + "is a Python\n", + "distribution for scientific and analytic computing distribution and\n", + "analysis environment, available for free and under a commercial\n", + "license.\n", + "\n", + "Furthermore, [Google's Colab](https://colab.research.google.com/notebooks/welcome.ipynb) is a free Jupyter notebook environment that requires \n", + "no setup and runs entirely in the cloud. Try it out!\n", + "\n", + "## Useful Python libraries\n", + "Here we list several useful Python libraries we strongly recommend (if you use anaconda many of these are already there)\n", + "\n", + "* [NumPy](https://www.numpy.org/) is a highly popular library for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays\n", + "\n", + "* [The pandas](https://pandas.pydata.org/) library provides high-performance, easy-to-use data structures and data analysis tools \n", + "\n", + "* [Xarray](http://xarray.pydata.org/en/stable/) is a Python package that makes working with labelled multi-dimensional arrays simple, efficient, and fun!\n", + "\n", + "* [Scipy](https://www.scipy.org/) (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering. \n", + "\n", + "* [Matplotlib](https://matplotlib.org/) is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms.\n", + "\n", + "* [Autograd](https://github.com/HIPS/autograd) can automatically differentiate native Python and Numpy code. It can handle a large subset of Python's features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives\n", + "\n", + "* [SymPy](https://www.sympy.org/en/index.html) is a Python library for symbolic mathematics. \n", + "\n", + "* [scikit-learn](https://scikit-learn.org/stable/) has simple and efficient tools for machine learning, data mining and data analysis\n", + "\n", + "* [TensorFlow](https://www.tensorflow.org/) is a Python library for fast numerical computing created and released by Google\n", + "\n", + "* [Keras](https://keras.io/) is a high-level neural networks API, written in Python and capable of running on top of TensorFlow, CNTK, or Theano\n", + "\n", + "* And many more such as [pytorch](https://pytorch.org/), [Theano](https://pypi.org/project/Theano/) etc \n", + "\n", + "## Installing R, C++, cython or Julia\n", + "\n", + "You will also find it convenient to utilize **R**. We will mainly\n", + "use Python during our lectures and in various projects and exercises.\n", + "Those of you\n", + "already familiar with **R** should feel free to continue using **R**, keeping\n", + "however an eye on the parallel Python set ups. Similarly, if you are a\n", + "Python afecionado, feel free to explore **R** as well. Jupyter/Ipython\n", + "notebook allows you to run **R** codes interactively in your\n", + "browser. The software library **R** is really tailored for statistical data analysis\n", + "and allows for an easy usage of the tools and algorithms we will discuss in these\n", + "lectures.\n", + "\n", + "To install **R** with Jupyter notebook \n", + "[follow the link here](https://mpacer.org/maths/r-kernel-for-ipython-notebook)\n", + "\n", + "\n", + "\n", + "\n", + "## Installing R, C++, cython, Numba etc\n", + "\n", + "\n", + "For the C++ aficionados, Jupyter/IPython notebook allows you also to\n", + "install C++ and run codes written in this language interactively in\n", + "the browser. Since we will emphasize writing many of the algorithms\n", + "yourself, you can thus opt for either Python or C++ (or Fortran or other compiled languages) as programming\n", + "languages.\n", + "\n", + "To add more entropy, **cython** can also be used when running your\n", + "notebooks. It means that Python with the jupyter notebook\n", + "setup allows you to integrate widely popular softwares and tools for\n", + "scientific computing. Similarly, the \n", + "[Numba Python package](https://numba.pydata.org/) delivers increased performance\n", + "capabilities with minimal rewrites of your codes. With its\n", + "versatility, including symbolic operations, Python offers a unique\n", + "computational environment. Your jupyter notebook can easily be\n", + "converted into a nicely rendered **PDF** file or a Latex file for\n", + "further processing. For example, convert to latex as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " pycod jupyter nbconvert filename.ipynb --to latex \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And to add more versatility, the Python package [SymPy](http://www.sympy.org/en/index.html) is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) and is entirely written in Python. \n", + "\n", + "Finally, if you wish to use the light mark-up language \n", + "[doconce](https://github.com/hplgit/doconce) you can convert a standard ascii text file into various HTML \n", + "formats, ipython notebooks, latex files, pdf files etc with minimal edits. These lectures were generated using **doconce**.\n", + "\n", + "\n", + "\n", + "## Numpy examples and Important Matrix and vector handling packages\n", + "\n", + "There are several central software libraries for linear algebra and eigenvalue problems. Several of the more\n", + "popular ones have been wrapped into ofter software packages like those from the widely used text **Numerical Recipes**. The original source codes in many of the available packages are often taken from the widely used\n", + "software package LAPACK, which follows two other popular packages\n", + "developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly here.\n", + "\n", + " * LINPACK: package for linear equations and least square problems.\n", + "\n", + " * LAPACK:package for solving symmetric, unsymmetric and generalized eigenvalue problems. From LAPACK's website it is possible to download for free all source codes from this library. Both C/C++ and Fortran versions are available.\n", + "\n", + " * BLAS (I, II and III): (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. Blas I is vector operations, II vector-matrix operations and III matrix-matrix operations. Highly parallelized and efficient codes, all available for download from .\n", + "\n", + "## Basic Matrix Features\n", + "\n", + "**Matrix properties reminder.**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathbf{A} =\n", + " \\begin{bmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\\\\n", + " a_{21} & a_{22} & a_{23} & a_{24} \\\\\n", + " a_{31} & a_{32} & a_{33} & a_{34} \\\\\n", + " a_{41} & a_{42} & a_{43} & a_{44}\n", + " \\end{bmatrix}\\qquad\n", + "\\mathbf{I} =\n", + " \\begin{bmatrix} 1 & 0 & 0 & 0 \\\\\n", + " 0 & 1 & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " 0 & 0 & 0 & 1\n", + " \\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The inverse of a matrix is defined by" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\mathbf{A}^{-1} \\cdot \\mathbf{A} = I\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
    Relations Name matrix elements
    $A = A^{T}$ symmetric $a_{ij} = a_{ji}$
    $A = \\left (A^{T} \\right )^{-1}$ real orthogonal $\\sum_k a_{ik} a_{jk} = \\sum_k a_{ki} a_{kj} = \\delta_{ij}$
    $A = A^{ * }$ real matrix $a_{ij} = a_{ij}^{ * }$
    $A = A^{\\dagger}$ hermitian $a_{ij} = a_{ji}^{ * }$
    $A = \\left (A^{\\dagger} \\right )^{-1}$ unitary $\\sum_k a_{ik} a_{jk}^{ * } = \\sum_k a_{ki}^{ * } a_{kj} = \\delta_{ij}$
    \n", + "\n", + "\n", + "\n", + "\n", + "### Some famous Matrices\n", + "\n", + " * Diagonal if $a_{ij}=0$ for $i\\ne j$\n", + "\n", + " * Upper triangular if $a_{ij}=0$ for $i > j$\n", + "\n", + " * Lower triangular if $a_{ij}=0$ for $i < j$\n", + "\n", + " * Upper Hessenberg if $a_{ij}=0$ for $i > j+1$\n", + "\n", + " * Lower Hessenberg if $a_{ij}=0$ for $i < j+1$\n", + "\n", + " * Tridiagonal if $a_{ij}=0$ for $|i -j| > 1$\n", + "\n", + " * Lower banded with bandwidth $p$: $a_{ij}=0$ for $i > j+p$\n", + "\n", + " * Upper banded with bandwidth $p$: $a_{ij}=0$ for $i < j+p$\n", + "\n", + " * Banded, block upper triangular, block lower triangular....\n", + "\n", + "### More Basic Matrix Features\n", + "\n", + "**Some Equivalent Statements.**\n", + "\n", + "For an $N\\times N$ matrix $\\mathbf{A}$ the following properties are all equivalent\n", + "\n", + " * If the inverse of $\\mathbf{A}$ exists, $\\mathbf{A}$ is nonsingular.\n", + "\n", + " * The equation $\\mathbf{Ax}=0$ implies $\\mathbf{x}=0$.\n", + "\n", + " * The rows of $\\mathbf{A}$ form a basis of $R^N$.\n", + "\n", + " * The columns of $\\mathbf{A}$ form a basis of $R^N$.\n", + "\n", + " * $\\mathbf{A}$ is a product of elementary matrices.\n", + "\n", + " * $0$ is not eigenvalue of $\\mathbf{A}$.\n", + "\n", + "\n", + "\n", + "\n", + "## Numpy and arrays\n", + "[Numpy](http://www.numpy.org/) provides an easy way to handle arrays in Python. The standard way to import this library is as" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here follows a simple example where we set up an array of ten elements, all determined by random numbers drawn according to the normal distribution," + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1.80432933 -0.34658746 -0.1683511 0.47440928 0.14478962 0.72574174\n", + " -0.32725137 -0.80229425 1.91533392 -0.20784711]\n", + "-0.3465874638427752\n" + ] + } + ], + "source": [ + "n = 10\n", + "x = np.random.normal(size=n)\n", + "print(x)\n", + "print(x[1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We defined a vector $x$ with $n=10$ elements with its values given by the Normal distribution $N(0,1)$.\n", + "Another alternative is to declare a vector as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1 2 3]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "x = np.array([1, 2, 3])\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we have defined a vector with three elements, with $x_0=1$, $x_1=2$ and $x_2=3$. Note that both Python and C++\n", + "start numbering array elements from $0$ and on. This means that a vector with $n$ elements has a sequence of entities $x_0, x_1, x_2, \\dots, x_{n-1}$. We could also let (recommended) Numpy to compute the logarithms of a specific array as" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.38629436 1.94591015 2.07944154]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "x = np.log(np.array([4, 7, 8]))\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the last example we used Numpy's unary function $np.log$. This function is\n", + "highly tuned to compute array elements since the code is vectorized\n", + "and does not require looping. We normaly recommend that you use the\n", + "Numpy intrinsic functions instead of the corresponding **log** function\n", + "from Python's **math** module. The looping is done explicitely by the\n", + "**np.log** function. The alternative, and slower way to compute the\n", + "logarithms of a vector would be to write" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1 1 2]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from math import log\n", + "x = np.array([4, 7, 8])\n", + "for i in range(0, len(x)):\n", + " x[i] = log(x[i])\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We note that our code is much longer already and we need to import the **log** function from the **math** module. \n", + "The attentive reader will also notice that the output is $[1, 1, 2]$. Python interprets automagically our numbers as integers (like the **automatic** keyword in C++). To change this we could define our array elements to be double precision numbers as" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.38629436 1.94591015 2.07944154]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "x = np.log(np.array([4, 7, 8], dtype = np.float64))\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "or simply write them as double precision numbers (Python uses 64 bits as default for floating point type variables), that is" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.38629436 1.94591015 2.07944154]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "x = np.log(np.array([4.0, 7.0, 8.0]))\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To check the number of bytes (remember that one byte contains eight bits for double precision variables), you can use simple use the **itemsize** functionality (the array $x$ is actually an object which inherits the functionalities defined in Numpy) as" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "8\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "x = np.log(np.array([4.0, 7.0, 8.0]))\n", + "print(x.itemsize)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Matrices in Python\n", + "\n", + "Having defined vectors, we are now ready to try out matrices. We can\n", + "define a $3 \\times 3 $ real matrix $\\hat{A}$ as (recall that we user\n", + "lowercase letters for vectors and uppercase letters for matrices)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1.38629436 1.94591015 2.07944154]\n", + " [1.09861229 2.30258509 2.39789527]\n", + " [1.38629436 1.60943791 1.94591015]]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ]))\n", + "print(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we use the **shape** function we would get $(3, 3)$ as output, that is verifying that our matrix is a $3\\times 3$ matrix. We can slice the matrix and print for example the first column (Python organized matrix elements in a row-major order, see below) as" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.38629436 1.09861229 1.38629436]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ]))\n", + "# print the first column, row-major order and elements start with 0\n", + "print(A[:,0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can continue this was by printing out other columns or rows. The example here prints out the second column" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.09861229 2.30258509 2.39789527]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ]))\n", + "# print the first column, row-major order and elements start with 0\n", + "print(A[1,:])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Numpy contains many other functionalities that allow us to slice, subdivide etc etc arrays. We strongly recommend that you look up the [Numpy website for more details](http://www.numpy.org/). Useful functions when defining a matrix are the **np.zeros** function which declares a matrix of a given dimension and sets all elements to zero" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "n = 10\n", + "# define a matrix of dimension 10 x 10 and set all elements to zero\n", + "A = np.zeros( (n, n) )\n", + "print(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "or initializing all elements to" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n", + " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "n = 10\n", + "# define a matrix of dimension 10 x 10 and set all elements to one\n", + "A = np.eye( n )\n", + "print(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "or as unitarily distributed random numbers (see the material on random number generators in the statistics part)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.43899866 0.46169685 0.82802838 0.01878861 0.57728067 0.27066734\n", + " 0.76768203 0.45868393 0.88154915 0.61056994]\n", + " [0.96580399 0.87602499 0.14852935 0.21224171 0.13320006 0.79846325\n", + " 0.20788158 0.69197632 0.16066764 0.66755371]\n", + " [0.47252801 0.81555965 0.58536962 0.32273634 0.72036017 0.31013823\n", + " 0.57539355 0.50350565 0.20874948 0.07492828]\n", + " [0.86223598 0.43597325 0.40770873 0.68604957 0.21101646 0.27044856\n", + " 0.1455994 0.60472182 0.19083044 0.10860756]\n", + " [0.40146508 0.27103868 0.26800926 0.21720673 0.88831113 0.51288871\n", + " 0.7187809 0.76198251 0.36040404 0.71476125]\n", + " [0.03966188 0.56233876 0.3487739 0.7690807 0.42767953 0.68674257\n", + " 0.42012295 0.4879373 0.73078312 0.25520193]\n", + " [0.82968903 0.67872721 0.1762172 0.54494737 0.62176734 0.43590014\n", + " 0.91153384 0.50347008 0.18704645 0.66579026]\n", + " [0.06237223 0.4835503 0.69195546 0.81822687 0.94712863 0.41172076\n", + " 0.45145424 0.94821617 0.20049451 0.0287913 ]\n", + " [0.47161189 0.91430425 0.61801367 0.67828384 0.38636346 0.18000367\n", + " 0.63048023 0.96683366 0.83713254 0.48704914]\n", + " [0.46758458 0.14590637 0.68284884 0.14853351 0.44160782 0.29308848\n", + " 0.55158921 0.60057337 0.62236916 0.64914015]]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "n = 10\n", + "# define a matrix of dimension 10 x 10 and set all elements to random numbers with x \\in [0, 1]\n", + "A = np.random.rand(n, n)\n", + "print(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we will see throughout these lectures, there are several extremely useful functionalities in Numpy.\n", + "As an example, consider the discussion of the covariance matrix. Suppose we have defined three vectors\n", + "$\\hat{x}, \\hat{y}, \\hat{z}$ with $n$ elements each. The covariance matrix is defined as" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\hat{\\Sigma} = \\begin{bmatrix} \\sigma_{xx} & \\sigma_{xy} & \\sigma_{xz} \\\\\n", + " \\sigma_{yx} & \\sigma_{yy} & \\sigma_{yz} \\\\\n", + " \\sigma_{zx} & \\sigma_{zy} & \\sigma_{zz} \n", + " \\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where for example" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\sigma_{xy} =\\frac{1}{n} \\sum_{i=0}^{n-1}(x_i- \\overline{x})(y_i- \\overline{y}).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Numpy function **np.cov** calculates the covariance elements using the factor $1/(n-1)$ instead of $1/n$ since it assumes we do not have the exact mean values. \n", + "The following simple function uses the **np.vstack** function which takes each vector of dimension $1\\times n$ and produces a $3\\times n$ matrix $\\hat{W}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\hat{W} = \\begin{bmatrix} x_0 & y_0 & z_0 \\\\\n", + " x_1 & y_1 & z_1 \\\\\n", + " x_2 & y_2 & z_2 \\\\\n", + " \\dots & \\dots & \\dots \\\\\n", + " x_{n-2} & y_{n-2} & z_{n-2} \\\\\n", + " x_{n-1} & y_{n-1} & z_{n-1}\n", + " \\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which in turn is converted into into the $3\\times 3$ covariance matrix\n", + "$\\hat{\\Sigma}$ via the Numpy function **np.cov()**. We note that we can also calculate\n", + "the mean value of each set of samples $\\hat{x}$ etc using the Numpy\n", + "function **np.mean(x)**. We can also extract the eigenvalues of the\n", + "covariance matrix through the **np.linalg.eig()** function." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-0.021274912445883344\n", + "3.8204481431138078\n", + "0.022212735017009457\n", + "[[1.01666993 2.97008469 2.38972956]\n", + " [2.97008469 9.62887642 7.08845086]\n", + " [2.38972956 7.08845086 8.53339228]]\n", + "[17.09071869 0.08198784 2.0062321 ]\n" + ] + } + ], + "source": [ + "# Importing various packages\n", + "import numpy as np\n", + "\n", + "n = 100\n", + "x = np.random.normal(size=n)\n", + "print(np.mean(x))\n", + "y = 4+3*x+np.random.normal(size=n)\n", + "print(np.mean(y))\n", + "z = x**3+np.random.normal(size=n)\n", + "print(np.mean(z))\n", + "W = np.vstack((x, y, z))\n", + "Sigma = np.cov(W)\n", + "print(Sigma)\n", + "Eigvals, Eigvecs = np.linalg.eig(Sigma)\n", + "print(Eigvals)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1. 0. 0. 0.]\n", + " [0. 1. 0. 0.]\n", + " [0. 0. 1. 0.]\n", + " [0. 0. 0. 1.]]\n", + " (0, 0)\t1.0\n", + " (1, 1)\t1.0\n", + " (2, 2)\t1.0\n", + " (3, 3)\t1.0\n" + ] + }, + { + "data": { + "image/png": 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\n", 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