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adding dft slides

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Morten Hjorth-Jensen
2023-10-25 15:38:49 +02:00
parent 248fa398fc
commit 9587aff02c
142 changed files with 2211 additions and 3328 deletions
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doc/LectureNotes/_build/html/chapter8.html
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@@ -333,6 +333,16 @@ const thebe_selector_output = ".output, .cell_output"
Week 42 Constructing a Neural Network code with introduction to Tensor flow
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="exercisesweek43.html">
Exercises weeks 43 and 44
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="week43.html">
Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
@@ -751,10 +761,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.10776220958055382
3.743189104728408
[[0.82379443 2.29894362]
[2.29894362 7.75174305]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.04570437990371566
4.420442688206847
[[ 1.01597952 3.06059304]
[ 3.06059304 10.1387933 ]]
</pre></div>
</div>
</div>
@@ -794,10 +804,10 @@ a more brute force way. Here we scale the mean values for each column of the des
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.0704374681593734
1.3273472571412799
[[1. 0.58076367]
[0.58076367 1. ]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07663067400487368
1.9423652864980914
[[1. 0.72782592]
[0.72782592 1. ]]
</pre></div>
</div>
</div>
@@ -826,30 +836,30 @@ this matrix we easily see that it is a positive definite matrix.</p>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.92200223 -1.78838813]
[-0.90854751 -2.66047048]
[ 0.83618601 2.91748202]
[-0.88821402 -4.10035098]
[ 0.44781662 2.48685204]
[ 1.20493234 2.32729105]
[ 1.02509184 2.42265837]
[-0.84210141 -3.82012236]
[-0.01031541 1.40111899]
[ 0.05715377 0.81392948]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.51761523 -1.42486342]
[ 1.91816586 6.87585634]
[-0.34694145 -1.09920915]
[ 0.31244861 1.08282867]
[ 1.12441319 3.24411906]
[-0.51892347 -1.08417181]
[-0.54509921 -2.1148557 ]
[ 0.26084008 0.60846694]
[ 0.01029574 0.21049575]
[-1.69758412 -6.29866668]]
0 1
0 -0.922002 -1.788388
1 -0.908548 -2.660470
2 0.836186 2.917482
3 -0.888214 -4.100351
4 0.447817 2.486852
5 1.204932 2.327291
6 1.025092 2.422658
7 -0.842101 -3.820122
8 -0.010315 1.401119
9 0.057154 0.813929
0 -0.517615 -1.424863
1 1.918166 6.875856
2 -0.346941 -1.099209
3 0.312449 1.082829
4 1.124413 3.244119
5 -0.518923 -1.084172
6 -0.545099 -2.114856
7 0.260840 0.608467
8 0.010296 0.210496
9 -1.697584 -6.298667
0 1
0 1.000000 0.920619
1 0.920619 1.000000
0 1.000000 0.993148
1 0.993148 1.000000
</pre></div>
</div>
</div>
@@ -906,37 +916,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.0 0.076527 0.079731 0.075684 0.075421 0.075030 0.066467 0.065808
2 0.0 0.079731 0.084207 0.080233 0.080607 0.080750 0.071252 0.070964
3 0.0 0.075684 0.080233 0.079381 0.079948 0.080284 0.072483 0.072285
4 0.0 0.075421 0.080607 0.079948 0.080953 0.081677 0.073541 0.073640
5 0.0 0.075030 0.080750 0.080284 0.081677 0.082746 0.074340 0.074708
6 0.0 0.066467 0.071252 0.072483 0.073541 0.074340 0.068082 0.068257
7 0.0 0.065808 0.070964 0.072285 0.073640 0.074708 0.068257 0.068650
8 0.0 0.065215 0.070694 0.072098 0.073720 0.075030 0.068406 0.068997
9 0.0 0.064696 0.070461 0.071942 0.073802 0.075331 0.068551 0.069320
10 0.0 0.057462 0.062071 0.064444 0.065735 0.066768 0.061869 0.062273
11 0.0 0.056898 0.061747 0.064145 0.065645 0.066870 0.061826 0.062390
12 0.0 0.056418 0.061484 0.063905 0.065593 0.066992 0.061813 0.062523
13 0.0 0.056019 0.061281 0.063722 0.065582 0.067139 0.061833 0.062675
14 0.0 0.055697 0.061138 0.063597 0.065614 0.067315 0.061888 0.062852
1 0.0 0.079243 0.085251 0.080541 0.083416 0.086394 0.074010 0.075867
2 0.0 0.085251 0.093570 0.084995 0.089008 0.093218 0.076658 0.079150
3 0.0 0.080541 0.084995 0.088240 0.090361 0.092452 0.084878 0.086337
4 0.0 0.083416 0.089008 0.090361 0.093080 0.095821 0.086090 0.087899
5 0.0 0.086394 0.093218 0.092452 0.095821 0.099275 0.087175 0.089365
6 0.0 0.074010 0.076658 0.084878 0.086090 0.087175 0.084042 0.084968
7 0.0 0.075867 0.079150 0.086337 0.087899 0.089365 0.084968 0.086108
8 0.0 0.077847 0.081832 0.087845 0.089793 0.091685 0.085877 0.087254
9 0.0 0.079975 0.084740 0.089414 0.091796 0.094163 0.086774 0.088416
10 0.0 0.067272 0.068624 0.079437 0.079971 0.080322 0.080193 0.080702
11 0.0 0.068609 0.070338 0.080572 0.081322 0.081908 0.081000 0.081647
12 0.0 0.070043 0.072194 0.081762 0.082754 0.083604 0.081821 0.082621
13 0.0 0.071587 0.074211 0.083015 0.084278 0.085427 0.082657 0.083630
14 0.0 0.073256 0.076413 0.084340 0.085908 0.087393 0.083511 0.084678
8 9 10 11 12 13 14
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.065215 0.064696 0.057462 0.056898 0.056418 0.056019 0.055697
2 0.070694 0.070461 0.062071 0.061747 0.061484 0.061281 0.061138
3 0.072098 0.071942 0.064444 0.064145 0.063905 0.063722 0.063597
4 0.073720 0.073802 0.065735 0.065645 0.065593 0.065582 0.065614
5 0.075030 0.075331 0.066768 0.066870 0.066992 0.067139 0.067315
6 0.068406 0.068551 0.061869 0.061826 0.061813 0.061833 0.061888
7 0.068997 0.069320 0.062273 0.062390 0.062523 0.062675 0.062852
8 0.069522 0.070009 0.062631 0.062894 0.063159 0.063434 0.063723
9 0.070009 0.070645 0.062963 0.063359 0.063747 0.064134 0.064527
10 0.062631 0.062963 0.057231 0.057361 0.057502 0.057657 0.057831
11 0.062894 0.063359 0.057361 0.057613 0.057864 0.058121 0.058388
12 0.063159 0.063747 0.057502 0.057864 0.058216 0.058567 0.058921
13 0.063434 0.064134 0.057657 0.058121 0.058567 0.059004 0.059439
14 0.063723 0.064527 0.057831 0.058388 0.058921 0.059439 0.059949
1 0.077847 0.079975 0.067272 0.068609 0.070043 0.071587 0.073256
2 0.081832 0.084740 0.068624 0.070338 0.072194 0.074211 0.076413
3 0.087845 0.089414 0.079437 0.080572 0.081762 0.083015 0.084340
4 0.089793 0.091796 0.079971 0.081322 0.082754 0.084278 0.085908
5 0.091685 0.094163 0.080322 0.081908 0.083604 0.085427 0.087393
6 0.085877 0.086774 0.080193 0.081000 0.081821 0.082657 0.083511
7 0.087254 0.088416 0.080702 0.081647 0.082621 0.083630 0.084678
8 0.088665 0.090123 0.081150 0.082248 0.083393 0.084594 0.085858
9 0.090123 0.091913 0.081538 0.082805 0.084141 0.085557 0.087063
10 0.081150 0.081538 0.077571 0.078106 0.078624 0.079125 0.079606
11 0.082248 0.082805 0.078106 0.078732 0.079353 0.079969 0.080577
12 0.083393 0.084141 0.078624 0.079353 0.080089 0.080832 0.081584
13 0.084594 0.085557 0.079125 0.079969 0.080832 0.081718 0.082632
14 0.085858 0.087063 0.079606 0.080577 0.081584 0.082632 0.083726
</pre></div>
</div>
</div>
@@ -1125,10 +1135,10 @@ We can write our own code or simply use either the functionaly of <strong>numpy<
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1
0 3.949162 1.987722
1 1.987722 2.004480
[[3.94916237 1.98772232]
[1.98772232 2.00447992]]
0 3.987648 2.034723
1 2.034723 2.038727
[[3.98764765 2.03472297]
[2.03472297 2.03872663]]
</pre></div>
</div>
</div>
@@ -1155,8 +1165,8 @@ Our own code here is not very elegant and asks for obvious improvements. It is t
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Centered covariance using own code
[[3.94916237 1.98772232]
[1.98772232 2.00447992]]
[[3.98764765 2.03472297]
[2.03472297 2.03872663]]
</pre></div>
</div>
<img alt="_images/chapter8_65_1.png" src="_images/chapter8_65_1.png" />
@@ -1216,16 +1226,16 @@ questions.</p>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Covariance matrix
5.189621963782685
0.7640203256838339
5.269217029290255
0.7571572558830478
First eigenvector
[0.84835621 0.52942586]
[0.84614892 0.53294653]
Second eigenvector
[-0.52942586 0.84835621]
[-0.53294653 0.84614892]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
[0.84835621 0.52942586]
[-0.84614892 -0.53294653]
</pre></div>
</div>
</div>