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Morten Hjorth-Jensen
2021-04-26 09:20:25 -04:00
parent 4446c1be47
commit c82f437bcf
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doc/LectureNotes/_build/html/chapter8.html
+80 -70
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@@ -128,6 +128,11 @@
1. Elements of Probability Theory and Statistical Data Analysis
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="linalg.html">
2. Linear Algebra, Handling of Arrays and more Python Features
</a>
</li>
</ul>
<p class="caption collapsible-parent">
<span class="caption-text">
@@ -206,6 +211,11 @@
2. Building a Feed Forward Neural Network
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter11.html">
3. Solving Differential Equations with Deep Learning
</a>
</li>
</ul>
</nav> <!-- To handle the deprecated key -->
@@ -516,10 +526,10 @@ 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>0.013770665200945059
4.0696182771562865
[[ 1.28864075 3.9567042 ]
[ 3.9567042 12.91108638]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.2310524795427768
3.1831903689627863
[[0.86117632 2.59603122]
[2.59603122 9.06044826]]
</pre></div>
</div>
</div>
@@ -559,10 +569,10 @@ 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>0.09677449095137611
2.1297860009663863
[[1. 0.72674076]
[0.72674076 1. ]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08745913868064381
2.1128123336365077
[[1. 0.6798478]
[0.6798478 1. ]]
</pre></div>
</div>
</div>
@@ -591,30 +601,30 @@ 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>[[ 1.10924603 3.83689962]
[-1.78744085 -5.79440072]
[-0.99810985 -3.0835973 ]
[ 0.02436339 -0.99150612]
[ 1.282947 4.23630419]
[-0.47573169 -0.92807223]
[-0.45955372 -1.52210478]
[-0.27330595 0.26924602]
[ 0.32511025 0.73840521]
[ 1.2524754 3.23882611]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 1.21030078 4.50152769]
[ 0.85231126 2.49259646]
[-0.27754082 -0.99161035]
[-0.05499028 -0.95681341]
[ 0.65405197 0.57844946]
[ 0.12802926 0.88441436]
[ 0.43424077 1.60051748]
[-1.57205214 -3.89834457]
[-0.77949144 -1.89899948]
[-0.59485937 -2.31173763]]
0 1
0 1.109246 3.836900
1 -1.787441 -5.794401
2 -0.998110 -3.083597
3 0.024363 -0.991506
4 1.282947 4.236304
5 -0.475732 -0.928072
6 -0.459554 -1.522105
7 -0.273306 0.269246
8 0.325110 0.738405
9 1.252475 3.238826
0 1
0 1.00000 0.98078
1 0.98078 1.00000
0 1.210301 4.501528
1 0.852311 2.492596
2 -0.277541 -0.991610
3 -0.054990 -0.956813
4 0.654052 0.578449
5 0.128029 0.884414
6 0.434241 1.600517
7 -1.572052 -3.898345
8 -0.779491 -1.898999
9 -0.594859 -2.311738
0 1
0 1.000000 0.957565
1 0.957565 1.000000
</pre></div>
</div>
</div>
@@ -671,37 +681,37 @@ 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 0.088871 0.091057 0.086480 0.086882 0.087207 0.076599 0.076736
2 0.0 0.091057 0.094219 0.089279 0.090116 0.090850 0.079397 0.079778
3 0.0 0.086480 0.089279 0.089816 0.090608 0.091280 0.082607 0.083021
4 0.0 0.086882 0.090116 0.090608 0.091649 0.092562 0.083598 0.084176
5 0.0 0.087207 0.090850 0.091280 0.092562 0.093708 0.084468 0.085206
6 0.0 0.076599 0.079397 0.082607 0.083598 0.084468 0.077844 0.078449
7 0.0 0.076736 0.079778 0.083021 0.084176 0.085206 0.078449 0.079175
8 0.0 0.076896 0.080176 0.083441 0.084757 0.085945 0.079053 0.079897
9 0.0 0.077088 0.080599 0.083875 0.085351 0.086696 0.079662 0.080623
10 0.0 0.066962 0.069634 0.074011 0.075111 0.076098 0.070962 0.071693
11 0.0 0.067119 0.069952 0.074388 0.075607 0.076712 0.071496 0.072320
12 0.0 0.067315 0.070309 0.074797 0.076135 0.077358 0.072056 0.072972
13 0.0 0.067553 0.070705 0.075243 0.076699 0.078039 0.072646 0.073655
14 0.0 0.067832 0.071144 0.075726 0.077300 0.078758 0.073267 0.074370
1 0.0 0.091583 0.077830 0.092209 0.086333 0.080182 0.084446 0.080360
2 0.0 0.077830 0.067325 0.077735 0.073465 0.068967 0.071391 0.068389
3 0.0 0.092209 0.077735 0.099350 0.092714 0.085784 0.094735 0.090145
4 0.0 0.086333 0.073465 0.092714 0.086992 0.080974 0.088533 0.084586
5 0.0 0.080182 0.068967 0.085784 0.080974 0.075877 0.082067 0.078752
6 0.0 0.084446 0.071391 0.094735 0.088533 0.082067 0.092739 0.088427
7 0.0 0.080360 0.068389 0.090145 0.084586 0.078752 0.088427 0.084585
8 0.0 0.076446 0.065511 0.085713 0.080765 0.075532 0.084250 0.080847
9 0.0 0.072627 0.062704 0.081361 0.076998 0.072349 0.080136 0.077151
10 0.0 0.076483 0.065094 0.088105 0.082612 0.076881 0.087850 0.084014
11 0.0 0.073208 0.062649 0.084453 0.079459 0.074213 0.084413 0.080946
12 0.0 0.070145 0.060358 0.081016 0.076483 0.071690 0.081166 0.078040
13 0.0 0.067263 0.058198 0.077760 0.073657 0.069286 0.078077 0.075268
14 0.0 0.064527 0.056149 0.074647 0.070949 0.066978 0.075114 0.072600
8 9 10 11 12 13 14
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.076896 0.077088 0.066962 0.067119 0.067315 0.067553 0.067832
2 0.080176 0.080599 0.069634 0.069952 0.070309 0.070705 0.071144
3 0.083441 0.083875 0.074011 0.074388 0.074797 0.075243 0.075726
4 0.084757 0.085351 0.075111 0.075607 0.076135 0.076699 0.077300
5 0.085945 0.086696 0.076098 0.076712 0.077358 0.078039 0.078758
6 0.079053 0.079662 0.070962 0.071496 0.072056 0.072646 0.073267
7 0.079897 0.080623 0.071693 0.072320 0.072972 0.073655 0.074370
8 0.080736 0.081579 0.072417 0.073137 0.073882 0.074657 0.075466
9 0.081579 0.082540 0.073144 0.073955 0.074793 0.075662 0.076565
10 0.072417 0.073144 0.065549 0.066186 0.066845 0.067528 0.068238
11 0.073137 0.073955 0.066186 0.066898 0.067632 0.068392 0.069179
12 0.073882 0.074793 0.066845 0.067632 0.068443 0.069279 0.070144
13 0.074657 0.075662 0.067528 0.068392 0.069279 0.070193 0.071137
14 0.075466 0.076565 0.068238 0.069179 0.070144 0.071137 0.072162
1 0.076446 0.072627 0.076483 0.073208 0.070145 0.067263 0.064527
2 0.065511 0.062704 0.065094 0.062649 0.060358 0.058198 0.056149
3 0.085713 0.081361 0.088105 0.084453 0.081016 0.077760 0.074647
4 0.080765 0.076998 0.082612 0.079459 0.076483 0.073657 0.070949
5 0.075532 0.072349 0.076881 0.074213 0.071690 0.069286 0.066978
6 0.084250 0.080136 0.087850 0.084413 0.081166 0.078077 0.075114
7 0.080847 0.077151 0.084014 0.080946 0.078040 0.075268 0.072600
8 0.077525 0.074225 0.080285 0.077563 0.074977 0.072501 0.070112
9 0.074225 0.071304 0.076603 0.074208 0.071924 0.069731 0.067608
10 0.080285 0.076603 0.084360 0.081287 0.078374 0.075595 0.072921
11 0.077563 0.074208 0.081287 0.078509 0.075868 0.073341 0.070901
12 0.074977 0.071924 0.078374 0.075868 0.073479 0.071184 0.068960
13 0.072501 0.069731 0.075595 0.073341 0.071184 0.069105 0.067084
14 0.070112 0.067608 0.072921 0.070901 0.068960 0.067084 0.065252
</pre></div>
</div>
</div>
@@ -890,10 +900,10 @@ 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 3.947193 2.023730
1 2.023730 2.048423
[[3.94719285 2.02373037]
[2.02373037 2.04842273]]
0 3.923640 1.961854
1 1.961854 1.947452
[[3.92363958 1.96185372]
[1.96185372 1.94745179]]
</pre></div>
</div>
</div>
@@ -920,8 +930,8 @@ 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
[[3.94719285 2.02373037]
[2.02373037 2.04842273]]
[[3.92363958 1.96185372]
[1.96185372 1.94745179]]
</pre></div>
</div>
<img alt="_images/chapter8_65_1.png" src="_images/chapter8_65_1.png" />
@@ -981,16 +991,16 @@ 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
5.233163823635816
0.7624517604393659
5.132179379442221
0.7389119925478163
First eigenvector
[0.84401218 0.536324 ]
[0.85141702 0.52448933]
Second eigenvector
[-0.536324 0.84401218]
[-0.52448933 0.85141702]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
[-0.84401218 -0.536324 ]
[0.85141702 0.52448933]
</pre></div>
</div>
</div>