coorected typo

doc/LectureNotes/_build/html/week35.html

@@ -1347,9 +1347,9 @@ In order to find the derivative of <span class="math notranslate nohighlight">\(
 <p>which means that (using our previous example) we have</p>
 <div class="math notranslate nohighlight">
 \[
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=bm{A}^T\boldsymbol{y}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=\boldsymbol{A}^T\boldsymbol{y}.
 \]</div>
-<p>Note that the resulting vector elements are the same for <span class="math notranslate nohighlight">\(\boldsymbol{z}^T\)</span> and <span class="math notranslate nohighlight">\(\boldsymbol{z}\)</span>, the only difference is that one if just the transpose of the other.</p>
+<p>Note that the resulting vector elements are the same for <span class="math notranslate nohighlight">\(\boldsymbol{z}^T\)</span> and <span class="math notranslate nohighlight">\(\boldsymbol{z}\)</span>, the only difference is that one is just the transpose of the other.</p>
 <p>Since <span class="math notranslate nohighlight">\(\alpha\)</span> is a scalar we have <span class="math notranslate nohighlight">\(\alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y}\)</span>. Defining now <span class="math notranslate nohighlight">\(\boldsymbol{z}=\boldsymbol{x}^T\boldsymbol{A}^T\)</span> we find that</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1592,7 +1592,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.9966579875073338
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.9935551267466322
 </pre></div>
 </div>
 </div>
@@ -1609,7 +1609,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.007652435292578527
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.010490200097725966
 </pre></div>
 </div>
 </div>
@@ -1624,31 +1624,23 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[3.25042813e-02 2.38298328e-02 2.64093905e-02 1.31145723e-02
- 7.85640706e-02 2.08298871e-02 2.08187418e-02 6.69029803e-04
- 2.18905573e-02 2.14957387e-02 2.32863661e-02 4.66181587e-03
- 8.93710544e-03 2.89564974e-03 2.51647799e-03 3.61336683e-02
- 1.11766707e-02 6.39623570e-02 7.54190070e-03 2.85193598e-03
- 4.90018622e-02 1.46957262e-02 4.86592590e-02 9.69161166e-05
- 1.11309850e-02 1.47605918e-02 1.80419748e-03 3.18023984e-02
- 2.92063704e-02 3.53149684e-02 1.18573920e-02 3.32775737e-03
- 1.71196799e-02 1.96079426e-02 1.69232893e-02 1.89273223e-02
- 3.13021533e-02 2.96574402e-03 4.06270382e-02 4.92293994e-02
- 1.07282462e-02 1.29064873e-02 8.37618253e-03 4.02472584e-02
- 2.44637348e-02 1.00149403e-02 2.21129518e-02 2.30674822e-03
- 4.87391702e-02 2.53371547e-02 8.26280707e-03 1.80203363e-02
- 2.38115471e-02 7.62038116e-02 4.34816464e-02 3.92213792e-02
- 6.68818255e-03 8.88623007e-03 8.28473779e-02 4.53859920e-02
- 8.26121775e-02 4.67869899e-03 1.62034461e-02 2.78672237e-02
- 8.98401894e-03 3.17303133e-02 3.51729923e-02 2.90612093e-03
- 5.70221196e-03 3.49065324e-02 3.22091393e-02 2.15706394e-02
- 1.40920261e-02 3.82602592e-03 4.59101492e-02 3.65313891e-02
- 1.52725477e-02 3.05989176e-02 1.28347954e-03 3.00674454e-02
- 8.92998014e-02 1.63727258e-02 3.77117804e-02 1.17886788e-02
- 8.76071777e-02 4.11958697e-02 4.99322932e-03 7.57875488e-02
- 1.16954396e-04 1.90884438e-02 1.41441328e-02 5.38923192e-02
- 9.21237677e-03 1.36654107e-02 9.03904224e-04 9.90027459e-03
- 3.01828101e-02 4.71038982e-02 3.87200322e-02 1.62397973e-02]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.0154132  0.05341376 0.03110433 0.00569304 0.00506878 0.0148722
+ 0.08128265 0.02279801 0.02093685 0.06532712 0.04539538 0.03257064
+ 0.02869709 0.08842405 0.05211842 0.07932386 0.02115366 0.04175792
+ 0.01811045 0.06077967 0.04565093 0.03645765 0.06066397 0.00485256
+ 0.01797226 0.02614999 0.01806634 0.02108223 0.0066334  0.05980771
+ 0.04400708 0.00630419 0.1383885  0.00044903 0.00641337 0.03058676
+ 0.00976807 0.02733896 0.05637138 0.02881541 0.0163562  0.03518305
+ 0.02460355 0.00280363 0.0044697  0.01549726 0.01692802 0.01292378
+ 0.03745017 0.02810512 0.02286429 0.02165757 0.02666129 0.00779268
+ 0.03131926 0.02339588 0.00461151 0.01516054 0.04771954 0.04964381
+ 0.00310577 0.07038555 0.02244542 0.00549812 0.03432913 0.02357982
+ 0.03663294 0.02518542 0.04143717 0.03388678 0.00780776 0.00132783
+ 0.02747654 0.04561434 0.00158754 0.02174822 0.03353115 0.00624452
+ 0.02947717 0.03378293 0.02430551 0.00728374 0.01379422 0.01427509
+ 0.04598223 0.0442411  0.07660514 0.03523894 0.05599355 0.08451695
+ 0.01631541 0.0314934  0.00085946 0.0174912  0.04138379 0.02711384
+ 0.06866315 0.01900861 0.03389626 0.00703161]
 </pre></div>
 </div>
 </div>
@@ -1717,15 +1709,15 @@ but now splitting the data into a training set and a test set.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.86544433  1.28573357  0.76075617  5.54611024 -2.45878472]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.99523653  0.19571155  3.70792235  2.56288447 -1.52977457]
 Training R2
-0.9958543328528107
+0.9957793953467874
 Training MSE
-0.011031108072207247
+0.009780101492052846
 Test R2
-0.9958824304846606
+0.9948937588794076
 Test MSE
-0.006546368424400406
+0.007661225358276448
 </pre></div>
 </div>
 </div>

doc/LectureNotes/_build/jupyter_execute/week35.py

@@ -292,10 +292,10 @@
 # which means that (using our previous example) we have
 
 # $$
-# \frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=bm{A}^T\boldsymbol{y}.
+# \frac{\partial \alpha}{\partial \boldsymbol{x}} = \boldsymbol{z}=\boldsymbol{A}^T\boldsymbol{y}.
 # $$
 
-# Note that the resulting vector elements are the same for $\boldsymbol{z}^T$ and $\boldsymbol{z}$, the only difference is that one if just the transpose of the other.
+# Note that the resulting vector elements are the same for $\boldsymbol{z}^T$ and $\boldsymbol{z}$, the only difference is that one is just the transpose of the other.
 # 
 # Since $\alpha$ is a scalar we have $\alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y}$. Defining now $\boldsymbol{z}=\boldsymbol{x}^T\boldsymbol{A}^T$ we find that