small adjustment

This commit is contained in:
Morten Hjorth-Jensen
2022-11-18 05:50:27 +01:00
parent e3034398b7
commit e93e980131
8 changed files with 293 additions and 287 deletions
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@@ -322,6 +322,7 @@ sol <span style="color: #666666">=</span> solvers<span style="color: #666666">.<
<span style="color: #408080; font-style: italic"># Extract optimal value and solution</span>
sol[<span style="color: #BA2121">&#39;x&#39;</span>]
sol[<span style="color: #BA2121">&#39;primal objective&#39;</span>]
<span style="color: #008000">print</span>(sol[<span style="color: #BA2121">&#39;x&#39;</span>] )
</pre>
</div>
</div>
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@@ -272,7 +272,7 @@ $$
With the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \).
</p>
<p>Using the <b>CVXOPT</b> library, the matrix \( P \) would then be defined by the </p>
<p>Using the <b>CVXOPT</b> library, the matrix \( P \) would then be defined by the above matrix while the KKT conditions would all be collected by the matrix \( G \).</p>
<p>
<!-- navigation buttons at the bottom of the page -->
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@@ -1566,6 +1566,7 @@ sol = solvers.qp(P,q,G,h)
<span style="color: #228B22"># Extract optimal value and solution</span>
sol[<span style="color: #CD5555">&#39;x&#39;</span>]
sol[<span style="color: #CD5555">&#39;primal objective&#39;</span>]
<span style="color: #658b00">print</span>(sol[<span style="color: #CD5555">&#39;x&#39;</span>] )
</pre>
</div>
</div>
@@ -1602,7 +1603,7 @@ $$
With the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \).
</p>
<p>Using the <b>CVXOPT</b> library, the matrix \( P \) would then be defined by the </p>
<p>Using the <b>CVXOPT</b> library, the matrix \( P \) would then be defined by the above matrix while the KKT conditions would all be collected by the matrix \( G \).</p>
</section>
<section>
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@@ -1432,6 +1432,7 @@ sol = solvers.qp(P,q,G,h)
<span style="color: #228B22"># Extract optimal value and solution</span>
sol[<span style="color: #CD5555">&#39;x&#39;</span>]
sol[<span style="color: #CD5555">&#39;primal objective&#39;</span>]
<span style="color: #658b00">print</span>(sol[<span style="color: #CD5555">&#39;x&#39;</span>] )
</pre>
</div>
</div>
@@ -1466,7 +1467,7 @@ $$
With the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \).
</p>
<p>Using the <b>CVXOPT</b> library, the matrix \( P \) would then be defined by the </p>
<p>Using the <b>CVXOPT</b> library, the matrix \( P \) would then be defined by the above matrix while the KKT conditions would all be collected by the matrix \( G \).</p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="basic-ideas-of-the-principal-component-analysis-pca">Basic ideas of the Principal Component Analysis (PCA) </h2>
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@@ -1509,6 +1509,7 @@ sol <span style="color: #666666">=</span> solvers<span style="color: #666666">.<
<span style="color: #408080; font-style: italic"># Extract optimal value and solution</span>
sol[<span style="color: #BA2121">&#39;x&#39;</span>]
sol[<span style="color: #BA2121">&#39;primal objective&#39;</span>]
<span style="color: #008000">print</span>(sol[<span style="color: #BA2121">&#39;x&#39;</span>] )
</pre>
</div>
</div>
@@ -1543,7 +1544,7 @@ $$
With the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \).
</p>
<p>Using the <b>CVXOPT</b> library, the matrix \( P \) would then be defined by the </p>
<p>Using the <b>CVXOPT</b> library, the matrix \( P \) would then be defined by the above matrix while the KKT conditions would all be collected by the matrix \( G \).</p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="basic-ideas-of-the-principal-component-analysis-pca">Basic ideas of the Principal Component Analysis (PCA) </h2>
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@@ -1140,6 +1140,7 @@ sol = solvers.qp(P,q,G,h)
# Extract optimal value and solution
sol['x']
sol['primal objective']
print(sol['x'] )
!ec
!split
@@ -1160,7 +1161,7 @@ subject to $\bm{y}^T\bm{\lambda}=0$. Here we defined the vectors $\bm{\lambda} =
$\bm{y}=[y_1,y_2,\dots,y_n]$.
With the slack constants this leads to the additional constraint $0\leq \lambda_i \leq C$.
Using the _CVXOPT_ library, the matrix $P$ would then be defined by the
Using the _CVXOPT_ library, the matrix $P$ would then be defined by the above matrix while the KKT conditions would all be collected by the matrix $G$.