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General update of several files with to do list

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mhjensen
2018-05-22 16:49:43 -04:00
parent 7a39d02fd6
commit 4e5fa98fe8
225 changed files with 13485 additions and 6123 deletions
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doc/pub/Regression/html/._Regression-bs000.html
+6 -4
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -193,7 +195,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>May 17, 2018</h4></center> <!-- date -->
<center><h4>May 22, 2018</h4></center> <!-- date -->
<br>
<p>
@@ -217,7 +219,7 @@ MathJax.Hub.Config({
<li><a href="._Regression-bs008.html">9</a></li>
<li><a href="._Regression-bs009.html">10</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs001.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs001.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -214,7 +216,7 @@ A regression model aims at finding a likelihood function \( p(y\vert \hat{x}) \)
<li><a href="._Regression-bs009.html">10</a></li>
<li><a href="._Regression-bs010.html">11</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs002.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs002.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -211,7 +213,7 @@ where \( \epsilon_i \) is the error in our approximation.
<li><a href="._Regression-bs010.html">11</a></li>
<li><a href="._Regression-bs011.html">12</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs003.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs003.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -211,7 +213,7 @@ $$
<li><a href="._Regression-bs011.html">12</a></li>
<li><a href="._Regression-bs012.html">13</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs004.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs004.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -231,7 +233,7 @@ $$
<li><a href="._Regression-bs012.html">13</a></li>
<li><a href="._Regression-bs013.html">14</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs005.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs005.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -216,7 +218,7 @@ $$
<li><a href="._Regression-bs013.html">14</a></li>
<li><a href="._Regression-bs014.html">15</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs006.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs006.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -222,7 +224,7 @@ The left-hand side of this equation forms know. Our error vector \( \hat{\epsilo
<li><a href="._Regression-bs014.html">15</a></li>
<li><a href="._Regression-bs015.html">16</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs007.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs007.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -217,7 +219,7 @@ $$
<li><a href="._Regression-bs015.html">16</a></li>
<li><a href="._Regression-bs016.html">17</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs008.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs008.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -220,7 +222,7 @@ $$
<li><a href="._Regression-bs016.html">17</a></li>
<li><a href="._Regression-bs017.html">18</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs009.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs009.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -236,7 +238,7 @@ $$
<li><a href="._Regression-bs017.html">18</a></li>
<li><a href="._Regression-bs018.html">19</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs010.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs010.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
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<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -224,7 +226,7 @@ $$
<li><a href="._Regression-bs018.html">19</a></li>
<li><a href="._Regression-bs019.html">20</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs011.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs011.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
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<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -226,7 +228,7 @@ meaning that the solution for \( \hat{\beta} \) is the one which minimizes the r
<li><a href="._Regression-bs019.html">20</a></li>
<li><a href="._Regression-bs020.html">21</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs012.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs012.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
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<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -237,7 +239,7 @@ We see that, as expected, a linear fit gives a seemingly (from the graph) good r
<li><a href="._Regression-bs020.html">21</a></li>
<li><a href="._Regression-bs021.html">22</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs013.html">&raquo;</a></li>
</ul>
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doc/pub/Regression/html/._Regression-bs013.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -228,7 +230,7 @@ plt<span style="color: #666666">.</span>show()
<li><a href="._Regression-bs021.html">22</a></li>
<li><a href="._Regression-bs022.html">23</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs014.html">&raquo;</a></li>
</ul>
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doc/pub/Regression/html/._Regression-bs014.html
+5 -3
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -211,7 +213,7 @@ Let us now try to assess the quality of our fit by studying various measures.
<li><a href="._Regression-bs022.html">23</a></li>
<li><a href="._Regression-bs023.html">24</a></li>
<li><a href="">...</a></li>
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<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs015.html">&raquo;</a></li>
</ul>
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doc/pub/Regression/html/._Regression-bs015.html
+6 -2
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -201,6 +203,8 @@ MathJax.Hub.Config({
<li><a href="._Regression-bs022.html">23</a></li>
<li><a href="._Regression-bs023.html">24</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs016.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/._Regression-bs016.html
+5 -2
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -219,6 +221,7 @@ where the matrix \( \hat{\Sigma} \) is a diagonal matrix with \( \sigma_i \) as
<li><a href="._Regression-bs022.html">23</a></li>
<li><a href="._Regression-bs023.html">24</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs017.html">&raquo;</a></li>
</ul>
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doc/pub/Regression/html/._Regression-bs017.html
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
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'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -223,6 +225,7 @@ where we have defined the matrix \( \hat{A} =\hat{X}/\hat{\Sigma} \) with matrix
<li><a href="._Regression-bs022.html">23</a></li>
<li><a href="._Regression-bs023.html">24</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs018.html">&raquo;</a></li>
</ul>
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doc/pub/Regression/html/._Regression-bs018.html
+5 -2
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
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('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
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<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -220,6 +222,7 @@ $$
<li><a href="._Regression-bs022.html">23</a></li>
<li><a href="._Regression-bs023.html">24</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs019.html">&raquo;</a></li>
</ul>
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doc/pub/Regression/html/Regression-bs.html
+6 -4
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@@ -97,7 +97,8 @@ Automatically generated HTML file from DocOnce source
2,
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'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
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<body>
@@ -158,7 +159,8 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._Regression-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs022.html#___sec21" style="font-size: 80%;">Simple regression model with gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs023.html#___sec22" style="font-size: 80%;">Simple regression model with stochastic gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">The singular value decompostion</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs024.html#___sec23" style="font-size: 80%;">Polynomial Regression</a></li>
<!-- navigation toc: --> <li><a href="._Regression-bs025.html#___sec24" style="font-size: 80%;">The singular value decompostion</a></li>
</ul>
</li>
@@ -193,7 +195,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>May 17, 2018</h4></center> <!-- date -->
<center><h4>May 22, 2018</h4></center> <!-- date -->
<br>
<p>
@@ -217,7 +219,7 @@ MathJax.Hub.Config({
<li><a href="._Regression-bs008.html">9</a></li>
<li><a href="._Regression-bs009.html">10</a></li>
<li><a href="">...</a></li>
<li><a href="._Regression-bs024.html">25</a></li>
<li><a href="._Regression-bs025.html">26</a></li>
<li><a href="._Regression-bs001.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/Regression/html/Regression-reveal.html
+34 -2
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@@ -148,7 +148,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>&nbsp;<br>
<center><h4>May 17, 2018</h4></center> <!-- date -->
<center><h4>May 22, 2018</h4></center> <!-- date -->
<br>
<p>
@@ -859,7 +859,39 @@ sgdreg.fit(x,y.ravel())
<section>
<h2 id="___sec23">The singular value decompostion </h2>
<h2 id="___sec23">Polynomial Regression </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># Importing various packages</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">math</span> <span style="color: #8B008B; font-weight: bold">import</span> exp, sqrt
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">random</span> <span style="color: #8B008B; font-weight: bold">import</span> random, seed
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
m = <span style="color: #B452CD">100</span>
x = <span style="color: #B452CD">2</span>*np.random.rand(m,<span style="color: #B452CD">1</span>)+<span style="color: #B452CD">4.</span>
y = <span style="color: #B452CD">4</span>+<span style="color: #B452CD">3</span>*x*x+ +x-np.random.randn(m,<span style="color: #B452CD">1</span>)
xb = np.c_[np.ones((m,<span style="color: #B452CD">1</span>)), x]
theta = np.linalg.inv(xb.T.dot(xb)).dot(xb.T).dot(y)
xnew = np.array([[<span style="color: #B452CD">0</span>],[<span style="color: #B452CD">2</span>]])
xbnew = np.c_[np.ones((<span style="color: #B452CD">2</span>,<span style="color: #B452CD">1</span>)), xnew]
ypredict = xbnew.dot(theta)
plt.plot(xnew, ypredict, <span style="color: #CD5555">&quot;r-&quot;</span>)
plt.plot(x, y ,<span style="color: #CD5555">&#39;ro&#39;</span>)
plt.axis([<span style="color: #B452CD">0</span>,<span style="color: #B452CD">2.0</span>,<span style="color: #B452CD">0</span>, <span style="color: #B452CD">15.0</span>])
plt.xlabel(<span style="color: #CD5555">r&#39;$x$&#39;</span>)
plt.ylabel(<span style="color: #CD5555">r&#39;$y$&#39;</span>)
plt.title(<span style="color: #CD5555">r&#39;Random numbers &#39;</span>)
plt.show()
</pre></div>
</section>
<section>
<h2 id="___sec24">The singular value decompostion </h2>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<p>
doc/pub/Regression/html/Regression-solarized.html
+35 -3
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@@ -117,7 +117,8 @@ div { text-align: justify; text-justify: inter-word; }
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('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
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<body>
@@ -159,7 +160,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>May 17, 2018</h4></center> <!-- date -->
<center><h4>May 22, 2018</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -795,7 +796,38 @@ sgdreg.fit(x,y.ravel())
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec23">The singular value decompostion </h2>
<h2 id="___sec23">Polynomial Regression </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># Importing various packages</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">math</span> <span style="color: #8B008B; font-weight: bold">import</span> exp, sqrt
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">random</span> <span style="color: #8B008B; font-weight: bold">import</span> random, seed
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
m = <span style="color: #B452CD">100</span>
x = <span style="color: #B452CD">2</span>*np.random.rand(m,<span style="color: #B452CD">1</span>)+<span style="color: #B452CD">4.</span>
y = <span style="color: #B452CD">4</span>+<span style="color: #B452CD">3</span>*x*x+ +x-np.random.randn(m,<span style="color: #B452CD">1</span>)
xb = np.c_[np.ones((m,<span style="color: #B452CD">1</span>)), x]
theta = np.linalg.inv(xb.T.dot(xb)).dot(xb.T).dot(y)
xnew = np.array([[<span style="color: #B452CD">0</span>],[<span style="color: #B452CD">2</span>]])
xbnew = np.c_[np.ones((<span style="color: #B452CD">2</span>,<span style="color: #B452CD">1</span>)), xnew]
ypredict = xbnew.dot(theta)
plt.plot(xnew, ypredict, <span style="color: #CD5555">&quot;r-&quot;</span>)
plt.plot(x, y ,<span style="color: #CD5555">&#39;ro&#39;</span>)
plt.axis([<span style="color: #B452CD">0</span>,<span style="color: #B452CD">2.0</span>,<span style="color: #B452CD">0</span>, <span style="color: #B452CD">15.0</span>])
plt.xlabel(<span style="color: #CD5555">r&#39;$x$&#39;</span>)
plt.ylabel(<span style="color: #CD5555">r&#39;$y$&#39;</span>)
plt.title(<span style="color: #CD5555">r&#39;Random numbers &#39;</span>)
plt.show()
</pre></div>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec24">The singular value decompostion </h2>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<p>
doc/pub/Regression/html/Regression.html
+35 -3
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@@ -122,7 +122,8 @@ div { text-align: justify; text-justify: inter-word; }
2,
None,
'___sec22'),
('The singular value decompostion', 2, None, '___sec23')]}
('Polynomial Regression', 2, None, '___sec23'),
('The singular value decompostion', 2, None, '___sec24')]}
end of tocinfo -->
<body>
@@ -164,7 +165,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>May 17, 2018</h4></center> <!-- date -->
<center><h4>May 22, 2018</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -800,7 +801,38 @@ sgdreg<span style="color: #666666">.</span>fit(x,y<span style="color: #666666">.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec23">The singular value decompostion </h2>
<h2 id="___sec23">Polynomial Regression </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># Importing various packages</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">math</span> <span style="color: #008000; font-weight: bold">import</span> exp, sqrt
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">random</span> <span style="color: #008000; font-weight: bold">import</span> random, seed
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
m <span style="color: #666666">=</span> <span style="color: #666666">100</span>
x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(m,<span style="color: #666666">1</span>)<span style="color: #666666">+4.</span>
y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">*</span>x<span style="color: #666666">+</span> <span style="color: #666666">+</span>x<span style="color: #666666">-</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(m,<span style="color: #666666">1</span>)
xb <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((m,<span style="color: #666666">1</span>)), x]
theta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(xb<span style="color: #666666">.</span>T<span style="color: #666666">.</span>dot(xb))<span style="color: #666666">.</span>dot(xb<span style="color: #666666">.</span>T)<span style="color: #666666">.</span>dot(y)
xnew <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([[<span style="color: #666666">0</span>],[<span style="color: #666666">2</span>]])
xbnew <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)), xnew]
ypredict <span style="color: #666666">=</span> xbnew<span style="color: #666666">.</span>dot(theta)
plt<span style="color: #666666">.</span>plot(xnew, ypredict, <span style="color: #BA2121">&quot;r-&quot;</span>)
plt<span style="color: #666666">.</span>plot(x, y ,<span style="color: #BA2121">&#39;ro&#39;</span>)
plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0</span>,<span style="color: #666666">2.0</span>,<span style="color: #666666">0</span>, <span style="color: #666666">15.0</span>])
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">r&#39;$x$&#39;</span>)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">r&#39;$y$&#39;</span>)
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">r&#39;Random numbers &#39;</span>)
plt<span style="color: #666666">.</span>show()
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<h2 id="___sec24">The singular value decompostion </h2>
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