added random walk example

2018-05-29 11:08:41 -04:00
parent 3a2abcd62b
commit d34d39836b
8 changed files with 608 additions and 101 deletions
@@ -82,7 +82,8 @@ div { text-align: justify; text-justify: inter-word; }
              ('Particle in one dimension and velocity distribution',
               3,
               None,
-               '___sec11')]}
+               '___sec11'),
+              ('Random walk model', 3, None, '___sec12')]}
 end of tocinfo -->

 <body>
@@ -126,8 +127,6 @@ MathJax.Hub.Config({
 <p>
 <center><h4>May 29, 2018</h4></center> <!-- date -->
 <br>
-<p>
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>

 <h2 id="___sec0">Introduction </h2>

@@ -169,9 +168,6 @@ introduce will serve as inputs to many of our discussions later, as
 well as allowing you to set up models and produce your own data and
 get started with programming.

-<p>
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>
-
 <h2 id="___sec1">Software and needed installations </h2>

 <p>
@@ -214,9 +210,6 @@ you can use <b>pip</b> as well and simply install Python as

 etc etc.

-<p>
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>
-
 <h2 id="___sec2">Python installers </h2>

 <p>
@@ -244,9 +237,6 @@ distribution for scientific and analytic computing distribution and
 analysis environment, available for free and under a commercial
 license.

-<p>
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>
-
 <h2 id="___sec3">Installing R, C++, cython or Julia </h2>

 <p>
@@ -265,9 +255,6 @@ texts.
 To install <b>R</b> with Jupyter notebook 
 <a href="https://mpacer.org/maths/r-kernel-for-ipython-notebook" target="_blank">follow the link here</a>

-<p>
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>
-
 <h2 id="___sec4">Installing R, C++, cython, Numba etc </h2>

 <p>
@@ -302,9 +289,6 @@ Finally, if you wish to use the light mark-up language
 <a href="https://github.com/hplgit/doconce" target="_blank">doconce</a> you can convert a standard ascii text file into various HTML 
 formats, ipython notebooks, latex files, pdf files etc with minimal edits.

-<p>
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>
-
 <h2 id="___sec5">Simple linear regression model using <b>scikit-learn</b> </h2>

 <p>
@@ -591,7 +575,6 @@ plt<span style="color: #666666">.</span>show()
 </pre></div>
 <p>
 Similarly, using <b>R</b>, we can perform similar studies. The following <b>R</b> code illustrates this.
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>

 <h2 id="___sec6">Non-Linear Least squares in R  </h2>
 <div class="alert alert-block alert-block alert-text-normal">
@@ -642,8 +625,6 @@ data <span style="color: #666666">=</span> {<span style="color: #BA2121">&#39;Na
 data_pandas <span style="color: #666666">=</span> pd<span style="color: #666666">.</span>DataFrame(data)
 display(data_pandas)
 </pre></div>
-<p>
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>

 <h2 id="___sec7">Examples </h2>

@@ -1305,6 +1286,101 @@ plt<span style="color: #666666">.</span>axis([<span style="color: #666666">-5</s
 plt<span style="color: #666666">.</span>grid(<span style="color: #008000">True</span>)
 plt<span style="color: #666666">.</span>show()
 </pre></div>
+
+<h3 id="___sec12">Random walk model </h3>
+
+<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: #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>
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> PolynomialFeatures
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LinearRegression
+
+steps<span style="color: #666666">=250</span>
+
+distance<span style="color: #666666">=0</span>
+x<span style="color: #666666">=0</span>
+distance_list<span style="color: #666666">=</span>[]
+steps_list<span style="color: #666666">=</span>[]
+<span style="color: #008000; font-weight: bold">while</span> x<span style="color: #666666">&lt;</span>steps:
+    distance<span style="color: #666666">+=</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randint(<span style="color: #666666">-1</span>,<span style="color: #666666">2</span>)
+    distance_list<span style="color: #666666">.</span>append(distance)
+    x<span style="color: #666666">+=1</span>
+    steps_list<span style="color: #666666">.</span>append(x)
+plt<span style="color: #666666">.</span>plot(steps_list,distance_list, color<span style="color: #666666">=</span><span style="color: #BA2121">&#39;green&#39;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;Random Walk Data&quot;</span>)
+
+steps_list<span style="color: #666666">=</span>np<span style="color: #666666">.</span>asarray(steps_list)
+distance_list<span style="color: #666666">=</span>np<span style="color: #666666">.</span>asarray(distance_list)
+
+X<span style="color: #666666">=</span>steps_list[:,np<span style="color: #666666">.</span>newaxis]
+
+<span style="color: #408080; font-style: italic">#Polynomial fits</span>
+
+<span style="color: #408080; font-style: italic">#Degree 2</span>
+poly_features<span style="color: #666666">=</span>PolynomialFeatures(degree<span style="color: #666666">=2</span>, include_bias<span style="color: #666666">=</span><span style="color: #008000">False</span>)
+X_poly<span style="color: #666666">=</span>poly_features<span style="color: #666666">.</span>fit_transform(X)
+
+lin_reg<span style="color: #666666">=</span>LinearRegression()
+poly_fit<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>fit(X_poly,distance_list)
+b<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>coef_
+c<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>intercept_
+<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;2nd degree coefficients:&quot;</span>)
+<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;zero power: &quot;</span>,c)
+<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;first power: &quot;</span>, b[<span style="color: #666666">0</span>])
+<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;second power: &quot;</span>,b[<span style="color: #666666">1</span>])
+
+z <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #666666">0</span>, steps, <span style="color: #666666">.01</span>)
+z_mod<span style="color: #666666">=</span>b[<span style="color: #666666">1</span>]<span style="color: #666666">*</span>z<span style="color: #666666">**2+</span>b[<span style="color: #666666">0</span>]<span style="color: #666666">*</span>z<span style="color: #666666">+</span>c
+
+fit_mod<span style="color: #666666">=</span>b[<span style="color: #666666">1</span>]<span style="color: #666666">*</span>X<span style="color: #666666">**2+</span>b[<span style="color: #666666">0</span>]<span style="color: #666666">*</span>X<span style="color: #666666">+</span>c
+plt<span style="color: #666666">.</span>plot(z, z_mod, color<span style="color: #666666">=</span><span style="color: #BA2121">&#39;r&#39;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;2nd Degree Fit&quot;</span>)
+plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;Polynomial Regression&quot;</span>)
+
+plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&quot;Steps&quot;</span>)
+plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&quot;Distance&quot;</span>)
+
+<span style="color: #408080; font-style: italic">#Degree 10</span>
+poly_features10<span style="color: #666666">=</span>PolynomialFeatures(degree<span style="color: #666666">=10</span>, include_bias<span style="color: #666666">=</span><span style="color: #008000">False</span>)
+X_poly10<span style="color: #666666">=</span>poly_features10<span style="color: #666666">.</span>fit_transform(X)
+
+poly_fit10<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>fit(X_poly10,distance_list)
+
+y_plot<span style="color: #666666">=</span>poly_fit10<span style="color: #666666">.</span>predict(X_poly10)
+plt<span style="color: #666666">.</span>plot(X, y_plot, color<span style="color: #666666">=</span><span style="color: #BA2121">&#39;black&#39;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;10th Degree Fit&quot;</span>)
+
+plt<span style="color: #666666">.</span>legend()
+plt<span style="color: #666666">.</span>show()
+
+
+<span style="color: #408080; font-style: italic">#Decision Tree Regression</span>
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.tree</span> <span style="color: #008000; font-weight: bold">import</span> DecisionTreeRegressor
+regr_1<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=2</span>)
+regr_2<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=5</span>)
+regr_3<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=7</span>)
+regr_1<span style="color: #666666">.</span>fit(X, distance_list)
+regr_2<span style="color: #666666">.</span>fit(X, distance_list)
+regr_3<span style="color: #666666">.</span>fit(X, distance_list)
+
+X_test <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #666666">0.0</span>, steps, <span style="color: #666666">0.01</span>)[:, np<span style="color: #666666">.</span>newaxis]
+y_1 <span style="color: #666666">=</span> regr_1<span style="color: #666666">.</span>predict(X_test)
+y_2 <span style="color: #666666">=</span> regr_2<span style="color: #666666">.</span>predict(X_test)
+y_3<span style="color: #666666">=</span>regr_3<span style="color: #666666">.</span>predict(X_test)
+
+<span style="color: #408080; font-style: italic"># Plot the results</span>
+plt<span style="color: #666666">.</span>figure()
+plt<span style="color: #666666">.</span>scatter(X, distance_list, s<span style="color: #666666">=2.5</span>, c<span style="color: #666666">=</span><span style="color: #BA2121">&quot;black&quot;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;data&quot;</span>)
+plt<span style="color: #666666">.</span>plot(X_test, y_1, color<span style="color: #666666">=</span><span style="color: #BA2121">&quot;red&quot;</span>,
+         label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;max_depth=2&quot;</span>, linewidth<span style="color: #666666">=2</span>)
+plt<span style="color: #666666">.</span>plot(X_test, y_2, color<span style="color: #666666">=</span><span style="color: #BA2121">&quot;green&quot;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;max_depth=5&quot;</span>, linewidth<span style="color: #666666">=2</span>)
+plt<span style="color: #666666">.</span>plot(X_test, y_3, color<span style="color: #666666">=</span><span style="color: #BA2121">&quot;m&quot;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;max_depth=7&quot;</span>, linewidth<span style="color: #666666">=2</span>)
+
+plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&quot;Data&quot;</span>)
+plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&quot;Darget&quot;</span>)
+plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;Decision Tree Regression&quot;</span>)
+plt<span style="color: #666666">.</span>legend()
+plt<span style="color: #666666">.</span>show()
+</pre></div>
 <p>

 <!-- ------------------- end of main content --------------- -->