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added random walk example

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mhjensen
2018-05-29 11:08:41 -04:00
parent 3a2abcd62b
commit d34d39836b
8 changed files with 608 additions and 101 deletions
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doc/pub/How2ReadData/html/How2ReadData-solarized.html
+97 -21
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@@ -77,7 +77,8 @@ 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>
@@ -121,8 +122,6 @@ 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>
@@ -164,9 +163,6 @@ 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>
@@ -209,9 +205,6 @@ 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>
@@ -239,9 +232,6 @@ 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>
@@ -260,9 +250,6 @@ 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>
@@ -297,9 +284,6 @@ 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>
@@ -586,7 +570,6 @@ plt.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">
@@ -637,8 +620,6 @@ data = {<span style="color: #CD5555">&#39;Name&#39;</span>: [<span style="color:
data_pandas = pd.DataFrame(data)
display(data_pandas)
</pre></div>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec7">Examples </h2>
@@ -1300,6 +1281,101 @@ plt.axis([-<span style="color: #B452CD">5</span>, <span style="color: #B452CD">5
plt.grid(<span style="color: #658b00">True</span>)
plt.show()
</pre></div>
<h3 id="___sec12">Random walk model </h3>
<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: #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>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.preprocessing</span> <span style="color: #8B008B; font-weight: bold">import</span> PolynomialFeatures
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LinearRegression
steps=<span style="color: #B452CD">250</span>
distance=<span style="color: #B452CD">0</span>
x=<span style="color: #B452CD">0</span>
distance_list=[]
steps_list=[]
<span style="color: #8B008B; font-weight: bold">while</span> x&lt;steps:
distance+=np.random.randint(-<span style="color: #B452CD">1</span>,<span style="color: #B452CD">2</span>)
distance_list.append(distance)
x+=<span style="color: #B452CD">1</span>
steps_list.append(x)
plt.plot(steps_list,distance_list, color=<span style="color: #CD5555">&#39;green&#39;</span>, label=<span style="color: #CD5555">&quot;Random Walk Data&quot;</span>)
steps_list=np.asarray(steps_list)
distance_list=np.asarray(distance_list)
X=steps_list[:,np.newaxis]
<span style="color: #228B22">#Polynomial fits</span>
<span style="color: #228B22">#Degree 2</span>
poly_features=PolynomialFeatures(degree=<span style="color: #B452CD">2</span>, include_bias=<span style="color: #658b00">False</span>)
X_poly=poly_features.fit_transform(X)
lin_reg=LinearRegression()
poly_fit=lin_reg.fit(X_poly,distance_list)
b=lin_reg.coef_
c=lin_reg.intercept_
<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">&quot;2nd degree coefficients:&quot;</span>)
<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">&quot;zero power: &quot;</span>,c)
<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">&quot;first power: &quot;</span>, b[<span style="color: #B452CD">0</span>])
<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">&quot;second power: &quot;</span>,b[<span style="color: #B452CD">1</span>])
z = np.arange(<span style="color: #B452CD">0</span>, steps, .<span style="color: #B452CD">01</span>)
z_mod=b[<span style="color: #B452CD">1</span>]*z**<span style="color: #B452CD">2</span>+b[<span style="color: #B452CD">0</span>]*z+c
fit_mod=b[<span style="color: #B452CD">1</span>]*X**<span style="color: #B452CD">2</span>+b[<span style="color: #B452CD">0</span>]*X+c
plt.plot(z, z_mod, color=<span style="color: #CD5555">&#39;r&#39;</span>, label=<span style="color: #CD5555">&quot;2nd Degree Fit&quot;</span>)
plt.title(<span style="color: #CD5555">&quot;Polynomial Regression&quot;</span>)
plt.xlabel(<span style="color: #CD5555">&quot;Steps&quot;</span>)
plt.ylabel(<span style="color: #CD5555">&quot;Distance&quot;</span>)
<span style="color: #228B22">#Degree 10</span>
poly_features10=PolynomialFeatures(degree=<span style="color: #B452CD">10</span>, include_bias=<span style="color: #658b00">False</span>)
X_poly10=poly_features10.fit_transform(X)
poly_fit10=lin_reg.fit(X_poly10,distance_list)
y_plot=poly_fit10.predict(X_poly10)
plt.plot(X, y_plot, color=<span style="color: #CD5555">&#39;black&#39;</span>, label=<span style="color: #CD5555">&quot;10th Degree Fit&quot;</span>)
plt.legend()
plt.show()
<span style="color: #228B22">#Decision Tree Regression</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.tree</span> <span style="color: #8B008B; font-weight: bold">import</span> DecisionTreeRegressor
regr_1=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">2</span>)
regr_2=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">5</span>)
regr_3=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">7</span>)
regr_1.fit(X, distance_list)
regr_2.fit(X, distance_list)
regr_3.fit(X, distance_list)
X_test = np.arange(<span style="color: #B452CD">0.0</span>, steps, <span style="color: #B452CD">0.01</span>)[:, np.newaxis]
y_1 = regr_1.predict(X_test)
y_2 = regr_2.predict(X_test)
y_3=regr_3.predict(X_test)
<span style="color: #228B22"># Plot the results</span>
plt.figure()
plt.scatter(X, distance_list, s=<span style="color: #B452CD">2.5</span>, c=<span style="color: #CD5555">&quot;black&quot;</span>, label=<span style="color: #CD5555">&quot;data&quot;</span>)
plt.plot(X_test, y_1, color=<span style="color: #CD5555">&quot;red&quot;</span>,
label=<span style="color: #CD5555">&quot;max_depth=2&quot;</span>, linewidth=<span style="color: #B452CD">2</span>)
plt.plot(X_test, y_2, color=<span style="color: #CD5555">&quot;green&quot;</span>, label=<span style="color: #CD5555">&quot;max_depth=5&quot;</span>, linewidth=<span style="color: #B452CD">2</span>)
plt.plot(X_test, y_3, color=<span style="color: #CD5555">&quot;m&quot;</span>, label=<span style="color: #CD5555">&quot;max_depth=7&quot;</span>, linewidth=<span style="color: #B452CD">2</span>)
plt.xlabel(<span style="color: #CD5555">&quot;Data&quot;</span>)
plt.ylabel(<span style="color: #CD5555">&quot;Darget&quot;</span>)
plt.title(<span style="color: #CD5555">&quot;Decision Tree Regression&quot;</span>)
plt.legend()
plt.show()
</pre></div>
<p>
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