added random walk example

doc/src/How2ReadData/How2ReadData.do.txt

@@ -3,7 +3,7 @@ AUTHOR: Morten Hjorth-Jensen {copyright, 1999-present|CC BY-NC} at Department of
 DATE: today
 
 
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+
 ===== Introduction =====
 
 Our emphasis throughout this series of lectures  
@@ -44,7 +44,7 @@ get started with programming.
 
 
 
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+
 ===== Software and needed installations =====
 
 We will make extensive use of Python as programming language and its
@@ -79,7 +79,7 @@ o sudo apt-get install python3  (or python for pyhton2.7)
 
 etc etc. 
 
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 ===== Python installers =====
 
 If you don't want to perform these operations separately and venture
@@ -103,7 +103,7 @@ analysis environment, available for free and under a commercial
 license.
 
 
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 ===== Installing R, C++, cython or Julia =====
 
 You will also find it convenient to utilize R. Although we will mainly
@@ -122,7 +122,7 @@ To install _R_ with Jupyter notebook
 
 
 
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 ===== Installing R, C++, cython, Numba etc =====
 
 
@@ -153,7 +153,7 @@ Finally, if you wish to use the light mark-up language
 "doconce":"https://github.com/hplgit/doconce" you can convert a standard ascii text file into various HTML 
 formats, ipython notebooks, latex files, pdf files etc with minimal edits.
 
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+
 ===== Simple linear regression model using _scikit-learn_ =====
 
 We start with perhaps our simplest possible example, using _scikit-learn_ to perform linear regression analysis on a data set produced by us. 
@@ -430,7 +430,8 @@ print (error(y))
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 Similarly, using _R_, we can perform similar studies. The following _R_ code illustrates this.
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+
 ===== Non-Linear Least squares in R  =====
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 !bc r
@@ -473,7 +474,7 @@ display(data_pandas)
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+
 ===== Examples =====
 
 We present here several examples, with pertinent Python codes that we
@@ -1026,3 +1027,96 @@ plt.show()
 
 
 
+
+=== Random walk model ===
+!bc pycod
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.preprocessing import PolynomialFeatures
+from sklearn.linear_model import LinearRegression
+
+steps=250
+
+distance=0
+x=0
+distance_list=[]
+steps_list=[]
+while x<steps:
+    distance+=np.random.randint(-1,2)
+    distance_list.append(distance)
+    x+=1
+    steps_list.append(x)
+plt.plot(steps_list,distance_list, color='green', label="Random Walk Data")
+
+steps_list=np.asarray(steps_list)
+distance_list=np.asarray(distance_list)
+
+X=steps_list[:,np.newaxis]
+
+#Polynomial fits
+
+#Degree 2
+poly_features=PolynomialFeatures(degree=2, include_bias=False)
+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_
+print ("2nd degree coefficients:")
+print ("zero power: ",c)
+print ("first power: ", b[0])
+print ("second power: ",b[1])
+
+z = np.arange(0, steps, .01)
+z_mod=b[1]*z**2+b[0]*z+c
+
+fit_mod=b[1]*X**2+b[0]*X+c
+plt.plot(z, z_mod, color='r', label="2nd Degree Fit")
+plt.title("Polynomial Regression")
+
+plt.xlabel("Steps")
+plt.ylabel("Distance")
+
+#Degree 10
+poly_features10=PolynomialFeatures(degree=10, include_bias=False)
+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='black', label="10th Degree Fit")
+
+plt.legend()
+plt.show()
+
+
+#Decision Tree Regression
+from sklearn.tree import DecisionTreeRegressor
+regr_1=DecisionTreeRegressor(max_depth=2)
+regr_2=DecisionTreeRegressor(max_depth=5)
+regr_3=DecisionTreeRegressor(max_depth=7)
+regr_1.fit(X, distance_list)
+regr_2.fit(X, distance_list)
+regr_3.fit(X, distance_list)
+
+X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]
+y_1 = regr_1.predict(X_test)
+y_2 = regr_2.predict(X_test)
+y_3=regr_3.predict(X_test)
+
+# Plot the results
+plt.figure()
+plt.scatter(X, distance_list, s=2.5, c="black", label="data")
+plt.plot(X_test, y_1, color="red",
+         label="max_depth=2", linewidth=2)
+plt.plot(X_test, y_2, color="green", label="max_depth=5", linewidth=2)
+plt.plot(X_test, y_3, color="m", label="max_depth=7", linewidth=2)
+
+plt.xlabel("Data")
+plt.ylabel("Darget")
+plt.title("Decision Tree Regression")
+plt.legend()
+plt.show()
+
+!ec