added gradient codes

doc/src/Splines/Splines.do.txt

@@ -539,3 +539,72 @@ which gives
 !eblock
 
 
+
+!split
+===== Gradient Descent codes =====
+!bc pycod
+
+# Importing various packages
+from math import exp, sqrt
+from random import random, seed
+import numpy as np
+import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d import Axes3D
+from matplotlib import cm
+from matplotlib.ticker import LinearLocator, FormatStrFormatter
+import sys
+
+x = 2*np.random.rand(100,1)
+y = 4+3*x+np.random.randn(100,1)
+
+xb = np.c_[np.ones((100,1)), x]
+theta_linreg = np.linalg.inv(xb.T.dot(xb)).dot(xb.T).dot(y)
+print(theta_linreg)
+theta = np.random.randn(2,1)
+
+eta = 0.1
+Niterations = 1000
+m = 100
+
+for iter in range(Niterations):
+    gradients = 2.0/m*xb.T.dot(xb.dot(theta)-y)
+    theta -= eta*gradients
+
+print(theta)
+xnew = np.array([[0],[2]])
+xbnew = np.c_[np.ones((2,1)), xnew]
+ypredict = xbnew.dot(theta)
+ypredict2 = xbnew.dot(theta_linreg)
+plt.plot(xnew, ypredict, "r-")
+plt.plot(xnew, ypredict2, "b-")
+plt.plot(x, y ,'ro')
+plt.axis([0,2.0,0, 15.0])
+plt.xlabel(r'$x$')
+plt.ylabel(r'$y$')
+plt.title(r'Random numbers ')
+plt.show()
+
+!ec
+
+!bc pycod
+# Importing various packages
+from math import exp, sqrt
+from random import random, seed
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.linear_model import SGDRegressor
+
+x = 2*np.random.rand(100,1)
+y = 4+3*x+np.random.randn(100,1)
+
+xb = np.c_[np.ones((100,1)), x]
+theta_linreg = np.linalg.inv(xb.T.dot(xb)).dot(xb.T).dot(y)
+print(theta_linreg)
+sgdreg = SGDRegressor(n_iter = 50, penalty=None, eta0=0.1)
+sgdreg.fit(x,y.ravel())
+print(sgdreg.intercept_, sgdreg.coef_)
+
+!ec
+
+
+