import matplotlib
import numpy as np
import matplotlib.cm as cm
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt

%matplotlib inline


features = np.array([0.8,0.9,1.0,1.1,1.4,\
	1.4,1.5,1.6,1.8,2.0,2.4,2.5,2.7,3.2,3.5])
target = np.array([70,83,74,93,89,58,85,114,95,100,138,111,124,161,172])

plt.plot(features,target,'o', markersize=10)
plt.show()

def cost(t0,t1):
    return (np.sum(((features*t1 +t0)- target)**2))/(2*len(features))

def cost_del_t0(t0,t1):
    return np.sum(((features*t1 +t0)- target))/len(features)

def cost_del_t1(t0,t1):
    return np.sum((features*t0) + (features**2)*t1\
     - features*target)/len(features)


#gradient Descent fixed alpha
def gra_de1(alpha, times, inicial0, inicial1):
    i0 = inicial0
    i1 = inicial1
    for i in range(times):
        temp0 = i0 - alpha*cost_del_t0(i0,i1)
        temp1 = i1 - alpha*cost_del_t1(i0,i1)
        i0 = temp0
        i1 = temp1
    return i0,i1



#gradient Descent decreasing alpha
def gra_de2(alpha, times, inicial0, inicial1):
    i0 = inicial0
    i1 = inicial1
    for i in range(times):
        alpha = alpha - alpha*(i/(times-1))
        temp0 = i0 - alpha*cost_del_t0(i0,i1)
        temp1 = i1 - alpha*cost_del_t1(i0,i1)
        i0 = temp0
        i1 = temp1
    return i0,i1


test1 = gra_de1(0.3, 500,0,0)

test2 = gra_de2(0.6, 500,0,0)

def hypothesis1(x):
    return test1[0] + test1[1]*x

def hypothesis2(x):
    return test2[0] + test2[1]*x

plt.plot(features, hypothesis1(features),\
	features,hypothesis2(features),features,target,'o', markersize=10)
plt.show()