%autosave 10

%matplotlib inline
from matplotlib import pyplot

import numpy

import csv

data = []
with open('data/ex1data1.txt', 'r') as f:
    data_reader = csv.reader(f, delimiter=',')
    for row in data_reader:
        data.append((float(row[0]), float(row[1])))
data = numpy.asarray(data)

data[:5]

pyplot.scatter(data[:,0], data[:,1])

theta = numpy.zeros(shape=(2,))
alpha = 0.001

m = len(data[:,0])
h = lambda theta, x: numpy.add(theta[0], theta[1]*x)
J = lambda theta: (1./(2.*m))*numpy.sum(numpy.power(h(theta,data[:,0])-data[:,1], 2))

feature_vector = numpy.column_stack((numpy.ones(shape=(m,)), data[:,0]))
nabla_J = lambda theta: (1./m)*numpy.sum(numpy.column_stack((h(theta,data[:,0])-data[:,1],h(theta,data[:,0])-data[:,1]))*feature_vector)

feature_vector[:5]

print('Before GD, J = %g' % J(theta))
for i in range(10000):
    theta = theta - alpha*nabla_J(theta)
print('After GD, J = %g' % J(theta))

theta