import numpy as np
from scipy.misc import imread, imsave, imresize
from matplotlib import pyplot as plt

from scipy.io import loadmat,whosmat
from numpy.linalg import inv




def linregpredictmat(xmat,thetavec):
  #Find the predicted value of y=xmat*theta

  t=1

  yhat = xmat.dot(thetavec)
  return yhat

def linregloss(y,yhat):
   #Compute the loss as mean squared error over all samples
   #
   m = len(y)
   n
   mseloss = np.sum((yhat-y)**2)/(2*m)

   mseloss1 = mseloss
   return mseloss1


def normalequations(xmat,y,thetavec):
  thetanorm=np.zeros(thetavec.shape)
  xinv = inv(xmat.T.dot(xmat))
  xprod = xinv.dot(xmat.T)
  res = xprod.dot(y)
  thetanorm = res
  
  return thetanorm


def gradientdescent(yhat,y,epsilon,thetavec,xmat,x):
  # Use gradient descent with learning rate epsilon to predict the next value of thetavec
  # First, compute theta0 and theta1 one at a time
  m = len(yhat)

  [mm, nn] = xmat.shape
  diffvec = yhat - y
  deltatheta = np.zeros(xmat.shape)
  deltatheta = xmat * diffvec[:, np.newaxis]
  corrvector = np.zeros(nn)
  nythetavectorized = np.zeros(thetavec.shape)

  for j in range(0, nn):
    corrvector[j] = epsilon * np.sum(deltatheta[:, j]) / m


  nythetavectorized = thetavec - corrvector

  return nythetavectorized








f = open('linregy.asc', 'r')
ydata = np.genfromtxt(f)

f = open('ex1data1.txt','r')
tmpdata = np.genfromtxt(f,delimiter=",")

x=tmpdata[:,0]
nofsamp=x.shape
ydata=tmpdata[:,1]
thetavec = np.zeros((2))







nofsamp = len(ydata)
xmat = np.zeros((nofsamp,2))
xmat[:,0]=np.ones(nofsamp).T
xmat[:,1]= x.T


theta0 = 0.0
theta1 = 0.0
thetavec[0] = theta0
thetavec[0]=theta1
maxit = 2500;
lossvec = np.zeros(maxit)
for it in range(1,maxit):

  yhat = linregpredictmat(xmat,thetavec)

  mseloss=linregloss(ydata,yhat)

  epsilon = 0.01
  thetavecny = gradientdescent(yhat,ydata, epsilon,thetavec,xmat,x)


  thetavec = thetavecny

  lossvec[it-1] = mseloss




#Control the answer using the normal equations
#thetanorm = normalequations(xmattest,ytest,thetavec)
thetanorm = normalequations(xmat,ydata,thetavec)

print thetavec
print thetanorm


ynormpred = linregpredictmat(xmat,thetanorm)


plt.plot(x,ydata,'ro',x,yhat,'b-',x,ynormpred,'g--')
plt.show()





plt.plot(lossvec[1:200])
plt.show()

#