/*
Program to implement the the Logistic Regression Using Gradient Descent.
Developed by: Akshaya Lakshmi VS 
RegisterNumber:  212222040005
*/

import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize

data = np.loadtxt("/content/ex2data1.txt", delimiter=',')
X = data[:,[0,1]]
y = data[:,2]

X[:5]

y[:5]

plt.figure()
plt.scatter(X[y == 1][:,0],X[y == 1][:,1], label="Admitted")
plt.scatter(X[y == 0][:,0],X[y == 0][:,1],label ="Not admitted")
plt.xlabel("Exam 1 score")
plt.ylabel("Exam 2 score")
plt.legend()
plt.show()

def sigmoid(z):
  return 1/(1+np.exp(-z))

plt.plot()
X_plot = np.linspace(-10,10,100)
plt.plot(X_plot,sigmoid(X_plot))
plt.show()

def costfunction(theta,X,y):
  h = sigmoid(np.dot(X,theta))
  j = -(np.dot(y,np.log(h)) + np.dot(1-y,np.log(1-h))) / X.shape[0]
  grad = np.dot(X.T, h-y)/ X.shape[0]
  return j,grad

X_train = np.hstack((np.ones((X.shape[0],1)),X))
theta =np.array([0,0,0])
j,grad = costfunction(theta,X_train,y)
print(j)
print(grad)

X_train = np.hstack((np.ones((X.shape[0],1)),X))
theta = np.array([-24,0.2,0.2])
j,grad = costfunction(theta,X_train,y)
print(j)
print(grad)

def cost(theta,X,y):
  h = sigmoid(np.dot(X,theta))
  j = -(np.dot(y,np.log(h)) + np.dot(1-y,np.log(1-h)))/X.shape[0]
  return j

def gradient(theta,X,y):
  h = sigmoid(np.dot(X,theta))
  grad = np.dot(X.T,h-y)/X.shape[0]
  return grad

X_train = np.hstack((np.ones((X.shape[0],1)),X))
theta = np.array([0,0,0])
res = optimize.minimize(fun=cost, x0=theta, args=(X_train,y),method='Newton-CG',jac=gradient)

print(res.fun)
print(res.x)

def plotDecisionBoundary(theta,X,y):
  x_min, x_max = X[:,0].min()-1, X[:,0].max() +1
  y_min, y_max = X[:,1].min()-1, X[:,1].max() +1
  xx,yy =np.meshgrid(np.arange(x_min, x_max,0.1),np.arange(y_min,y_max, 0.1))
  X_plot = np.c_[xx.ravel(), yy.ravel()]
  X_plot = np.hstack((np.ones((X_plot.shape[0],1)),X_plot))
  y_plot = np.dot(X_plot,theta).reshape(xx.shape)
  plt.figure()
  plt.scatter(X[y == 1][:,0],X[y== 1][:,1],label="Admitted")
  plt.scatter(X[y== 0][:,0],X[y ==0][:,1],label="Not admitted")
  plt.contour(xx,yy,y_plot,levels =[0])
  plt.xlabel("Exam 1 score")
  plt.ylabel("Exam 2 score")
  plt.legend()
  plt.show()

plotDecisionBoundary(res.x,X,y)

prob = sigmoid(np.dot(np.array([1,45,85]),res.x))
print(prob)

def predict(theta,X):
  X_train = np.hstack((np.ones((X.shape[0],1)),X))
  prob=sigmoid(np.dot(X_train,theta))
  return (prob >=0.5).astype(int)

np.mean(predict(res.x,X)==y)