/*
Program to implement the the Logistic Regression Using Gradient Descent.
Developed by: 
RegisterNumber:  
import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize    #to remove unwanted data and memory storage

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

X[:5]

y[:5]

Visualizing the data
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()

Sigmoid fuction
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 costFuction(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=costFuction(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=costFuction(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)
*/