#!/usr/bin/python
# -*- coding: utf-8 -*-

## Logistic Regression from scratch

# In[62]:

# In[63]:

# importing all the required libraries

''' Implementing logistic regression for classification problem 
 Helpful resources : 1.Coursera ML course 2.https://medium.com/@martinpella/logistic-regression-from-scratch-in-python-124c5636b8ac'''

import numpy as np
import matplotlib.pyplot as plt

# get_ipython().run_line_magic('matplotlib', 'inline')

from sklearn import datasets


# In[67]:

# sigmoid function or logistic function is used as a hypothesis function in classification problems

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


def cost_function(h, y):
 return (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()


# here alpha is the learning rate, X is the feature matrix,y is the target matrix

def logistic_reg(
 alpha,
 X,
 y,
 max_iterations=70000,
 ):
 converged = False
 iterations = 0
 theta = np.zeros(X.shape[1])

 while not converged:
 z = np.dot(X, theta)
 h = sigmoid_function(z)
 gradient = np.dot(X.T, h - y) / y.size
 theta = theta - alpha * gradient

 z = np.dot(X, theta)
 h = sigmoid_function(z)
 J = cost_function(h, y)

 iterations += 1 # update iterations

 if iterations == max_iterations:
 print ('Maximum iterations exceeded!')
 print ('Minimal cost function J=', J)
 converged = True

 return theta


# In[68]:

if __name__ == '__main__':
 iris = datasets.load_iris()
 X = iris.data[:, :2]
 y = (iris.target != 0) * 1

 alpha = 0.1
 theta = logistic_reg(alpha, X, y, max_iterations=70000)
 print (theta)


 def predict_prob(X):
 return sigmoid_function(np.dot(X, theta)) # predicting the value of probability from the logistic regression algorithm


 plt.figure(figsize=(10, 6))
 plt.scatter(X[y == 0][:, 0], X[y == 0][:, 1], color='b', label='0')
 plt.scatter(X[y == 1][:, 0], X[y == 1][:, 1], color='r', label='1')
 (x1_min, x1_max) = (X[:, 0].min(), X[:, 0].max())
 (x2_min, x2_max) = (X[:, 1].min(), X[:, 1].max())
 (xx1, xx2) = np.meshgrid(np.linspace(x1_min, x1_max),
 np.linspace(x2_min, x2_max))
 grid = np.c_[xx1.ravel(), xx2.ravel()]
 probs = predict_prob(grid).reshape(xx1.shape)
 plt.contour(
 xx1,
 xx2,
 probs,
 [0.5],
 linewidths=1,
 colors='black',
 )

 plt.legend()