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

# # Cost function

# In[1]:


import numpy as np


# In[2]:


def costFunction(X, y, theta):
    m = len(y)
    hypothesis = X @ theta
    err = hypothesis - y
    return ((1 / (2 * m)) * (np.transpose(err) @ err).item((0, 0)))


# Let's run it against some fake housing data:

# In[3]:


X = np.array([
    [1, 3000],
    [1, 4000],
    [1, 5000],
])

y = np.array([
    [1550000],
    [2050000],
    [2550000],
])

bad_theta = np.array([
    [0],
    [0],
])

good_theta = np.array([
    [50000],
    [500],
])

print("With bad theta values  - cost:", costFunction(X, y, bad_theta))

print("With good theta values - cost:", costFunction(X, y, good_theta))