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

# # Table of Contents
#  <p>

# In[1]:


get_ipython().run_line_magic('matplotlib', 'inline')
import math,sys,os,numpy as np
from numpy.random import random
from matplotlib import pyplot as plt, rcParams, animation, rc
from __future__ import print_function, division
from ipywidgets import interact, interactive, fixed
from ipywidgets.widgets import *
rc('animation', html='html5')
rcParams['figure.figsize'] = 3, 3
get_ipython().run_line_magic('precision', '4')
np.set_printoptions(precision=4, linewidth=100)


# In[2]:


def lin(a,b,x): return a*x+b


# In[3]:


a=3.
b=8.


# In[4]:


n=30
x = random(n)
y = lin(a,b,x)


# In[5]:


x


# In[6]:


y


# In[7]:


plt.scatter(x,y)


# In[8]:


def sse(y,y_pred): return ((y-y_pred)**2).sum()
def loss(y,a,b,x): return sse(y, lin(a,b,x))
def avg_loss(y,a,b,x): return np.sqrt(loss(y,a,b,x)/n)


# In[9]:


a_guess=-1.
b_guess=1.
avg_loss(y, a_guess, b_guess, x)


# In[ ]:


lr=0.01
# d[(y-(a*x+b))**2,b] = 2 (b + a x - y)      = 2 (y_pred - y)
# d[(y-(a*x+b))**2,a] = 2 x (b + a x - y)    = x * dy/db


# In[ ]:


def upd():
    global a_guess, b_guess
    y_pred = lin(a_guess, b_guess, x)
    dydb = 2 * (y_pred - y)
    dyda = x*dydb
    a_guess -= lr*dyda.mean()
    b_guess -= lr*dydb.mean()


# In[ ]:


fig = plt.figure(dpi=100, figsize=(5, 4))
plt.scatter(x,y)
line, = plt.plot(x,lin(a_guess,b_guess,x))
plt.close()

def animate(i):
    line.set_ydata(lin(a_guess,b_guess,x))
    for i in range(10): upd()
    return line,

ani = animation.FuncAnimation(fig, animate, np.arange(0, 40), interval=100)
ani


# In[ ]: