# download the software
import urllib

urllib.urlretrieve('https://github.com/sods/ods/archive/master.zip', 'master.zip')

# unzip the software
import zipfile
zip = zipfile.ZipFile('./master.zip', 'r')
for name in zip.namelist():
    zip.extract(name, '.')

# add the module location to the python path.    
import sys
sys.path.append("./ods-master/")

#import pods
#pods.notebook.code_toggle()

import pods
pods.notebook.display_google_book(id='spcAAAAAMAAJ', page=72) 

data = pods.datasets.olympic_marathon_men()
x = data['X']
y = data['Y']

print(x)
print(y)

%matplotlib inline 
import pylab as plt

plt.plot(x, y, 'rx')
plt.xlabel('year')
plt.ylabel('pace in min/km')

m = -0.4
c = 80 

# set c to the minimum
c = (y - m*x).mean()
print c

m = ((y - c)*x).sum()/(x**2).sum()
print m

import numpy as np
x_test = np.linspace(1890, 2020, 130)[:, None]

f_test = m*x_test + c

plt.plot(x_test, f_test, 'b-')
plt.plot(x, y, 'rx')

for i in np.arange(10):
    m = ((y - c)*x).sum()/(x*x).sum()
    c = (y-m*x).sum()/y.shape[0]
print(m)
print(c)

f_test = m*x_test + c
plt.plot(x_test, f_test, 'b-')
plt.plot(x, y, 'rx')

# Question 3 Answer Code
# Write code for you answer to this question in this box
# Do not delete these comments, otherwise you will get zero for this answer.
# Make sure your code has run and the answer is correct *before* submitting your notebook for marking.


# define the vector w
w = np.zeros(shape=(2, 1))
w[0] = m
w[1] = c

X = np.hstack((np.ones_like(x), x))
print(X)

f = np.dot(X, w) # np.dot does matrix multiplication in python

resid = (y-f)
E = np.dot(resid.T, resid) # matrix multiplication on a single vector is equivalent to a dot product.
print "Error function is:", E

np.linalg.solve?

w = np.linalg.solve(np.dot(X.T, X), np.dot(X.T, y))
print w

m = w[1]; c=w[0]
f_test = m*x_test + c
print(m)
print(c)
plt.plot(x_test, f_test, 'b-')
plt.plot(x, y, 'rx')

data = pods.datasets.movie_body_count()
movies = data['Y']

print ', '.join(movies.columns)

select_features = ['Year', 'Body_Count', 'Length_Minutes']
X = movies[select_features]
X['Eins'] = 1 # add a column for the offset
y = movies[['IMDB_Rating']]

import pandas as pd
w = pd.DataFrame(data=np.linalg.solve(np.dot(X.T, X), np.dot(X.T, y)),  # solve linear regression here
                 index = X.columns,  # columns of X become rows of w
                 columns=['regression_coefficient']) # the column of X is the value of regression coefficient

(y - np.dot(X, w)).hist()

w

from IPython.display import YouTubeVideo
YouTubeVideo('ui-uNlFHoms')

from IPython.display import YouTubeVideo
YouTubeVideo('78YNphT90-k')

import scipy as sp
Q, R = np.linalg.qr(X)
w = sp.linalg.solve_triangular(R, np.dot(Q.T, y)) 
w = pd.DataFrame(w, index=X.columns)
w