%%! 
pip install --upgrade ipython

# 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 numpy as np # import numpy for the arrays.

def quadratic(x):
    """Take in a vector of input values and return the design matrix associated 
    with the basis functions."""
    return np.hstack([np.ones((n, 1)), x, x**2])


# ensure plots appear in the notebook.
%matplotlib inline 
import pylab as plt

# first let's generate some inputs
n = 100
x = np.zeros((n, 1))  # create a data set of zeros
x[:, 0] = np.linspace(-1, 1, n) # fill it with values between -1 and 1

Phi = quadratic(x)

fig, ax = plt.subplots(figsize=(12,4))
ax.set_ylim([-1.2, 1.2]) # set y limits to ensure basis functions show.
ax.plot(x[:,0], Phi[:, 0], 'r-', label = '$\phi=1$')
ax.plot(x[:,0], Phi[:, 1], 'g-', label = '$\phi = x$')
ax.plot(x[:,0], Phi[:, 2], 'b-', label = '$\phi = x^2$')
ax.legend(loc='lower right')
ax.set_title('Quadratic Basis Functions')

def polynomial(x, num_basis=4, data_limits=[-1., 1.]):
    Phi = np.zeros((x.shape[0], num_basis))
    for i in xrange(num_basis):
        Phi[:, i:i+1] = x**i
    return Phi

import pods
pods.notebook.display_prediction(basis=polynomial, num_basis=4)

fig, ax = plt.subplots(figsize=(12,4))
plt.close(fig)
from IPython.display import display
display(fig)

def rbf(x, num_basis=4, data_limits=[-1., 1.]):
    centres=np.linspace(data_limits[0], data_limits[1], num_basis)
    width = (centres[1]-centres[0])/2.
    Phi = np.zeros((x.shape[0], num_basis))
    for i in xrange(num_basis):
        Phi[:, i:i+1] = np.exp(-0.5*((x-centres[i])/width)**2)
    return Phi

pods.notebook.display_prediction(basis=rbf, num_basis=4)

def fourier(x, num_basis=4, data_limits=[-1., 1.]):
    tau = 2*np.pi
    span = float(data_limits[1]-data_limits[0])
    Phi = np.zeros((x.shape[0], num_basis))
    for i in xrange(num_basis):
        count = float((i+1)/2)
        frequency = count/span
        if i % 2:
            Phi[:, i:i+1] = np.sin(tau*frequency*x)
        else:
            Phi[:, i:i+1] = np.cos(tau*frequency*x)
    return Phi

pods.notebook.display_prediction(basis=fourier, num_basis=4)

data = pods.datasets.olympic_marathon_men()
y = data['Y']
x = data['X']
y -= y.mean()
y /= y.std()

def polynomial(x, num_basis=4, data_limits=[-1., 1.]):
    centre = data_limits[0]/2. + data_limits[1]/2.
    span = data_limits[1] - data_limits[0]
    z = x - centre
    z = 2*z/span
    Phi = np.zeros((x.shape[0], num_basis))
    for i in xrange(num_basis):
        Phi[:, i:i+1] = z**i
    return Phi
import pods
#x[:, 0] = np.linspace(1888, 2020, 1000)
fig, ax = plt.subplots(figsize=(12,4))

ax.plot(x, y, 'rx')
pods.notebook.display_prediction(basis=dict(rbf=rbf, polynomial=polynomial, fourier=fourier), 
                                 data_limits=(1888, 2020),
                                 fig=fig, ax=ax,
                                 offset=0.,
                                 wlim = (-4., 4., 0.001),
                                 num_basis=4)

# Question 3 Answer Code
# provide the answers so that the code runs correctly otherwise you will loose marks!

# (a) polynomial
###### Edit these lines #####
w_0 =
w_1 = 
w_2 = 
w_3 =
##############################
w_polynomial = np.asarray([[w_0], [w_1], [w_2], [w_3]]) 

# (b) rbf
###### Edit these lines #####
w_0 =
w_1 = 
w_2 = 
w_3 =
##############################
w_rbf = np.asarray([[w_0], [w_1], [w_2], [w_3]]) 

# (c) fourier
###### Edit these lines #####
w_0 =
w_1 = 
w_2 = 
w_3 =
##############################
w_fourier = np.asarray([[w_0], [w_1], [w_2], [w_3]]) 

np.asarray([[1, 2, 3, 4]]).shape

# Question 5 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.


from IPython.display import YouTubeVideo
YouTubeVideo('PoNbOnUnOao')