This codes related to other imolement code the one before:

# Various tools for data manipulation.

import numpy as np

import math

class MyUtils:

def rand_matrix(nb_rows = 1, nb_cols = 1):

''' return a nb_row x nb_col matrix of random numbers from (-1,1)

'''

X = np.random.rand(nb_rows, nb_cols) * np.sign(np.random.rand(nb_rows, nb_cols)-0.5)

return X

def normalize_0_1(X):

''' Normalize the value of every feature into the [0,1] range, using formula: x = (x-x_min)/(x_max - x_min)

1) First shift all feature values to be non-negative by subtracting the min of each column

if that min is negative.

2) Then divide each feature value by the max of the column if that max is not zero.

X: n x d matrix of samples, excluding the x_0 = 1 feature. X can have negative numbers.

return: the n x d matrix of samples where each feature value belongs to [0,1]

'''

n, d = X.shape

X_norm = X.astype('float64') # Have a copy of the data in float

for i in range(d):

col_min = min(X_norm[:,i])

col_max = max(X_norm[:,i])

gap = col_max - col_min

if gap:

X_norm[:,i] = (X_norm[:,i] - col_min) / gap

else:

X_norm[:,i] = 0 #X_norm[:,i] - X_norm[:,i]

return X_norm

def normalize_neg1_pos1(X):

''' Normalize the value of every feature into the [-1,+1] range.

X: n x d matrix of samples, excluding the x_0 = 1 feature. X can have negative numbers.

return: the n x d matrix of samples where each feature value belongs to [-1,1]

'''

# To be implemented

n, d = X.shape

X_norm = X.astype('float64') # Have a copy of the data in float

for i in range(d):

col_min = min(X_norm[:,i])

col_max = max(X_norm[:,i])

col_mid = (col_max + col_min) / 2

gap = (col_max - col_min) / 2

if gap:

X_norm[:,i] = (X_norm[:,i] - col_mid) / gap

else:

X_norm[:,i] = 0 #X_norm[:,i] - X_norm[:,i]

return X_norm

def z_transform(X, degree = 2):

''' Transforming traing samples to the Z space

X: n x d matrix of samples, excluding the x_0 = 1 bias feature

degree: the degree of the Z space

return: the n x d' matrix of samples in the Z space, excluding the z_0 = 1 feature.

It can be mathematically calculated: d' = \sum_{k=1}^{degree} (k+d-1) \choose (d-1)

'''

if degree == 1:

return X

### BEGIN YOUR SOLUTION

raise NotImplementedError()

### END YOUR SOLUTION