CS590 HW3 Prob 2-a

CS590_HW3_Prob2.py

import numpy as np

def binarize(num):
    binnum = bin(num)[2:]
    if len(binnum) < 3:
        rem_num = 3 - len(binnum)
        return '0'*rem_num + binnum
    else:
        return binnum

def f(binnum):
    count_zero = 0
    count_one = 0
    for elem in binnum:
        if elem == '0':
            count_zero += 1
        else:
            count_one += 1
    if count_one > count_zero:
        return -1
    else:
        return 1

def Fourier_basis(bin_s, bin_x):
    lincom = 0
    for elem_s, elem_x in zip(bin_s, bin_x):
        lincom += int(elem_s) * int(elem_x)
    return (-1)**(lincom)

def Fourier_Matrix(bindom):
    FM = np.zeros((len(bindom),len(bindom)))
    N = len(bindom)
    for s in range(len(bindom)):
        for x in range(len(bindom)):
            bin_s = bindom[s]
            bin_x = bindom[x]
            FM[x,s] = 1/N * Fourier_basis(bin_s,bin_x)
    return FM



domain_N = list(range(0,8))
bindom = [binarize(x) for x in domain_N]
fval = [f(x) for x in bindom]
FM = Fourier_Matrix(bindom)
FC = np.matrix(fval) * np.matrix(FM)

print(FC)