HW3.1-Gaussian Features

"""
Gaussian Features
Date:23.06.2019
Author:Yulian Sun
"""
import numpy as np
import math
import matplotlib.pyplot as plt
from numpy import linalg as la
file = np.loadtxt('../linRegData.txt', dtype=float)
trainingSet = file[0:20]
testingSet = file[20:150]

def gaussian(x,mu,sigma_sq):
    equ1 = 1 / np.sqrt(2 * np.pi * sigma_sq)
    gaus = equ1 * np.exp(-(x - mu) ** 2 / (2* sigma_sq) )
    return gaus

# calculate gaussian,plot matrix Phi
def fit_gaussian(dataset,mean,sigma_sq):
    input =dataset[:,0]
    n = len(dataset)
    phi = np.empty((n, 10))
    equ = np.empty((n, 10))
    sum = np.empty((n, 1))
    for i in range(n):
        for k in range(len(mean)):
            equ[i][k] = gaussian(input[i],mean[k],sigma_sq)
            sum[i] = np.sum(equ[i,:],axis=0)

        phi[i,:] = equ[i,:]/sum[i]
    Phi = np.array(phi).reshape(n,10)
    return Phi

sigma_sq = 0.02
mean = np.linspace(0,2,10)
data = np.zeros((1000,2))
data[:,0] = np.linspace(0,2,1000).T

Phi = fit_gaussian(data,mean,sigma_sq)
print(Phi)
for i in range(10):
    plt.plot(data[:,0],Phi[:,i],label='mu{}'.format(i))

plt.legend()
plt.show()