linear_regression.py

# coding:utf-8
import numpy as np
import math
import random
import matplotlib.pyplot as plt

def sinpi(x):
    return math.sin(2*math.pi * x)

def base(x, n):
    return x**n

def makeData(N):
    l = []
    for i in range(N):
        x = random.random()
        error = np.random.normal(0,0.1)
        l.append((x,sinpi(x)+error))
    return l

def main():
    N = 100
    M = 8
    data = makeData(N)
    phi = [[base(data[i][0], j) for j in range(M)] for i in range(N)]
    phi = np.matrix(phi)
    t = np.matrix([x[1] for x in data]).T
    w = np.linalg.inv(phi.T.dot(phi)).dot(phi.T).dot(t)

    def f(v):
        s = 0
        for i in range(M):
            s += base(v,i)*w[i,0]
        return s

    x = np.arange(0,1,0.01)
    y = f(x)
    plt.plot(x, y)
    plt.scatter([x[0] for x in data], [x[1] for x in data], c="red")
    plt.show()



if __name__=='__main__':
    main()