【数值计算】梯度下降法

为了睡觉，我写简单点

反正就是个记录

梯度下降

快速梯度下降

"""
Numerical Computation & Optimization
homework1: gradient
cww97
Name: Chen WeiWen
stuID: 10152510217
2017/12/14
from cww970329@qq.com
to num_com_opt@163.com
"""
import numpy as np
N = 1000


def gradient(A, b):
    x = np.mat(np.zeros([N, 1]))
    #while np.linalg.norm(A*x-b) > 1e-2:
    for cnt in range(3000):
        gx = A * x - b
        s = 5e-4 * sum(A[i].T * gx[i] for i in range(N))
        x -= s
    return x


def fast_gradient(A, b):
    x = np.mat(np.zeros([N, 1]))
    x_old, a_old, a = np.copy(x), 0, 1
    for cnt in range(1000):
        a_new = 0.5 + 0.5 * np.sqrt(1+4*a*a)
        t = (a-1) / a_new
        y_new = (1+t) * x - t * x_old
        gy = A * y_new - b
        s = 3e-4 * sum(A[i].T * gy[i] for i in range(N))
        x_new = y_new - s
        a_old, a, x_old, x = a, a_new, x, x_new
        # make you dont feel boring when waiting
        print(cnt, np.linalg.norm(A*x-b))
    return x


if __name__ == '__main__':
    A = np.mat(np.random.normal(size=(N, N)))
    x = np.mat(np.ones([N, 1]))
    b = A * x
    print('A =
', A, '
x = ', x.T, '.T
b = ', b.T, '.T')
    print('梯度下降：')
    print(gradient(A, b).T)
    print('快速梯度下降：')
    print(fast_gradient(A, b).T)