线性回归 | 梯度下降前序 求解函数最小值

求解y=x²最小值

# -*- coding: UTF-8 -*-
"""
    梯度下降求解y=x**2的最小值
"""
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt

# 设置字符集，防止中文乱码
mpl.rcParams['font.sans-serif'] = [u'simHei']
mpl.rcParams['axes.unicode_minus'] = False

# 原函数
def f(x):
    return x ** 2

# 导数
def h(x):
    return 2 * x

# 画图
def draw_gd(X, Y, x, f_current):
    figure = plt.figure()
    X2 = np.arange(-2.1, 2.15, 0.05)
    Y2 = X2 ** 2

    plt.plot(X2, Y2, '-', color='#666666', linewidth=2)
    plt.plot(X, Y, 'ro--')
    plt.title(u'y=x^2函数求解最小值，最终解为：x=%.2f,y=%.2f' % (x, f_current))
    plt.show()

# 梯度下降求解y=x**2的最小值
def gd():
    X = []
    Y = []

    x = 2
    step = 0.8
    f_change = f(x)
    f_current = f(x)
    X.append(x)
    Y.append(f_current)

    while f_change > 1e-10:
        x = x - step * h(x)
        f_change = np.abs(f_current - f(x))
        f_current = f(x)

        X.append(x)
        Y.append(f_current)
    print("result: ", (x, f_current))
    draw_gd(X, Y, x, f_current)

if __name__ == '__main__':
    gd()

函数y=x^2最小值

求解z=x²+y²最小值

# -*- coding: UTF-8 -*-
"""
    梯度下降求解y=x**2的最小值
"""
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

# 设置字符集，防止中文乱码
mpl.rcParams['font.sans-serif'] = [u'simHei']
mpl.rcParams['axes.unicode_minus'] = False

# 原函数
def f(x, y):
    return x**2 + y**2

# 偏导
def h(t):
    return 2 * t

# 画图
def draw(X, Y, Z, x, y, f_current):
    figure = plt.figure()
    axes = Axes3D(figure)
    X2 = np.arange(-2, 2, 0.2)
    Y2 = np.arange(-2, 2, 0.2)
    X2, Y2 = np.meshgrid(X2, Y2)
    Z2 = f(X2, Y2)

    axes.plot_surface(X2, Y2, Z2, rstride=1, cstride=1, cmap='rainbow')
    axes.plot(X, Y, Z, 'ro--')
    axes.set_title(u'z=x^2+y^2函数求解最小值，最终解为：x=%.2f,y=%.2f,z=%.2f' 
        % (x, y, f_current))
    plt.show()

# 梯度下降求解z=x**2+y**2的最小值
def gd():
    X = []
    Y = []
    Z = []

    x = 2
    y = 2
    step = 0.1
    f_change = f(x, y)
    f_current = f(x, y)
    X.append(x)
    Y.append(y)
    Z.append(f_current)
    while f_change > 1e-10:
        x = x - step * h(x)
        y = y - step * h(y)
        f_change = np.abs(f_current - f(x, y))
        f_current = f(x, y)

        X.append(x)
        Y.append(y)
        Z.append(f_current)
    print("result: ", (x, y, f_current))
    draw(X, Y, Z, x, y, f_current)

if __name__ == '__main__':
    gd()

函数z=x^2+y^2最小值