<filename>code/basic-knowledge/GDDoubleVariable.py
# -*- coding: utf-8 -*-#
'''
# Name:         GDDoubleVariable
# Description:  GDDoubleVariable 双变量梯度下降
# Author:       super
# Date:         2020/5/7
'''

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D


def target_function(x, y):
    '''
    目标函数
    :param x:
    :param y:
    :return:
    '''
    J = x ** 2 + np.sin(y) ** 2
    return J


def derivative_function(theta):
    '''
    目标函数的两个偏导数
    :param theta:
    :return:
    '''
    x = theta[0]
    y = theta[1]
    return np.array([2 * x, 2 * np.sin(y) * np.cos(y)])


def show_3d_surface(x, y, z):
    fig = plt.figure()
    ax = Axes3D(fig)

    u = np.linspace(-3, 3, 100)
    v = np.linspace(-3, 3, 100)
    # 以参数中每个点为中心，生成网格
    X, Y = np.meshgrid(u, v)
    R = np.zeros((len(u), len(v)))
    for i in range(len(u)):
        for j in range(len(v)):
            R[i, j] = X[i, j] ** 2 + np.sin(Y[i, j]) ** 2

    ax.plot_surface(X, Y, R, cmap='rainbow')
    plt.plot(x, y, z, c='black')
    plt.show()


if __name__ == '__main__':
    theta = np.array([3, 1])
    eta = 0.1
    error = 1e-2

    X = []
    Y = []
    Z = []
    for i in range(100):
        print(theta)
        x = theta[0]
        y = theta[1]
        z = target_function(x, y)
        X.append(x)
        Y.append(y)
        Z.append(z)
        print("%d: x=%f, y=%f, z=%f" % (i, x, y, z))
        d_theta = derivative_function(theta)
        print("    ", d_theta)
        theta = theta - eta * d_theta
        if z < error:
            break
    show_3d_surface(X, Y, Z)
<filename>code/basic-knowledge/GDDoubleVariable.py
# -*- coding: utf-8 -*-#
'''
# Name:         GDDoubleVariable
# Description:  GDDoubleVariable 双变量梯度下降
# Author:       super
# Date:         2020/5/7
'''

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D


def target_function(x, y):
    '''
    目标函数
    :param x:
    :param y:
    :return:
    '''
    J = x ** 2 + np.sin(y) ** 2
    return J


def derivative_function(theta):
    '''
    目标函数的两个偏导数
    :param theta:
    :return:
    '''
    x = theta[0]
    y = theta[1]
    return np.array([2 * x, 2 * np.sin(y) * np.cos(y)])


def show_3d_surface(x, y, z):
    fig = plt.figure()
    ax = Axes3D(fig)

    u = np.linspace(-3, 3, 100)
    v = np.linspace(-3, 3, 100)
    # 以参数中每个点为中心，生成网格
    X, Y = np.meshgrid(u, v)
    R = np.zeros((len(u), len(v)))
    for i in range(len(u)):
        for j in range(len(v)):
            R[i, j] = X[i, j] ** 2 + np.sin(Y[i, j]) ** 2

    ax.plot_surface(X, Y, R, cmap='rainbow')
    plt.plot(x, y, z, c='black')
    plt.show()


if __name__ == '__main__':
    theta = np.array([3, 1])
    eta = 0.1
    error = 1e-2

    X = []
    Y = []
    Z = []
    for i in range(100):
        print(theta)
        x = theta[0]
        y = theta[1]
        z = target_function(x, y)
        X.append(x)
        Y.append(y)
        Z.append(z)
        print("%d: x=%f, y=%f, z=%f" % (i, x, y, z))
        d_theta = derivative_function(theta)
        print("    ", d_theta)
        theta = theta - eta * d_theta
        if z < error:
            break
    show_3d_surface(X, Y, Z)
# -*- coding: utf-8 -*-# # Name:         GDDoubleVariable # Description:  GDDoubleVariable 双变量梯度下降 # Author:       super # Date:         2020/5/7 目标函数     :param x:     :param y:     :return: 目标函数的两个偏导数     :param theta:     :return: # 以参数中每个点为中心，生成网格