tensorflow 2.0 学习 Himmelblua函数求极值

Posted 2020-11-24 heze

Himmelblua函数在（-6，6），（-6，6）的二维平面上求极值

函数的数学表达式：f(x, y) = (x**2 + y -11)**2 + (x + y**2 -7)**2； 如下图所示

等高线如下图所示：

代码如下：

# encoding: utf-8

import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.axes_grid1 import ImageGrid


# Himmelblau function
def himmelblua(x):
    return (x[0] ** 2 + x[1] - 11) ** 2 + (x[0] + x[1] ** 2 - 7) ** 2


# 产生三维数据
x = np.arange(-6, 6, 0.1)           # 创建等差数组，步长为0.1
y = np.arange(-6, 6, 0.1)
print(‘x, y range:‘, x.shape, y.shape)
X, Y = np.meshgrid(x, y)
print(‘X, Y maps:‘, X.shape, Y.shape)
Z = himmelblua([X, Y])
max = np.max(Z)
min = np.min(Z)

# 画三维图
fig = plt.figure(‘himmelblua‘)
ax = fig.gca(projection=‘3d‘)       # 设置3D坐标轴
ax.plot_surface(X, Y, Z)            # 3D曲面图
ax.view_init(60, -30)
ax.set_xlabel(‘x‘)
ax.set_ylabel(‘y‘)
plt.show()

# 画等高线图
N = np.arange(min, max, (max-min)/200)
fig = plt.figure(‘contour‘)
ct = plt.contour(Z, N, linewidth=2, cmap=mpl.cm.jet)        # 计算等高差
plt.clabel(ct, inline=True, fmt=‘%1.1f‘, fontsize=10)
plt.colorbar(ct)
plt.xlabel(‘x‘)
plt.ylabel(‘y‘)
plt.savefig(‘contour-himmelblua.png‘)
plt.show()

# 初始化参数
x = tf.constant([4., 0.])

# 寻找极小值数值解
for step in range(200):
    with tf.GradientTape() as tape:
        tape.watch([x])
        y = himmelblua(x)
    grads = tape.gradient(y, [x])[0]
    x -= 0.01*grads
    if step % 20 ==19:
        print(‘step {}: x={}, f(x)={}‘.format(step, x.numpy(), y.numpy()))

经过迭代后的值越来越精确，这里就不表了！