microproduct/soilMoisture_geo_sar/test_tool/minimize.py

# -*- coding: UTF-8 -*-
"""
@Project ：onestar 
@File ：minimize.py
@Contact：
@Author ：SHJ
@Date ：2021/11/24 15:46 
@Version ：1.0.0
"""
from scipy.optimize import minimize
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import pyplot as plt
#目标函数：
def func(args):
    fun = lambda x: 10 - x[0]**2 - x[1]**2
    return fun

#约束条件，包括等式约束和不等式约束
def con(args):
    cons = ({'type': 'ineq', 'fun': lambda x: x[1]-x[0]**2},
    {'type': 'eq', 'fun': lambda x: x[0]+x[1]})
    return cons



#画三维模式图
def draw3D():
    fig = plt.figure()
    ax = Axes3D(fig)
    x_arange = np.arange(-5.0, 5.0)
    y_arange = np.arange(-5.0, 5.0)
    X, Y = np.meshgrid(x_arange, y_arange)
    Z1 = 10 - X**2 - Y**2
    Z2 = Y - X**2
    Z3 = X + Y
    plt.xlabel('x')
    plt.ylabel('y')
    ax.plot_surface(X, Y, Z1, rstride=1, cstride=1, cmap='rainbow')
    ax.plot_surface(X, Y, Z2, rstride=1, cstride=1, cmap='rainbow')
    ax.plot_surface(X, Y, Z3, rstride=1, cstride=1, cmap='rainbow')
    plt.show()
    #画等高线图

def drawContour():
    x_arange = np.linspace(-3.0, 4.0, 256)
    y_arange = np.linspace(-3.0, 4.0, 256)
    X, Y = np.meshgrid(x_arange, y_arange)
    Z1 = 10 - X**2 - Y**2
    Z2 = Y - X**2
    Z3 = X + Y
    plt.xlabel('x')
    plt.ylabel('y')
    plt.contourf(X, Y, Z1, 8, alpha=0.75, cmap='rainbow')
    plt.contourf(X, Y, Z2, 8, alpha=0.75, cmap='rainbow')
    plt.contourf(X, Y, Z3, 8, alpha=0.75, cmap='rainbow')
    C1 = plt.contour(X, Y, Z1, 8, colors='black')
    C2 = plt.contour(X, Y, Z2, 8, colors='blue')
    C3 = plt.contour(X, Y, Z3, 8, colors='red')
    plt.clabel(C1, inline=1, fontsize=10)
    plt.clabel(C2, inline=1, fontsize=10)
    plt.clabel(C3, inline=1, fontsize=10)
    plt.show()

    # 目标函数：
    def func1(args):
        fun = lambda x: 10 - x[0] ** 2 - x[1] ** 2
        return fun

def samper():
    args = ()
    args1 = ()
    cons = con(args1)
    x0 = np.array((1.0, 2.0)) #设置初始值，初始值的设置很重要，很容易收敛到另外的极值点中，建议多试几个值
    #求解#
    res = minimize(func(args), x0, method='SLSQP', constraints=cons)
    #####
    print(res.fun)
    print(res.success)
    print(res.x)
    # draw3D()
    drawContour()

def samper1():
    fun = lambda x: np.abs(np.abs((0.7- (x[0] -0.49)**0.5)/(0.7- (x[0] +0.49)**0.5)) - 0.5*np.abs((0.7- (x[1] -0.49)**0.5)/(0.7- (x[1] +0.49)**0.5)))
    # fun = lambda x: np.abs(x[0]**2 -x[1]**2)
    x_min = 1
    x_max = 20
    cons = ({'type': 'ineq', 'fun': lambda x: x[0] - x_min},
            {'type': 'ineq', 'fun': lambda x: -x[0] + x_max},
            {'type': 'ineq', 'fun': lambda x: x[1] - x_min},
            {'type': 'ineq', 'fun': lambda x: -x[1] + x_max})
    bnds = ((0, 30), (0, 30))
    res = minimize(fun, (3, 3), method='SLSQP', bounds=bnds,constraints=cons)
    print("res::",res)

    x_arange = np.linspace(0, 25, 256)
    y_arange = np.linspace(0, 25, 256)
    X, Y = np.meshgrid(x_arange, y_arange)
    Z1 = np.abs(np.abs((0.7- (X -0.49)**0.5)/(0.7- (X +0.49)**0.5)) - 0.5*np.abs((0.7- (Y -0.49)**0.5)/(0.7- (Y +0.49)**0.5)))
    # Z1 = np.abs(X**2 - Y**2)
    plt.xlabel('x')
    plt.ylabel('y')
    plt.contourf(X, Y, Z1, 8, alpha=0.75, cmap='rainbow')
    C1 = plt.contour(X, Y, Z1, 8, colors='black')
    plt.clabel(C1, inline=1, fontsize=10)
    plt.show()



if __name__ == "__main__":
    # samper1()
    s1 = 0.9414927
    c1 = 0.24188292
    s2 = 0.9414927
    c2 = 0.24188292
    t = 1.0
    x_min = 1
    x_max = 20
    bnds = ((x_min, x_max), (x_min, x_max))
    x_mid = 0.5 * (x_max - x_min)
    x = [9,8]
    a = (s2 - x[1]*(1 + s2))
    b = np.abs((x[1] - 1)*(s2 - x[1]*(1 + s2)) / (x[1] * c2 + (x[1] - s2) ** 0.5) ** 2)- t * np.abs((x[0] - 1)*(s1 - x[0]*(1 + s1)) / (x[0] * c1 + (x[0] - s1) ** 0.5) ** 2)

    fun = lambda x: np.abs(
        np.abs((x[1] - 1)*(s2 - x[1]*(1 + s2)) / (x[1] * c2 + (x[1] - s2) ** 0.5) ** 2)
        - t * np.abs((x[0] - 1)*(s1 - x[0]*(1 + s1)) / (x[0] * c1 + (x[0] - s1) ** 0.5) ** 2)
    )
    res = minimize(fun, (x_mid, x_mid), method='SLSQP', bounds=bnds)
    print("res::", res)

    x_arange = np.linspace(0, 25, 256)
    y_arange = np.linspace(0, 25, 256)
    X, Y = np.meshgrid(x_arange, y_arange)

    Z1 = np.abs(
        np.abs((Y - 1)*(s2 - Y*(1 + s2)) / (Y * c2 + (Y - s2) ** 0.5) ** 2)
        - t * np.abs((X - 1)*(s1 - X*(1 + s1)) / (X * c1 + (X - s1) ** 0.5) ** 2)
    )
    # Z1 = np.abs(X**2 - Y**2)
    plt.xlabel('x')
    plt.ylabel('y')
    plt.contourf(X, Y, Z1, 8, alpha=0.75, cmap='rainbow')
    C1 = plt.contour(X, Y, Z1, 8, colors='black')
    plt.clabel(C1, inline=1, fontsize=10)
    plt.show()


    print('done')