156 lines
4.6 KiB
Python
156 lines
4.6 KiB
Python
# -*- coding: UTF-8 -*-
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"""
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@Project ：onestar
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@File ：minimize.py
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@Contact：
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@Author ：SHJ
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@Date ：2021/11/24 15:46
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@Version ：1.0.0
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"""
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from scipy.optimize import minimize
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import numpy as np
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from mpl_toolkits.mplot3d import Axes3D
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from matplotlib import pyplot as plt
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#目标函数：
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def func(args):
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fun = lambda x: 10 - x[0]**2 - x[1]**2
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return fun
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#约束条件，包括等式约束和不等式约束
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def con(args):
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cons = ({'type': 'ineq', 'fun': lambda x: x[1]-x[0]**2},
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{'type': 'eq', 'fun': lambda x: x[0]+x[1]})
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return cons
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#画三维模式图
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def draw3D():
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fig = plt.figure()
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ax = Axes3D(fig)
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x_arange = np.arange(-5.0, 5.0)
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y_arange = np.arange(-5.0, 5.0)
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X, Y = np.meshgrid(x_arange, y_arange)
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Z1 = 10 - X**2 - Y**2
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Z2 = Y - X**2
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Z3 = X + Y
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plt.xlabel('x')
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plt.ylabel('y')
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ax.plot_surface(X, Y, Z1, rstride=1, cstride=1, cmap='rainbow')
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ax.plot_surface(X, Y, Z2, rstride=1, cstride=1, cmap='rainbow')
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ax.plot_surface(X, Y, Z3, rstride=1, cstride=1, cmap='rainbow')
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plt.show()
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#画等高线图
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def drawContour():
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x_arange = np.linspace(-3.0, 4.0, 256)
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y_arange = np.linspace(-3.0, 4.0, 256)
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X, Y = np.meshgrid(x_arange, y_arange)
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Z1 = 10 - X**2 - Y**2
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Z2 = Y - X**2
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Z3 = X + Y
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plt.xlabel('x')
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plt.ylabel('y')
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plt.contourf(X, Y, Z1, 8, alpha=0.75, cmap='rainbow')
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plt.contourf(X, Y, Z2, 8, alpha=0.75, cmap='rainbow')
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plt.contourf(X, Y, Z3, 8, alpha=0.75, cmap='rainbow')
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C1 = plt.contour(X, Y, Z1, 8, colors='black')
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C2 = plt.contour(X, Y, Z2, 8, colors='blue')
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C3 = plt.contour(X, Y, Z3, 8, colors='red')
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plt.clabel(C1, inline=1, fontsize=10)
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plt.clabel(C2, inline=1, fontsize=10)
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plt.clabel(C3, inline=1, fontsize=10)
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plt.show()
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# 目标函数：
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def func1(args):
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fun = lambda x: 10 - x[0] ** 2 - x[1] ** 2
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return fun
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def samper():
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args = ()
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args1 = ()
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cons = con(args1)
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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
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#求解#
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res = minimize(func(args), x0, method='SLSQP', constraints=cons)
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#####
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print(res.fun)
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print(res.success)
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print(res.x)
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# draw3D()
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drawContour()
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def samper1():
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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)))
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# fun = lambda x: np.abs(x[0]**2 -x[1]**2)
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x_min = 1
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x_max = 20
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cons = ({'type': 'ineq', 'fun': lambda x: x[0] - x_min},
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{'type': 'ineq', 'fun': lambda x: -x[0] + x_max},
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{'type': 'ineq', 'fun': lambda x: x[1] - x_min},
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{'type': 'ineq', 'fun': lambda x: -x[1] + x_max})
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bnds = ((0, 30), (0, 30))
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res = minimize(fun, (3, 3), method='SLSQP', bounds=bnds,constraints=cons)
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print("res::",res)
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x_arange = np.linspace(0, 25, 256)
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y_arange = np.linspace(0, 25, 256)
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X, Y = np.meshgrid(x_arange, y_arange)
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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)))
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# Z1 = np.abs(X**2 - Y**2)
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plt.xlabel('x')
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plt.ylabel('y')
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plt.contourf(X, Y, Z1, 8, alpha=0.75, cmap='rainbow')
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C1 = plt.contour(X, Y, Z1, 8, colors='black')
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plt.clabel(C1, inline=1, fontsize=10)
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plt.show()
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if __name__ == "__main__":
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# samper1()
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s1 = 0.9414927
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c1 = 0.24188292
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s2 = 0.9414927
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c2 = 0.24188292
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t = 1.0
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x_min = 1
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x_max = 20
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bnds = ((x_min, x_max), (x_min, x_max))
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x_mid = 0.5 * (x_max - x_min)
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x = [9,8]
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a = (s2 - x[1]*(1 + s2))
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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)
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fun = lambda x: np.abs(
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np.abs((x[1] - 1)*(s2 - x[1]*(1 + s2)) / (x[1] * c2 + (x[1] - s2) ** 0.5) ** 2)
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- t * np.abs((x[0] - 1)*(s1 - x[0]*(1 + s1)) / (x[0] * c1 + (x[0] - s1) ** 0.5) ** 2)
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)
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res = minimize(fun, (x_mid, x_mid), method='SLSQP', bounds=bnds)
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print("res::", res)
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x_arange = np.linspace(0, 25, 256)
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y_arange = np.linspace(0, 25, 256)
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X, Y = np.meshgrid(x_arange, y_arange)
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Z1 = np.abs(
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np.abs((Y - 1)*(s2 - Y*(1 + s2)) / (Y * c2 + (Y - s2) ** 0.5) ** 2)
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- t * np.abs((X - 1)*(s1 - X*(1 + s1)) / (X * c1 + (X - s1) ** 0.5) ** 2)
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)
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# Z1 = np.abs(X**2 - Y**2)
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plt.xlabel('x')
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plt.ylabel('y')
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plt.contourf(X, Y, Z1, 8, alpha=0.75, cmap='rainbow')
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C1 = plt.contour(X, Y, Z1, 8, colors='black')
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plt.clabel(C1, inline=1, fontsize=10)
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plt.show()
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print('done')
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