浙江建设职业技术学院网站,南宁专业网站制作,外贸公司图片,wordpress加速网站插件今天想写一个最优传输的简单实现#xff0c;结果学歪了#xff0c;学到线性规划去了#xff0c;这里我发现了一个宝藏网站 虽然是讲计量经济的#xff0c;但是里面提供的公式和代码我很喜欢#xff0c;有时间可以好好读一下 https://python.quantecon.org/lp_intro.html
…今天想写一个最优传输的简单实现结果学歪了学到线性规划去了这里我发现了一个宝藏网站 虽然是讲计量经济的但是里面提供的公式和代码我很喜欢有时间可以好好读一下 https://python.quantecon.org/lp_intro.html
参考博客 https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linprog.html
https://python.quantecon.org/lp_intro.html
example1 图解法
import numpy as np
from scipy.optimize import linprog
import matplotlib.pyplot as plt
from matplotlib.patches import Polygonfig, ax plt.subplots(figsize(8, 6))
ax.grid()# Draw constraint lines
ax.hlines(0, -1, 17.5)
ax.vlines(0, -1, 12)
ax.plot(np.linspace(-1, 17.5, 100), 6-0.4*np.linspace(-1, 17.5, 100), colorc)## 画一条直线
ax.plot(np.linspace(-1, 5.5, 100), 10-2*np.linspace(-1, 5.5, 100), colorc) ## 画一条直线
ax.text(1.5, 8, $2x_1 5x_2 \leq 30$, size12)
ax.text(10, 2.5, $4x_1 2x_2 \leq 20$, size12)
ax.text(-2, 2, $x_2 \geq 0$, size12)
ax.text(2.5, -0.7, $x_1 \geq 0$, size12)# Draw the feasible region
feasible_set Polygon(np.array([[0, 0],[0, 6],[2.5, 5],[5, 0]]),colorcyan)
ax.add_patch(feasible_set)# Draw the objective function
ax.plot(np.linspace(-1, 5.5, 100), 3.875-0.75*np.linspace(-1, 5.5, 100), colororange)
ax.plot(np.linspace(-1, 5.5, 100), 5.375-0.75*np.linspace(-1, 5.5, 100), colororange)
ax.plot(np.linspace(-1, 5.5, 100), 6.875-0.75*np.linspace(-1, 5.5, 100), colororange)
ax.arrow(-1.6, 5, 0, 2, width 0.05, head_width0.2, head_length0.5, colororange)
ax.text(5.7, 1, $z 3x_1 4x_2$, size12)# Draw the optimal solution
ax.plot(2.5, 5, *, colorblack)
ax.text(2.7, 5.2, Optimal Solution, size12)plt.show()结果如下这个图还蛮好看的
python代码 - solution
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import linprog
from quantecon.optimize.linprog_simplex import linprog_simplex
import ot
from scipy.stats import betabinom
import networkx as nx
# Define parameters# Construct parameters
c_ex1 np.array([3, 4])# Inequality constraints
A_ex1 np.array([[2, 5],[4, 2]])
b_ex1 np.array([30,20])# Solve the problem
# we put a negative sign on the objective as linprog does minimization
res_ex1 linprog(-c_ex1, A_ubA_ex1, b_ubb_ex1)res_ex1结果如下
matlab代码-solution
%% example1
clc;
clear;
c[-3,-4]; % 价值向量
a_inequ[2,5;4,2]; % a、b对应不等式的左边和右边
b_inequ[30;20];
a_eq[]; % aeq和beq对应等式的左边和右边
b_eq[];
[x,y]linprog(c,a_inequ,b_inequ,a_eq,b_eq,zeros(2,1));
fprintf(x[%3f,%3f]\n,x);
fprintf(y[%3f]\n,y);
%结果如下
example2 python代码
from scipy.optimize import linprog
c [-1, 4]
A [[-3, 1], [1, 2]]
b [6, 4]
x0_bounds (None, None)
x1_bounds (-3, None)
res linprog(c, A_ubA, b_ubb, bounds[x0_bounds, x1_bounds])
print(res.fun)
print(res.x)结果如下
matlab代码 %%example2
clc;
clear;
c[-1,4]; % 价值向量
a_inequ[-3,1;1,2]; % a、b对应不等式的左边和右边
b_inequ[6;4];
a_eq[]; % aeq和beq对应等式的左边和右边
b_eq[];
lb [-inf,-3]; % 这里不要写成了lb[-3,-inf],否则无界
ub [];
[x,y]linprog(c,a_inequ,b_inequ,a_eq,b_eq,lb,ub);
fprintf(x[%3f,%3f]\n,x);
fprintf(y[%3f]\n,y);example3 python代码 from scipy.optimize import linprog
import numpy as npc [-1,-1/3]
a_inequ np.array([[1, 1],[1 ,1/4],[1 ,-1],[-1/4, -1],[-1, -1],[-1 ,1]])b_inequ np.array([2, 1, 2 ,1 ,-1 ,2]);a_eq np.array([[1, 1/4]]);
b_eq np.array([1/2]);x0_bounds [-1,1.5];
x1_bounds [-0.5,1.25];res linprog(c, A_uba_inequ, b_ubb_inequ,A_eqa_eq,b_eqb_eq, bounds[x0_bounds, x1_bounds])print(res.x)
print(res.fun)结果如下
matlab代码
clc;
clear;
c [-1 -1/3];
a_inequ [1 1; 1 1/4;1 -1; -1/4 -1;-1 -1;-1 1];
b_inequ [2 1 2 1 -1 2];
a_eq [1 1/4];
b_eq 1/2;
lb [-1,-0.5];
ub [1.5,1.25];
[x,y] linprog(c,a_inequ,b_inequ,a_eq,b_eq,lb,ub);
fprintf(x[%3f,%3f]\n,x);
fprintf(y[%3f]\n,y);嘿嘿先到这里吧
