parent
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commit
95f484af5c
@ -1,61 +0,0 @@
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%27页例题
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clc; clear; close all;
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n = 10000; % 使用较小的 n 值以便更容易可视化
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x = unifrnd(0, 12, [1, n]);
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y = unifrnd(0, 9, [1, n]);
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ans=sum(y < x.^2 & x <= 3)+sum(y < 12 - x & x >= 3);
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ans=ans/n;
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% 找出满足条件的点
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condition1 = y < x.^2 & x <= 3;
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condition2 = y < 12 - x & x >= 3;
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condition_met = condition1 | condition2; % 满足任一条件的点
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condition_not_met = ~condition_met; % 不满足任何条件的点
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% 创建图形窗口
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figure;
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hold on;%在同一张图上绘图
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% 绘制不满足任何条件的点
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scatter(x(condition_not_met), y(condition_not_met), 'k.'); % k----黑色 .----绘制样式
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%scatter绘制散点图
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%x(condition_not_met) 会返回一个新的向量，其中只包含 x 中对应 condition_not_met 为 true 的元素。
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% 绘制满足第一个条件的点
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scatter(x(condition1), y(condition1), 'r.'); % 红色
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% 绘制满足第二个条件的点
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scatter(x(condition2), y(condition2), 'b.'); % 蓝色
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% 添加图例和标签
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legend('不满足任何条件的点', '满足 y < x^2 且 x <= 3 的点', '满足 y < 12 - x 且 x >= 3 的点');
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xlabel('x');
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ylabel('y');
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title('随机生成的点和满足条件的点');
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hold off;
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%蒙特卡洛法求圆周率qw
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clc;clear;close all;
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n=10^5;
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x=unifrnd(-1,1,[1,n]);
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y=unifrnd(-1,1,[1,n]);
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con1=x.^2+y.^2<=1;
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con2=~con1;
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ans=sum(x.^2+y.^2<=1);
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ans=ans/n*4;
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figure ;
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hold on;
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scatter(x(con1),y(con1),'r.');
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scatter(x(con2),y(con2),'k.');
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hold off;
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@ -1,3 +0,0 @@
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function f=fun1(x)
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f=x(1)*x(1)+x(2)*x(2)-x(1)*x(2)-2*x(1)-5*x(2);
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end
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@ -1,15 +0,0 @@
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function f=fun2(x)
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a=[1.25,8.75,0.5,5.75,3,7.25];
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b=[1.25,0.75,4.75,5,6.5,7.25];
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f1 = 0; % 初始化f1
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f2 = 0; % 初始化f2
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for i=1:6
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s=sqrt((a(i)-x(13))^2+(b(i)-x(14))^2);
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f1=x(i)*s+f1;
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end
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for i=7:12
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s=sqrt((a(i-6)-x(15))^2+(b(i-6)-x(16))^2);
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f2=s*x(i)+f2;
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end
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f=f1+f2;
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end
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@ -1,49 +0,0 @@
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%整数规划
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%P23 ej2.5
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%optimproblem解法
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clc; clear; close all; format long g;
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prob=optimproblem;
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x=optimvar('x',6,'LowerBound',0,'Type','integer');
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prob.Objective=sum(x);
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cnt=[35,40,50,45,55,30];
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con=optimconstr(6);
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con(1)=x(1)+x(6)>=35;
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for i=1:5
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con(i+1)=x(i)+x(i+1)>=cnt(i+1);
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end
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prob.Constraints.con=con;
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[sol,fval,flag,out]=solve(prob);
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X=sol.x;
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%linprog解法
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clc; clear; close all; format long g;
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f=[1,1,1,1,1,1];
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intcon=[1:6];
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A=zeros(6,6);
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A(1,1)=-1;
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A(1,6)=-1;
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for i=1:5
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A(i+1,i)=-1;
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A(i+1,i+1)=-1;
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end
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lb=zeros(6,1);%注意不是lb=0
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b=[-35;-40;-50;-45;-55;-30];
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[x,fval]=intlinprog(f,intcon,A,b,[],[],lb);
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%01规划
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%背包问题
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f=-[540,200,180,350,60,150,280,450,320,120];
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intcon=1:10;
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lb=zeros(10);
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ub=ones(10);
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A=[6,3,4,5,1,2,3,5,4,2];
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b=30;
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[x,fval]=intlinprog(f,intcon,A,b,[],[],lb,ub);
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@ -1,140 +0,0 @@
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%投资利益与风险1998A题
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%模型一 给定风险承受程度，求最大利益
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f=[-0.05,-0.27,-0.19,-0.185,-0.185];
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%A矩阵
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%A=[0,0.025,0.015,0.055,0.026]; %错误
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%b=[1,1,1,1,1];
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A=[zeros(4,1),diag([0.025,0.015,0.055,0.026])];%不等式约束条件矩阵
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%Aeq、beq
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Aeq=[1,1.01,1.02,1.045,1.065];
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beq=1;
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%lb
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%lb=0; %错误
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lb=zeros(5,1);
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%可承担风险率a
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a=(0:0.001:0.05);
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%保存最优解
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Q=zeros(1,length(a));
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xx=[];%空矩阵存放最优解对应x的值
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for i=1:length(a)
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b=a(i)*ones(4,1);
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[x,y]=linprog(f,A,b,Aeq,beq,lb);
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Q(i)=-y;%注意取负！！！
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xx=[xx;x'];
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end
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plot(a,Q,'*r');
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xlabel("风险率");
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ylabel("最大收益");
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%模型二 收益、风险按权重组合
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% f0=[-0.05,-0.27,-0.19,-0.185,-0.185];
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% w=(0:0.1:1);
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% Aeq=[1,1.01,1.02,1.045,1.065,0];
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% beq=1;
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% lb=0;
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% xx=[];
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% Q=zeros(1,length(w));
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% A=[zeros(5,1),diag([0.025,0.025,0.055,0.065,0])];
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% b=ones(5,1);
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% for i=1:length(w)
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% f=[-w(i)*f0,1-w(i)];
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% b=x(end)*b;
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% [x,y]=linprog(f,A,b,Aeq,beq,lb);
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% Q(i)=-y;
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% xx=[xx,x'];
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% end
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% plot(w,Q,'*r');
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%模型二 收益、风险按权重组合
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clc; clear; close all; format long g;
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M = 10000;
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prob = optimproblem;
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x = optimvar('x', 6, 1, 'LowerBound', 0);
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r = [0.05, 0.28, 0.21, 0.23, 0.25];
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p = [0, 0.01, 0.02, 0.045, 0.065];
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q = [0, 0.025, 0.015, 0.055, 0.026]';
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%w = 0:0.1:1;
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w = 0.7:0.03:1;
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V = [];
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Q = [];
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X = [];
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prob.Constraints.con1 = (1 + p) * x(1:end-1) == M;
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prob.Constraints.con2 = (q(2:end).* x(2:end-1))<= x(end); %下标从1开始
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for i = 1:length(w)
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prob.Objective = w(i) * x(end) - (1 - w(i)) * (r - p) * x(1:end-1); %注意大小写
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[sol, fval, flag, out] = solve(prob);
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xx = sol.x;
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V = [V, max(q.* xx(1:end-1))];
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Q = [Q, (r - p) * xx(1:end-1)];
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X = [X, xx];
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plot(V, Q, '*-');
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grid on;
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xlabel('风险');
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ylabel('收益');
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end
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%模型三：达到一定盈利水平，极小化风险
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clc; clear; close all; format long g;
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M=10000;
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k=1500:100:3000;
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prob = optimproblem;
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x = optimvar('x', 5, 1, 'LowerBound', 0);%下界为0
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r = [0.05, 0.28, 0.21, 0.23, 0.25];
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p = [0, 0.01, 0.02, 0.045, 0.065];
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q = [0, 0.025, 0.015, 0.055, 0.026]';
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V = [];
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Q = [];
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X = [];
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t = optimvar('t', 'LowerBound', 0);
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%prob.Objective=max(q.*x);%极小化风险
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for i=1:length(k)
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prob.Objective = t; % 极小化风险
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prob.Constraints.con1 = (1 + p) * x == M;
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prob.Constraints.con2=((r-p)*x>=k(i));%达到一定盈利水平
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prob.Constraints.con3=(q.*x<=t);
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[sol,fval,flag,out]=solve(prob);
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if flag==1
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xx=sol.x;
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X=[X,xx];
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Q=[Q,(r-p)*xx];
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V=[V,fval];
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else
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xx=-1*ones(5,1);
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X=[X,xx];
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Q=[Q,-1];
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V=[V,-1];
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end
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end
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plot(k,V,'*-');
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@ -1,40 +1,40 @@
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clc; clear; close all; format long g;
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prob=optimproblem;
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x=optimvar('x',9,1,'LowerBound',0,'Type','integer');
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p=[0.25,0.35,0.50];
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r=[1.25,2.00,2.80];
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ot=[5,10,0;7,9,12;6,8,0;4,0,11;7,0,0];
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total=1000:200:3000;
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odp=[300/6000,321/10000,250/4000,783/7000,200/4000];
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X=[];
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Q=[];
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for i=1:length(total)
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% prob.Objective=(ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7))*odp(1)+(ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9))*odp(2)+(ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8)))*odp(3)+(ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9))*odp(4)+(ot(5,1)*(x(3)+x(6)))*odp(5)-(r(1)-p(1))*ones(1,6)*x(1:6)-(r(2)-p(2))*ones(1,2)*x(7:8)-(r(3)-p(3))*x(9);
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dp1=(ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7))*odp(1);
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dp2=(ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9))*odp(2);
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dp3=(ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8)))*odp(3);
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dp4=(ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9))*odp(4);
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dp5=(ot(5,1)*(x(3)+x(6)))*odp(5);
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dp=dp1+dp2+dp3+dp4+dp5;
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prob.Objective=dp-(r(1)-p(1))*ones(1,6)*x(1:6)-(r(2)-p(2))*ones(1,2)*x(7:8)-(r(3)-p(3))*x(9);
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prob.Constraints.con1=p(1)*ones(1,6)*x(1:6)+p(2)*ones(1,2)*x(7:8)+p(3)*x(9)+dp<=total(i);%总费用
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prob.Constraints.con2=ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7)<=6000;%A1
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prob.Constraints.con3=ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9)<=10000;
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prob.Constraints.con4=ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8))<=4000;
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prob.Constraints.con5=ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9)<=7000;
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prob.Constraints.con6=ot(5,1)*(x(3)+x(6))<=4000;
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[sol,fval,flag,out]=solve(prob);
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xx=sol.x;
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X=[X,xx];
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Q=[Q,-fval];
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end
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plot(total,Q,'*-');
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clc; clear; close all; format long g;
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prob=optimproblem;
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x=optimvar('x',9,1,'LowerBound',0,'Type','integer');
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p=[0.25,0.35,0.50];
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r=[1.25,2.00,2.80];
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ot=[5,10,0;7,9,12;6,8,0;4,0,11;7,0,0];
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total=1000:200:3000;
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odp=[300/6000,321/10000,250/4000,783/7000,200/4000];
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X=[];
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Q=[];
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for i=1:length(total)
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% prob.Objective=(ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7))*odp(1)+(ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9))*odp(2)+(ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8)))*odp(3)+(ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9))*odp(4)+(ot(5,1)*(x(3)+x(6)))*odp(5)-(r(1)-p(1))*ones(1,6)*x(1:6)-(r(2)-p(2))*ones(1,2)*x(7:8)-(r(3)-p(3))*x(9);
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dp1=(ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7))*odp(1);
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dp2=(ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9))*odp(2);
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dp3=(ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8)))*odp(3);
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dp4=(ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9))*odp(4);
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dp5=(ot(5,1)*(x(3)+x(6)))*odp(5);
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dp=dp1+dp2+dp3+dp4+dp5;
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prob.Objective=dp-(r(1)-p(1))*ones(1,6)*x(1:6)-(r(2)-p(2))*ones(1,2)*x(7:8)-(r(3)-p(3))*x(9);
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prob.Constraints.con1=p(1)*ones(1,6)*x(1:6)+p(2)*ones(1,2)*x(7:8)+p(3)*x(9)+dp<=total(i);%总费用
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prob.Constraints.con2=ot(1,1)*ones(1,3)*x(1:3)+ot(1,2)*x(7)<=6000;%A1
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prob.Constraints.con3=ot(2,1)*ones(1,3)*x(4:6)+ot(2,2)*x(8)+ot(2,3)*x(9)<=10000;
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prob.Constraints.con4=ot(3,1)*(x(1)+x(4))+ot(3,2)*(x(7)+x(8))<=4000;
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prob.Constraints.con5=ot(4,1)*(x(2)+x(5))+ot(4,3)*x(9)<=7000;
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prob.Constraints.con6=ot(5,1)*(x(3)+x(6))<=4000;
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[sol,fval,flag,out]=solve(prob);
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xx=sol.x;
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X=[X,xx];
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Q=[Q,-fval];
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end
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plot(total,Q,'*-');
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Reference in new issue