ex.m

一个matlab的线性规划的工具箱

% Test M-file for lp_solve
clc;
echo on;

% Test and Demonstrate the use of lp_solve

echo off;
disp('Press any key to continue.');
pause
echo on;

clc;
% Example 1 from the lp_solve distribution
f = [-1, 2]';
A = [2, 1;-4, 4];
b = [5, 5];
e = -[1, 1];
xint = [1, 2];
[v,x] = lp_solve(f,sparse(A),b,e,[],[],[])

echo off;
disp('End of Ex1. Expected Solution: v=3, x=[1, 2]. Press any key to continue.');
pause
echo on;

clc;
% Example 2
f = [50, 100];
A = sparse([10, 5;4, 10; 1, 1.5]);
b = [2500, 2000, 450];
e = [-1, -1, -1];

[v,x] = lp_solve(f,A,b,e)

echo off;
disp('End of Ex2. Press any key to continue.');
pause
echo on;

clc;
% Example 3
f = -[40, 36];
vub = [8, 10];
A = sparse([5, 3]);
b = [45];
e = 1;

[v,x] = lp_solve(f,A,b,e,[],vub)

echo off;
disp('End of Ex3. Press any key to continue.');
pause
echo on;

clc;
% Example 4
f = [10, 6, 4];
A = [1, 1, 1;10, 4, 5;2, 2, 6];
A = sparse(A);
b = [100, 600, 300];
e = [-1, -1, -1];
xint = [2];

[v,x] = lp_solve(f,A,b,e,[],[],xint)

echo off;
disp('End of Ex4. Press any key to continue.');
pause
echo on;

clc;
% Example 5
% Integer programming example, page 218 of Ecker & Kupferschmid
f = -[3, -7, -12];
a = [-3, 6, 8;6, -3, 7;-6, 3, 3];
a = sparse(a);
b = [12, 8, 5];
e = [-1, -1, -1];
xint = [1, 2, 3];

[v,x] = lp_solve(f,a,b,e,[],[],xint)

echo off;
disp('End of Ex5. Press any key to continue.');
pause
echo on;

clc;
% Example 6
% 0-1 programming example, page 228 233 of Ecker & Kupferschmid
f = -[2, 3, 7, 7];
a = [1, 1, -2, -5;-1, 2, 1, 4];
a = sparse(a);
b = [2, -3];
e = [1, 1];
xint = [1, 2, 3, 4];
vub = [1, 1, 1, 1];

[v,x] = lp_solve(f,a,b,e,[],vub,xint)

echo off;
disp('End of Ex6. Press any key to continue.');
pause
echo on;

clc;
% Example 7
% 0-1 programming example, page 238 of Ecker & Kupferschmid
f = -[1, 2, 3, 7, 8, 8];
a = [5, -3, 2, -3, -1, 2; -1, 0, 2, 1, 3, -3;1, 2, -1, 0, 5, -1];
b = [-5, -1, 3];
e = [1, 1, 1];
xint = [1, 2, 3, 4, 5, 6];
vub = [1, 1, 1, 1, 1, 1];

[v,x] = lp_solve(f,sparse(a),b,e,[],vub,xint)

echo off;
disp('End of Ex7. Press any key to continue.');
pause
echo on;

clc;
% Example 8
% A knapsack problem
% The problem is to maximize the sum of objects

n = 5; 		% Number of objects
f = ones(n,1);

% subject to a constraint not to fill up the bag
a = rand(1,n);
b = [1];
e = [-1];
xint = 1:n;
vub = ones(n,1);

[v,x] = lp_solve(f,sparse(a),b,e,[],vub,xint)

echo off;
disp('End of Ex8. Note that model is random, so solution is also random. Press any key to continue.');
pause
echo on;

clc;
% Example 9
% L1 Data fitting example with integer constraint on the intercept
n = 40;
t = (0:n-1)';
y = 3.5 -.2*t;
y = y + 0.5*randn(size(y));

m = [ones(n,1),t(:)];
a = [m,-m,speye(n)];
f = -[sum(m),sum(-m),2*ones(1,n)];
e = ones(n,1);

vub = [10, 10, 10, 10, 5*ones(1,n)];

[v,x] = lp_solve(f,sparse(a),y,e,[],vub,[1,3]);

p = x(1:2)-x(3:4);
err = y-m*p;
plot(t,y,'o',t,m*p);
xlabel('t');
ylabel('y');

echo off;
disp('End of Ex9. Press any key to continue.');
pause
echo on;

clc;
% Example 10
% Now solve bigger problem

n = 200;
m = 100;
a = rand(m,n);
idx = find(a<0.8);
a(idx) = zeros(length(idx),1);
a = sparse(a);
z = rand(n,1);
b = a*z;

[v,x] = lp_solve(-ones(1,n),a,b,zeros(m,1));

plot(a*x-b);
title('Residuals');
xlabel('Equation Number');
echo off;
disp('End of Ex10. Note that model is random, so solution is also random. Press any key to continue.');
pause
echo on;

clc;
% Example 11
% ex2.lp from the lp_solve distribution
f=[8, 15];
a = [10, 21;2, 1];
a = sparse(a);
b = [156, 22];
e = [-1, -1];
[v,x] = lp_solve(f,a,b,e)
echo off;
disp('End of Ex11. Expected Solution: v=119.625, x=[9.5625, 2.875]. Press any key to continue.');
pause
echo on;

clc;
% Example 12
% ex3.lp from the lp_solve distribution
f=[3, 13];
a = [2, 9;11, -8];
a = sparse(a);
b = [40, 82];
e = [-1, -1];
[v,x] = lp_solve(f,a,b,e)
echo off;
disp('End of Ex12. Expected Solution: v=58.8, x=[9.2, 2.4]. Press any key to continue.');
pause
echo on;

clc;
% Example 13
% ex6.lp from the lp_solve distribution
f=[592, 381, 273, 55, 48, 37, 23];
a = [3534, 2356, 1767, 589, 528, 451, 304];
a = sparse(a);
b = [119567];
e = [-1];
xint = [1, 2, 3, 4, 5, 6, 7];
vub = [];
[v,x] = lp_solve(f,a,b,e,[],vub,xint)
echo off;
disp('End of Ex13. Expected Solution: v=19979, x=[32,2,1,0,0,0,0]. Press any key to continue.');
pause
echo on;

clc;
% Example 14
% ex7.lp from the lp_solve distribution
% This works as a test for autoscale options, it will NOT
% work properly without scaling
f=[0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1];
echo off;
disp('a=[...large, 29x16...]');
a=[0,0,0,0,0,0,0,+100,0,0,0,0,0,-406.9903088236362691532121971,...
0,+406.9903088236362691532121971;0,0,0,0,0,0,0,+100,0,0,0,0,...
0,-319.0773778073742619199038018,0,+319.0773778073742619199038018;...
0,0,0,0,0,0,0,+99.9999999999999857891452848,0,0,0,0,0,-287.8545880453748964100668672,...
0,+287.8545880453748964100668672;0,0,0,0,0,0,0,+100,0,0,0,0,...
0,-329.7778359794653511016804259,0,+329.7778359794653511016804259;...
0,0,0,0,0,0,0,+100,0,0,0,0,0,-329.7778359794653511016804259,...
0,+329.7778359794653511016804259;0,0,0,0,0,0,0,+100,0,0,0,0,...
0,-352.0403706295338110976445023,0,+352.0403706295338110976445023;...
0,0,0,0,0,0,0,+99.9999999999999857891452848,0,0,0,0,0,-287.8545880453748964100668672,...
0,+287.8545880453748964100668672;0,0,0,0,0,0,0,+100,0,0,0,0,...
0,-322.6669947786614898177504074,0,+322.6669947786614898177504074;...
0,0,0,0,0,0,0,+99.9999999999999857891452848,0,0,0,0,0,-287.8545880453748964100668672,...
0,+287.8545880453748964100668672;0,+100,+200.5050277777777978371887002,...
+200.5050277777777978371887002,0,+100,+281.5962205081120259819726925,...
0,0,+100,+281.5962205081120259819726925,+114.8098208928219747804178041,...
-237.0370370370370380896929419,0,+237.0370370370370380896929419,...
0;+100,+133.3333333333333143855270464,+267.3400370370370069394994061,...
+375.4616273441493490281573031,+100,+133.3333333333333143855270464,...
+267.3400370370370069394994061,0,+100,+133.3333333333333143855270464,...