yalmiptest.m

matlab波形优化算法经常要用到的matlab toolbox工具箱:yalmip

Y = sdpvar(2,2);
F = set([Y Y*(A-B*L)';(A-B*L)*Y Y]);
F = F+set('L*Y*L''<1');
sol = solvesdp(F,-logdet(Y),ops);
Y = double(Y);
pass = ismember(sol.problem,[0 3 4 5]);
if pass
    result = resultstring(Y,[2.9957 -4.1514;-4.1514 6.2918]);
else
    result = 'N/A';
end
%pass = pass & (sum(sum(abs(Y-[2.9957 -4.15;-4.15 6.29])))<0.01);

function [pass,sol,result] = lyapell2(ops)
A = [1 0;0.4 1];
B = [0.4;0.08]; 
L = [1.9034 1.1501];  
Y = sdpvar(2,2);
F = set('[Y Y*(A-B*L)'';(A-B*L)*Y Y]>0');
F = F+set('L*Y*L''<1');
sol = solvesdp(F,-logdet(Y),ops);
Y = double(Y);
pass = ismember(sol.problem,[0 3 4 5]);
if pass
    result = resultstring(Y,[2.9957 -4.1514;-4.1514 6.2918]);
else
    result = 'N/A';
end

function [pass,sol,result] = complete(ops)
x = sdpvar(1,1);
y = sdpvar(1,1);
z = sdpvar(1,1);

X = [x 1 2;1 y 3;2 3 100];

F = set(X>0);
F = F+set(x>10);
F = F+set(y>0); 
F = F+set(z>0);
F = F+set(x<1000);
F = F+set(y<1000); 
F = F+set(z<1000);
sol = solvesdp(F,x+y+z,ops);
x   = double(x);
y   = double(y);
z   = double(z);

pass = ismember(sol.problem,[0 3 4 5]);
result = 'N/A';
if pass
    result = resultstring([x;y;z],[10;0.1787;0]);
else
    result = 'N/A';
end


function [pass,sol,result] = complete_2(ops)
x = sdpvar(1,1);
%y = sdpvar(1,1);
z = sdpvar(1,1);

X = [x 2;2 z];

F = set('X>0');
F = F+set('x>0');
F = F+set('z>0');
F = F+set('x<10');
F = F+set('z<10');
sol = solvesdp(F,x+z,ops);
x   = double(x);
%y   = double(y);
z   = double(z);

pass = ismember(sol.problem,[0 3 4 5]);
result = 'N/A';
if pass
    result = resultstring([x;z],[2;2]);
else
    result = 'N/A';
end



function [pass,sol,result]  = maxcut(ops)
% Upper bound on maxcut of a n-cycle
n = 15;
Q = zeros(n);
for i = 1:n-1
    Q(i,i+1) = 1;Q(i+1,i)  = 1;
end
Q(n,1) = 1;Q(1,n) = 1;  
Q = 0.25*(diag(Q*ones(n,1))-Q);

t = sdpvar(1,1);
tau = sdpvar(n,1);

F = set('t>0');

M = [-Q zeros(n,1);zeros(1,n) t];

for i = 1:n
    ei = zeros(n,1);ei(i,1) = 1;
    M = M+tau(i)*[ei*ei' zeros(n,1);zeros(1,n) -1];
end

F = F+set(M>0);
sol = solvesdp(F,t,ops);

t   = double(t);
tau = double(t);

pass = ismember(sol.problem,[0 3 4 5]);
if pass
    result = resultstring(t,14.8361);
else
    result = 'N/A';
end


function [pass,sol,result] = socptest1(ops)
x = sdpvar(2,1);
a = [0;1];
b = [1;1];
F = set('||x-a||<1');
F = F+set('||x-b||<1');
sol = solvesdp(F,sum(x),ops);
pass = ismember(sol.problem,[0 3 4 5]); 

x = double(x);

if pass
    result = resultstring(sum(x),0.58578);
else
    result = 'N/A';
end



function [pass,sol,result] = socptest2(ops)
z = sdpvar(3,1);
x = sdpvar(3,1);
y = sdpvar(3,1);
a = [0;1;0];
b = [1;1;0];
F = set('||x-a||<1');
F = F+set('||x-b||<1');
F = F+set('x(1)==0.35');
F = F+set('z(2:3)==[5;6]');
sol = solvesdp(F,sum(x),ops);
pass = ismember(sol.problem,[0 3 4 5]); 

x = double(x);
y = double(y);
z = double(z);

if pass
    result = resultstring(sum(x),0.27592);
else
    result = 'N/A';
end



function [pass,sol,result] = socptest3(ops)
z = sdpvar(2,1);
x = sdpvar(2,1);
y = sdpvar(3,1);
a = [0;1];
b = [1;1];
F = set('||x-a||<1');
F = F+set('||x-b||<1');
F = F+set('x(1)==0.35');
F = F+set('z(1,end)>5');
F = F+set('z(2,end)<100');
F = F+set('z(2)==5');

sol = solvesdp(F,sum(x),ops);
pass = ismember(sol.problem,[0 3 4 5]); 

x = double(x);
y = double(y);
z = double(z);
if pass
    result = resultstring(sum(x),0.59);
else
    result = 'N/A';
end



function [pass,sol,result] = feasiblelp(ops)
N = 5;
A = [2 -1;1 0];
B = [1;0];
C = [0.5 0.5];
[H,S] = create_CHS(A,B,C,N);
x = [2;0];
t = sdpvar(2*N,1);
U = sdpvar(N,1);   
Y = H*x+S*U; 
F = set(U<1)+set(U>-1);
F = F+set(Y(N)>-1);  
F = F+set(Y(N)<1); 
F = F+set([Y;U]<t)+set([Y;U]>-t);
sol = solvesdp(F,sum(t),ops);
pass = ismember(sol.problem,[0 3 4 5]); 
if pass
    result = resultstring(sum(t),12.66666);
else
    result = 'N/A';
end

function [pass,sol,result] = feasibleqp(ops)
N = 5;
A = [2 -1;1 0];
B = [1;0];
C = [0.5 0.5];
[H,S] = create_CHS(A,B,C,N);
x = [2;0];
U = sdpvar(N,1);   
Y = H*x+S*U; 
F = set(U<1)+set(U>-1);
F = F+set(Y(N)>-1);  
F = F+set(Y(N)<1); 
sol = solvesdp(F,Y'*Y+U'*U,ops);
pass = ismember(sol.problem,[0 3 4 5]); 
if pass
    result = resultstring(Y'*Y+U'*U,26.35248);
else
    result = 'N/A';
end


function [pass,sol,result] = infeasibleqp(ops)
N = 5;
A = [2 -1;1 0];
B = [1;0];
C = [0.5 0.5];
[H,S] = create_CHS(A,B,C,N);
x = [2;0];
U = sdpvar(N,1);   
Y = H*x+S*U; 
F = set(U<1)+set(U>-1);
F = F+set(Y(N)>-1);  
F = F+set(Y(N)<1); 
F = F + set(U>0);
sol = solvesdp(F,Y'*Y+U'*U,ops);
pass = ismember(sol.problem,[1]); 
result = 'N/A';



function [pass,sol,result] = infeasiblesdp(ops)
A = magic(6);
A = A*A';
P = sdpvar(6,6);
sol = solvesdp(set(A'*P+P*A < -P) + set(P>eye(6)),trace(P),ops); 
pass = (sol.problem==1);
result = 'N/A';

function [pass,sol,result]=toepapprox(ops)

n = 5;
P = magic(n);
Z = sdpvar(n,n,'toeplitz');
t = sdpvar(n,n,'full');
F = set(P-Z<t)+set(P-Z>-t);
sol = solvesdp(F,sum(sum(t)),ops);
pass = ismember(sol.problem,[0 3 4 5]); 
result = 'N/A';
if pass
    result = resultstring(sum(sum(t)),156);
else
    result = 'N/A';
end


function [pass,sol,result]=toepapprox2(ops)

n = 5;
P = magic(n);
Z = sdpvar(n,n,'toeplitz');
t = sdpvar(n,n,'full');
resid = P-Z;resid = resid(:);
sol = solvesdp([],resid'*resid,ops);
pass = ismember(sol.problem,[0 3 4 5]); 
result = 'N/A';
if pass
    result = resultstring(resid'*resid,1300);
else
    result = 'N/A';
end

function [pass,sol,result]=momenttest(ops)

x1 = sdpvar(1,1);
x2 = sdpvar(1,1);
x3 = sdpvar(1,1);

objective = -2*x1+x2-x3;

F = set(x1*(4*x1-4*x2+4*x3-20)+x2*(2*x2-2*x3+9)+x3*(2*x3-13)+24>0);
F = F + set(4-(x1+x2+x3)>0);
F = F + set(6-(3*x2+x3)>0);
F = F + set(x1>0);
F = F + set(2-x1>0);
F = F + set(x2>0);
F = F + set(x3>0);
F = F + set(3-x3>0);
sol = solvemoment(F,objective,ops);
pass = ismember(sol.problem,[0 3 4 5]); 
result = 'N/A';
if pass
    result = resultstring(objective,-6);
else
    result = 'N/A';
end

function [pass,sol,result]=sostest(ops)

yalmip('clear')
x = sdpvar(1,1);
y = sdpvar(1,1);
t = sdpvar(1,1);
F = set(sos(1+x^7+x^8+y^4-t));
sol = solvesos(F,-t,ops);
pass = ismember(sol.problem,[0 3 4 5]); 
result = 'N/A';
if pass
    result = resultstring(t,0.9509);
else
    result = 'N/A';
end

function [pass,sol,result]=bmitest(ops)

A = [-1 2;-3 -4];
P = sdpvar(2,2);
alpha = sdpvar(1,1);
F = set(P>eye(2))+set(A'*P+P*A < -2*alpha*P)+set(alpha > 0);
sol = solvesdp(F,-alpha,ops);
pass = ismember(sol.problem,[0 3 4 5]); 
result = 'N/A';
if pass
    result = resultstring(alpha,2.5);
else
    result = 'N/A';
end


function [pass,sol,result]=circuit1(ops)
x = sdpvar(7,1);

% Data
a     = ones(7,1);
alpha = ones(7,1);
beta  = ones(7,1);
gamma = ones(7,1);
f = [1 0.8 1 0.7 0.7 0.5 0.5]';
e = [1 2 1 1.5 1.5 1 2]';
Cout6 = 10;
Cout7 = 10;

% Model
C = alpha+beta.*x;
A = sum(a.*x);
P = sum(f.*e.*x);
R = gamma./x;

D1 = R(1)*(C(4));
D2 = R(2)*(C(4)+C(5));
D3 = R(3)*(C(5)+C(7));
D4 = R(4)*(C(6)+C(7));
D5 = R(5)*(C(7));
D6 = R(6)*Cout6;
D7 = R(7)*Cout7;

% Constraints
F = set(x > 1) + set(P < 20) + set(A < 100);

% Objective
D = max((D1+D4+D6),(D1+D4+D7),(D2+D4+D6),(D2+D4+D7),(D2+D5+D7),(D3+D5+D6),(D3+D7));

sol = solvesdp(F,D,ops);

pass = ismember(sol.problem,[0 3 4 5]); 
result = 'N/A';
if pass
    result = resultstring(D,7.8936);
else
    result = 'N/A';
end





function result = resultstring(x,xopt)
if norm(double(x(:))-xopt(:))<1e-3*(1+norm(xopt(:)))
    result = 'Correct';
else
    result = 'Incorrect';
end

function assert(a)
if ~a
    error('Assertion failed!');
end