source: proiecte/pmake3d/make3d_original/Make3dSingleImageStanford_version0.1/third_party/opt/yalmip/yalmiptest.m @ 37

function out = yalmiptest(prefered_solver,auto)
%YALMIPTEST Runs a number of test problems.
%
%   YALMIPTEST is recommended when a new solver or a new version
%   of YALMIP installed.
%
%   EXAMPLES
%    YALMIPTEST               % Without argument, default solver used
%    YALMIPTEST('solver tag') % Test with specified solver
%    YALMIPTEST(options)      % Test with specific options structure from
%
%   See also SDPSETTINGS, YALMIPDEMO

% Author Johan Löfberg 
% $Id: yalmiptest.m,v 1.27 2006/05/16 14:44:27 joloef Exp $


if ~exist('sedumi2pen.m')
    disp('Add /yalmip/extras to your path first...')
    return
end

if ~exist('bmibnb.m')
    disp('Add /yalmip/modules/ with sub-directories to your path first...')
    return
end

if ~exist('pwa_yalmip.m')
    disp('Add /yalmip/operators to your path first...')
    return
end

if ~exist('callsedumi.m')
    disp('Add /yalmip/solvers to your path first...')
    return
end

detected = which('yalmip.m','-all');
if length(detected)>1
    disp('You seem to have multiple installations of YALMIP in your path. Please correct this...');
    detected
    return
end

donttest = 0;
if (nargin==1) & isa(prefered_solver,'char') & strcmp(prefered_solver,'test')
    donttest = 0;
    prefered_solver = '';    
else
    donttest = 1;
end

if nargin==0
    prefered_solver = '';
else
    if ~(isa(prefered_solver,'struct') | isa(prefered_solver,'char'))
        error('Argument should be a solver tag, or a sdpsettings structure');
    end
    if isa(prefered_solver,'char') 
        donttest = 1;
    end
end

if ~(exist('callsedumi')==2)
    disp('The directory yalmip/solvers is not in your path.')
    disp('Put yalmip/, yalmip/solvers, yalmip/extras and yalmip/demos in your MATLAB path.');
    return
end

foundstring = {'not found','found'};
teststring = {'-failed','+passed'};
if ~donttest
    header = {'Solver','Version/module','Status','Unit test'};
else
    header = {'Solver','Version/module','Status'};
end    

[solvers,found] = getavailablesolvers(0);
solvers = solvers([find(found);find(~found)]);
found = [found(find(found));found(find(~found))];
j = 1;
for i = 1:length(solvers)
    if solvers(i).show
        data{j,1} = upper(solvers(i).tag); 
        data{j,2} = solvers(i).version;
        data{j,3} = foundstring{found(i)+1};   
        if ~donttest
            if found(i)
                if options.verbose
                    disp(['Testing ' solvers(i).tag '...']);    
                end
                try
                    if solvers(i).maxdet
                        pass = lyapell(sdpsettings('solver',solvers(i).tag,'verbose',0));            
                    else
                        if solvers(i).sdp
                            pass = stabtest(sdpsettings('solver',solvers(i).tag,'verbose',0));
                        else
                            pass = feasiblelp(sdpsettings('solver',solvers(i).tag,'verbose',0));
                        end
                    end
                    data{j,4} = teststring{pass+1};
                catch
                    data{j,4} = '-failed';
                end
            else
                data{j,4} = 'not tested';
            end
        end
        j = j+1;
    end
end

if isa(prefered_solver,'char')
    ops = sdpsettings('Solver',prefered_solver);
else
    ops = prefered_solver;
end

if ~((nargin==2) & (ops.verbose==0))    
table({'Searching for installed solvers'},header,data);
disp(' ')
end
if nargin<2
    disp('Press any key to continue test')
    pause
end

i=1;
test{i}.fcn  = 'testsdpvar';
test{i}.desc = 'sdpvar/set methods';
i = i+1;

test{i}.fcn  = 'feasiblelp'; 
test{i}.desc = 'LP';
i = i+1;

test{i}.fcn  = 'toepapprox'; 
test{i}.desc = 'LP';
i = i+1;

test{i}.fcn  = 'feasibleqp'; 
test{i}.desc = 'QP';
i = i+1;

test{i}.fcn  = 'toepapprox2'; 
test{i}.desc = 'QP';
i = i+1;


test{i}.fcn  = 'socptest1'; 
test{i}.desc = 'SOCP';
i = i+1;

test{i}.fcn  = 'socptest2'; 
test{i}.desc = 'SOCP'; 
i = i+1;

test{i}.fcn  = 'socptest3'; 
test{i}.desc = 'SOCP';   
i = i+1;

test{i}.fcn  = 'complete';
test{i}.desc = 'SDP';
i = i+1;

test{i}.fcn  = 'complete_2'; 
test{i}.desc = 'SDP';
i = i+1;

test{i}.fcn  = 'maxcut';
test{i}.desc = 'SDP';
i = i+1;

test{i}.fcn  = 'feasible'; 
test{i}.desc = 'SDP';
i = i+1;

test{i}.fcn  = 'lyapell'; 
test{i}.desc = 'MAXDET';
i = i+1;

test{i}.fcn  = 'lyapell2'; 
test{i}.desc = 'MAXDET';
i = i+1;

%test{i}.fcn  = 'circuit1'; 
%test{i}.desc = 'GP';
%i = i+1;

test{i}.fcn  = 'infeasible'; 
test{i}.desc = 'Infeasible LP';
i = i+1;

test{i}.fcn  = 'infeasibleqp'; 
test{i}.desc = 'Infeasible QP';
i = i+1;

test{i}.fcn  = 'infeasiblesdp'; 
test{i}.desc = 'Infeasible SDP';
i = i+1;

test{i}.fcn  = 'momenttest'; 
test{i}.desc = 'Moment relaxation';
i = i+1;

test{i}.fcn  = 'sostest'; 
test{i}.desc = 'Sum-of-squares';
i = i+1;

test{i}.fcn  = 'bmitest'; 
test{i}.desc = 'Bilinear SDP';
i = i+1;



pass_strings = {'Error','Passed','Solver not available'};

tt = cputime;

% Run test-problems
for i = 1:length(test)
    try
        t=cputime;           
        if ops.verbose
            disp(' ');
            disp(['Testing function ' test{i}.fcn]);
            disp(' ');
        end       
        [pp,ss,res] = eval([test{i}.fcn '(ops)']);
        pass(i) = pp;
        sols{i} = ss.info;
        results{i}=res;
        ttime(i) = cputime-t;
    catch
        pass(i) = 0;   
        results{i} = 'NAN';
        sols{i} = 'Unknown problem in YALMIP';
        ttime(i) = cputime-tt;
    end
end
totaltime = cputime-tt;

clear data;
header = {'Test','Solution', 'Solver message'};
for i = 1:length(pass)
    thetime =  num2str(ttime(i),4);
    data{i,1} = test{i}.desc;
    data{i,2} = results{i};
    data{i,3} = sols{i};
end
if ops.verbose
    disp(' ');
end
formats{1}.data.just = 'right';
formats{2}.data.just = 'right';
formats{3}.data.just = 'right';

formats{1}.header.just = 'right';
formats{2}.header.just = 'right';
formats{3}.header.just = 'right';

clc
table([],header,data,formats)


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

% Test the sdpvar implementation
pass = 1;
sol.info = yalmiperror(0,'YALMIP');
try
    x = sdpvar(2,2);
    x = sdpvar(2,2,'symmetric');
    x = sdpvar(2,2,'full');
    x = sdpvar(2,2,'toeplitz');
    x = sdpvar(2,2,'hankel');
    x = sdpvar(2,2,'skew');
    if ~ishermitian(sdpvar(2,2,'hermitian','complex'))
        error('bug')
    end
    if ~issymmetric(sdpvar(2,2,'symmetric','complex'))
        error('bug')
    end
    if ~isreal(real(sdpvar(2,2,'symmetric','complex')))
        error('bug')
    end
    if isreal(sqrt(-1)*real(sdpvar(2,2,'symmetric','complex')))
        error('bug')
    end
    x = sdpvar(2,1,'','co');
    if ~isreal(x'*x)
        error('bug')
    end
    x = sdpvar(2,2,'','co');
    if ~isreal(diag(x'*x))
        error('bug')
    end
    x = sdpvar(1,1);
    y = sdpvar(2,2);
    x*eye(2);
    eye(2)*x;
    y*3;
    3*y;
    x = sdpvar(2,3);
    y = sdpvar(2,3);
    setsdpvar(x,randn(2,3));
    z = replace(x,x(1,1:2),[8 9]);
    z = x+y;
    z = x-y;
    z = x+1;
    z = x-1;
    z = x+ones(2,3);
    z = x-ones(2,3);
    z = ones(2,3)-x;
    z = ones(2,3)-x;
    z = eye(2)*x;
    z = x*eye(3);
    z = diag(x);
    z = trace(x);
    z = diff(x);
    z = fliplr(x);
    z = flipud(x);
    z = kron(x,eye(3));
    z = kron(eye(3),x);
    z = rot90(x);
    z = sum(x);
    z = diff(x);
    z = x';
    z = x.';
    z = tril(x);
    z = triu(x);
    z = [x y];
    z = [x;y];
    sdpvar x y
    diag([x y])*[x^-1;y^-1];
    assert(isequal([x x;x x]*x,[x x;x x].*x))
    assert(isequal(trace([x x;x x]*[x y;y x]),x*x+x*y+y*x+x*x))
    
    % Regression ??
    yalmip('clear')
    sdpvar x

    (1+x+x^4)*(1-x^2); 
    
    % Regression complex multiplcation
    A = randn(10,5)+sqrt(-1)*randn(10,5);
    b = randn(10,1)+sqrt(-1)*randn(10,1);
    x = sdpvar(5,1);
    res = A*x-b;
    assert(nnz(clean([res res]'*[res res]-res'*res,1e-8))==0)
    assert(isreal(clean(res'*res,1e-8)))
    
    sdpvar x(1,1,'full','complex');
    assert(isreal(x*x'))
    
%     x = sdpvar(4,1);
%     sdpvar i a   
%     y = [i a];
%     y(1)
%    % i = sdpvar(1,1);
%    % a = sdpvar(1,1);
%    % [i a]
%     
%     
%     
%     size(x([i j]))
%     assert(all(size(x([i j])) == [2 1]))
%     assert(all(size(x(1,[i j])) == [1 2]))
%    % assert(all(size(x(1,[i j])) == [1 2]));
%    % x(1,[i j]);
   % x([i j],1);
   % x([i j],[i j]);
    
    
    
    result = 'N/A';
catch
    sol.info = 'Problems';
    result = 'N/A';
    pass = 0;
end


function [pass,sol,result] = feasible(ops) 
t = sdpvar(1,1);
Y = sdpvar(2,2);
F = set('Y<t*eye(2)');
F = F+set('Y>[1 0.2;0.2 1]');
sol = solvesdp(F,t,ops);
pass = ismember(sol.problem,[0 3 4 5]);
if pass
    result = resultstring(t,1.2);
else
    result = 'N/A';
end
    


function [pass,sol,result] = infeasible(ops)
t = sdpvar(1,1);
Y = sdpvar(2,2);
F = set('t>0');
F = F+set('t<-10');
sol = solvesdp(F,t,ops);
pass = ~(sol.problem==0);
result = 'N/A';

function [pass,sol,result] = lyapell(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]);
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