284 lines
8.1 KiB
Mathematica
284 lines
8.1 KiB
Mathematica
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function [pres,dres] = check(F)
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% CHECK(F) Displays/calculates constraint residuals on constraint F
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%
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% [pres,dres] = check(F)
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%
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% pres : Primal constraint residuals
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% dres : Dual constraint residuals
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%
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% If no output argument is supplied, tabulated results are displayed
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%
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% Primal constraint residuals are calculated as:
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%
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% Semidefinite constraint F(x)>=0 : min(eig(F))
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% Element-wise constraint F(x)>=0 : min(min(F))
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% Equality constraint F==0 : -max(max(abs(F)))
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% Second order cone t>=||x|| : t-||x||
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% Exponential cone constraint : x(3) - exp(x(1)/x(2))*x(2)
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% Integrality constraint on x : max(abs(x-round(x)))
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% Sum-of-square constraint : Minus value of largest (absolute value) coefficient
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% in the polynomial p-v'*v
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%
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% Dual constraints are evaluated similarily.
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%
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% See also SOLVESDP, SOLVESOS, SOSD, DUAL
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% Check if solution avaliable
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currsol = evalin('caller','yalmip(''getsolution'')');
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if isempty(currsol)
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disp('No solution available.')
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return
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end
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F = flatten(F);
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nlmi = length(F.LMIid);
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spaces = [' '];
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if (nlmi == 0)
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if nargout == 0
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disp('empty LMI')
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else
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pres = [];
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dres = [];
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end
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return
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end
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lmiinfo{1} = 'Matrix inequality';
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lmiinfo{2} = 'Elementwise inequality';
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lmiinfo{3} = 'Equality constraint';
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lmiinfo{4} = 'Second order cone constraint';
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lmiinfo{5} = 'Rotated Lorentz constraint';
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lmiinfo{7} = 'Integer constraint';
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lmiinfo{8} = 'Binary constraint';
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lmiinfo{9} = 'KYP constraint';
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lmiinfo{10} = 'Eigenvalue constraint';
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lmiinfo{11} = 'SOS constraint';
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lmiinfo{15} = 'Uncertainty declaration';
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lmiinfo{54} = 'Vectorized second order cone constraints';
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lmiinfo{55} = 'Complementarity constraint';
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lmiinfo{56} = 'Logic constraint';
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header = {'ID','Constraint','Primal residual','Dual residual','Tag'};
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if nargout==0
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disp(' ');
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end
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% Checkset is very slow for multiple SOS
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% The reason is that REPLACE has to be called
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% for every SOS. Instead, precalc on one vector
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p=[];
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ParVar=[];
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soscount=1;
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for j = 1:nlmi
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if F.clauses{j}.type==11
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pi = F.clauses{j}.data;
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[v,ParVari] = sosd(pi);
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if isempty(v)
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p=[p;0];
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else
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p=[p;pi];
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ParVar=unique([ParVar(:);ParVari(:)]);
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end
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end
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end
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if ~isempty(ParVar)
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ParVar = recover(ParVar);
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p = replace(p,ParVar,double(ParVar));
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end
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for j = 1:nlmi
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constraint_type = F.clauses{j}.type;
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if constraint_type~=11 && constraint_type~=56
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F0 = double(F.clauses{j}.data);
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end
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if ~((constraint_type == 56) || (constraint_type==11)) && any(isnan(F0(:)))
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res(j,1) = NaN;
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else
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switch F.clauses{j}.type
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case {1,9}
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if isa(F0,'intval')
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res(j,1) = full(min(inf_(veigsym(F0))));
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else
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res(j,1) = full(min(real(eig(F0))));
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end
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case 2
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if isa(F0,'intval')
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res(j,1) = full(min(min(inf_(F0))));
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else
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res(j,1) = full(min(min(F0)));
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end
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case 3
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res(j,1) = -full(max(max(abs(F0))));
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case 4
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res(j,1) = full(F0(1)-norm(F0(2:end)));
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case 5
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res(j,1) = full(2*F0(1)*F0(2)-norm(F0(3:end))^2);
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case 7
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res(j,1) = -full(max(max(abs(F0-round(F0)))));
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case 8
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res(j,1) = -full(max(max(abs(F0-round(F0)))));
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res(j,1) = min(res(j,1),-(any(F0>1) | any(F0<0)));
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case 21
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res(j,1) = F0(3) - F0(2)*exp(F0(1)/F0(2));
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case 54
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res(j,1) = inf;
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for k = 1:size(F0,2)
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res(j,1) = min(res(j,1),full(F0(1,k)-norm(F0(2:end,k))));
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end
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case 11
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if 0
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p = F.clauses{j}.data;
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[v,ParVar] = sosd(p);
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if ~isempty(ParVar)
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ParVar = recover(ParVar);
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p = replace(p,ParVar,double(ParVar));
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end
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if isempty(v)
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res(j,1)=nan;
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else
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h = p-v'*v;
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res(j,1) = full(max(max(abs(getbase(h)))));
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end
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else
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%p = F.clauses{j}.data;
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[v,ParVar] = sosd(F.clauses{j}.data);
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if isempty(v)
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res(j,1)=nan;
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else
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h = p(soscount)-v'*v;
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res(j,1) = full(max(max(abs(getbase(h)))));
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end
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soscount=soscount+1;
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end
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case 56
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res(j,1) = logicSatisfaction(F.clauses{j}.data);
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otherwise
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res(j,1) = nan;
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end
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end
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% Get the internal index
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LMIid = F.LMIid(j);
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dual = yalmip('dual',LMIid);
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if isempty(dual) | any(isnan(dual))
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resdual(j,1) = NaN;
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else
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switch F.clauses{j}.type
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case {1,9}
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resdual(j,1) = min(eig(dual));
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case 2
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resdual(j,1) = min(min(dual));
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case 3
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resdual(j,1) = -max(max(abs(dual)));
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case 4
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resdual(j,1) = dual(1)-norm(dual(2:end));
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case 5
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resdual(j,1) = 2*dual(1)*dual(2)-norm(dual(3:end))^2;
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case 7
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resdual(j,1) = nan;
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case 54
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resdual(j,1) = inf;
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for k = 1:size(dual,2)
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resdual(j,1) = min(resdual(j,1),full(dual(1,k)-norm(dual(2:end,k))));
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end
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otherwise
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gap = nan;
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end
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end
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if nargout==0
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data{j,1} = ['#' num2str(j)];
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data{j,2} = lmiinfo{F.clauses{j}.type};
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data{j,3} = res(j,1);
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data{j,4} = resdual(j,1);
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data{j,5} = F.clauses{j}.handle;
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if ~islinear(F.clauses{j}.data)
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if is(F.clauses{j}.data,'sigmonial')
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classification = 'sigmonial';
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elseif is(F.clauses{j}.data,'bilinear')
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classification = 'bilinear';
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elseif is(F.clauses{j}.data,'quadratic')
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classification = 'quadratic';
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else
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classification = 'polynomial';
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end
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data{j,2} = [data{j,2} ' (' classification ')'];
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end
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end
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end
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if nargout>0
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pres = res;
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dres = resdual;
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else
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keep = ones(1,5);
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if length([data{:,5}])==0
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keep(5) = 0;
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end
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header = {header{:,find(keep)}};
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temp = {data{:,find(keep)}};
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data = reshape(temp,length(temp)/nnz(keep),nnz(keep));
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post{1} = 'A primal-dual optimal solution would show non-negative residuals.';
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post{end+1} = 'In practice, many solvers converge to slightly infeasible';
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post{end+1} = 'solutions, which may cause some residuals to be negative.';
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post{end+1} = 'It is up to the user to judge the importance and impact of';
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post{end+1} = 'slightly negative residuals (i.e. infeasibilities)';
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post{end+1} = 'https://yalmip.github.io/command/check/';
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post{end+1} = 'https://yalmip.github.io/faq/solutionviolated/';
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yalmiptable('',header,data,[],post);
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disp(' ');
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end
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function res = logicSatisfaction(clause);
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a = clause{2};
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b = clause{3};
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if isa(a,'sdpvar')
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aval = double(a);
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if is(a,'binary')
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atruth = aval == 1;
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else
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atruth = aval>=0;
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end
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elseif isa(a,'lmi') | isa(a,'constraint')
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aval = check(lmi(a));
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atruth = aval >= 0;
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end
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if isa(b,'sdpvar')
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bval = double(b);
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if is(b,'binary')
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btruth = bval == 1;
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else
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btruth = bval>=0;
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end
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elseif isa(b,'lmi') | isa(b,'constraint')
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bval = check(lmi(b));
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btruth = bval >= 0;
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end
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if isnan(aval) | isnan(bval)
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res = nan;
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else
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switch clause{1}
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case 'implies'
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if all(btruth >= atruth)
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res = 1;
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else
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res = -1;
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end
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case 'iff'
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if all(btruth == atruth);
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res = 1;
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else
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res = -1;
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end
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otherwise
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res = nan;
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end
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end
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