77 lines
2.3 KiB
Mathematica
77 lines
2.3 KiB
Mathematica
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function [P,x] = polyhedron(X,options)
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% polyhedron Converts constraint to MPT polyhedron object
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%
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% P = polyhedron(F)
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% [P,x] = polyhedron(F)
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%
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% P : polyhedron object (Requires the Multi-parametric Toolbox)
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% x : sdpvar object defining the variables in the polyhedron
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% F : Constraint object with linear inequalities
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if nargin < 2
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options = sdpsettings;
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elseif isempty(options)
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options = sdpsettings;
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end
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[p,recoverdata,solver,diagnostic,F] = compileinterfacedata(X,[],[],[],options,0);
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if p.K.q(1) > 0 | p.K.s(1) > 0 | any(p.variabletype)
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error('Polyhedron can only be applied to MILP-representable constraints.')
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end
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if isempty(p.binary_variables) & isempty(p.integer_variables)
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Aeq = -p.F_struc(1:p.K.f,2:end);
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beq = p.F_struc(1:p.K.f,1);
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A = -p.F_struc(p.K.f+1:end,2:end);
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b = p.F_struc(p.K.f+1:end,1);
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P = Polyhedron('A',A,'b',b,'Ae',Aeq,'be',beq);
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x = recover(p.used_variables);
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else
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nBin = length(p.binary_variables);
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[pBinary,removeEQ,removeLP] = extractOnly(p,p.binary_variables);
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p.F_struc = [p.F_struc(removeEQ,:);p.F_struc(p.K.f+removeLP,:)];
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p.K.f = length(removeEQ);
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p.K.l = length(removeLP);
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p.used_variables(p.binary_variables)=[];
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x = recover(p.used_variables);
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P = [];
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for i = 0:2^nBin-1;
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comb = dec2decbin(i,nBin);
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if checkfeasiblefast(pBinary,comb(:),1e-6)
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pi = p;
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H = -p.F_struc(:,2:end);
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K = p.F_struc(:,1);
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K = K-H(:,p.binary_variables)*comb(:);
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H(:,p.binary_variables)=[];
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Aeq = H(1:p.K.f,:);
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beq = H(1:p.K.f);
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A = H(p.K.f+1:end,:);
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b = K(p.K.f+1:end);
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Pi = Polyhedron('A',A,'b',b,'Ae',Aeq,'be',beq);
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P = [P Pi];
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end
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end
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end
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function pLP = extractLP(p);
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pLP = p;
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pLP.F_struc = pLP.F_struc(1:p.K.f+p.K.l,:);
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pLP.K.q = 0;
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pLP.K.s = 0;
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function [pRed,removeEQ,removeLP] = extractOnly(p,these);
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pRed = p;
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p.F_struc(:,1+these) = 0;
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removeEQ = find(any(p.F_struc(1:pRed.K.f,2:end),2));
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removeLP = find(any(p.F_struc(1+pRed.K.f:end,2:end),2));
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pRed.F_struc(pRed.K.f+removeLP,:)=[];
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pRed.F_struc(removeEQ,:)=[];
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pRed.K.f = pRed.K.f - length(removeEQ);
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pRed.K.l = pRed.K.l - length(removeLP);
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pRed.F_struc = pRed.F_struc(:,[1 1+these]);
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pRed.lb = pRed.lb(these);
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pRed.ub = pRed.ub(these);
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