121 lines
3.2 KiB
Mathematica
121 lines
3.2 KiB
Mathematica
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function YESNO = ismember_internal(x,p)
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%ISMEMBER_INTERNAL Helper for ISMEMBER
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if isa(x,'sdpvar') & (isa(p,'polytope') | isa(p,'Polyhedron'))
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if length(p) == 1
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[H,K,Ae,be] = poly2data(p);
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if min(size(x))>1
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error('first argument should be a vector');
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end
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if length(x) == size(H,2)
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x = reshape(x,length(x),1);
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YESNO = [H*x <= K,Ae*x == be];
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return
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else
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disp('The polytope in the ismember condition has wrong dimension')
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error('Dimension mismatch.');
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end
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else
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d = binvar(length(p),1);
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YESNO = (sum(d)==1);
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[L,U] = safe_bounding_box(p(1));
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for i = 1:length(p)
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[Li,Ui] = safe_bounding_box(p(i));
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L = min([L Li],[],2);
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U = max([U Ui],[],2);
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end
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for i = 1:length(p)
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[H,K,Ae,be] = poly2data(p(i));
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% Merge equalities into inequalities
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H = [H;Ae;-Ae];
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K = [K;be;-be];
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if min(size(x))>1
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error('first argument should be a vector');
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end
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if length(x) == size([H],2)
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x = reshape(x,length(x),1);
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lhs = H*x-K;
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% Derive bounds based on YALMIPs knowledge on bounds on
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% involved variables
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[M,m] = derivebounds(lhs);
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% Strengthen by using MPTs bounding box
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%[temp,L,U] = bounding_box(p(i));
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Hpos = (H>0);
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Hneg = (H<0);
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M = min([M (H.*Hpos*U+H.*Hneg*L-K)],[],2);
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YESNO = YESNO + (H*x-K <= M.*(1-extsubsref(d,i)));
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else
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error('Dimension mismatch.');
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end
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end
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end
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return
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end
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if isa(x,'sdpvar') & isa(p,'double')
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x = reshape(x,prod(x.dim),1);
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if numel(p)==1
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F = (x == p);
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else
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if size(p,1)==length(x) & size(p,2)>1
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Delta = binvar(size(p,2),1);
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F = [sum(Delta) == 1, x == p*Delta];
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if all(all(p == fix(p)))
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% Check if x implicitly is constrained to be integer
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B = getbase(x);
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if all(all(B == fix(B)))
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if all(sum(B | B,2)<= 1)
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F = [F, integer(x)];
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end
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end
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end
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else
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p = p(:);
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Delta = binvar(length(x),length(p),'full');
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F = [sum(Delta,2) == 1, x == Delta*p];
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if all(all(p == fix(p)))
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% Check if x implicitly is constrained to be integer
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B = getbase(x);
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if all(all(B == fix(B)))
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if all(sum(B | B,2)<= 1)
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F = [F, integer(x)];
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end
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end
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end
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end
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end
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YESNO = F;
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return
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end
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function [H,K,Ae,be] = poly2data(p);
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if isa(p,'polytope')
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[H,K] = double(p);
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Ae = [];
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be = [];
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else
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p = p.minHRep();
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H = p.A;
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K = p.b;
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Ae = p.Ae;
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be = p.be;
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end
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function [L,U] = safe_bounding_box(P)
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if isa(P,'polytope')
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[temp,L,U] = bounding_box(P);
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else
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S = outerApprox(P);
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L = S.Internal.lb;
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U = S.Internal.ub;
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end
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