108 lines
2.8 KiB
Mathematica
108 lines
2.8 KiB
Mathematica
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function [Fimage,objimage,x,y] = imagemodel(F,obj,options)
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% IMAGEMODEL Explicitely removes equality constraints from model.
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%
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% [Fi,hi,x,y] = imagemodel(F,h)
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%
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% Input
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% F : Constraint in form F(x)>0, Ax=b
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% h : objective function h(x)
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%
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% Output
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% Fi : Constraints in form F(y)>0
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% hi : objective function h(y)
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% x : original variables
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% z : old variables expressed in basis y
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%
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% To obtain a solution in the original variables x, use assign(x,double(y))
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%
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% Note that this reduction is automatically done when you call solvesdp and use
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% a solver that cannot handle equality constraints. Hence, there is typically no
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% reason to use this command, unless some further manipulations are going
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% to be done.
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%
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% See also DUALIZE, PRIMALIZE
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% Check for unsupported problems
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F = flatten(F);
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err = 0;
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p1 = ~(isreal(F) & isreal(obj));
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p2 = ~(islinear(F) & islinear(obj));
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p3 = any(is(F,'integer')) | any(is(F,'binary'));
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if p1 | p2 | p3
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if nargout == 5
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Fdual = lmi([]);objdual = [];y = []; X = []; t = []; err = 1;
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else
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problems = {'Cannot imagalize complex-valued problems','Cannot imagalize nonlinear problems','Cannot imagalize discrete problems'};
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error(problems{min(find([p1 p2 p3]))});
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end
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end
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if nargin < 3
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options = sdpsettings('solver','sedumi','remove',1);
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else
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options = sdpsettings(options,'remove',1);
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end
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if any(is(F,'equality'))
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[model,recoverdata,solver,diagnostic,F] = compileinterfacedata(F,[],[],obj,options,0);
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if ~isempty(model.F_struc)
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model.F_struc(abs(model.F_struc) <= 1e-12)=0;
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end
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if isfield(diagnostic,'problem')
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if diagnostic.problem == 1
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warning('Problem is infeasible');
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Fimage = [];
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objimage = [];
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x = [];
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y = [];
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return
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end
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end
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if isempty(model)
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Fimage = [];
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objimage = [];
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x = [];
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y = [];
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warning('Reduced problem does not have free variables. Optimal solution computed');
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return
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end
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else
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Fimage = F;
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objimage = obj;
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x = recover(unique([depends(obj) depends(F)]));
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y = x;
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return
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end
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y = sdpvar(length(model.c),1);
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vecF = model.F_struc*[1;y];
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K = model.K;
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Fimage = lmi([]);
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start = 1;
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if model.K.l > 0
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Fimage = Fimage + lmi(vecF(start:start+K.l-1) >= 0);
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start = start + K.l;
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end
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if model.K.q(1) > 0
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for i = 1:length(model.K.q)
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z = vecF(start:start+K.q(i)-1)
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Fimage = Fimage + lmi(cone(z(2:end),z(1)));
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start = start + K.q(i);
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end
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end
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if model.K.s(1)>0
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for i = 1:length(model.K.s)
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z = vecF(start:start+K.s(i)^2-1);
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Fimage = Fimage + lmi(reshape(z,K.s(i),K.s(i)));
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start = start + K.s(i)^2;
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end
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end
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objimage = model.c'*y+y'*model.Q*y+model.f;
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x = recover(recoverdata.used_variables);
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y = recoverdata.H*y+recoverdata.x_equ;
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