362 lines
12 KiB
Mathematica
362 lines
12 KiB
Mathematica
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function y = times(X,Y)
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%TIMES (overloaded)
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% Check dimensions
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[n,m]=size(X);
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if ~((prod(size(X))==1) || (prod(size(Y))==1))
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if ~((n==size(Y,1) && (m ==size(Y,2))))
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error('Matrix dimensions must agree.')
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end
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end;
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% Convert block objects
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if isa(X,'blkvar')
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X = sdpvar(X);
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end
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if isa(Y,'blkvar')
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Y = sdpvar(Y);
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end
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if isnumeric(X)
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if any(isnan(X))
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error('Multiplying NaN with an SDPVAR makes no sense.');
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end
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end
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if isnumeric(Y)
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if any(isnan(Y))
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error('Multiplying NaN with an SDPVAR makes no sense.');
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end
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end
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if isempty(X)
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YY = full(reshape(Y.basis(:,1),Y.dim(1),Y.dim(2)));
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y = X.*YY;
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return
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elseif isempty(Y)
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XX = full(reshape(X.basis(:,1),X.dim(1),X.dim(2)));
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y = XX.*Y;
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return
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end
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if (isa(X,'sdpvar') && isa(Y,'sdpvar'))
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X = flush(X);
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Y = flush(Y);
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if (X.typeflag==5) && (Y.typeflag==5)
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error('Product of norms not allowed');
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end
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if numel(X)==1 && numel(Y) > 1
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X = repmat(X,size(Y));
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elseif numel(Y)==1 && numel(X) > 1
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Y = repmat(Y,size(X));
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end
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try
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y = check_for_special_case(Y,X);
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if ~isempty(y)
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return
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end
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% Check for the case x.*y where x and y are unit variables
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[mt,variable_type,hashedMT,hash] = yalmip('monomtable');
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if length(X.lmi_variables)==numel(X)
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if length(Y.lmi_variables) == numel(Y)
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if numel(X)==numel(Y)
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% This looks promising. write as (x0+X)*(y0+Y)
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X0 = reshape(X.basis(:,1),X.dim);
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Y0 = reshape(Y.basis(:,1),Y.dim);
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Xsave = X;
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Ysave = Y;
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X.basis(:,1)=0;
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Y.basis(:,1)=0;
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if nnz(X.basis)==numel(X)
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if nnz(Y.basis)==numel(Y)
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D = [spalloc(numel(Y),1,0) speye(numel(Y))];
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if isequal(X.basis,D)
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if isequal(Y.basis,D)
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% Pew.
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Z = X;
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generated_monoms = mt(X.lmi_variables,:) + mt(Y.lmi_variables,:);
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generated_hash = generated_monoms*hash;
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keep = zeros(1,numel(X));
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if all(generated_hash) && all(diff(sort([generated_hash;hashedMT])))
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Z.lmi_variables = size(mt,1)+(1:numel(X));
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keep = keep + 1;
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else
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for i = 1:numel(X)
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if generated_hash(i)
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before = find(abs(hashedMT-generated_hash(i))<eps);
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if isempty(before)
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% mt = [mt;generated_monoms(i,:)];
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keep(i) = 1;
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Z.lmi_variables(i) = size(mt,1)+nnz(keep);
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else
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Z.lmi_variables(i) = before;
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end
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else
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Z.lmi_variables(i) = 0;
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end
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end
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end
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if any(keep)
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keep = find(keep);
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mt = [mt;generated_monoms(keep,:)];
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yalmip('setmonomtable',mt,[],[hashedMT;generated_hash(keep)],hash);
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end
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if any(diff(Z.lmi_variables)<0)
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[i,j]=sort(Z.lmi_variables);
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Z.lmi_variables = Z.lmi_variables(j);
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Z.basis(:,2:end) = Z.basis(:,j+1);
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end
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if Z.lmi_variables(1)==0
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i = find(Z.lmi_variables == 0);
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Z.basis(:,1) = sum(Z.basis(:,1+i),2);
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Z.basis(:,1+i)=[];
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end
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Z.conicinfo = [0 0];
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Z.extra.opname='';
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Z = Z + X0.*Y0 + X0.*Y + X.*Y0;
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Z = flush(Z);
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y = clean(Z);
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return
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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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X = Xsave;
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Y = Ysave;
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end
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end
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x_isscalar = (X.dim(1)*X.dim(2)==1);
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y_isscalar = (Y.dim(1)*Y.dim(2)==1);
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all_lmi_variables = uniquestripped([X.lmi_variables Y.lmi_variables]);
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Z = X;Z.dim(1) = 1;Z.dim(2) = 1;Z.lmi_variables = all_lmi_variables;Z.basis = [];
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% Awkward code due to bug in ML6.5
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Xbase = reshape(X.basis(:,1),X.dim(1),X.dim(2));
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Ybase = reshape(Y.basis(:,1),Y.dim(1),Y.dim(2));
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if x_isscalar
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Xbase = sparse(full(Xbase));
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end
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if y_isscalar
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Ybase = sparse(full(Ybase));
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end
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index_Y = zeros(length(all_lmi_variables),1);
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index_X = zeros(length(all_lmi_variables),1);
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for j = 1:length(all_lmi_variables)
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indexy = find(all_lmi_variables(j)==Y.lmi_variables);
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indexx = find(all_lmi_variables(j)==X.lmi_variables);
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if ~isempty(indexy)
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index_Y(j) = indexy;
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end
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if ~isempty(indexx)
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index_X(j) = indexx;
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end
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end
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ny = Y.dim(1);
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my = Y.dim(2);
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nx = X.dim(1);
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mx = X.dim(2);
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% Linear terms
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base = Xbase.*Ybase;
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Z.basis = base(:);
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x_base_not_zero = nnz(Xbase)>0;
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y_base_not_zero = nnz(Ybase)>0;
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for i = 1:length(all_lmi_variables)
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base = 0;
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if index_Y(i) && x_base_not_zero
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base = Xbase.*getbasematrixwithoutcheck(Y,index_Y(i));
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end
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if index_X(i) && y_base_not_zero
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base = base + getbasematrixwithoutcheck(X,index_X(i)).*Ybase;
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end
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Z.basis(:,i+1) = base(:);
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end
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% Nonlinear terms
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i = i+1;
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ix=1;
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new_mt = [];
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%mt = yalmip('monomtable');
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nvar = length(all_lmi_variables);
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local_mt = mt(all_lmi_variables,:);
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theyvars = find(index_Y);
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thexvars = find(index_X);
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hash = randn(size(mt,2),1);
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mt_hash = mt*hash;
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for ix = thexvars(:)'
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% if mx==1
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Xibase = X.basis(:,1+index_X(ix));
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% else
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% Xibase = reshape(X.basis(:,1+index_X(ix)),nx,mx);
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% end
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mt_x = local_mt(ix,:);
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y_basis = Y.basis(:,1+index_Y(theyvars));
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x_basis = repmat(Xibase,1,length(theyvars(:)'));
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if y_isscalar && ~x_isscalar
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y_basis = repmat(y_basis,nx*mx,1);
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elseif x_isscalar && ~y_isscalar
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x_basis = repmat(x_basis,ny*my,1);
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end
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allBase = x_basis.*y_basis;
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jjj = 1;
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usedatall = find(any(allBase,1));
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% for iy = theyvars(:)'
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for iy = theyvars(usedatall(:))'
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% ff=Y.basis(:,1+index_Y(iy));
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% Yibase = reshape(ff,ny,my);
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% prodbase = Xibase.*Yibase;
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prodbase = allBase(:,usedatall(jjj));jjj = jjj+1;
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% prodbase = reshape(prodbase,ny,my);
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if (norm(prodbase,inf)>1e-12)
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mt_y = local_mt(iy,:);
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% Idiot-hash the lists
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new_hash = (mt_x+mt_y)*hash;
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if abs(new_hash)<eps%if nnz(mt_x+mt_y)==0
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Z.basis(:,1) = Z.basis(:,1) + prodbase(:);
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else
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before = find(abs(mt_hash-(mt_x+mt_y)*hash)<eps);
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if isempty(before)
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mt = [mt;mt_x+mt_y];
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mt_hash = [mt_hash;(mt_x+mt_y)*hash];
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Z.lmi_variables = [Z.lmi_variables size(mt,1)];
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else
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Z.lmi_variables = [Z.lmi_variables before];
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end
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Z.basis(:,i+1) = prodbase(:);i = i+1;
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end
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end
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end
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end
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% Fucked up order
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if any(diff(Z.lmi_variables)<0)
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[i,j]=sort(Z.lmi_variables);
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Z.lmi_variables = Z.lmi_variables(j);
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Z.basis(:,2:end) = Z.basis(:,j+1);
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end
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% FIX : Speed up
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if length(Z.lmi_variables) ~=length(unique(Z.lmi_variables))
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un_Z_vars = unique(Z.lmi_variables);
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newZbase = Z.basis(:,1);
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for i = 1:length(un_Z_vars)
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newZbase = [newZbase sum(Z.basis(:,find(un_Z_vars(i)==Z.lmi_variables)+1),2)];
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end
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Z.basis = newZbase;
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Z.lmi_variables = un_Z_vars;
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end
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yalmip('setmonomtable',mt);
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if ~(x_isscalar || y_isscalar)
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Z.dim(1) = X.dim(1);
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Z.dim(2) = Y.dim(2);
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else
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Z.dim(1) = max(X.dim(1),Y.dim(1));
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Z.dim(2) = max(X.dim(2),Y.dim(2));
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end
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catch
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error(lasterr)
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end
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% Reset info about conic terms
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Z.conicinfo = [0 0];
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Z.extra.opname='';
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Z = flush(Z);
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y = clean(Z);
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return
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end
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if isa(X,'sdpvar')
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Z = X;
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X = Y;
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Y = Z;
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end
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y = Y;
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if prod(Y.dim)==1
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y.basis = X(:)*(y.basis);
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y.dim = size(X);
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% Might be an nd-array
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y.dim = [numel(X) 1];
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else
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y.basis = [(Y.basis.')*diag(sparse(X(:)))].';
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end
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% Reset info about conic terms
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y.conicinfo = [0 0];
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y.extra.opname='';
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y = flush(y);
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y = clean(y);
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if numel(y)==numel(X)
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y = reshape(y,size(X));
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else
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y = reshape(y,size(Y));
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end
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function y = check_for_special_case(Y,X);
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y = [];
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if (min(size(X))>1) || (min(size(Y))>1)
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return
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end
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if ~all(size(Y)==size(X))
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return
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end
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entropies = zeros(length(Y),1);
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if is(X,'linear')
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argst = yalmip('getarguments',Y);
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if length(argst)~=length(X)
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return
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end
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if length(argst) == 1
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args{1} = argst;
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else
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args = argst;
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end
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for i = 1:length(args)
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if isempty(args{i})
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return
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end
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if isequal(args{i}.fcn,'log')
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S(1).subs={i};
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S(1).type='()';
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Z = subsref(X,S);
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if isequal(Z.basis,args{i}.arg{1}.basis)
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if isequal(Z.lmi_variables,args{i}.arg{1}.lmi_variables)
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entropies(i) = 1;
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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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if all(entropies)
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y = -ventropy(X);
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end
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