273 lines
11 KiB
Mathematica
273 lines
11 KiB
Mathematica
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function y = subsasgn(X,I,Y)
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%SUBASGN (overloaded)
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try
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if strcmp('()',I.type)
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X_is_spdvar = isa(X,'sdpvar') | isa(X,'ndsdpvar');
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Y_is_spdvar = isa(Y,'sdpvar') | isa(Y,'ndsdpvar');
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if islogical(I.subs{1})
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I.subs{1} = double(find(I.subs{1}));
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end
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if any(I.subs{1} <=0)
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error('Index into matrix is negative or zero.');
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end
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switch 2*X_is_spdvar+Y_is_spdvar
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case 1
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% This code does not work properly
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% Only work if b is undefined!!?!!
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% generally ugly code...
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y = Y;
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[n_y,m_y] = size(Y);
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y_lmi_variables = y.lmi_variables;
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try
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X0 = subsasgn(full(X),I,full(reshape(Y.basis(:,1),n_y,m_y)));
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dim = size(X0);
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y.basis = reshape(X0,prod(dim),1);
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X = full(X)*0;
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for i = 1:length(y_lmi_variables)
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X0 = subsasgn(X,I,full(reshape(Y.basis(:,i+1),n_y,m_y)));
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y.basis(:,i+1) = reshape(X0,prod(dim),1);
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end
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y.dim = dim;
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% Reset info about conic terms
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y.conicinfo = [0 0];
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y.basis = sparse(y.basis);
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if length(dim)>2
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y = ndsdpvar(y);
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end
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y = flush(y);
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catch
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error(lasterr)
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end
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case 2
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if ~isempty(Y)
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if isa(Y,'uint8') || isa(Y,'uint16') || isa(Y,'uint32') || isa(Y,'uint64')
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Y = sparse(double(Y));
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elseif isnumeric(Y)
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Y = sparse(Y);
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else
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Y = sparse(double(Y));
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end
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end
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y = X;
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% Special code for speed
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% elements in vector replaced with constants
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if min(X.dim(1),X.dim(2))==1 & (length(I.subs)==1)
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y = X;
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if isempty(Y)
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y.basis(I.subs{1},:) = [];
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if X.dim(1) == 1
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y.dim(2) = y.dim(2) - length(unique(I.subs{1}));
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else
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y.dim(1) = y.dim(1) - length(unique(I.subs{1}));
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end
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else
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y.basis(I.subs{1},1) = Y;
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y.basis(I.subs{1},2:end) = 0;
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end
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if prod(y.dim)~=size(y.basis,1)
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% Ah bugger, the dimension of the object was changed)
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aux = X.basis(:,1);
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aux = reshape(aux,X.dim);
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aux(I.subs{1})=Y;
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y.dim = size(aux);
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end
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y = clean(y);
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% Reset info about conic terms
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if isa(y,'sdpvar')
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y.conicinfo = [0 0];
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y = flush(y);
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end
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return;
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end
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x_lmi_variables = X.lmi_variables;
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lmi_variables = [];
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n = y.dim(1);
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m = y.dim(2);
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subX = sparse(subsasgn(full(reshape(X.basis(:,1),n,m)),I,Y));
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y.basis = subX(:);
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if isa(I.subs{1},'char')
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I.subs{1} = 1:n;
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end
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if length(I.subs)>1
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if isa(I.subs{2},'char')
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I.subs{2} = 1:m;
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end
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end
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if length(I.subs)>1
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if length(I.subs{1})==1 & length(I.subs{2})~=1
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I.subs{1} = repmat(I.subs{1},size(I.subs{2},1),size(I.subs{2},2));
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elseif length(I.subs{2})==1 & length(I.subs{1})~=1
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I.subs{2} = repmat(I.subs{2},size(I.subs{1},1),size(I.subs{1},2));
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end
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end
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if length(I.subs)>1
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ii = kron(I.subs{1}(:),ones(length(I.subs{2}),1));
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jj = kron(ones(length(I.subs{1}),1),I.subs{2}(:));
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LinearIndex = sub2ind([n m],ii,jj);
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else
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LinearIndex = I.subs{1};
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end
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if isempty(Y)
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X.basis = X.basis(:,2:end);
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X.basis(LinearIndex,:) = [];
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y.basis = [y.basis(:,1) X.basis];
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else
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X.basis(LinearIndex,2:end)=sparse(0);
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y.basis = [y.basis(:,1) X.basis(:,2:end)];
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end
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y.dim(1) = size(subX,1);
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y.dim(2) = size(subX,2);
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y = clean(y);
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if isa(y,'sdpvar')
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% Reset info about conic terms
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y.conicinfo = [0 0];
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y = flush(y);
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end
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case 3
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z = X;
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x_lmi_variables = X.lmi_variables;
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y_lmi_variables = Y.lmi_variables;
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% In a first run, we fix the constant term and null terms in the X basis
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lmi_variables = [];
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nx = X.dim(1);
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mx = X.dim(2);
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ny = Y.dim(1);
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my = Y.dim(2);
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if (mx==1) & (my == 1) & isempty(setdiff(y_lmi_variables,x_lmi_variables)) & (max(I.subs{1}) < nx) & length(I.subs)==1 & length(unique(I.subs{1}))==length(I.subs{1}) ;
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% Fast specialized code for Didier
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y = specialcode(X,Y,I);
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return
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end
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subX = subsasgn(reshape(X.basis(:,1),nx,mx),I,reshape(Y.basis(:,1),ny,my));
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[newnx, newmx] = size(subX);
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j = 1;
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yz = reshape(1:ny*my,ny,my);
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subX2 = subsasgn(reshape(zeros(nx*mx,1),nx,mx),I,yz);
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subX2 = subX2(:);
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[ix,jx,sx] = find(subX2);
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yz = 0*reshape(Y.basis(:,1),ny,my);
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lmi_variables = zeros(1,length(x_lmi_variables));
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A = reshape(1:nx*mx,nx,mx);
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B = reshape(1:newnx*newmx,newnx,newmx);
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rm = B(1:nx,1:mx);rm = rm(:);
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[iix,jjx,ssx] = find(X.basis(:,2:end));
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z.basis = [subX(:) sparse(rm(iix),jjx,ssx,newnx*newmx,size(X.basis,2)-1)];
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z.basis(ix,2:end) = 0;
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keep = find(any(z.basis(:,2:end),1));
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z.basis = z.basis(:,[1 1+keep]);
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lmi_variables2 = x_lmi_variables(keep);
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z.lmi_variables = lmi_variables2;
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lmi_variables = lmi_variables2;
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all_lmi_variables = union(lmi_variables,y_lmi_variables);
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in_z = ismembcYALMIP(all_lmi_variables,lmi_variables);
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in_y = ismembcYALMIP(all_lmi_variables,y_lmi_variables);
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z_ind = 2;
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y_ind = 2;
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basis = spalloc(size(z.basis,1),1+length(all_lmi_variables),0);
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basis(:,1) = z.basis(:,1);
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nz = size(subX,1);
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mz = size(subX,2);
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template = full(0*reshape(X.basis(:,1),nx,mx));
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in_yin_z = 2*in_y + in_z;
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if all(in_yin_z<3)
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case1 = find(in_yin_z==1);
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if ~isempty(case1)
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basis(:,case1+1) = z.basis(:,2:1+length(case1));
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in_yin_z(case1) = 0;
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end
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end
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% Let's identify the indices at which we need to intervene
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case1 = find(in_yin_z==1);
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checkI = union(find(in_yin_z >= 2), setdiff(case1,case1+1));
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if size(checkI,1) > size(checkI,2)
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% Sometimes the in_yin_z vector is vertical (not
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% always though), so we make sure that checkI, on
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% which we'll iterate, is horizontal.
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checkI = checkI';
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end
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for i = checkI
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switch in_yin_z(i)
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case 1
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% We look for the end of the block of ones
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% starting at i
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iend = i + find([in_yin_z(i+1:end) 0] ~= 1, 1, 'first')-1;
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basis(:,i+1:iend+1) = z.basis(:,z_ind:z_ind+(iend-i));z_ind = z_ind+(iend-i)+1;
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case 2
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temp = sparse(subsasgn(template,I,full(reshape(Y.basis(:,y_ind),ny,my))));
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basis(:,i+1) = temp(:);
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y_ind = y_ind+1;
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case 3
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Z1 = z.basis(:,z_ind);
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Z4 = Y.basis(:,y_ind);
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Z3 = reshape(Z4,ny,my);
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Z2 = sparse(subsasgn(0*reshape(full(X.basis(:,1)),nx,mx),I,Z3));
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temp = reshape(Z1,nz,mz)+Z2;
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basis(:,i+1) = temp(:);
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z_ind = z_ind+1;
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y_ind = y_ind+1;
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otherwise
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end
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end;
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z.dim(1) = nz;
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z.dim(2) = mz;
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z.basis = basis;
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z.lmi_variables = all_lmi_variables(:)';
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y = z;
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% Reset info about conic terms
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y.conicinfo = [0 0];
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y = flush(y);
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otherwise
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end
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else
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error('Reference type not supported');
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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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function y = specialcode(X,Y,I)
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y = X;
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X_basis = X.basis;
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Y_basis = Y.basis;
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ind = I.subs{1};ind = ind(:);
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yvar_in_xvar = zeros(length(Y.lmi_variables),1);
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for i = 1:length(Y.lmi_variables);
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yvar_in_xvar(i) = find(X.lmi_variables==Y.lmi_variables(i));
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end
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y.basis(ind,:) = 0;
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mapper = [1 1+yvar_in_xvar(:)'];mapper = mapper(:);
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[i,j,k] = find(y.basis);
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[ib,jb,kb] = find(Y_basis);
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i = [i(:);ind(ib(:))];
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j = [j(:);mapper(jb(:))];
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k = [k(:);kb(:)];
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y.basis = sparse(i,j,k,size(y.basis,1),size(y.basis,2));
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y = clean(y);
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