306 lines
9.5 KiB
Mathematica
306 lines
9.5 KiB
Mathematica
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function [A,b] = generate_kernel_representation_data(N,N_unique,exponent_m2,exponent_p,p,options,p_base_parametric,ParametricIndicies,MonomIndicies,FirstRun)
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persistent saveData
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exponent_p_parametric = exponent_p(:,ParametricIndicies);
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exponent_p_monoms = exponent_p(:,MonomIndicies);
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pcoeffs = getbase(p);
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if any(exponent_p_monoms(1,:))
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pcoeffs=pcoeffs(:,2:end); % No constant term in p
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end
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b = [];
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parametric = full((~isempty(ParametricIndicies) & any(any(exponent_p_parametric))));
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% For problems with a lot of similar cones, this saves some time
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reuse = 0;
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if ~isempty(saveData) && isequal(saveData.N,N) & ~FirstRun
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n = saveData.n;
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ind = saveData.ind;
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if isequal(saveData.N_unique,N_unique) & isequal(saveData.exponent_m2,exponent_m2)% & isequal(saveData.epm,exponent_p_monoms)
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reuse = 1;
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end
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else
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% Congruence partition sizes
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for k = 1:size(N,1)
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n(k) = size(N{k},1);
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end
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% Save old SOS definition
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saveData.N = N;
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saveData.n = n;
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saveData.N_unique = N_unique;
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saveData.exponent_m2 = exponent_m2;
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saveData.N_unique = N_unique;
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end
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if reuse & options.sos.reuse
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% Get old stuff
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if size(exponent_m2{1},2)==2 % Stupid (sos(parametric)) case
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ind = spalloc(1,1,0);
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ind(1)=1;
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allj = 1:size(exponent_p_monoms,1);
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used_in_p = ones(size(exponent_p_monoms,1),1);
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else
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allj = [];
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used_in_p = zeros(size(exponent_p_monoms,1),1);
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hash = randn(size(exponent_p_monoms,2),1);
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p_hash = exponent_p_monoms*hash;
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exponent_p_monoms_hash = exponent_p_monoms*hash;
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for i = 1:size(N_unique,1)
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monom = sparse(N_unique(i,3:end));
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j = find(exponent_p_monoms_hash == (monom*hash));
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if isempty(j)
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b = [b 0];
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allj(end+1,1) = 0;
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else
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used_in_p(j) = 1;
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allj(end+1,1:length(j)) = j(:)';
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end
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end
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ind = saveData.ind;
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end
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else
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allj = [];
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used_in_p = zeros(size(exponent_p_monoms,1),1);
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if size(exponent_m2{1},2)==2 % Stupid (sos(parametric)) case
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ind = spalloc(1,1,0);
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ind(1)=1;
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allj = 1:size(exponent_p_monoms,1);
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used_in_p = ones(size(exponent_p_monoms,1),1);
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else
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% To speed up some searching, we random-hash data
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hash = randn(size(exponent_p_monoms,2),1);
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for k = 1:length(exponent_m2)
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if isempty(exponent_m2{k})
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exp_hash{k}=[];
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else
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exp_hash{k} = sparse((exponent_m2{k}(:,3:end)))*hash; % SPARSE NEEDED DUE TO STRANGE NUMERICS IN MATLAB ON 0s (the stuff will differ on last bit in hex format)
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end
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end
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p_hash = exponent_p_monoms*hash;
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ind = spalloc(size(N_unique,1),sum(n.^2),0);
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for i = 1:size(N_unique,1)
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monom = N_unique(i,3:end);
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monom_hash = sparse(monom)*hash;
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LHS = 0;
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start = 0;
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for k = 1:size(N,1)
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j = find(exp_hash{k} == monom_hash);
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if ~isempty(j)
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pos=exponent_m2{k}(j,1:2);
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nss = pos(:,1);
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mss = pos(:,2);
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indicies = nss+(mss-1)*n(k);
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ind(i,indicies+start) = ind(i,indicies+start) + 1;
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end
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start = start + (n(k))^2;
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% start = start + (matrixSOSsize*n(k))^2;
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end
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j = find(p_hash == monom_hash);
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if isempty(j)
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allj(end+1,1) = 0;
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else
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used_in_p(j) = 1;
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allj(end+1,1:length(j)) = j(:)';
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end
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end
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end
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end
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saveData.ind = ind;
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% Some parametric terms in p(x,t) do not appear in v'Qv
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% So these have to be added 0*Q = b
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not_dealt_with = find(used_in_p==0);
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while ~isempty(not_dealt_with)
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%j = findrows(exponent_p_monoms,exponent_p_monoms(not_dealt_with(1),:));
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j = find(p_hash == p_hash(not_dealt_with(1)));
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allj(end+1,1:length(j)) = j(:)';
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used_in_p(j) = 1;
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not_dealt_with = find(used_in_p==0);
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ind(end+1,1)=0;
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end
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matrixSOSsize = length(p);
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if parametric
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% Inconsistent behaviour in MATLAB
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if size(allj,1)==1
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uu = [0;p_base_parametric];
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b = sum(uu(allj+1))';
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else
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b = [];
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for i = 1:matrixSOSsize
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for j = i:matrixSOSsize
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if i~=j
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uu = [0;2*p_base_parametric(:,(i-1)*matrixSOSsize+j)];
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else
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uu = [0;p_base_parametric(:,(i-1)*matrixSOSsize+j)];
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end
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b = [b sum(uu(allj+1),2)'];
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end
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end
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end
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else
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if matrixSOSsize == 1
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uu = [zeros(size(pcoeffs,1),1) pcoeffs]';
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b = sum(uu(allj+1,:),2)';
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else
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b = [];
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for i = 1:matrixSOSsize
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for j = i:matrixSOSsize
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if i~=j
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uu = [0;2*pcoeffs((i-1)*matrixSOSsize+j,:)'];
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else
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uu = [0;pcoeffs((i-1)*matrixSOSsize+j,:)'];
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end
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b = [b;sum(uu(allj+1,:),2)'];
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end
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end
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end
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% uu = [0;pcoeffs(:)];
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% b = sum(uu(allj+1),2)';
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end
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b = b';
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dualbase = ind;
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j = 1;
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A = cell(size(N,1),1);
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for k = 1:size(N,1)
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if matrixSOSsize==1
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A{k} = dualbase(:,j:j+n(k)^2-1);
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else
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% Quick fix for matrix SOS case, should be optimized
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A{k} = inflate(dualbase(:,j:j+n(k)^2-1),matrixSOSsize,n(k));
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end
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j = j + n(k)^2;
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end
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b = b(:);
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function newAi = inflate(Ai,matrixSOSsize,n);
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% Quick fix for matrix SOS case, should be optimized
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newAi = [];
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newAi = [];
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newAj = [];
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newAk = [];
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top = 1;
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for i = 1:matrixSOSsize
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for r = i:matrixSOSsize
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for m = 1:size(Ai,1)
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ai = reshape(Ai(m,:),n,n);
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if 1
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% V = spalloc(matrixSOSsize,matrixSOSsize,2);
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% V(i,r)=1;
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% V(r,i)=1;
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% aii = kron(V,ai);
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% aii = aii(:);
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% [ii,jj,kk] = find(aii);
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% newAj = [newAj ii(:)'];
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% newAi = [newAi repmat(top,1,length(ii))];
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% newAk = [newAk kk(:)'];
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[dnewAj,dnewAi,dnewAk] = inflatelocal(ai,matrixSOSsize,r,i,top);
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newAj = [newAj dnewAj];
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newAi = [newAi dnewAi];
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newAk = [newAk dnewAk];
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% newAi = [newAi;ai(:)'];
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else
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[dnewAjC,dnewAiC,dnewAkC] = inflatelocal(ai,matrixSOSsize,r,i,top);
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[dnewAj,dnewAi,dnewAk] = inflatelocalnew(ai,matrixSOSsize,r,i,top,n);
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AA=reshape(full(sparse(dnewAi*0+1,dnewAj,dnewAk,1,(matrixSOSsize*n)^2)),n*matrixSOSsize,[]);
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AA2=reshape(full(sparse(dnewAiC*0+1,dnewAjC,dnewAkC,1,(matrixSOSsize*n)^2)),n*matrixSOSsize,[]);
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if norm(AA-AA2)>0
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1
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end
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newAj = [newAj dnewAj];
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newAi = [newAi dnewAi];
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newAk = [newAk dnewAk];
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%
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% [ii,jj,kk] = find(ai-diag(diag(ai)));
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% iii = [(i-1)*n+ii;(r-1)*n+jj]
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% jjj = [(r-1)*n+jj;(i-1)*n+ii]
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% kkk = [kk;kk];
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% indexi = repmat(top,1,length(iii));
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% index = iii+(jjj-1)*matrixSOSsize*n
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% newAj = [newAj index(:)'];
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% newAi = [newAi indexi];
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% newAk = [newAk kkk(:)'];
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%
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% [ii,jj,kk] = find(diag(diag(ai)));
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% iii = [(i-1)*n+ii]
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% jjj = [(r-1)*n+jj]
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% kkk = [kk];
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% indexi = repmat(top,1,length(iii));
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% index = iii+(jjj-1)*matrixSOSsize*n
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% newAj = [newAj index(:)'];
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% newAi = [newAi indexi];
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% newAk = [newAk kkk(:)'];
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end
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%sparse(indexi,index,kkk,1,(n*nA)^2)
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top = top+1;
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end
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end
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end
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newAi = sparse(newAi,newAj,newAk,top-1,(matrixSOSsize*n)^2);
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function [Z,Q1,R] = sparsenull(A)
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[Q,R] = qr(A');
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n = max(find(sum(abs(R),2)));
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Q1 = Q(:,1:n);
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R = R(1:n,:);
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Z = Q(:,n+1:end); % New basis
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function [dnewAj,dnewAi,dnewAk] = inflatelocal(ai,matrixSOSsize,r,i,top)
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V = spalloc(matrixSOSsize,matrixSOSsize,2);
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V(i,r)=1;
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V(r,i)=1;
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aii = kron(V,ai);
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aii = aii(:);
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[ii,jj,kk] = find(aii);
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dnewAj = ii(:)';
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dnewAi = repmat(top,1,length(ii));
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dnewAk = kk(:)';
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% newAi = [newAi;ai(:)'];
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function [dnewAj,dnewAi,dnewAk] = inflatelocalnew(ai,matrixSOSsize,r,i,top,n)
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if r==i
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[ii,jj,kk] = find(ai-diag(diag(ai)));
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else
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[ii,jj,kk] = find(ai);
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end
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iii = [(i-1)*n+ii;(r-1)*n+jj];
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jjj = [(r-1)*n+jj;(i-1)*n+ii];
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kkk = [kk;kk];
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indexi = repmat(top,1,length(iii));
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index = iii+(jjj-1)*matrixSOSsize*n;
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dnewAj = [ index(:)'];
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dnewAi = [ indexi];
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dnewAk = [ kkk(:)'];
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[ii,jj,kk] = find(diag(diag(ai)));
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iii = [(i-1)*n+ii];
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jjj = [(r-1)*n+jj];
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kkk = [kk];
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indexi = repmat(top,1,length(iii));
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index = iii+(jjj-1)*matrixSOSsize*n;
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dnewAj = [dnewAj index(:)'];
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dnewAi = [dnewAi indexi];
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dnewAk = [dnewAk kkk(:)'];
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