253 lines
7.1 KiB
Mathematica
253 lines
7.1 KiB
Mathematica
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function [base,v] = matrixcoefficients(p,x)
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%MATRIXCOEFFICIENTS Extends coefficients, beta
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% FIX: CURRENTLY UNSTABLE!
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if nargout>1 & (max(size(p))>1)
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% error('For matrix inputs, only the coefficients can be returned. Request feature if you need this...');
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end
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% Hack to make sure we get the basis w.r.t all variables and 1
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% This has to be fixed soon (to make robust opt. module fast)
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p = p + pi + sum(x)*1e-5;
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if nargin==1
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allvar = depends(p);
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xvar = allvar;
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x = recover(xvar);
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else
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xvar = intersect(depends(x),depends(p));
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end
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% Try to debug this!
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p = p(:);
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base = [];
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v = [];
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allvar = depends(p);%(ii));
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allvar_recovered = recover(allvar);
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t = setdiff(allvar,xvar);
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t_recovered = recover(t);
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ParametricIndicies = find(ismember(allvar,t));
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map = find(~ismember(allvar,t));
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for ii = 1:length(p)
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pii = p(ii);
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[exponent_p,p_base] = getexponentbase(pii,allvar_recovered);
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tempbase = parameterizedbase(pii,[],t_recovered,ParametricIndicies,exponent_p,p_base);
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[i,j,k] = unique(full(exponent_p(:,map)),'rows');
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V = sparse(1:length(k),k,1,length(tempbase),max(k))';
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base{ii} = V*tempbase - [pi;repmat(1e-5,length(x),1)];
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keepthese = j(1:max(k));
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v{ii} = recovermonoms(exponent_p(keepthese,map),x);%recover(xvar));
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end
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function p_base_parametric = parameterizedbase(p,z, params,ParametricIndicies,exponent_p,p_base)
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% Check for linear parameterization
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parametric_basis = exponent_p(:,ParametricIndicies);
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if all(sum(parametric_basis,2)==0)
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p_base_parametric = full(p_base(:));
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return
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end
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if all(sum(parametric_basis,2)<=1)
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p_base_parametric = full(p_base(:));
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n = length(p_base_parametric);
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ii = [];
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vars = [];
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js = sum(parametric_basis,1);
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for i = 1:size(parametric_basis,2)
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if js(i)
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j = find(parametric_basis(:,i));
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ii = [ii j(:)'];
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vars = [vars repmat(i,1,js(i))];
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end
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end
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k = setdiff1D(1:n,ii);
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if isempty(k)
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p_base_parametric = p_base_parametric.*sparse(ii,repmat(1,1,n),params(vars));
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else
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pp = params(vars); % Must do this, bug in ML 6.1 (x=sparse(1);x([1 1]) gives different result in 6.1 and 7.0!)
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temp = sparse([ii k(:)'],repmat(1,1,n),[pp(:)' ones(1,1,length(k))]);
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p_base_parametric = p_base_parametric.*temp;
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end
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else
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% Bummer, nonlinear parameterization sucks...
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for i = 1:length(p_base)
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j = find(exponent_p(i,ParametricIndicies));
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if ~isempty(j)
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temp = p_base(i);
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for k = 1:length(j)
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if exponent_p(i,ParametricIndicies(j(k)))==1
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temp = temp*params(j(k));
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else
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temp = temp*params(j(k))^exponent_p(i,ParametricIndicies(j(k)));
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end
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end
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xx{i} = temp;
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else
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xx{i} = p_base(i);
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end
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end
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p_base_parametric = stackcell(sdpvar(1,1),xx)';
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end
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%
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%
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%
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%
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%
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% function [base,v] = coefficients(p,x)
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% %COEFFICIENTS Extract coefficients and monomials from polynomials
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% %
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% % [c,v] = COEFFICIENTS(p,x) extracts the coefficents
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% % of a polynomial p(x) = c'*v(x)
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% %
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% % INPUT
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% % p : SDPVAR object
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% % x : SDPVAR object
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% %
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% % OUTPUT
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% % c : SDPVAR object
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% % v : SDPVAR object
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% %
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% % EXAMPLE
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% % sdpvar x y s t
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% % p = x^2+x*y*(s+t)+s^2+t^2; % define p(x,y), parameterized with s and t
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% % [c,v] = coefficients(p,[x y]);
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% % sdisplay([c v])
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% %
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% % See also SDPVAR
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%
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% % Author Johan L<EFBFBD>fberg
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% % $Id: matrixcoefficients.m,v 1.4 2006-08-09 12:14:04 joloef Exp $
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%
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%
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% if length(p) > 1%size(p,2) > 1
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% error('Coefficents can only be applied to column vectors');
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% end
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%
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% allvar = depends(p);
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% if nargin==1
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% xvar = allvar;
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% x = recover(xvar);
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% else
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% xvar = depends(x);
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% end
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%
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% pvar = recover(depends(p));
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%
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% base = [];
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% for i = 1:length(p)
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% [bi{i},vi{i}] = coefficientsi(p(i),xvar,pvar,allvar);
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% end
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%
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% % Fix the lengths of the basis to use same basis for all elements
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% if length(bi)>1
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% allvars = [];
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% for i = 1:length(bi)
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% bivar{i} = getvariables(vi{i});
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% if isequal(vi{i}(1),1)
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% bivar{i} = [0 bivar{i}];
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% end
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% allvars = unique([allvars bivar{i}]);
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% end
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% v = recover(allvars);
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% c = zeros(length(p),length(allvars))';
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% ci = [];
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% cj = [];
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% cv = [];
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% for i = 1:length(bi)
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% index = find(ismember(allvars,bivar{i}));
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% ci = [ci index];
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% cj = [cj repmat(i,1,length(index))];
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% cv = [cv bi{i}'];
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% end
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% base = sparse(ci,cj,cv);
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% else
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% base = bi{1};
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% v = vi{1};
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% end
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%
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%
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% function [base,v] = coefficientsi(p,xvar,pvar,allvar)
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%
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% % Try to debug this!
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% t = setdiff(allvar,xvar);
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% [exponent_p,p_base] = getexponentbase(p,pvar);
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% ParametricIndicies = find(ismember(allvar,t));
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% % FIX : don't define it here, wait until sparser below. Speed!!
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% tempbase = parameterizedbase(p,[],recover(t),ParametricIndicies,exponent_p,p_base);
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% [i,j,k] = unique(full(exponent_p(:,find(~ismember(allvar,t)))),'rows');
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% %V = sparse(max(k),length(tempbase));
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% %for i = 1:max(k)
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% % V(i,find(k==i)) = 1;
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% %end
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% V = sparse(1:length(k),k,1,length(tempbase),max(k))';
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% base = V*tempbase;
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% if nargout == 2
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% keepthese = j(1:max(k));
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% v = recovermonoms(exponent_p(keepthese,find(~ismember(allvar,t))),recover(xvar));
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% end
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%
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%
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% function p_base_parametric = parameterizedbase(p,z, params,ParametricIndicies,exponent_p,p_base)
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%
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% % Check for linear parameterization
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% parametric_basis = exponent_p(:,ParametricIndicies);
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% if all(sum(parametric_basis,2)==0)
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% p_base_parametric = full(p_base(:));
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% return
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% end
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% if all(sum(parametric_basis,2)<=1)
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% p_base_parametric = full(p_base(:));
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% n = length(p_base_parametric);
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% ii = [];
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% vars = [];
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% js = sum(parametric_basis,1);
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% for i = 1:size(parametric_basis,2)
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% if js(i)
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% j = find(parametric_basis(:,i));
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% ii = [ii j(:)'];
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% vars = [vars repmat(i,1,js(i))];
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% end
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% end
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% k = setdiff1D(1:n,ii);
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% if isempty(k)
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% p_base_parametric = p_base_parametric.*sparse(ii,repmat(1,1,n),params(vars));
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% else
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% pp = params(vars); % Must do this, bug in ML 6.1 (x=sparse(1);x([1 1]) gives different result in 6.1 and 7.0!)
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% p_base_parametric = p_base_parametric.*sparse([ii k(:)'],repmat(1,1,n),[pp(:)' ones(1,1,length(k))]);
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% end
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% else
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% % Bummer, nonlinear parameterization sucks...
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% for i = 1:length(p_base)
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% j = find(exponent_p(i,ParametricIndicies));
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% if ~isempty(j)
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% temp = p_base(i);
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% for k = 1:length(j)
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% if exponent_p(i,ParametricIndicies(j(k)))==1
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% temp = temp*params(j(k));
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% else
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% temp = temp*params(j(k))^exponent_p(i,ParametricIndicies(j(k)));
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% end
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% end
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% xx{i} = temp;
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% else
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% xx{i} = p_base(i);
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% end
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% end
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% p_base_parametric = stackcell(sdpvar(1,1),xx)';
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% end
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