120 lines
4.4 KiB
Mathematica
120 lines
4.4 KiB
Mathematica
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%%*******************************************************************
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%% NTrhsfun: compute the right-hand side vector of the
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%% Schur complement equation for the NT direction.
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%%
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%% SDPT3: version 3.1
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%% Copyright (c) 1997 by
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%% K.C. Toh, M.J. Todd, R.H. Tutuncu
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%% Last Modified: 16 Sep 2004
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%%*******************************************************************
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function [rhs,EinvRc,hRd] = NTrhsfun(blk,At,par,X,Z,rp,Rd,sigmu,hRd,dX,dZ);
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spdensity = par.spdensity;
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m = length(rp);
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if (nargin > 8)
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corrector = 1;
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else
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corrector = 0;
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hRd = zeros(m,1);
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end
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hEinvRc = zeros(m,1);
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EinvRc = cell(size(blk,1),1);
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rhsfree = [];
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%%
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for p = 1:size(blk,1)
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pblk = blk(p,:);
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n = sum(pblk{2}); numblk = length(pblk{2});
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if strcmp(pblk{1},'l')
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Rq = sparse(n,1);
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if (corrector)
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if (norm(par.parbarrier{p}) <= inf)
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Rq = dX{p}.*dZ{p};
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end
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else
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tmp = par.dd{p}.*Rd{p};
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tmp2 = mexMatvec(At{p},tmp,1);
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hRd = hRd + tmp2;
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end
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if iscell(sigmu)
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EinvRc{p} = sigmu{p}./Z{p}-X{p} -Rq./Z{p};
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else
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EinvRc{p} = sigmu./Z{p}-X{p} -Rq./Z{p};
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end
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tmp2 = mexMatvec(At{p},EinvRc{p},1);
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hEinvRc = hEinvRc + tmp2;
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elseif strcmp(pblk{1},'q')
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Rq = sparse(n,1);
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if (corrector)
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if (norm(par.parbarrier{p}) <= inf)
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w = sqrt(par.gamz{p}./par.gamx{p});
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hdx = qops(pblk,w,par.ff{p},5,dX{p});
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hdz = qops(pblk,w,par.ff{p},6,dZ{p});
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hdxdz = Arrow(pblk,hdx,hdz);
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vv = qops(pblk,w,par.ff{p},5,X{p});
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Vihdxdz = Arrow(pblk,vv,hdxdz,1);
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Rq = qops(pblk,w,par.ff{p},6,Vihdxdz);
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end
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else
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tmp = par.dd{p}.*Rd{p} + qops(pblk,qops(pblk,Rd{p},par.ee{p},1),par.ee{p},3);
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tmp2 = mexMatvec(At{p},tmp,1);
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hRd = hRd + tmp2;
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end
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if iscell(sigmu)
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EinvRc{p} = qops(pblk,-sigmu{p}./(par.gamz{p}.*par.gamz{p}),Z{p},4) -X{p}-Rq;
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else
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EinvRc{p} = qops(pblk,-sigmu./(par.gamz{p}.*par.gamz{p}),Z{p},4) -X{p}-Rq;
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end
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tmp2 = mexMatvec(At{p},EinvRc{p},1);
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hEinvRc = hEinvRc + tmp2;
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elseif strcmp(pblk{1},'s')
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n2 = pblk{2}.*(pblk{2}+1)/2;
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Rq = sparse(n,n);
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if (corrector)
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if (norm(par.parbarrier{p}) <= inf)
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hdZ = Prod3(pblk,par.G{p},dZ{p},par.G{p}',1);
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hdX = spdiags(-par.sv{p},0,n,n)-hdZ;
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tmp = Prod2(pblk,hdX,hdZ,0);
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tmp = 0.5*(tmp+tmp');
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if (numblk == 1)
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d = par.sv{p};
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e = ones(pblk{2},1);
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Rq = 2*tmp./(d*e'+e*d');
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if (nnz(Rq) <= spdensity*n2); Rq = sparse(Rq); end
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else
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Rq = sparse(n,n);
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s = [0, cumsum(pblk{2})];
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for i = 1:numblk
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pos = [s(i)+1 : s(i+1)];
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d = par.sv{p}(pos); e = ones(length(pos),1);
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Rq(pos,pos) = 2*tmp(pos,pos)./(d*e' + e*d');
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end
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end
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end
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else
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tmp = Prod3(pblk,par.W{p},Rd{p},par.W{p},1,par.nzlistAy{p});
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tmp2 = AXfun(pblk,At(p,:),par.permA(p,:),{tmp});
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hRd = hRd + tmp2;
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end
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if iscell(sigmu)
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ss = [0,cumsum(pblk{2})];
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sigmuvec = zeros(n,1);
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for k = 1:length(pblk{2});
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sigmuvec(ss(k)+1:ss(k+1)) = sigmu{p}(k)*ones(pblk{2}(k),1);
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end
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tmp = spdiags(sigmuvec./par.sv{p} -par.sv{p},0,n,n);
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else
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tmp = spdiags(sigmu./par.sv{p} -par.sv{p},0,n,n);
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end
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EinvRc{p} = Prod3(pblk,par.G{p}',tmp-Rq,par.G{p},1);
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tmp2 = AXfun(pblk,At(p,:),par.permA(p,:),EinvRc(p));
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hEinvRc = hEinvRc + tmp2;
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elseif strcmp(pblk{1},'u')
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rhsfree = [rhsfree; Rd{p}];
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end
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end
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%%
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rhs = rp + hRd - hEinvRc;
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rhs = full([rhs; rhsfree]);
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%%*******************************************************************
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