68 lines
2.2 KiB
Mathematica
68 lines
2.2 KiB
Mathematica
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%%*****************************************************************
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%% NTpred: Compute (dX,dy,dZ) for NT direction.
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%%
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%% compute SVD of Xchol*Zchol via eigenvalue decompostion of
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%% Zchol * X * Zchol' = V * diag(sv2) * V'.
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%% compute W satisfying W*Z*W = X.
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%% W = G'*G, where G = diag(sqrt(sv)) * (invZchol*V)'
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%%*****************************************************************
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%% SDPT3: version 4.0
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%% Copyright (c) 1997 by
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%% Kim-Chuan Toh, Michael J. Todd, Reha H. Tutuncu
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%% Last Modified: 16 Sep 2004
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%%*****************************************************************
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function [par,dX,dy,dZ,coeff,L,hRd] = ...
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NTpred(blk,At,par,rp,Rd,sigmu,X,Z,Zchol,invZchol);
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global schurfun schurfun_par
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%%
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%% compute NT scaling matrix
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%%
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[par.W,par.G,par.sv,par.gamx,par.gamz,par.dd,par.ee,par.ff] = ...
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NTscaling(blk,X,Z,Zchol,invZchol);
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%%
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%% compute schur matrix
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%%
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m = length(rp);
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schur = sparse(m,m);
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UU = []; EE = []; Afree = [];
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dX = cell(size(blk,1),1); dy = []; dZ = cell(size(blk,1),1);
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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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if strcmp(pblk{1},'l')
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[schur,UU,EE] = schurmat_lblk(blk,At,par,schur,UU,EE,p,par.dd);
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elseif strcmp(pblk{1},'q');
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[schur,UU,EE] = schurmat_qblk(blk,At,par,schur,UU,EE,p,par.dd,par.ee);
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elseif strcmp(pblk{1},'s')
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if isempty(schurfun{p})
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schur = schurmat_sblk(blk,At,par,schur,p,par.W);
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elseif isstr(schurfun{p})
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schurtmp = sparse(m,m);
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if ~isempty(par.permZ{p})
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Wp = par.W{p}(par.permZ{p},par.permZ{p});
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else
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Wp = par.W{p};
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end
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eval(['schurtmp = ',schurfun{p},'(Wp,Wp,schurfun_par(p,:));']);
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schur = schur + schurtmp;
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end
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elseif strcmp(pblk{1},'u')
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Afree = [Afree, At{p}'];
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end
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end
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%%
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%% compute rhs
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%%
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[rhs,EinvRc,hRd] = NTrhsfun(blk,At,par,X,Z,rp,Rd,sigmu);
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%%
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%% solve linear system
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%%
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[xx,coeff,L] = linsysolve(par,schur,UU,Afree,EE,rhs);
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%%
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%% compute (dX,dZ)
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%%
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[dX,dy,dZ] = NTdirfun(blk,At,par,Rd,EinvRc,xx,m);
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%%**********************************************************************
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