232 lines
8.0 KiB
Mathematica
232 lines
8.0 KiB
Mathematica
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%%*******************************************************************
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%% HKMpred: Compute (dX,dy,dZ) for the H..K..M direction.
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%%
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%% SDPT3: version 3.0
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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: 2 Feb 01
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%%*******************************************************************
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function [dX,dy,dZ,schur,L,UU,VV,E,SMWmat,hRd] = ...
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HKMpred(blk,At,par,rp,Rd,sigmu,X,Z,invZchol);
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global matlabversion ispc_hp_ibm
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global spdensity iter solve_ok existMA47symb existspcholsymb
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global nnzmat nnzmatold matfct_options matfct_options_old use_SCM
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global Lsymb cachesize
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global Zinv gamz dd
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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 = []; VV = []; E = []; SMWmat = []; Afree = [];
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existsdpblk = 0; exist_free_vars = 0;
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dX = cell(size(blk,1),1); dy = []; dZ = cell(size(blk,1),1);
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Zinv = 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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n = sum(pblk{2});
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numblk = length(pblk{2});
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if strcmp(pblk{1},'l')
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Zinv{p} = 1./Z{p};
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dd{p} = X{p}./Z{p};
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[schur,UU,VV] = schurmat_lblkold(blk,At,schur,UU,VV,p,dd);
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elseif strcmp(pblk{1},'q');
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gaptmp = qops(pblk,X{p},Z{p},1);
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gamz2 = qops(pblk,Z{p},Z{p},2);
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gamz{p} = sqrt(gamz2);
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Zinv{p} = qops(pblk,-1./gamz2,Z{p},4);
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dd{p} = qops(pblk,gaptmp./gamz2,ones(n,1),4);
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[schur,UU,VV] = schurmat_qblkold(blk,At,schur,UU,VV,p,dd,Zinv,X);
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elseif strcmp(pblk{1},'s')
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existsdpblk = 1;
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if (numblk == 1)
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Zinv{p} = Prod2(pblk,full(invZchol{p}),invZchol{p}',1);
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else
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Zinv{p} = Prod2(pblk,invZchol{p},invZchol{p}',1);
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end
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schur = schurmat_sblk(blk,At,par,schur,p,X,Zinv);
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elseif strcmp(pblk{1},'u')
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exist_free_vars = 1;
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Afree = [Afree At{p}'];
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end
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end
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diagschur = diag(schur);
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if (existsdpblk);
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pertdiag = 1e-16*sqrt(m)*norm(diagschur);
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for k=1:m; schur(k,k) = abs(schur(k,k)) + pertdiag; end;
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else
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pertdiag = 1e-16*max(diagschur);
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for k=1:m; schur(k,k) = abs(schur(k,k)) + pertdiag; end;
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end
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%%
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[rhs,EinvRc,hRd] = HKMrhsfun(blk,At,par,X,Z,rp,Rd,sigmu);
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%%
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%% determine matrix factorization to use
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%%
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if (exist_free_vars)
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tmp = [zeros(size(Afree,2),1); ones(size(UU,2),1)];
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UU = [Afree UU]; VV = [Afree VV];
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E = spdiags(tmp,0,length(tmp),length(tmp));
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else
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E = speye(size(UU,2));
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end
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rhs = [rhs; zeros(m+size(UU,2)-length(rhs),1)];
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if (iter <= 2)
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if (size(UU,2) < min(500,0.1*m));
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use_SCM = 1;
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else
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use_SCM = 0;
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if (norm(UU-VV,'fro') < 1e-13) & (existMA47symb) & (size(UU,2) < 0.25*m)
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matfct_options = 'MA47';
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else
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matfct_options = 'splu';
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end
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end
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end
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%%
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%% Cholesky factorization
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%%
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if (iter == 1); existMA47symb = 1; nnzmatold = 0; end
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nnzmat = mexnnz(schur);
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nnzmatdiff = (nnzmat ~= nnzmatold);
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if use_SCM
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if (nnzmat > spdensity*m^2);
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if issparse(schur); schur = full(schur); end;
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matfct_options = 'chol';
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else
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if ~issparse(schur), schur = sparse(schur); end;
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matfct_options = 'spchol';
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end
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if strcmp(matfct_options,'chol')
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L = [];
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if (matlabversion >= 6)
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if (ispc_hp_ibm), [schur,indef] = chol(schur);
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else, indef = mexchol_(schur);
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end
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else
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[schur,indef] = chol(schur);
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end
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if indef;
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solve_ok = -2;
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fprintf(' chol: Schur complement matrix not positive definite.\n');
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else
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[xx,solve_ok,SMWmat] = schursysolve(schur,schur,UU,VV,E,rhs,matfct_options);
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end
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elseif strcmp(matfct_options,'spchol')
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if (nnzmatdiff | ~strcmp(matfct_options,matfct_options_old))
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[Lsymb,flag] = symbcholfun(schur,cachesize);
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if (flag)
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solve_ok = -2;
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existspcholsymb = 0;
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fprintf(' spchol: symbolic factorization fails.\n');
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else
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existspcholsymb = 1;
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end
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end
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if (existspcholsymb)
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L = sparcholfun(Lsymb,schur);
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L.d(find(L.skip)) = inf;
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if ~isempty(UU) & any(L.skip);
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solve_ok = -3;
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fprintf(' spchol: fail to solve Schur complement equation\n');
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fprintf(' via the Sherman-Morrison update.\n');
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else
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[xx,solve_ok,SMWmat] = schursysolve(schur,L,UU,VV,E,rhs,matfct_options);
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end
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end
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end
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end
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if (solve_ok <= 0)
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if ~(existsdpblk & size(UU,2)==0)
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use_SCM = 0;
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matfct_options = 'splu';
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if (size(UU,2) > 0)
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fprintf(' switch to augmented system.\n');
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else
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fprintf(' switch to LU factorization.\n');
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end
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else
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return;
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end
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end
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%%
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%% LU or symmetric indefinite factorization
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%%
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if ~use_SCM
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raugmat = [schur UU; VV' -E];
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if (nnzmat > spdensity*m^2);
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matfct_options = 'lu';
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end
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%%
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if strcmp(matfct_options,'lu')
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if issparse(raugmat); raugmat = full(raugmat); end
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[L.l,L.u,L.p] = lu(raugmat);
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xx = L.u \ (L.l \ (L.p*rhs));
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end
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if strcmp(matfct_options,'MA47')
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if ~issparse(raugmat); raugmat = sparse(raugmat); end
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if (nnzmatdiff | ~strcmp(matfct_options,matfct_options_old))
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nnztmp = (nnz(raugmat) + nnz(diag(raugmat)))/2;
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[keep,Jcn,flag,info] = mexMA47syb(nnztmp,raugmat);
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if (flag)
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existMA47symb = 0;
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fprintf(' MA47: symbolic factorization fails, switch to LU.\n');
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matfct_options = 'splu';
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else
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existMA47symb = 1;
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Lsymb.keep = keep; Lsymb.Jcn = Jcn;
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Lsymb.La = 2*info(1); Lsymb.Liw = 2*info(2);
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end
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end
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if (existMA47symb)
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[L.a,L.iw,flag] = mexMA47fct(raugmat, ...
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Lsymb.keep,Lsymb.Jcn,Lsymb.La,Lsymb.Liw,[1e-10,0]);
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xx = mexMA47slv(length(rhs),L.a,L.iw,rhs);
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if (flag == 0)
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solve_ok = 1;
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else
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existMA47symb = 0;
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fprintf(' MA47: solver fails, switch to LU. \n');
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matfct_options = 'splu';
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end
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end
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end
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if strcmp(matfct_options,'splu')
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if ~issparse(raugmat); raugmat = sparse(raugmat); end
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if (nnzmatdiff | ~strcmp(matfct_options,matfct_options_old))
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Lsymb.perm = symmmd(raugmat);
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end
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L.perm = Lsymb.perm;
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if (matlabversion >= 6.5)
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[L.l,L.u,L.p,L.q] = lu(raugmat(L.perm,L.perm));
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elseif (exist('umfpack2')==3)
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[L.l,L.u,pp,qq] = umfpack2(raugmat(L.perm,L.perm));
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len = length(pp);
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L.p = spconvert([(1:len)' pp' ones(len,1)]);
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L.q = spconvert([qq' (1:len)' ones(len,1)]);
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else
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[L.l,L.u,L.p] = lu(raugmat(L.perm,L.perm));
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L.q = speye(length(raugmat));
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end
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xx(L.perm,1) = L.q*( L.u \ (L.l \ (L.p*rhs(L.perm))));
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if any(xx == inf)
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solve_ok = 0;
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fprintf(' LU: fails to solve the augmented system.\n');
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else
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solve_ok = 1;
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end
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end
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end
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nnzmatold = nnzmat; matfct_options_old = matfct_options;
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%%
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%% compute (dX,dZ)
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%%
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if (any(isnan(xx)) | any(isinf(xx)))
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error(' solution of linear system contains NaN or inf');
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end
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[dX,dy,dZ] = HKMdirfun(blk,At,par,Rd,EinvRc,X,xx);
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%%*******************************************************************
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