195 lines
7.0 KiB
Matlab
Executable File
195 lines
7.0 KiB
Matlab
Executable File
%%*****************************************************************
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%% linsysolve: solve linear system to get dy, and direction
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%% corresponding to unrestricted variables.
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%%
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%% [xx,coeff,L,resnrm] = linsysolve(schur,UU,EE,Bmat,rhs);
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%%
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%% child functions: mybicgstable.m
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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 [xx,coeff,L,resnrm] = HSDlinsysolve(par,schur,UU,EE,Bmat,rhs)
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global solve_ok msg
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global nnzmat nnzmatold matfct_options matfct_options_old use_LU
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spdensity = par.spdensity;
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printlevel = par.printlevel;
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iter = par.iter;
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m = length(schur);
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if (iter==1); use_LU = 0; matfct_options_old = ''; end
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if isempty(nnzmatold); nnzmatold = 0; end
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%%
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%% diagonal perturbation
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%% old: pertdiag = 1e-15*max(1,diagschur);
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%%
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diagschur = abs(full(diag(schur)));
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const = 1e-2/max(1,norm(par.dy2));
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alpha = max(1e-14,min(1e-10,const*norm(par.rp))/(1+norm(diagschur.*par.dy2)));
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pertdiag = alpha*max(1e-8,diagschur); %% Note: alpha is close to 1e-15.
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schur = mexschurfun(schur,pertdiag);
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%%if (printlevel); fprintf(' %3.1e ',alpha); end
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if (par.depconstr) | (min(diagschur) < min([1e-20*max(diagschur), 1e-4]))
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lambda = 0.1*min(1e-14,const*norm(par.rp)/(1+norm(par.diagAAt.*par.dy2)));
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schur = mexschurfun(schur,lambda*par.diagAAt);
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%%if (printlevel); fprintf('*'); end
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end
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if (max(diagschur)/min(diagschur) > 1e14) & (par.blkdim(2) == 0) ...
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& (iter > 10)
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tol = 1e-6;
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idx = find(diagschur < tol); len = length(idx);
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pertdiagschur = zeros(m,1);
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if (len > 0 & len < 5) & (norm(rhs(idx)) < tol)
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pertdiagschur(idx) = 1*ones(length(idx),1);
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schur = mexschurfun(schur,pertdiagschur);
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if (printlevel); fprintf('#'); end
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end
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end
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%%
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%%
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%%
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UU = [UU, Bmat];
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if ~isempty(EE)
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len = max(max(EE(:,1)),max(EE(:,2)));
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else
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len = 0;
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end
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tmp = [len+1,len+3,-1; len+2,len+4,1; len+3,len+1,1; len+4,len+2,-1;
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len+2,len+2,par.addschur]; %% this is the -inverse
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EE = [EE; tmp];
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ncolU = size(UU,2);
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%%
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%% assemble coefficient matrix
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%%
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if isempty(EE)
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coeff.mat22 = [];
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else
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coeff.mat22 = spconvert(EE);
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end
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coeff.mat12 = UU;
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coeff.mat11 = schur; %% important to use perturbed schur matrix
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%%
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%% pad rhs with zero vector
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%% decide which solution methods to use
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%%
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rhs = [rhs; zeros(m+ncolU-length(rhs),1)];
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if (ncolU > 300); use_LU = 1; end
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%%
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%% Cholesky factorization
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%%
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L = []; resnrm = []; xx = inf*ones(m,1);
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if (~use_LU)
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nnzmat = mexnnz(coeff.mat11);
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nnzmatdiff = (nnzmat ~= nnzmatold);
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solve_ok = 1; solvesys = 1;
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if (nnzmat > spdensity*m^2) | (m < 500)
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matfct_options = 'chol';
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else
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matfct_options = 'spchol';
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end
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if (printlevel > 2); fprintf(' %s',matfct_options); end
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L.matdim = length(schur);
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if strcmp(matfct_options,'chol')
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if issparse(schur); schur = full(schur); end;
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if (iter<=5); %%--- to fix strange anonmaly in Matlab
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schur = mexschurfun(schur,1e-20,2);
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end
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L.matfct_options = 'chol';
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[L.R,indef] = chol(schur);
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L.perm = [1:m];
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elseif strcmp(matfct_options,'spchol')
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if ~issparse(schur); schur = sparse(schur); end;
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L.matfct_options = 'spchol';
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[L.R,indef,L.perm] = chol(schur,'vector');
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L.Rt = L.R';
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end
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if (indef)
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solve_ok = -2; solvesys = 0;
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msg = 'HSDlinsysolve: Schur complement matrix not positive definite';
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if (printlevel); fprintf('\n %s',msg); end
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end
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if (solvesys)
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if (ncolU)
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tmp = coeff.mat12'*linsysolvefun(L,coeff.mat12)-coeff.mat22;
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if issparse(tmp); tmp = full(tmp); end
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[L.Ml,L.Mu,L.Mp] = lu(tmp);
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tol = 1e-16;
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condest = max(abs(diag(L.Mu)))/min(abs(diag(L.Mu)));
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idx = find(abs(diag(L.Mu)) < tol);
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if ~isempty(idx) | (condest > 1e50*sqrt(norm(par.diagAAt))); %% old: 1e30
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solvesys = 0; solve_ok = -4;
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use_LU = 1;
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msg = 'SMW too ill-conditioned, switch to LU factor';
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if (printlevel); fprintf('\n %s, %2.1e.',msg,condest); end
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end
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end
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if (solvesys)
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[xx,resnrm,solve_ok] = HSDbicgstab(coeff,rhs,L,[],[],printlevel);
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if (solve_ok<=0) & (printlevel)
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fprintf('\n warning: HSDbicgstab fails: %3.1f.',solve_ok);
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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 (m < 6000 & strcmp(matfct_options,'chol')) | ...
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(m < 1e5 & strcmp(matfct_options,'spchol'))
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use_LU = 1;
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if (printlevel); fprintf('\n switch to LU factor'); end
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end
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end
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end
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%%
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%% LU factorization
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%%
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if (use_LU)
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nnzmat = mexnnz(coeff.mat11)+mexnnz(coeff.mat12);
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nnzmatdiff = (nnzmat ~= nnzmatold);
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solve_ok = 1;
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if ~isempty(coeff.mat22)
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raugmat = [coeff.mat11, coeff.mat12; coeff.mat12', coeff.mat22];
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else
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raugmat = coeff.mat11;
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end
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if (nnzmat > spdensity*m^2) | (m+ncolU < 500)
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matfct_options = 'lu';
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else
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matfct_options = 'splu';
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end
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if (printlevel > 2); fprintf(' %s ',matfct_options); end
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L.matdim = length(raugmat);
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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.matfct_options = 'lu';
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[L.L,L.U,L.p] = lu(raugmat,'vector');
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elseif strcmp(matfct_options,'splu')
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if ~issparse(raugmat); raugmat = sparse(raugmat); end
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L.matfct_options = 'splu';
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[L.L,L.U,L.p,L.q,L.s] = lu(raugmat,'vector');
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L.s = full(diag(L.s));
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elseif strcmp(matfct_options,'ldl')
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if issparse(raugmat); raugmat = full(raugmat); end
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L.matfct_options = 'ldl';
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[L.L,L.D,L.p] = ldl(raugmat,'vector');
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L.D = sparse(L.D);
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elseif strcmp(matfct_options,'spldl')
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if ~issparse(raugmat); raugmat = sparse(raugmat); end
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L.matfct_options = 'spldl';
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[L.L,L.D,L.p,L.s] = ldl(raugmat,'vector');
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L.s = full(diag(L.s));
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L.Lt = L.L';
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end
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[xx,resnrm,solve_ok] = HSDbicgstab(coeff,rhs,L,[],[],printlevel);
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if (solve_ok<=0) & (printlevel)
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fprintf('\n warning: HSDbicgstab fails: %3.1f,',solve_ok);
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end
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end
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if (printlevel>=3); fprintf('%2.0f ',length(resnrm)-1); end
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%%
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nnzmatold = nnzmat; matfct_options_old = matfct_options;
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%%***************************************************************
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