234 lines
8.0 KiB
Mathematica
234 lines
8.0 KiB
Mathematica
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%%***************************************************************
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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,Afree,EE,rhs);
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%%
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%% child functions: symqmr.m, mybicgstable.m, linsysolvefun.m
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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 [xx,coeff,L,resnrm] = linsysolve(par,schur,UU,Afree,EE,rhs);
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global solve_ok existspcholsymb
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global nnzmat nnzmatold matfct_options matfct_options_old use_LU
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global Lsymb
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%%global switch2LU existMA47symb
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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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if (iter==1); use_LU = 0; end
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%%if (iter==1); existMA47symb = 1; switch2LU = 0; end
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if isempty(nnzmatold); nnzmatold = 0; end
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%%
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%% schur = schur + rho*diagschur + lam*AAt
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%%
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m = length(schur);
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diagschur = max(0,full(diag(schur)));
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minrho(1) = max(1e-15, 1e-4/3.0^iter);
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minlam(1) = max(1e-10, 1e-2/2.0^iter);
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minrho(2) = max(1e-04, 1/1.5^iter);
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rho = min(minrho(1),minrho(2)*(1+norm(rhs))/(1+norm(diagschur.*par.y)));
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lam = min(minlam(1),0.1*rho*norm(diagschur)/par.normAAt);
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mexschurfun(schur,rho*diagschur);
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mexschurfun(schur,lam*par.AAt);
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fprintf(' %2.1e %2.1e ',rho,lam);
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%%
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%% old strategy
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%%
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%%diagschur = full(abs(diag(schur)));
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%%if (par.depconstr)
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%% pertdiag = 1e-15*max(1,diagschur);
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%%else
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%% pertdiag = 1e-15*max(1e-4,diagschur);
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%%end
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%%mexschurfun(schur,pertdiag);
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%%
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%% assemble coefficient matrix
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%%
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len = size(Afree,2);
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if ~isempty(EE)
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EE(:,[1 2]) = len + EE(:,[1 2]); %% adjust for ublk
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end
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EE = [(1:len)' (1:len)' zeros(len,1); EE];
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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 = [Afree, UU];
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coeff.mat11 = schur; %% important to use perturbed schur matrix
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ncolU = size(coeff.mat12,2);
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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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if strcmp(matfct_options,'chol')
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if issparse(schur); schur = full(schur); end;
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L.matfct_options = 'chol';
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L.perm = [1:m];
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if (iter<=5); %% to fix strange anonmaly in Matlab
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mexschurfun(schur,1e-20,2);
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end
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[L.L,indef] = chol(schur);
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if (indef)
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solve_ok = -2; solvesys = 0;
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fprintf('\n chol: Schur complement matrix not pos. def.');
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end
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elseif strcmp(matfct_options,'spchol')
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if ~issparse(schur), schur = sparse(schur); end;
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if (nnzmatdiff | ~strcmp(matfct_options,matfct_options_old))
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[Lsymb,flag] = symbcholfun(schur,par.cachesize);
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if (flag)
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solve_ok = -2; solvesys = 0;
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existspcholsymb = 0;
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fprintf('\n spchol: symbolic factorization fails.');
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use_LU = 1;
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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.matfct_options = 'spchol';
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L.d(find(L.skip)) = 1e20;
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if any(L.skip) & (ncolU)
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solve_ok = -3; solvesys = 0;
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existspcholsymb = 0;
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use_LU = 1;
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if (printlevel)
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fprintf('\n spchol: L.skip exists but ncolU > 0.');
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fprintf('\n switch to symmetric indefinite or LU factor.');
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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 (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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pertdiag = zeros(ncolU,1);
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tol = 1e-16;
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idx = find(abs(diag(L.Mu)) < tol);
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if ~isempty(idx); fprintf('**'); end
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end
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[xx,resnrm,solve_ok] = symqmr(coeff,rhs,L);
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if (solve_ok<=0) & (printlevel)
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fprintf('\n warning: symqmr fails: %3.1f.',solve_ok);
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end
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end
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if (solve_ok < 0)
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if (m < 5000 & strcmp(matfct_options,'chol')) | ...
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(m < 10000 & strcmp(matfct_options,'spchol'))
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use_LU = 1;
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%%switch2LU = 1;
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if (printlevel)
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fprintf('\n switch to symmetric indefinite or LU factor.');
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end
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end
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end
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end
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%%
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%% symmetric indefinite or LU factorization
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%%
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existMA47symb = 0; %% to avoid using MA47
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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; solvesys = 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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elseif (existMA47symb) & (ncolU < 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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if (printlevel>2); fprintf(' %s ',matfct_options); end
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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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L.matfct_options = 'lu';
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L.p = sparse(L.p);
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idx = find(abs(diag(L.u)) < 1e-20);
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if ~isempty(idx)
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if (printlevel); fprintf('\n lu: matrix is singular'); end
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solvesys = 0;
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end
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[ii,jj] = find(L.p); [dummy,idx] = sort(ii); L.perm = jj(idx);
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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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[Lsymb,flag] = symbMA47(raugmat);
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if (flag)
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existMA47symb = 0;
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fprintf('\n MA47: symbolic factor fails, switch to splu.');
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matfct_options = 'splu';
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else
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existMA47symb = 1;
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end
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end
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if (existMA47symb)
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[L,flag] = MA47fct(Lsymb,raugmat);
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L.matfct_options = 'MA47';
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if (flag)
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existMA47symb = 0;
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fprintf('\n MA47: solver fails, switch to splu.');
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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 = symamd(raugmat);
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end
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L.perm = Lsymb.perm;
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L.matfct_options = 'splu';
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if (par.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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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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end
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if (solvesys)
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[xx,resnrm,solve_ok] = mybicgstab(coeff,rhs,L);
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if (solve_ok<=0) & (printlevel)
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fprintf('\n warning: bicgstab 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 (printlevel>=3); fprintf(' %2.0d',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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