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/******************************************************* |
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* |
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* Copyright 2003-2007 by ACceSS MNRF |
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* Copyright 2007 by University of Queensland |
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* |
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* http://esscc.uq.edu.au |
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* Primary Business: Queensland, Australia |
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* Licensed under the Open Software License version 3.0 |
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* http://www.opensource.org/licenses/osl-3.0.php |
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* |
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*******************************************************/ |
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|
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/* TFQMR iterations */ |
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#include "SystemMatrix.h" |
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#include "Paso.h" |
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#include "Solver.h" |
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#include "PasoUtil.h" |
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#ifdef _OPENMP |
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#include <omp.h> |
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#endif |
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#ifdef PASO_MPI |
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#include <mpi.h> |
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#endif |
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|
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/* |
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* |
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* Purpose |
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* ======= |
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* |
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* MINRES solves the linear system A*x = b |
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* |
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* Convergence test: norm( b - A*x )< TOL. |
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* For other measures, see the above reference. |
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* |
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* Arguments |
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* ========= |
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* |
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* r (input) DOUBLE PRECISION array, dimension N. |
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* On entry, residual of inital guess x |
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* |
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* x (input/output) DOUBLE PRECISION array, dimension N. |
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* On input, the initial guess. |
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* |
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* ITER (input/output) INT |
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* On input, the maximum iterations to be performed. |
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* On output, actual number of iterations performed. |
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* |
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* INFO (output) INT |
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* |
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* = SOLVER_NO_ERROR: Successful exit. Iterated approximate solution returned. |
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* = SOLVER_MAXITER_REACHED |
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* = SOLVER_INPUT_ERROR Illegal parameter: |
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* = SOLVER_MEMORY_ERROR : |
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* = SOLVER_NEGATIVE_NORM_ERROR : |
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* |
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* ============================================================== |
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*/ |
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|
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/* #define PASO_DYNAMIC_SCHEDULING_MVM */ |
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|
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#if defined PASO_DYNAMIC_SCHEDULING_MVM && defined __OPENMP |
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#define USE_DYNAMIC_SCHEDULING |
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#endif |
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|
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err_t Paso_Solver_MINRES( |
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Paso_SystemMatrix * A, |
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double * r, |
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double * x, |
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dim_t *iter, |
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double *tol, |
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double * tolerance, |
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Paso_Performance* pp) { |
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|
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/* Local variables */ |
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|
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dim_t num_iter=0,maxit; |
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bool_t breakFlag=FALSE, maxIterFlag=FALSE, convergeFlag=FALSE; |
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err_t status = SOLVER_NO_ERROR; |
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dim_t n = Paso_SystemMatrix_getTotalNumRows(A); |
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double *w=NULL, *w1=NULL, *w2=NULL, *r1=NULL, *r2=NULL, *y=NULL, *v=NULL; |
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|
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double Anorm,ynorm,oldb,dbar,epsln,phibar,rhs1,rhs2,rnorm,tnorm2,ynorm2,cs,sn,eps,s,alfa,denom,z,beta1,beta; |
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double gmax,gmin,oldeps,delta,gbar,gamma,phi; |
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double norm_of_residual; |
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|
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/* */ |
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/*-----------------------------------------------------------------*/ |
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/* */ |
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/* Start of Calculation : */ |
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/* --------------------- */ |
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/* */ |
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/* */ |
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w=TMPMEMALLOC(n,double); |
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w1=TMPMEMALLOC(n,double); |
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w2=TMPMEMALLOC(n,double); |
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r1=TMPMEMALLOC(n,double); |
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r2=TMPMEMALLOC(n,double); |
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y=TMPMEMALLOC(n,double); |
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v=TMPMEMALLOC(n,double); |
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|
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if (w ==NULL || w1== NULL || w2== NULL || r1 == NULL || r2== NULL || y==NULL || v==NULL ) { |
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status=SOLVER_MEMORY_ERROR; |
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} |
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maxit = *iter; |
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/* Test the input parameters. */ |
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if (n < 0 || maxit<=0 ) { |
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status=SOLVER_INPUT_ERROR; |
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} |
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Paso_Copy(n,r1,r); |
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Performance_startMonitor(pp,PERFORMANCE_PRECONDITIONER); |
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Paso_Solver_solvePreconditioner(A,y,r1); |
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Performance_stopMonitor(pp,PERFORMANCE_PRECONDITIONER); |
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beta1=Paso_InnerProduct(n,r1,y,A->mpi_info); |
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if (beta1<0) { |
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status=SOLVER_NEGATIVE_NORM_ERROR; |
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} |
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if (beta1>0) { |
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beta1=sqrt(beta1); |
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} |
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Performance_startMonitor(pp,PERFORMANCE_SOLVER); |
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|
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Paso_zeroes(n,w); |
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Paso_zeroes(n,w2); |
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Paso_Copy(n,r2,r1); |
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Anorm = 0; |
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ynorm = 0; |
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oldb = 0; |
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beta = beta1; |
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dbar = 0; |
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epsln = 0; |
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phibar = beta1; |
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rhs1 = beta1; |
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rhs2 = 0; |
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rnorm = phibar; |
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tnorm2 = 0; |
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ynorm2 = 0; |
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cs = -1; |
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sn = 0; |
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eps = 0.0001; |
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|
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while (!(convergeFlag || maxIterFlag || breakFlag || (status !=SOLVER_NO_ERROR) )) |
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{ |
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s=1/beta; |
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Paso_Update(n, 0., v, s, y); |
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Performance_stopMonitor(pp,PERFORMANCE_SOLVER); |
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Performance_startMonitor(pp,PERFORMANCE_MVM); |
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Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(ONE, A, v,ZERO,y); |
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Performance_stopMonitor(pp,PERFORMANCE_MVM); |
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Performance_startMonitor(pp,PERFORMANCE_SOLVER); |
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if (num_iter >= 1) { |
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Paso_Update(n, 1., y, -(beta/oldb), r1); |
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} |
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alfa = Paso_InnerProduct(n,v,y,A->mpi_info); |
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Paso_Update(n, 1., y, -(alfa/beta), r2); |
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Paso_Copy(n,r1,r2); |
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Paso_Copy(n,r2,y); |
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Performance_stopMonitor(pp,PERFORMANCE_SOLVER); |
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Performance_startMonitor(pp,PERFORMANCE_PRECONDITIONER); |
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Paso_Solver_solvePreconditioner(A,y,r2); |
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Performance_stopMonitor(pp,PERFORMANCE_PRECONDITIONER); |
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Performance_startMonitor(pp,PERFORMANCE_SOLVER); |
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oldb = beta; |
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beta = Paso_InnerProduct(n,y,r2,A->mpi_info); |
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if (beta<0) { |
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status=SOLVER_NEGATIVE_NORM_ERROR; |
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} |
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beta = sqrt( beta ); |
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tnorm2 = tnorm2 + alfa*alfa + oldb*oldb + beta*beta; |
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if (num_iter==0) { |
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gmax = ABS(alfa); |
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gmin = gmax; |
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} |
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/* Apply previous rotation Qk-1 to get |
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[deltak epslnk+1] = [cs sn][dbark 0 ] |
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[gbar k dbar k+1] [sn -cs][alfak betak+1]. */ |
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oldeps = epsln; |
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delta = cs * dbar + sn * alfa ; |
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gbar = sn * dbar - cs * alfa ; |
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epsln = sn * beta ; |
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dbar = - cs * beta; |
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gamma = sqrt(gbar*gbar+beta*beta) ; |
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gamma = MAX(gamma,eps) ; |
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cs = gbar / gamma ; |
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sn = beta / gamma ; |
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phi = cs * phibar ; |
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phibar = sn * phibar ; |
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/* Update x. */ |
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denom = 1/gamma ; |
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Paso_Copy(n,w1,w2); |
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Paso_Copy(n,w2,w); |
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Paso_LinearCombination(n,w,denom,v,-(denom*oldeps),w1); |
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Paso_Update(n, 1., w, -(delta*denom), w2) ; |
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Paso_Update(n, 1., x, phi, w) ; |
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/* Go round again. */ |
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gmax = MAX(gmax,gamma); |
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gmin = MIN(gmin,gamma); |
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z = rhs1 / gamma; |
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ynorm2 = z*z + ynorm2; |
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rhs1 = rhs2 - delta*z; |
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rhs2 = - epsln*z; |
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Anorm = sqrt( tnorm2 ) ; |
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ynorm = sqrt( ynorm2 ) ; |
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rnorm = phibar; |
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maxIterFlag = (num_iter > maxit); |
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norm_of_residual=rnorm; |
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convergeFlag=(norm_of_residual<Anorm*ynorm*(*tolerance)); |
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if (maxIterFlag) { |
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status = SOLVER_MAXITER_REACHED; |
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} else if (breakFlag) { |
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status = SOLVER_BREAKDOWN; |
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} |
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++(num_iter); |
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/*printf("residual norm %.10f < %.10f %.10f %.10f \n",rnorm,Anorm*ynorm*(*tolerance), Anorm*ynorm, (*tolerance));*/ |
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} |
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/* end of iteration */ |
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Performance_stopMonitor(pp,PERFORMANCE_SOLVER); |
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TMPMEMFREE(w); |
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TMPMEMFREE(w1); |
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TMPMEMFREE(w2); |
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TMPMEMFREE(r1); |
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TMPMEMFREE(r2); |
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TMPMEMFREE(y); |
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TMPMEMFREE(v); |
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*iter=num_iter; |
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*tol=norm_of_residual; |
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|
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/* End of MINRES */ |
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return status; |
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} |
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