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/* $Id$ */ |
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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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/* PCG iterations */ |
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|
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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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|
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#ifdef _OPENMP |
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#include <omp.h> |
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#endif |
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|
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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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* PCG solves the linear system A*x = b using the |
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* preconditioned conjugate gradient method plus a smoother |
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* A has to be symmetric. |
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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_BREAKDOWN: If parameters rHO or OMEGA become smaller |
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* = SOLVER_MEMORY_ERROR : If parameters rHO or OMEGA become smaller |
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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_PCG( |
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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 * tolerance, |
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Paso_Performance* pp) { |
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|
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/* Local variables */ |
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dim_t num_iter=0,maxit,num_iter_global, chunk_size=-1, len,rest, n_chunks, np, ipp; |
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register double ss,ss1; |
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dim_t i0, istart, iend; |
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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 *resid = tolerance, *rs=NULL, *p=NULL, *v=NULL, *x2=NULL ; |
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double tau_old,tau,beta,delta,gamma_1,gamma_2,alpha,sum_1,sum_2,sum_3,sum_4,sum_5,tol; |
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#ifdef PASO_MPI |
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double loc_sum[2], sum[2]; |
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#endif |
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double norm_of_residual,norm_of_residual_global; |
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register double d; |
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char* chksz_chr; |
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np=omp_get_max_threads(); |
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|
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#ifdef USE_DYNAMIC_SCHEDULING |
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chksz_chr=getenv("PASO_CHUNK_SIZE_PCG"); |
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if (chksz_chr!=NULL) sscanf(chksz_chr, "%d",&chunk_size); |
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chunk_size=MIN(MAX(1,chunk_size),n/np); |
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n_chunks=n/chunk_size; |
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if (n_chunks*chunk_size<n) n_chunks+=1; |
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#else |
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len=n/np; |
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rest=n-len*np; |
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#endif |
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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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rs=TMPMEMALLOC(n,double); |
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p=TMPMEMALLOC(n,double); |
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v=TMPMEMALLOC(n,double); |
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x2=TMPMEMALLOC(n,double); |
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|
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/* Test the input parameters. */ |
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|
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if (n < 0) { |
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status = SOLVER_INPUT_ERROR; |
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} else if (rs==NULL || p==NULL || v==NULL || x2==NULL) { |
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status = SOLVER_MEMORY_ERROR; |
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} else { |
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maxit = *iter; |
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tol = *resid; |
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Performance_startMonitor(pp,PERFORMANCE_SOLVER); |
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/* initialize data */ |
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#pragma omp parallel private(i0, istart, iend, ipp) |
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{ |
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#ifdef USE_DYNAMIC_SCHEDULING |
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#pragma omp for schedule(dynamic, 1) |
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for (ipp=0; ipp < n_chunks; ++ipp) { |
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istart=chunk_size*ipp; |
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iend=MIN(istart+chunk_size,n); |
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#else |
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#pragma omp for schedule(static) |
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for (ipp=0; ipp <np; ++ipp) { |
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istart=len*ipp+MIN(ipp,rest); |
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iend=len*(ipp+1)+MIN(ipp+1,rest); |
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#endif |
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#pragma ivdep |
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for (i0=istart;i0<iend;i0++) { |
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rs[i0]=r[i0]; |
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x2[i0]=x[i0]; |
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p[i0]=0; |
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v[i0]=0; |
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} |
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#ifdef USE_DYNAMIC_SCHEDULING |
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} |
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#else |
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} |
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#endif |
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} |
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num_iter=0; |
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/* start of iteration */ |
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while (!(convergeFlag || maxIterFlag || breakFlag)) { |
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++(num_iter); |
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/* v=prec(r) */ |
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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,v,r); |
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Performance_stopMonitor(pp,PERFORMANCE_PRECONDITIONER); |
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Performance_startMonitor(pp,PERFORMANCE_SOLVER); |
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/* tau=v*r */ |
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sum_1 = 0; |
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#pragma omp parallel private(i0, istart, iend, ipp, ss) |
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{ |
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ss=0; |
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#ifdef USE_DYNAMIC_SCHEDULING |
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#pragma omp for schedule(dynamic, 1) |
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for (ipp=0; ipp < n_chunks; ++ipp) { |
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istart=chunk_size*ipp; |
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iend=MIN(istart+chunk_size,n); |
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#else |
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#pragma omp for schedule(static) |
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for (ipp=0; ipp <np; ++ipp) { |
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istart=len*ipp+MIN(ipp,rest); |
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iend=len*(ipp+1)+MIN(ipp+1,rest); |
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#endif |
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#pragma ivdep |
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for (i0=istart;i0<iend;i0++) ss+=v[i0]*r[i0]; |
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#ifdef USE_DYNAMIC_SCHEDULING |
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} |
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#else |
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} |
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#endif |
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#pragma omp critical |
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{ |
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sum_1+=ss; |
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} |
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} |
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#ifdef PASO_MPI |
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/* In case we have many MPI processes, each of which may have several OMP threads: |
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OMP master participates in an MPI reduction to get global sum_1 */ |
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loc_sum[0] = sum_1; |
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MPI_Allreduce(loc_sum, &sum_1, 1, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); |
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#endif |
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tau_old=tau; |
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tau=sum_1; |
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/* p=v+beta*p */ |
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#pragma omp parallel private(i0, istart, iend, ipp,beta) |
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{ |
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#ifdef USE_DYNAMIC_SCHEDULING |
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#pragma omp for schedule(dynamic, 1) |
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for (ipp=0; ipp < n_chunks; ++ipp) { |
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istart=chunk_size*ipp; |
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iend=MIN(istart+chunk_size,n); |
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#else |
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#pragma omp for schedule(static) |
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for (ipp=0; ipp <np; ++ipp) { |
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istart=len*ipp+MIN(ipp,rest); |
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iend=len*(ipp+1)+MIN(ipp+1,rest); |
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#endif |
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if (num_iter==1) { |
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#pragma ivdep |
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for (i0=istart;i0<iend;i0++) p[i0]=v[i0]; |
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} else { |
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beta=tau/tau_old; |
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#pragma ivdep |
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for (i0=istart;i0<iend;i0++) p[i0]=v[i0]+beta*p[i0]; |
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} |
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#ifdef USE_DYNAMIC_SCHEDULING |
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} |
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#else |
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} |
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#endif |
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} |
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/* v=A*p */ |
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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, p,ZERO,v); |
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Performance_stopMonitor(pp,PERFORMANCE_MVM); |
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Performance_startMonitor(pp,PERFORMANCE_SOLVER); |
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/* delta=p*v */ |
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sum_2 = 0; |
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#pragma omp parallel private(i0, istart, iend, ipp,ss) |
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{ |
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ss=0; |
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#ifdef USE_DYNAMIC_SCHEDULING |
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#pragma omp for schedule(dynamic, 1) |
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for (ipp=0; ipp < n_chunks; ++ipp) { |
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istart=chunk_size*ipp; |
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iend=MIN(istart+chunk_size,n); |
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#else |
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#pragma omp for schedule(static) |
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for (ipp=0; ipp <np; ++ipp) { |
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istart=len*ipp+MIN(ipp,rest); |
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iend=len*(ipp+1)+MIN(ipp+1,rest); |
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#endif |
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#pragma ivdep |
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for (i0=istart;i0<iend;i0++) ss+=v[i0]*p[i0]; |
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#ifdef USE_DYNAMIC_SCHEDULING |
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} |
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#else |
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} |
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#endif |
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#pragma omp critical |
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{ |
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sum_2+=ss; |
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} |
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} |
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#ifdef PASO_MPI |
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loc_sum[0] = sum_2; |
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MPI_Allreduce(loc_sum, &sum_2, 1, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); |
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#endif |
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delta=sum_2; |
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alpha=tau/delta; |
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|
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if (! (breakFlag = (ABS(delta) <= TOLERANCE_FOR_SCALARS))) { |
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/* smoother */ |
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sum_3 = 0; |
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sum_4 = 0; |
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#pragma omp parallel private(i0, istart, iend, ipp,d, ss, ss1) |
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{ |
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ss=0; |
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ss1=0; |
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#ifdef USE_DYNAMIC_SCHEDULING |
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#pragma omp for schedule(dynamic, 1) |
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for (ipp=0; ipp < n_chunks; ++ipp) { |
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istart=chunk_size*ipp; |
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iend=MIN(istart+chunk_size,n); |
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#else |
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#pragma omp for schedule(static) |
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for (ipp=0; ipp <np; ++ipp) { |
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istart=len*ipp+MIN(ipp,rest); |
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iend=len*(ipp+1)+MIN(ipp+1,rest); |
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#endif |
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#pragma ivdep |
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for (i0=istart;i0<iend;i0++) { |
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r[i0]-=alpha*v[i0]; |
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d=r[i0]-rs[i0]; |
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ss+=d*d; |
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ss1+=d*rs[i0]; |
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} |
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#ifdef USE_DYNAMIC_SCHEDULING |
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} |
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#else |
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} |
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#endif |
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#pragma omp critical |
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{ |
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sum_3+=ss; |
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sum_4+=ss1; |
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} |
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} |
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#ifdef PASO_MPI |
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loc_sum[0] = sum_3; |
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loc_sum[1] = sum_4; |
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MPI_Allreduce(loc_sum, sum, 2, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); |
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sum_3=sum[0]; |
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sum_4=sum[1]; |
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#endif |
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sum_5 = 0; |
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#pragma omp parallel private(i0, istart, iend, ipp, ss, gamma_1,gamma_2) |
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{ |
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gamma_1= ( (ABS(sum_3)<= ZERO) ? 0 : -sum_4/sum_3) ; |
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gamma_2= ONE-gamma_1; |
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ss=0; |
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#ifdef USE_DYNAMIC_SCHEDULING |
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#pragma omp for schedule(dynamic, 1) |
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for (ipp=0; ipp < n_chunks; ++ipp) { |
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istart=chunk_size*ipp; |
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iend=MIN(istart+chunk_size,n); |
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#else |
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#pragma omp for schedule(static) |
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for (ipp=0; ipp <np; ++ipp) { |
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istart=len*ipp+MIN(ipp,rest); |
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iend=len*(ipp+1)+MIN(ipp+1,rest); |
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#endif |
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#pragma ivdep |
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for (i0=istart;i0<iend;i0++) { |
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rs[i0]=gamma_2*rs[i0]+gamma_1*r[i0]; |
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x2[i0]+=alpha*p[i0]; |
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x[i0]=gamma_2*x[i0]+gamma_1*x2[i0]; |
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ss+=rs[i0]*rs[i0]; |
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} |
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#ifdef USE_DYNAMIC_SCHEDULING |
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} |
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#else |
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} |
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#endif |
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#pragma omp critical |
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{ |
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sum_5+=ss; |
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} |
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} |
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#ifdef PASO_MPI |
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loc_sum[0] = sum_5; |
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MPI_Allreduce(loc_sum, &sum_5, 1, MPI_DOUBLE, MPI_SUM, A->mpi_info->comm); |
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#endif |
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norm_of_residual=sqrt(sum_5); |
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convergeFlag = norm_of_residual <= tol; |
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maxIterFlag = num_iter == maxit; |
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breakFlag = (ABS(tau) <= TOLERANCE_FOR_SCALARS); |
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} |
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} |
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/* end of iteration */ |
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num_iter_global=num_iter; |
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norm_of_residual_global=norm_of_residual; |
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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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Performance_stopMonitor(pp,PERFORMANCE_SOLVER); |
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TMPMEMFREE(rs); |
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TMPMEMFREE(x2); |
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TMPMEMFREE(v); |
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TMPMEMFREE(p); |
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*iter=num_iter_global; |
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*resid=norm_of_residual_global; |
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} |
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/* End of PCG */ |
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return status; |
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} |
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