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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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/* |
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Crude modifications and translations for Paso by Matt Davies and Lutz Gross |
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*/ |
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|
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#include "Paso.h" |
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#include "SystemMatrix.h" |
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#include "Solver.h" |
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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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/* -- Iterative template routine -- |
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* Univ. of Tennessee and Oak Ridge National Laboratory |
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* October 1, 1993 |
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* Details of this algorithm are described in "Templates for the |
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* Solution of Linear Systems: Building Blocks for Iterative |
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* Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, |
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* Eijkhout, Pozo, Romine, and van der Vorst, SIAM Publications, |
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* 1993. (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps). |
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* |
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* Purpose |
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* ======= |
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* |
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* BICGSTAB solves the linear system A*x = b using the |
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* BiConjugate Gradient Stabilized iterative method with |
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* preconditioning. |
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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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* A (input) |
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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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* RESID (input/output) DOUBLE PRECISION |
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* On input, the allowable convergence measure for |
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* norm( b - A*x ) |
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* On output, the final value of this measure. |
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* |
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* return value |
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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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err_t Paso_Solver_BiCGStab( |
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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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|
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/* Local variables */ |
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double *rtld=NULL,*p=NULL,*v=NULL,*t=NULL,*phat=NULL,*shat=NULL,*s=NULL, *buf1=NULL, *buf0=NULL; |
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double beta,norm_of_residual,sum_1,sum_2,sum_3,sum_4,norm_of_residual_global; |
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double alpha, omega, omegaNumtr, omegaDenumtr, rho, tol, rho1; |
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dim_t num_iter=0,maxit,num_iter_global; |
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dim_t i0; |
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bool_t breakFlag=FALSE, maxIterFlag=FALSE, convergeFlag=FALSE; |
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dim_t status = SOLVER_NO_ERROR; |
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double *resid = tolerance; |
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dim_t n = Paso_SystemMatrix_getTotalNumRows(A); |
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|
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/* Executable Statements */ |
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|
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/* allocate memory: */ |
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rtld=TMPMEMALLOC(n,double); |
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p=TMPMEMALLOC(n,double); |
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v=TMPMEMALLOC(n,double); |
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t=TMPMEMALLOC(n,double); |
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phat=TMPMEMALLOC(n,double); |
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shat=TMPMEMALLOC(n,double); |
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s=TMPMEMALLOC(n,double); |
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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 (rtld==NULL || p==NULL || v==NULL || t==NULL || phat==NULL || shat==NULL || s==NULL) { |
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status = SOLVER_MEMORY_ERROR; |
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} else { |
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|
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/* now bicgstab starts : */ |
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maxit = *iter; |
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tol = *resid; |
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|
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#pragma omp parallel firstprivate(maxit,tol) \ |
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private(rho,omega,num_iter,norm_of_residual,beta,alpha,rho1, convergeFlag,maxIterFlag,breakFlag) |
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{ |
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num_iter =0; |
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convergeFlag=FALSE; |
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maxIterFlag=FALSE; |
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breakFlag=FALSE; |
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|
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/* initialize arrays */ |
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|
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#pragma omp for private(i0) schedule(static) |
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for (i0 = 0; i0 < n; i0++) { |
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rtld[i0]=0; |
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p[i0]=0; |
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v[i0]=0; |
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t[i0]=0; |
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phat[i0]=0; |
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shat[i0]=0; |
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} |
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#pragma omp for private(i0) schedule(static) |
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for (i0 = 0; i0 < n; i0++) rtld[i0] = r[i0]; |
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|
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/* Perform BiConjugate Gradient Stabilized iteration. */ |
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|
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L10: |
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++(num_iter); |
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#pragma omp barrier |
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#pragma omp master |
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{ |
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sum_1 = 0; |
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sum_2 = 0; |
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sum_3 = 0; |
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sum_4 = 0; |
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omegaNumtr = 0.0; |
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omegaDenumtr = 0.0; |
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} |
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#pragma omp barrier |
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#pragma omp for private(i0) reduction(+:sum_1) schedule(static) |
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for (i0 = 0; i0 < n; i0++) sum_1 += rtld[i0] * r[i0]; |
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rho = sum_1; |
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if (! (breakFlag = (ABS(rho) <= TOLERANCE_FOR_SCALARS))) { |
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/* Compute vector P. */ |
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|
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if (num_iter > 1) { |
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beta = rho / rho1 * (alpha / omega); |
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#pragma omp for private(i0) schedule(static) |
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for (i0 = 0; i0 < n; i0++) p[i0] = r[i0] + beta * (p[i0] - omega * v[i0]); |
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} else { |
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#pragma omp for private(i0) schedule(static) |
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for (i0 = 0; i0 < n; i0++) p[i0] = r[i0]; |
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} |
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/* Compute direction adjusting vector PHAT and scalar ALPHA. */ |
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Paso_Solver_solvePreconditioner(A,&phat[0], &p[0]); |
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Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(ONE, A, &phat[0],ZERO, &v[0]); |
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|
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#pragma omp for private(i0) reduction(+:sum_2) schedule(static) |
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for (i0 = 0; i0 < n; i0++) sum_2 += rtld[i0] * v[i0]; |
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if (! (breakFlag = (ABS(sum_2) <= TOLERANCE_FOR_SCALARS))) { |
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alpha = rho / sum_2; |
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|
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#pragma omp for private(i0) reduction(+:sum_3) schedule(static) |
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for (i0 = 0; i0 < n; i0++) { |
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r[i0] -= alpha * v[i0]; |
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s[i0] = r[i0]; |
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sum_3 += s[i0] * s[i0]; |
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} |
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norm_of_residual = sqrt(sum_3); |
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|
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/* Early check for tolerance. */ |
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if ( (convergeFlag = (norm_of_residual <= tol)) ) { |
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#pragma omp for private(i0) schedule(static) |
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for (i0 = 0; i0 < n; i0++) x[i0] += alpha * phat[i0]; |
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maxIterFlag = FALSE; |
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breakFlag = FALSE; |
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} else { |
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/* Compute stabilizer vector SHAT and scalar OMEGA. */ |
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Paso_Solver_solvePreconditioner(A,&shat[0], &s[0]); |
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Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(ONE, A, &shat[0],ZERO,&t[0]); |
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|
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#pragma omp for private(i0) reduction(+:omegaNumtr,omegaDenumtr) schedule(static) |
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for (i0 = 0; i0 < n; i0++) { |
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omegaNumtr +=t[i0] * s[i0]; |
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omegaDenumtr += t[i0] * t[i0]; |
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} |
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if (! (breakFlag = (ABS(omegaDenumtr) <= TOLERANCE_FOR_SCALARS))) { |
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omega = omegaNumtr / omegaDenumtr; |
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#pragma omp for private(i0) reduction(+:sum_4) schedule(static) |
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for (i0 = 0; i0 < n; i0++) { |
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x[i0] += alpha * phat[i0] + omega * shat[i0]; |
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r[i0] -= omega * t[i0]; |
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sum_4 += r[i0] * r[i0]; |
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} |
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norm_of_residual = sqrt(sum_4); |
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convergeFlag = norm_of_residual <= tol; |
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maxIterFlag = num_iter == maxit; |
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breakFlag = (ABS(omega) <= TOLERANCE_FOR_SCALARS); |
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} |
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} |
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} |
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if (!(convergeFlag || maxIterFlag || breakFlag)) { |
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rho1 = rho; |
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goto L10; |
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} |
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} |
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/* end of iteration */ |
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#pragma omp master |
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{ |
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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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} |
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} /* end of parallel region */ |
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} |
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TMPMEMFREE(rtld); |
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TMPMEMFREE(p); |
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TMPMEMFREE(v); |
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TMPMEMFREE(t); |
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TMPMEMFREE(phat); |
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TMPMEMFREE(shat); |
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TMPMEMFREE(s); |
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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 BICGSTAB */ |
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return status; |
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} |
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