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/*
-- MAGMA (version 2.9.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2025
@author Hartwig Anzt
@precisions normal z -> s d c
*/
#include "magmasparse_internal.h"
#define RTOLERANCE lapackf77_dlamch( "E" )
#define ATOLERANCE lapackf77_dlamch( "E" )
#define r(i) r.dval+i*dofs
#define b(i) b.dval+i*dofs
#define h(i) h.dval+i*dofs
#define p(i) p.dval+i*dofs
#define q(i) q.dval+i*dofs
/**
Purpose
-------
Solves a system of linear equations
A * X = B
where A is a complex Hermitian N-by-N positive definite matrix A.
This is a GPU implementation of the block preconditioned Conjugate
Gradient method.
Arguments
---------
@param[in]
A magma_z_matrix
input matrix A
@param[in]
b magma_z_matrix
RHS b - can be a block
@param[in,out]
x magma_z_matrix*
solution approximation
@param[in,out]
solver_par magma_z_solver_par*
solver parameters
@param[in]
precond_par magma_z_preconditioner*
preconditioner
@param[in]
queue magma_queue_t
Queue to execute in.
@ingroup magmasparse_zposv
********************************************************************/
extern "C" magma_int_t
magma_zbpcg(
magma_z_matrix A, magma_z_matrix b, magma_z_matrix *x,
magma_z_solver_par *solver_par,
magma_z_preconditioner *precond_par,
magma_queue_t queue )
{
magma_int_t info = 0;
magma_int_t i, num_vecs = b.num_rows/A.num_rows;
// prepare solver feedback
solver_par->solver = Magma_PCG;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
solver_par->info = MAGMA_SUCCESS;
// local variables
magmaDoubleComplex c_zero = MAGMA_Z_ZERO, c_one = MAGMA_Z_ONE;
magma_int_t dofs = A.num_rows;
// GPU workspace
magma_z_matrix r={Magma_CSR}, rt={Magma_CSR}, p={Magma_CSR}, q={Magma_CSR}, h={Magma_CSR};
// solver variables
magmaDoubleComplex *alpha={0}, *beta={0};
alpha = NULL;
beta = NULL;
double *nom={0}, *nom0={0}, *r0={0}, *gammaold={0}, *gammanew={0}, *den={0}, *res={0}, *residual={0}, *nomb={0};
nom = NULL;
nom0 = NULL;
r0 = NULL;
gammaold = NULL;
gammanew = NULL;
den = NULL;
res = NULL;
residual = NULL;
nomb = NULL;
CHECK( magma_zmalloc_cpu(&alpha, num_vecs));
CHECK( magma_zmalloc_cpu(&beta, num_vecs));
CHECK( magma_dmalloc_cpu(&residual, num_vecs));
CHECK( magma_dmalloc_cpu(&nom, num_vecs));
CHECK( magma_dmalloc_cpu(&nom0, num_vecs));
CHECK( magma_dmalloc_cpu(&r0, num_vecs));
CHECK( magma_dmalloc_cpu(&gammaold, num_vecs));
CHECK( magma_dmalloc_cpu(&gammanew, num_vecs));
CHECK( magma_dmalloc_cpu(&den, num_vecs));
CHECK( magma_dmalloc_cpu(&res, num_vecs));
CHECK( magma_dmalloc_cpu(&residual, num_vecs));
CHECK( magma_dmalloc_cpu(&nomb, num_vecs));
CHECK( magma_zvinit( &r, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
CHECK( magma_zvinit( &rt, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
CHECK( magma_zvinit( &p, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
CHECK( magma_zvinit( &q, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
CHECK( magma_zvinit( &h, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
// solver setup
CHECK( magma_zresidualvec( A, b, *x, &r, nom0, queue));
// preconditioner
CHECK( magma_z_applyprecond_left( MagmaNoTrans, A, r, &rt, precond_par, queue ));
CHECK( magma_z_applyprecond_right( MagmaNoTrans, A, rt, &h, precond_par, queue ));
magma_zcopy( dofs*num_vecs, h.dval, 1, p.dval, 1, queue ); // p = h
for( i=0; i<num_vecs; i++) {
nom[i] = MAGMA_Z_REAL( magma_zdotc( dofs, r(i), 1, h(i), 1, queue ) );
nom0[i] = magma_dznrm2( dofs, r(i), 1, queue );
nomb[i] = magma_dznrm2( dofs, b(i), 1, queue );
}
CHECK( magma_z_spmv( c_one, A, p, c_zero, q, queue )); // q = A p
for( i=0; i<num_vecs; i++)
den[i] = MAGMA_Z_REAL( magma_zdotc( dofs, p(i), 1, q(i), 1, queue ) ); // den = p dot q
solver_par->init_res = nom0[0];
if ( (r0[0] = nom[0] * solver_par->rtol) < ATOLERANCE )
r0[0] = ATOLERANCE;
// check positive definite
if (den[0] <= 0.0) {
printf("Operator A is not postive definite. (Ar,r) = %f\n", den[0]);
info = MAGMA_NONSPD;
goto cleanup;
}
if ( nom[0] < r0[0] ) {
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
goto cleanup;
}
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = (real_Double_t)nom0[0];
solver_par->timing[0] = 0.0;
}
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// start iteration
do
{
solver_par->numiter++;
// preconditioner
CHECK( magma_z_applyprecond_left( MagmaNoTrans, A, r, &rt, precond_par, queue ));
CHECK( magma_z_applyprecond_right( MagmaNoTrans, A, rt, &h, precond_par, queue ));
for( i=0; i<num_vecs; i++)
gammanew[i] = MAGMA_Z_REAL( magma_zdotc( dofs, r(i), 1, h(i), 1, queue ) ); // gn = < r,h>
if ( solver_par->numiter==1 ) {
magma_zcopy( dofs*num_vecs, h.dval, 1, p.dval, 1, queue ); // p = h
} else {
for( i=0; i<num_vecs; i++) {
beta[i] = MAGMA_Z_MAKE(gammanew[i]/gammaold[i], 0.); // beta = gn/go
magma_zscal( dofs, beta[i], p(i), 1, queue ); // p = beta*p
magma_zaxpy( dofs, c_one, h(i), 1, p(i), 1, queue ); // p = p + h
}
}
CHECK( magma_z_spmv( c_one, A, p, c_zero, q, queue )); // q = A p
solver_par->spmv_count++;
// magma_z_bspmv_tuned( dofs, num_vecs, c_one, A, p.dval, c_zero, q.dval, queue );
for( i=0; i<num_vecs; i++) {
den[i] = MAGMA_Z_REAL(magma_zdotc( dofs, p(i), 1, q(i), 1, queue) );
// den = p dot q
alpha[i] = MAGMA_Z_MAKE(gammanew[i]/den[i], 0.);
magma_zaxpy( dofs, alpha[i], p(i), 1, x->dval+dofs*i, 1, queue ); // x = x + alpha p
magma_zaxpy( dofs, -alpha[i], q(i), 1, r(i), 1, queue ); // r = r - alpha q
gammaold[i] = gammanew[i];
res[i] = magma_dznrm2( dofs, r(i), 1, queue );
}
if ( solver_par->verbose > 0 ) {
tempo2 = magma_sync_wtime( queue );
if ( (solver_par->numiter)%solver_par->verbose==0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res[0];
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
if ( res[0]/nom0[0] < solver_par->rtol ) {
break;
}
}
while ( solver_par->numiter+1 <= solver_par->maxiter );
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
CHECK( magma_zresidual( A, b, *x, residual, queue ));
solver_par->iter_res = res[0];
solver_par->final_res = residual[0];
if ( solver_par->numiter < solver_par->maxiter ) {
solver_par->info = MAGMA_SUCCESS;
} else if ( solver_par->init_res > solver_par->final_res ) {
if ( solver_par->verbose > 0 ) {
if ( (solver_par->numiter)%solver_par->verbose==0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res[0];
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_SLOW_CONVERGENCE;
if( solver_par->iter_res < solver_par->rtol*nomb[0] ){
info = MAGMA_SUCCESS;
}
}
else {
if ( solver_par->verbose > 0 ) {
if ( (solver_par->numiter)%solver_par->verbose==0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res[0];
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_DIVERGENCE;
}
for( i=0; i<num_vecs; i++) {
printf("%.4e ",res[i]);
}
printf("\n");
for( i=0; i<num_vecs; i++) {
printf("%.4e ",residual[i]);
}
printf("\n");
cleanup:
magma_zmfree(&r, queue );
magma_zmfree(&rt, queue );
magma_zmfree(&p, queue );
magma_zmfree(&q, queue );
magma_zmfree(&h, queue );
magma_free_cpu(alpha);
magma_free_cpu(beta);
magma_free_cpu(nom);
magma_free_cpu(nom0);
magma_free_cpu(r0);
magma_free_cpu(gammaold);
magma_free_cpu(gammanew);
magma_free_cpu(den);
magma_free_cpu(res);
magma_free_cpu(nomb);
solver_par->info = info;
return info;
} /* magma_zbpcg */
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