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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" )
/**
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 Iterative Refinement method.
The inner solver is passed via the preconditioner argument.
Arguments
---------
@param[in]
A magma_z_matrix
input matrix A
@param[in]
b magma_z_matrix
RHS b
@param[in,out]
x magma_z_matrix*
solution approximation
@param[in,out]
solver_par magma_z_solver_par*
solver parameters
@param[in,out]
precond_par magma_z_preconditioner*
inner solver
@param[in]
queue magma_queue_t
Queue to execute in.
@ingroup magmasparse_zgesv
********************************************************************/
extern "C" magma_int_t
magma_ziterref(
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 = MAGMA_NOTCONVERGED;
// some useful variables
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
// prepare solver feedback
solver_par->solver = Magma_ITERREF;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
magma_int_t dofs = A.num_rows*b.num_cols;
// solver variables
double nom, nom0;
// workspace
magma_z_matrix r={Magma_CSR}, z={Magma_CSR};
CHECK( magma_zvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
double residual;
CHECK( magma_zresidual( A, b, *x, &residual, queue ));
solver_par->init_res = residual;
// solver setup
magma_zscal( dofs, c_zero, x->dval, 1, queue ); // x = 0
//CHECK( magma_zresidualvec( A, b, *x, &r, nom, queue));
magma_zcopy( dofs, b.dval, 1, r.dval, 1, queue ); // r = b
nom0 = magma_dznrm2( dofs, r.dval, 1, queue ); // nom0 = || r ||
nom = nom0 * nom0;
solver_par->init_res = nom0;
if( nom0 < solver_par->atol ||
nom0/solver_par->init_res < solver_par->rtol ){
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
info = MAGMA_SUCCESS;
goto cleanup;
}
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = nom0;
solver_par->timing[0] = 0.0;
}
// start iteration
for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter;
solver_par->numiter++ ) {
magma_zscal( dofs, MAGMA_Z_MAKE(1./nom, 0.), r.dval, 1, queue ); // scale it
CHECK( magma_z_precond( A, r, &z, precond_par, queue )); // inner solver: A * z = r
magma_zscal( dofs, MAGMA_Z_MAKE(nom, 0.), z.dval, 1, queue ); // scale it
magma_zaxpy( dofs, c_one, z.dval, 1, x->dval, 1, queue ); // x = x + z
CHECK( magma_z_spmv( c_neg_one, A, *x, c_zero, r, queue )); // r = - A x
solver_par->spmv_count++;
magma_zaxpy( dofs, c_one, b.dval, 1, r.dval, 1, queue ); // r = r + b
nom = magma_dznrm2( dofs, r.dval, 1, queue ); // nom = || r ||
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) nom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
if( nom < solver_par->atol ||
nom/solver_par->init_res < solver_par->rtol ){
break;
}
}
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
CHECK( magma_zresidualvec( A, b, *x, &r, &residual, queue));
solver_par->final_res = residual;
solver_par->iter_res = nom;
if ( solver_par->numiter < solver_par->maxiter ) {
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) nom;
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->atol ||
solver_par->iter_res/solver_par->init_res < solver_par->rtol ){
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) nom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_DIVERGENCE;
}
cleanup:
magma_zmfree(&r, queue );
magma_zmfree(&z, queue );
solver_par->info = info;
return info;
} /* magma_ziterref */
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