bvec_zcompute.c

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/**
 *
 * @file bvec_zcompute.c
 *
 *  Functions computing operations on the BCSC.
 *
 * @copyright 2004-2024 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria,
 *                      Univ. Bordeaux. All rights reserved.
 *
 * @version 6.4.0
 * @author Mathieu Faverge
 * @author Pierre Ramet
 * @author Xavier Lacoste
 * @author Gregoire Pichon
 * @author Theophile Terraz
 * @author Tony Delarue
 * @author Vincent Bridonneau
 * @date 2024-07-05
 * @generated from /builds/solverstack/pastix/bcsc/bvec_zcompute.c, normal z -> z, Tue Oct  8 14:17:55 2024
 *
 **/
#include "common.h"
#include <math.h>
#include "lapacke.h"
#include "bcsc/bcsc.h"
#include "bcsc_z.h"
#include "order/order_internal.h"
#include "frobeniusupdate.h"
#include "cblas.h"
#include "blend/solver.h"
 
#if defined(PASTIX_WITH_MPI)
void
bvec_zmpi_frb_merge( double       *dist,
                     double       *loc,
                     int          *len,
                     MPI_Datatype *dtype )
{
    assert( *len == 2 );
    frobenius_merge( dist[0], dist[1], loc, loc+1 );
    (void)len;
    (void)dtype;
}
#endif
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Compute the norm 2 of a vector. (Sequential version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          Provide information to the parallel version, to know the global
 *          context (Number of thread, barrier, ...).
 *
 * @param[in] n
 *          The size of the vector x.
 *
 * @param[in] x
 *          The vector x of size n.
 *
 *******************************************************************************
 *
 * @retval the norm 2 of x.
 *
 *******************************************************************************/
double
bvec_znrm2_seq( pastix_data_t            *pastix_data,
                pastix_int_t              n,
                const pastix_complex64_t *x )
{
    SolverMatrix  *solvmtx = pastix_data->solvmatr;
    SolverCblk    *scblk;
    pastix_bcsc_t *bcsc    = pastix_data->bcsc;
    bcsc_cblk_t   *bcblk   = bcsc->cscftab;
    pastix_int_t   cblknbr, colnbr;
    double         data[] = { 0., 1. }; /* Scale, Sum */
    double         norm;
    const double  *valptr;
    pastix_int_t   i, j;
 
    cblknbr = bcsc->cscfnbr;
    for( i = 0; i < cblknbr; i++, bcblk++ ) {
        scblk  = solvmtx->cblktab + bcblk->cblknum;
        colnbr = cblk_colnbr( scblk );
        valptr = (const double*)(x + scblk->lcolidx);
 
        for( j=0; j < colnbr; j++, valptr++ )
        {
            /* Real part */
            frobenius_update( 1, data, data + 1, valptr );
#if defined(PRECISION_z) || defined(PRECISION_c)
            /* Imaginary part */
            valptr++;
            frobenius_update( 1, data, data + 1, valptr );
#endif
        }
    }
 
#if defined(PASTIX_WITH_MPI)
    {
        MPI_Op merge;
 
        MPI_Op_create( (MPI_User_function *)bvec_zmpi_frb_merge, 1, &merge );
        MPI_Allreduce( MPI_IN_PLACE, data, 2, MPI_DOUBLE, merge, solvmtx->solv_comm );
        MPI_Op_free( &merge );
    }
#endif
 
    norm = data[0] * sqrt( data[1] );
 
    (void)n;
    return norm;
}
 
struct z_argument_nrm2_s
{
    pastix_int_t              n;
    const pastix_complex64_t *x;
    pastix_atomic_lock_t      lock;
    double                    scale;
    double                    sumsq;
};
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Compute the norm 2 of a vector. (Parallel version)
 *
 *******************************************************************************
 *
 * @param[in] ctx
 *          The context of the current thread
 *
 * @param[inout] args
 *          The parameter that providenumber of elements of x,
 *          and the vector which norm2 is to be computed, and the norm value
 *
 *******************************************************************************/
static inline void
pthread_bvec_znrm2( isched_thread_t *ctx,
                   void            *args )
{
    struct z_argument_nrm2_s *arg = (struct z_argument_nrm2_s*)args;
    pastix_int_t              n = arg->n;
    const pastix_complex64_t *x = arg->x;
    double                    scale = 0.;
    double                    sumsq = 1.;
    double                   *valptr = (double*)x;
    pastix_int_t              i, rank, size;
    pastix_int_t              begin, end;
 
    size = ctx->global_ctx->world_size;
    rank = ctx->rank;
 
    begin = (n / size) * rank;
    if (rank == (size - 1)) {
        end = n; /* One iteration more */
    } else {
        end = (n / size) * (rank + 1);
    }
 
    valptr += begin;
#if defined(PRECISION_z) || defined(PRECISION_c)
    valptr += begin;
#endif /* defined(PRECISION_z) || defined(PRECISION_c) */
 
    for( i = begin; i < end; i++, valptr++ )
    {
        frobenius_update( 1, &scale, &sumsq, valptr );
#if defined(PRECISION_z) || defined(PRECISION_c)
        valptr ++;
        frobenius_update( 1, &scale, &sumsq, valptr );
#endif
    }
 
    /* If we computed something */
    if ( scale != 0. ) {
        pastix_atomic_lock( &(arg->lock) );
        frobenius_merge( scale, sumsq, &(arg->scale), &(arg->sumsq) );
        pastix_atomic_unlock( &(arg->lock) );
    }
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Compute the norm 2 of a vector. (Parallel version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          Provide information to the parallel version, to know the global
 *          context (Number of thread, barrier, ...).
 *
 * @param[in] x
 *          The vector which norm2 is to be computed
 *
 * @param[in] n
 *          The number of elements of x
 *
 *******************************************************************************
 *
 * @return The norm 2 of the vector
 *
 *******************************************************************************/
double
bvec_znrm2_smp( pastix_data_t            *pastix_data,
                pastix_int_t              n,
                const pastix_complex64_t *x )
{
    struct z_argument_nrm2_s arg = { n, x, PASTIX_ATOMIC_UNLOCKED, 0., 1. };
    isched_parallel_call( pastix_data->isched, pthread_bvec_znrm2, &arg );
 
#if defined(PASTIX_WITH_MPI)
    {
        MPI_Op merge;
 
        MPI_Op_create( (MPI_User_function *)bvec_zmpi_frb_merge, 1, &merge );
        MPI_Allreduce( MPI_IN_PLACE, &(arg.scale), 2, MPI_DOUBLE, merge, pastix_data->solvmatr->solv_comm );
        MPI_Op_free( &merge );
    }
#endif
 
    return arg.scale * sqrt( arg.sumsq );
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Scale a vector by the scalar alpha. (Sequential version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          Provide information to the parallel version, to know the global
 *          context (Number of thread, barrier, ...).
 *
 * @param[in] n
 *          The size of the vector x.
 *
 * @param[in] alpha
 *          The scalar to scale the vector x.
 *
 * @param[inout] x
 *          The vector x to scale.
 *
 *******************************************************************************/
void
bvec_zscal_seq( pastix_data_t      *pastix_data,
                pastix_int_t        n,
                pastix_complex64_t  alpha,
                pastix_complex64_t *x )
{
#if defined(PASTIX_WITH_MPI) && 0
    SolverMatrix  *solvmtx = pastix_data->solvmatr;
    SolverCblk    *scblk   = solvmtx->cblktab;
    pastix_bcsc_t *bcsc    = pastix_data->bcsc;
    bcsc_cblk_t   *bcblk   = bcsc->cscftab;
    pastix_int_t   i, cblknbr;
 
    cblknbr = bcsc->cscfnbr;
    for( i = 0; i < cblknbr; i++, bcblk++ ) {
        scblk  = solvmtx->cblktab + bcblk->cblknum;
        n = cblk_colnbr( scblk );
 
        cblas_zscal( n, CBLAS_SADDR(alpha), x + scblk->lcolidx, 1 );
    }
#else
    (void)pastix_data;
    cblas_zscal( n, CBLAS_SADDR(alpha), x, 1 );
#endif
 
}
 
struct z_argument_scal_s
{
  pastix_int_t        n;
  pastix_complex64_t  alpha;
  pastix_complex64_t *x;
};
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Scale a vector (Parallel version)
 *
 *******************************************************************************
 *
 * @param[in] ctx
 *          The information about number of thread and rank of the actual thread
 *
 * @param[inout] args
 *          The argument providing number of elements of the vector, the scaling
 *          parameter and, and the vector to be scaled
 *
 *******************************************************************************/
static inline void
pthread_bvec_zscal( isched_thread_t *ctx,
                    void            *args )
{
    struct z_argument_scal_s *arg   = (struct z_argument_scal_s*)args;
    pastix_complex64_t       *x     = arg->x;
    pastix_int_t              n     = arg->n;
    pastix_complex64_t        alpha = arg->alpha;
    pastix_int_t              size  = ctx->global_ctx->world_size;
    pastix_int_t              rank;
    pastix_int_t              begin, end;
 
    if( x == NULL ) {
        return;
    }
 
    rank = (pastix_int_t)ctx->rank;
    begin = (n/size) * rank;
    if (rank == (size - 1)) {
        end = n;
    } else {
        end = (n/size) * (rank + 1);
    }
 
    if ( (end - begin) > 0 ) {
        cblas_zscal( end - begin, CBLAS_SADDR(alpha), x + begin, 1 );
    }
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Scale a vector (Parallel version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[in] n
 *          The number of elements of the vector
 *
 * @param[in] alpha
 *          The scaling parameter
 *
 * @param[inout] x
 *          The vector to be scaled
 *
 *******************************************************************************/
void
bvec_zscal_smp( pastix_data_t      *pastix_data,
                pastix_int_t        n,
                pastix_complex64_t  alpha,
                pastix_complex64_t *x )
{
    struct z_argument_scal_s arg = {n, alpha, x};
    isched_parallel_call( pastix_data->isched, pthread_bvec_zscal, &arg );
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Compute y <- alpha * x + y. (Sequential version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
-*
 * @param[in] n
 *          The size of the vectors.
 *
 * @param[in] alpha
 *          A scalar.
 *
 * @param[in] x
 *          The vector x.
 *
 * @param[inout] y
 *          The vector y.
 *
 *******************************************************************************/
void
bvec_zaxpy_seq( pastix_data_t            *pastix_data,
                pastix_int_t              n,
                pastix_complex64_t        alpha,
                const pastix_complex64_t *x,
                pastix_complex64_t       *y)
{
#if defined(PASTIX_WITH_MPI) && 0
    SolverMatrix  *solvmtx = pastix_data->solvmatr;
    SolverCblk    *scblk   = solvmtx->cblktab;
    pastix_bcsc_t *bcsc    = pastix_data->bcsc;
    bcsc_cblk_t   *bcblk   = bcsc->cscftab;
    pastix_int_t   i, cblknbr;
 
    cblknbr = bcsc->cscfnbr;
    for( i = 0; i < cblknbr; i++, bcblk++ ){
        scblk   = solvmtx->cblktab + bcblk->cblknum;
        n = cblk_colnbr( scblk );
 
        cblas_zaxpy( n, CBLAS_SADDR(alpha),
                     x + scblk->lcolidx, 1,
                     y + scblk->lcolidx, 1 );
    }
#else
    (void)pastix_data;
    cblas_zaxpy( n, CBLAS_SADDR(alpha), x, 1, y, 1 );
#endif
}
 
struct z_argument_axpy_s
{
    pastix_int_t              n;
    pastix_complex64_t        alpha;
    const pastix_complex64_t *x;
    pastix_complex64_t       *y;
};
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc_internal
 *
 * @brief Compute y <- alpha * x + y (Parallel version).
 *
 *******************************************************************************
 *
 * @param[in] ctx
 *          The context about the current thread
 *
 * @param[inout] args
 *          The parameter providing the size of the vectors, a scalar,
 *          the vectors x and y.
 *
 *******************************************************************************/
static inline void
pthread_bvec_zaxpy( isched_thread_t *ctx,
                    void            *args)
{
    struct z_argument_axpy_s  *arg = (struct z_argument_axpy_s*)args;
    pastix_int_t               n = arg->n;
    pastix_complex64_t         alpha = arg->alpha;
    const pastix_complex64_t  *x = arg->x;
    pastix_complex64_t        *y = arg->y;
    pastix_int_t               rank, size;
    pastix_int_t               begin, end;
 
    if( (y == NULL) || (x == NULL) ) {
        return;
    }
 
    if( alpha == (pastix_complex64_t)0.0 ) {
        return;
     }
 
    size = (pastix_int_t)ctx->global_ctx->world_size;
    rank = (pastix_int_t)ctx->rank;
 
    begin = (n/size) * rank;
    if (rank  == (size - 1)) {
        end = n;
    } else {
        end = (n/size) * (rank + 1);
    }
 
    if ( (end - begin) > 0 ) {
        cblas_zaxpy( end - begin, CBLAS_SADDR(alpha), x + begin, 1, y + begin, 1 );
    }
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Perform y = alpha * x + y (Parallel version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[in] n
 *          The number of elements of vectors x and y
 *
 * @param[in] alpha
 *          The scalar to scale x
 *
 * @param[in] x
 *          The vector to be scaled
 *
 * @param[inout] y
 *          The resulting solution
 *
 *******************************************************************************/
void
bvec_zaxpy_smp( pastix_data_t            *pastix_data,
                pastix_int_t              n,
                pastix_complex64_t        alpha,
                const pastix_complex64_t *x,
                pastix_complex64_t       *y )
{
    struct z_argument_axpy_s args = {n, alpha, x, y};
    isched_parallel_call( pastix_data->isched, pthread_bvec_zaxpy, &args );
}
 
struct z_argument_dotc_s
{
    pastix_int_t              n;
    const pastix_complex64_t *x;
    const pastix_complex64_t *y;
    pastix_atomic_lock_t      lock;
    pastix_complex64_t        sum;
};
 
#if defined(PRECISION_z) || defined(PRECISION_c)
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Compute the scalar product conj(x).y (Sequential version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[in] n
 *          The size of the vectors.
 *
 * @param[in] x
 *          The vector x.
 *
 * @param[in] y
 *          The vector y.
 *
 *******************************************************************************
 *
 * @retval the scalar product of conj(x) and y.
 *
 *******************************************************************************/
pastix_complex64_t
bvec_zdotc_seq( pastix_data_t            *pastix_data,
                pastix_int_t              n,
                const pastix_complex64_t *x,
                const pastix_complex64_t *y )
{
    SolverMatrix             *solvmtx = pastix_data->solvmatr;
    SolverCblk               *scblk   = solvmtx->cblktab;
    pastix_bcsc_t            *bcsc    = pastix_data->bcsc;
    bcsc_cblk_t              *bcblk   = bcsc->cscftab;
    pastix_int_t              i, j, cblknbr;
    const pastix_complex64_t *xptr;
    const pastix_complex64_t *yptr;
    pastix_complex64_t        r = 0.0;
 
    cblknbr = bcsc->cscfnbr;
    for( i = 0; i < cblknbr; i++, bcblk++ ) {
        scblk  = solvmtx->cblktab + bcblk->cblknum;
        n = cblk_colnbr( scblk );
 
        xptr = x + scblk->lcolidx;
        yptr = y + scblk->lcolidx;
        for( j=0; j<n; j++, xptr++, yptr++ ) {
            r += conj(*xptr) * (*yptr);
        }
    }
 
#if defined(PASTIX_WITH_MPI)
    MPI_Allreduce( MPI_IN_PLACE, &r, 1, PASTIX_MPI_COMPLEX64,
                   MPI_SUM, solvmtx->solv_comm );
#endif
 
    return r;
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc_internal
 *
 * @brief Compute the scalar product conj(x).y. (Parallel version)
 *
 *******************************************************************************
 *
 * @param[in] ctx
 *          The context of the current thread
 *
 * @param[in] args
 *          The argument provding the vectors x and y and their size.
 *
 *******************************************************************************/
static inline void
pthread_bvec_zdotc( isched_thread_t *ctx,
                    void            *args )
{
    struct z_argument_dotc_s *arg  = (struct z_argument_dotc_s*)args;
    pastix_int_t n = arg->n;
    int i;
    const pastix_complex64_t *xptr = arg->x;
    const pastix_complex64_t *yptr = arg->y;
    pastix_int_t begin, end, rank, size;
    pastix_complex64_t r = 0.0;
 
    rank = (pastix_int_t)ctx->rank;
    size = (pastix_int_t)ctx->global_ctx->world_size;
 
    begin = (n/size) * rank;
    if (rank != size - 1) {
        end = (n/size) * (rank + 1);
    } else { /*The last one computes the calcul for the rest of the sum*/
        end = n;
    }
 
    xptr += begin;
    yptr += begin;
 
    for ( i = begin; i < end; i++, xptr++, yptr++ )
    {
        r += conj(*xptr) * (*yptr);
    }
 
    if ( cabs(r) > 0. ) {
        pastix_atomic_lock( &(arg->lock) );
        arg->sum += r;
        pastix_atomic_unlock( &(arg->lock) );
    }
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Compute a scalar product between complex vectors: conj(x).y
 * (Parallel version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[in] n
 *          The number of elements of vectors x, y and r
 *
 * @param[in] y
 *          The first vector of the scalar product
 *
 * @param[in] n
 *          The second vector of the scalar product
 *
 * @param[out] r
 *          The result of the scalar product
 *
 *******************************************************************************/
pastix_complex64_t
bvec_zdotc_smp( pastix_data_t            *pastix_data,
                pastix_int_t              n,
                const pastix_complex64_t *x,
                const pastix_complex64_t *y )
{
    struct z_argument_dotc_s arg = {n, x, y, PASTIX_ATOMIC_UNLOCKED, 0.0};
    isched_parallel_call( pastix_data->isched, pthread_bvec_zdotc, &arg );
 
#if defined(PASTIX_WITH_MPI)
    MPI_Allreduce( MPI_IN_PLACE, &(arg.sum), 1, PASTIX_MPI_COMPLEX64,
                   MPI_SUM, pastix_data->solvmatr->solv_comm );
#endif
 
    return arg.sum;
}
#endif
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Compute the scalar product x.y. (Sequential version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[in] x
 *          The vector x.
 *
 * @param[in] y
 *          The vector y.
 *
 * @param[in] n
 *          The size of the vectors.
 *
 *******************************************************************************
 *
 * @retval the scalar product of x and y.
 *
 *******************************************************************************/
pastix_complex64_t
bvec_zdotu_seq( pastix_data_t            *pastix_data,
                pastix_int_t              n,
                const pastix_complex64_t *x,
                const pastix_complex64_t *y )
{
    SolverMatrix             *solvmtx = pastix_data->solvmatr;
    SolverCblk               *scblk   = solvmtx->cblktab;
    pastix_bcsc_t            *bcsc    = pastix_data->bcsc;
    bcsc_cblk_t              *bcblk   = bcsc->cscftab;
    pastix_int_t              i, j, cblknbr;
    const pastix_complex64_t *xptr;
    const pastix_complex64_t *yptr;
    pastix_complex64_t        r = 0.0;
 
    cblknbr = bcsc->cscfnbr;
    for( i = 0; i < cblknbr; i++, bcblk++ ) {
        scblk  = solvmtx->cblktab + bcblk->cblknum;
        n = cblk_colnbr( scblk );
 
        xptr = x + scblk->lcolidx;
        yptr = y + scblk->lcolidx;
        for( j=0; j<n; j++, xptr++, yptr++ ) {
            r += (*xptr) * (*yptr);
        }
    }
 
#if defined(PASTIX_WITH_MPI)
    MPI_Allreduce( MPI_IN_PLACE, &r, 1, PASTIX_MPI_COMPLEX64,
                   MPI_SUM, solvmtx->solv_comm );
#endif
 
    return r;
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc_internal
 *
 * @brief Compute the scalar product x.y. (Parallel version)
 *
 *******************************************************************************
 *
 * @param[in] ctx
 *          The context of the current thread.
 *
 * @param[in] args
 *          The argument providing the vectors x and y and their size n.
 *
 *******************************************************************************/
static inline void
pthread_bvec_zdotu( isched_thread_t *ctx,
                    void            *args )
{
    struct z_argument_dotc_s *arg = (struct z_argument_dotc_s*)args;
    int i;
    pastix_int_t              n = arg->n;
    const pastix_complex64_t *x = arg->x;
    const pastix_complex64_t *y = arg->y;
    const pastix_complex64_t *xptr;
    const pastix_complex64_t *yptr;
    pastix_complex64_t        r = 0.0;
    pastix_int_t              size, rank;
    pastix_int_t              begin, end;
 
    rank = (pastix_int_t)ctx->rank;
    size = (pastix_int_t)ctx->global_ctx->world_size;
 
    begin = (n / size) * rank;
    if ( rank == (size - 1)) {
        end = n;
    } else {
        end = (n / size) * (rank + 1);
    }
 
    xptr = x + begin;
    yptr = y + begin;
 
    for (i=begin; i<end; i++, xptr++, yptr++)
    {
        r += (*xptr) * (*yptr);
    }
 
    if ( cabs(r) > 0. ) {
        pastix_atomic_lock( &(arg->lock) );
        arg->sum += r;
        pastix_atomic_unlock( &(arg->lock) );
    }
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Compute a regular scalar product x.y (Parallel version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[in] n
 *          The number of elements of vectors x, y and r
 *
 * @param[in] x
 *          The first vector of the scalar product
 *
 * @param[in] y
 *          The second vector of the scalar product
 *
 *******************************************************************************
 *
 * @return The allocated vector
 *
 *******************************************************************************/
pastix_complex64_t
bvec_zdotu_smp( pastix_data_t            *pastix_data,
                pastix_int_t              n,
                const pastix_complex64_t *x,
                const pastix_complex64_t *y )
{
    struct z_argument_dotc_s arg = {n, x, y, PASTIX_ATOMIC_UNLOCKED, 0.0};
    isched_parallel_call( pastix_data->isched, pthread_bvec_zdotu, &arg );
 
#if defined(PASTIX_WITH_MPI)
    MPI_Allreduce( MPI_IN_PLACE, &(arg.sum), 1, PASTIX_MPI_COMPLEX64,
                   MPI_SUM, pastix_data->solvmatr->solv_comm );
#endif
 
    return arg.sum;
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Copy a vector y = x (Sequential version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[in] n
 *          The number of elements of vectors x and y
 *
 * @param[in] x
 *          The vector to be copied
 *
 * @param[inout] y
 *          The vector copy of x
 *
 *******************************************************************************/
void
bvec_zcopy_seq( pastix_data_t            *pastix_data,
                pastix_int_t              n,
                const pastix_complex64_t *x,
                pastix_complex64_t       *y )
{
#if defined(PASTIX_WITH_MPI) && 0
    SolverMatrix  *solvmtx = pastix_data->solvmatr;
    SolverCblk    *scblk   = solvmtx->cblktab;
    pastix_bcsc_t *bcsc    = pastix_data->bcsc;
    bcsc_cblk_t   *bcblk   = bcsc->cscftab;
    pastix_int_t   i, cblknbr;
 
    cblknbr = bcsc->cscfnbr;
    for( i = 0; i < cblknbr; i++, bcblk++ ) {
        scblk  = solvmtx->cblktab + bcblk->cblknum;
        n = cblk_colnbr( scblk );
 
        memcpy( y + scblk->lcolidx, x + scblk->lcolidx, n * sizeof(pastix_complex64_t) );
    }
#else
    (void)pastix_data;
    memcpy( y, x, n * sizeof(pastix_complex64_t) );
#endif
}
 
struct argument_copy_s {
    pastix_int_t              n;
    const pastix_complex64_t *x;
    pastix_complex64_t       *y;
};
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc_internal
 *
 * @brief Copy a vector y = x (parallel version)
 *
 *        Perform the coopy of x into y.
 *
 *******************************************************************************
 *
 * @param[in] ctx
 *          The context of the current thread
 *
 * @param[inout] args
 *          The argument containing the vector copy and the one to copy and their
 *          size.
 *
 *******************************************************************************/
static inline void
pthread_bvec_zcopy( isched_thread_t *ctx,
                    void            *args )
{
    struct argument_copy_s   *arg = (struct argument_copy_s*)args;
    pastix_int_t              n = arg->n;
    pastix_int_t              size, rank;
    pastix_int_t              begin, end;
 
    size = (pastix_int_t)ctx->global_ctx->world_size;
    rank = (pastix_int_t)ctx->rank;
 
    begin = (n/size) * rank;
 
    if (rank == (size - 1)) {
        end = n;
    } else {
        end = (n/size) * (rank + 1);
    }
 
    if ( (end - begin) > 0 ) {
        memcpy( arg->y + begin, arg->x + begin, (end - begin) * sizeof(pastix_complex64_t) );
    }
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Copy a vector y = x (parallel version)
 *
 *        Initialise argument for the parallel function
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[in] n
 *          The number of elements of vectors x and y
 *
 * @param[in] x
 *          The vector to be copied
 *
 * @param[inout] y
 *          The vector copy of x
 *
 *******************************************************************************/
void
bvec_zcopy_smp( pastix_data_t            *pastix_data,
                pastix_int_t              n,
                const pastix_complex64_t *x,
                pastix_complex64_t       *y )
{
    struct argument_copy_s args = {n, x, y};
    isched_parallel_call( pastix_data->isched, pthread_bvec_zcopy, &args );
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Solve A x = b with A the sparse matrix
 *
 * In Complex64 and Double precision and if mixed-precision is enabled, solve
 * SA sx = sb with SA the sparse matrix previously initialized respectively
 * in Complex32 or Float precision.
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The PaStiX data structure that describes the solver instance.
 *
 * @param[inout] b
 *          On entry, the right hand side
 *          On exit, the solution of the problem A x = b
 * @param[inout] work
 *          On entry, if mixed-precision is disabled or incompatible with the
 * sparse matrix's precision, the normal solve function is called and work must
 * be NULL. On exit, works stays NULL
 *          If mixed-precision is enabled, work must be allocated as a vector
 * half the size of b, so that the solve function can be performed in
 * in mixed-precision. On exit, work is undefined.
 *
 *******************************************************************************/
void bcsc_zspsv( pastix_data_t      *pastix_data,
                 pastix_complex64_t *b,
                 pastix_complex32_t *work )
{
    struct pastix_rhs_s rhsb = {
        .allocated  = 0,
        .flttype    = PastixComplex64,
        .m          = pastix_data->bcsc->n,
        .n          = 1,
        .ld         = pastix_data->bcsc->n,
        .b          = b,
        .cblkb      = NULL,
        .rhs_comm   = NULL,
        .Ploc2Pglob = NULL,
    };
    int rc;
 
    pastix_data->iparm[IPARM_VERBOSE]--;
 
#if defined(PRECISION_z) || defined(PRECISION_d)
    if ( pastix_data->iparm[IPARM_MIXED] )
    {
        pastix_int_t n    = rhsb.m;
        pastix_int_t nrhs = rhsb.n;
 
        rhsb.flttype = PastixComplex32;
        rhsb.b = work;
 
        /* Copying b into work at half the precision */
        rc = LAPACKE_zlag2c_work( LAPACK_COL_MAJOR, n, nrhs,
                                  b, n, work, n );
        assert( rc == 0 );
 
        pastix_subtask_solve( pastix_data, &rhsb );
 
        /* Reverting to normal precision after solving */
        rc = LAPACKE_clag2z_work( LAPACK_COL_MAJOR, n, nrhs,
                                  work, n, b, n );
        assert( rc == 0 );
    }
    else
#endif
    {
        assert(work == NULL);
        pastix_subtask_solve( pastix_data, &rhsb );
    }
 
    if ( rhsb.cblkb != NULL ) {
        free( rhsb.cblkb );
    }
    pastix_data->iparm[IPARM_VERBOSE]++;
    (void)rc;
    (void)work;
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Compute \f[ y = \alpha A x + \beta y \f] (Sequential version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[in] m
 *          The number of rows of the matrix A, and the size of y.
 *
 * @param[in] n
 *          The number of columns of the matrix A, and the size of x.
 *
 * @param[in] alpha
 *          The scalar alpha.
 *
 * @param[in] A
 *          The dense matrix A of size lda-by-n.
 *
 * @param[in] lda
 *          The leading dimension of the matrix A. lda >= max(1,m)
 *
 * @param[in] x
 *          The vector x of size n.
 *
 * @param[in] beta
 *          The scalar beta.
 *
 * @param[inout] y
 *          On entry, the initial vector y of size m.
 *          On exit, the updated vector.
 *
 *******************************************************************************/
void
bvec_zgemv_seq( pastix_data_t            *pastix_data,
                pastix_int_t              m,
                pastix_int_t              n,
                pastix_complex64_t        alpha,
                const pastix_complex64_t *A,
                pastix_int_t              lda,
                const pastix_complex64_t *x,
                pastix_complex64_t        beta,
                pastix_complex64_t       *y )
{
#if defined(PASTIX_WITH_MPI) && 0
    SolverMatrix  *solvmtx = pastix_data->solvmatr;
    SolverCblk    *scblk   = solvmtx->cblktab;
    pastix_bcsc_t *bcsc    = pastix_data->bcsc;
    bcsc_cblk_t   *bcblk   = bcsc->cscftab;
    pastix_int_t   i, cblknbr;
 
    cblknbr = bcsc->cscfnbr;
    for( i = 0; i < cblknbr; i++, bcblk++ ) {
        scblk  = solvmtx->cblktab + bcblk->cblknum;
        m = cblk_colnbr( scblk );
 
        cblas_zgemv( CblasColMajor, CblasNoTrans, m, n,
                     CBLAS_SADDR(alpha), A + scblk->lcolidx, lda, x, 1,
                     CBLAS_SADDR(beta), y + scblk->lcolidx, 1 );
    }
#else
    (void)pastix_data;
    cblas_zgemv( CblasColMajor, CblasNoTrans, m, n,
                 CBLAS_SADDR(alpha), A, lda, x, 1,
                 CBLAS_SADDR(beta), y, 1 );
#endif
 
}
 
struct z_gemv_s
{
    pastix_int_t              m;
    pastix_int_t              n;
    pastix_complex64_t        alpha;
    const pastix_complex64_t *A;
    pastix_int_t              lda;
    const pastix_complex64_t *x;
    pastix_complex64_t        beta;
    pastix_complex64_t       *y;
};
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc_internal
 *
 * @brief Compute \f[ y = \alpha A x + \beta y \f] (Parallel version)
 *
 *        This is the function called by bvec_zgemv_smp to perform gemv
 *        (Parallel version)
 *
 *******************************************************************************
 *
 * @param[in] ctx
 *          Information about number of thread and rank of current thread.
 *
 * @param[inout] args
 *          The number of rows (m) and columns (n) of the matrix A, vecteors y
 *          (size m) and x (size n), scalars alpha and beta. The dense matrix A
 *          of size lda-by-n, and its leading dimension lda >= max(1,m), and
 *          the vector x of size n. The result is stored in y.
 *
 *******************************************************************************/
static inline void
pthread_bvec_zgemv( isched_thread_t *ctx,
                    void            *args )
{
    struct z_gemv_s          *arg   = (struct z_gemv_s*)args;
    pastix_int_t              m     = arg->m;
    pastix_int_t              sub_m;
    pastix_int_t              n     = arg->n;
    pastix_complex64_t        alpha = arg->alpha;
    const pastix_complex64_t *A     = arg->A;
    const pastix_complex64_t *Aptr;
    pastix_int_t              lda   = arg->lda;
    const pastix_complex64_t *x     = arg->x;
    const pastix_complex64_t *xptr;
    pastix_complex64_t        beta  = arg->beta;
    pastix_complex64_t       *y     = arg->y;
    pastix_complex64_t       *yptr;
    pastix_int_t              size, rank;
 
    size = (pastix_int_t)ctx->global_ctx->world_size;
    rank = (pastix_int_t)ctx->rank;
 
    sub_m = (m / size);
 
    /* Subdivision of A */
    Aptr = A + sub_m * rank;
 
    xptr = x;
    yptr = y + sub_m * rank;
 
    if (rank == (size - 1)) {
        sub_m += m % size; /* Last thread has to do more tasks */
    }
 
    if ( sub_m > 0 ) {
        cblas_zgemv( CblasColMajor, CblasNoTrans, sub_m, n,
                     CBLAS_SADDR(alpha), Aptr, lda, xptr, 1,
                     CBLAS_SADDR(beta), yptr, 1 );
    }
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Compute \f[ y = \alpha A x + \beta y \f] (Parallel version)
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[in] m
 *          The number of rows of the matrix A, and the size of y.
 *
 * @param[in] n
 *          The number of columns of the matrix A, and the size of x.
 *
 * @param[in] alpha
 *          The scalar alpha.
 *
 * @param[in] A
 *          The dense matrix A of size lda-by-n.
 *
 * @param[in] lda
 *          The leading dimension of the matrix A. lda >= max(1,m)
 *
 * @param[in] x
 *          The vector x of size n.
 *
 * @param[in] beta
 *          The scalar beta.
 *
 * @param[inout] y
 *          On entry, the initial vector y of size m.
 *          On exit, the updated vector.
 *
 *******************************************************************************/
void
bvec_zgemv_smp( pastix_data_t            *pastix_data,
                pastix_int_t              m,
                pastix_int_t              n,
                pastix_complex64_t        alpha,
                const pastix_complex64_t *A,
                pastix_int_t              lda,
                const pastix_complex64_t *x,
                pastix_complex64_t        beta,
                pastix_complex64_t       *y )
{
    struct z_gemv_s arg = {m, n, alpha, A, lda, x, beta, y};
 
    isched_parallel_call( pastix_data->isched, pthread_bvec_zgemv, &arg );
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Set to 0 remote coefficients
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[inout] y
 *          On entry, the initial vector y of size m.
 *          On exit, the y vector with remote section set to 0.
 *
 *******************************************************************************/
void
bvec_znullify_remote( const pastix_data_t *pastix_data,
                      pastix_complex64_t  *y )
{
#if defined( PASTIX_WITH_MPI )
    const SolverMatrix *solvmtx = pastix_data->solvmatr;
    const SolverCblk   *cblk = solvmtx->cblktab;
    pastix_int_t        cblknbr;
    pastix_int_t        i, lastindex = 0;
    pastix_int_t        n = pastix_data->csc->gNexp;
 
    cblknbr = solvmtx->cblknbr;
    for ( i = 0; i < cblknbr; i++, cblk++ ) {
        if ( cblk->cblktype & (CBLK_FANIN|CBLK_RECV) ) {
            continue;
        }
 
        if ( cblk->fcolnum != lastindex ) {
            /* Set to 0 all remote data bewtween previous local cblk, and current cblk */
            memset(
                y + lastindex, 0, ( cblk->fcolnum - lastindex ) * sizeof( pastix_complex64_t ) );
        }
        lastindex = cblk->lcolnum + 1;
    }
 
    if ( lastindex < n ) {
        /* Set to 0 all remote data bewtween previous local cblk, and current cblk */
        memset( y + lastindex, 0, ( n - lastindex ) * sizeof( pastix_complex64_t ) );
    }
#endif
    (void)pastix_data;
    (void)y;
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Gather a distributed right hand side (bvec storage) on all nodes.
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[inout] y
 *          On entry, the local portion of the vector y.
 *          On exit, the complete vector y.
 *
 *******************************************************************************
 *
 * @retval TODO
 *
 *******************************************************************************/
const pastix_complex64_t *
bvec_zgather_remote( const pastix_data_t      *pastix_data,
                     const pastix_complex64_t *y )
{
#if defined( PASTIX_WITH_MPI )
    const SolverMatrix       *solvmtx = pastix_data->solvmatr;
    const SolverCblk         *cblk    = solvmtx->cblktab;
    pastix_complex64_t       *yglobal = NULL;
    pastix_complex64_t       *yto, *ytmp;
    const pastix_complex64_t *yfr;
    pastix_int_t              c, i, cblki, cblknbr;
    MPI_Request               request_c = MPI_REQUEST_NULL;
    MPI_Request               request_n = MPI_REQUEST_NULL;
    pastix_int_t             *all_n, *all_cblknbr, *indices;
    pastix_int_t              max_n       = 0;
    pastix_int_t              max_cblknbr = 0;
    pastix_int_t              gn = pastix_data->bcsc->gN;
    pastix_int_t              ln = pastix_data->bcsc->n;
    pastix_int_t              lcblknbr, colnbr;
 
    if ( ln != 0 ) {
        yglobal = malloc( gn * sizeof(pastix_complex64_t) );
#if !defined(NDEBUG)
        memset( yglobal, 0xff, gn * sizeof(pastix_complex64_t) );
#endif
    }
    all_n       = malloc( pastix_data->procnbr * sizeof(pastix_int_t) );
    all_cblknbr = malloc( pastix_data->procnbr * sizeof(pastix_int_t) );
 
    MPI_Allgather( &ln, 1, PASTIX_MPI_INT,
                   all_n, 1, PASTIX_MPI_INT, pastix_data->pastix_comm );
    lcblknbr = solvmtx->cblknbr - solvmtx->faninnbr - solvmtx->recvnbr;
    MPI_Allgather( &lcblknbr, 1, PASTIX_MPI_INT,
                   all_cblknbr, 1, PASTIX_MPI_INT, pastix_data->pastix_comm );
 
    for( c=0; c<pastix_data->procnbr; c++ )
    {
        max_n       = pastix_imax( max_n,       all_n[c]       );
        max_cblknbr = pastix_imax( max_cblknbr, all_cblknbr[c] );
    }
 
    ytmp    = malloc( max_n * sizeof(pastix_complex64_t) );
    indices = malloc( max_cblknbr * 2 * sizeof(pastix_int_t) );
 
    for( c=0; c<pastix_data->procnbr; c++ )
    {
        if ( all_n[c] == 0 ) {
            continue;
        }
 
        if ( c == pastix_data->procnum ) {
            MPI_Ibcast( (pastix_complex64_t*)y, ln, PASTIX_MPI_COMPLEX64, c, pastix_data->pastix_comm, &request_n );
 
            cblknbr = solvmtx->cblknbr;
            cblk    = solvmtx->cblktab;
            cblki   = 0;
            for ( i = 0; i < cblknbr; i++, cblk++ ) {
                if ( cblk->cblktype & (CBLK_FANIN|CBLK_RECV) ) {
                    continue;
                }
 
                yfr = y       + cblk->lcolidx;
                yto = yglobal + cblk->fcolnum;
 
                memcpy( yto, yfr, cblk_colnbr( cblk ) * sizeof( pastix_complex64_t ) );
 
                indices[ 2*cblki   ] = cblk->fcolnum;
                indices[ 2*cblki+1 ] = cblk->lcolnum;
                cblki++;
            }
            assert( cblki == lcblknbr );
 
            MPI_Ibcast( indices, 2 * lcblknbr, PASTIX_MPI_INT, c, pastix_data->pastix_comm, &request_c );
            MPI_Wait( &request_n, MPI_STATUS_IGNORE );
            MPI_Wait( &request_c, MPI_STATUS_IGNORE );
        }
        else {
            MPI_Ibcast( ytmp, all_n[c], PASTIX_MPI_COMPLEX64, c, pastix_data->pastix_comm, &request_n );
            MPI_Ibcast( indices, all_cblknbr[c] * 2, PASTIX_MPI_INT, c, pastix_data->pastix_comm, &request_c );
            MPI_Wait( &request_n, MPI_STATUS_IGNORE );
            MPI_Wait( &request_c, MPI_STATUS_IGNORE );
 
            /* If ln = 0, there are no local computation so no need to store in yglobal */
            if ( ln != 0 ) {
                yfr = ytmp;
                for ( i = 0; i < all_cblknbr[c]; i++ ) {
                    yto = yglobal + indices[2*i];
 
                    colnbr = indices[2*i+1] - indices[2*i] + 1;
                    memcpy( yto, yfr, colnbr * sizeof( pastix_complex64_t ) );
 
                    yfr += colnbr;
                }
            }
        }
    }
 
    free( all_n );
    free( all_cblknbr );
    free( ytmp );
    free( indices );
 
    return yglobal;
#else
    (void)pastix_data;
    return y;
#endif
}
 
/**
 *******************************************************************************
 *
 * @ingroup bcsc
 *
 * @brief Apply an all reduce of the vector on all nodes
 *
 *******************************************************************************
 *
 * @param[in] pastix_data
 *          The information about sequential and parallel version (Number of
 *          thread, ...).
 *
 * @param[inout] y
 *          On entry, the initial vector y of size m.
 *          On exit, the y vector with remote section set to 0.
 *
 *******************************************************************************/
void
bvec_zallreduce( const pastix_data_t *pastix_data,
                 pastix_complex64_t  *y )
{
#if defined( PASTIX_WITH_MPI )
    /* Reduce the partial sums on all nodes */
    MPI_Allreduce( MPI_IN_PLACE,
                   y, pastix_data->csc->gNexp,
                   PASTIX_MPI_COMPLEX64, MPI_SUM,
                   pastix_data->inter_node_comm );
#endif
    (void)pastix_data;
    (void)y;
}