core_zpxtrfsp.c

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/**
 *
 * @file core_zpxtrfsp.c
 *
 * PaStiX kernel routines for LL^t factorization.
 *
 * @copyright 2011-2023 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria,
 *                      Univ. Bordeaux. All rights reserved.
 *
 * @version 6.3.1
 * @author Mathieu Faverge
 * @author Pierre Ramet
 * @author Xavier Lacoste
 * @date 2023-10-23
 * @generated from /builds/solverstack/pastix/kernels/core_zpxtrfsp.c, normal z -> z, Thu Nov 23 09:55:47 2023
 *
 **/
#include "common.h"
#include "cblas.h"
#include "blend/solver.h"
#include "pastix_zcores.h"
#include "kernels_trace.h"
 
#ifndef DOXYGEN_SHOULD_SKIP_THIS
#define MAXSIZEOFBLOCKS 64
static pastix_complex64_t zone  =  1.0;
static pastix_complex64_t mzone = -1.0;
#endif /* DOXYGEN_SHOULD_SKIP_THIS */
 
/**
 *******************************************************************************
 *
 * @ingroup kernel_blas_lapack_null
 *
 * @brief Compute the sequential static pivoting LL^t factorization of the
 * matrix n-by-n A = L * L^t .
 *
 *******************************************************************************
 *
 * @param[in] n
 *          The number of rows and columns of the matrix A.
 *
 * @param[inout] A
 *          The matrix A to factorize with LL^t factorization. The matrix
 *          is of size lda -by- n.
 *
 * @param[in] lda
 *          The leading dimension of the matrix A.
 *
 * @param[inout] nbpivots
 *          Pointer to the number of piovting operations made during
 *          factorization. It is updated during this call
 *
 * @param[in] criterion
 *          Threshold use for static pivoting. If diagonal value is under this
 *          threshold, its value is replaced by the threshold and the number of
 *          pivots is incremented.
 *
 *******************************************************************************
 *
 * @warning This routine will fail if it discovers a null or negative value on
 *          the diagonal during factorization.
 *
 *******************************************************************************/
static inline void
core_zpxtf2sp( pastix_int_t        n,
               pastix_complex64_t *A,
               pastix_int_t        lda,
               pastix_int_t       *nbpivots,
               double              criterion )
{
    pastix_int_t k;
    pastix_complex64_t *Akk = A;   /* A [k  ][k] */
    pastix_complex64_t *Amk = A+1; /* A [k+1][k] */
    pastix_complex64_t  alpha;
 
    for (k=0; k<n; k++){
        if ( cabs(*Akk) < criterion ) {
            (*Akk) = (pastix_complex64_t)criterion;
            (*nbpivots)++;
        }
 
        *Akk = csqrt(*Akk);
        alpha = 1.0 / (*Akk);
 
        /* Scale the diagonal to compute L((k+1):n,k) */
        cblas_zscal(n-k-1, CBLAS_SADDR( alpha ), Amk, 1 );
 
        /* Move to next Akk */
        Akk += (lda+1);
 
        cblas_zsyrk( CblasColMajor, CblasLower, CblasNoTrans,
                     n-k-1, 1,
                     CBLAS_SADDR( mzone ), Amk, lda,
                     CBLAS_SADDR(  zone ), Akk, lda );
 
        /* Move to next Amk */
        Amk = Akk+1;
    }
}
 
/**
 *******************************************************************************
 *
 * @brief Compute the block static pivoting LL^t factorization of the matrix
 * n-by-n A = L * L^t .
 *
 *******************************************************************************
 *
 * @param[in] n
 *          The number of rows and columns of the matrix A.
 *
 * @param[inout] A
 *          The matrix A to factorize with LL^t factorization. The matrix
 *          is of size lda -by- n.
 *
 * @param[in] lda
 *          The leading dimension of the matrix A.
 *
 * @param[inout] nbpivots
 *          Pointer to the number of piovting operations made during
 *          factorization. It is updated during this call
 *
 * @param[in] criterion
 *          Threshold use for static pivoting. If diagonal value is under this
 *          threshold, its value is replaced by the threshold and the nu,ber of
 *          pivots is incremented.
 *
 *******************************************************************************
 *
 * @warning This routine will fail if it discovers a null or negative value on
 *          the diagonal during factorization.
 *
 *******************************************************************************/
void
core_zpxtrfsp( pastix_int_t        n,
               pastix_complex64_t *A,
               pastix_int_t        lda,
               pastix_int_t       *nbpivots,
               double              criterion )
{
    pastix_int_t k, blocknbr, blocksize, matrixsize;
    pastix_complex64_t *tmp,*tmp1,*tmp2;
 
    /* diagonal supernode is divided into MAXSIZEOFBLOCK-by-MAXSIZEOFBLOCKS blocks */
    blocknbr = pastix_iceil( n, MAXSIZEOFBLOCKS );
 
    for (k=0; k<blocknbr; k++) {
 
        blocksize = pastix_imin(MAXSIZEOFBLOCKS, n-k*MAXSIZEOFBLOCKS);
        tmp  = A+(k*MAXSIZEOFBLOCKS)*(lda+1);      /* Lk,k     */
 
        /* Factorize the diagonal block Akk*/
        core_zpxtf2sp(blocksize, tmp, lda, nbpivots, criterion);
 
        if ((k*MAXSIZEOFBLOCKS+blocksize) < n) {
 
            tmp1 = tmp  + blocksize;       /* Lk+1,k   */
            tmp2 = tmp1 + blocksize * lda; /* Lk+1,k+1 */
 
            matrixsize = n-(k*MAXSIZEOFBLOCKS+blocksize);
 
            /* Compute the column L(k+1:n,k) = (L(k,k)D(k,k))^{-1}A(k+1:n,k)    */
            /* 1) Compute A(k+1:n,k) = A(k+1:n,k)L(k,k)^{-T} = D(k,k)L(k+1:n,k) */
                        /* input: L(k,k) in tmp, A(k+1:n,k) in tmp1   */
                        /* output: A(k+1:n,k) in tmp1                 */
            cblas_ztrsm(CblasColMajor,
                        CblasRight, CblasLower,
                        CblasTrans, CblasNonUnit,
                        matrixsize, blocksize,
                        CBLAS_SADDR(zone), tmp,  lda,
                                           tmp1, lda);
 
            /* Update Ak+1k+1 = Ak+1k+1 - Lk+1k * Lk+1kT */
            cblas_zsyrk(CblasColMajor, CblasLower, CblasNoTrans,
                        matrixsize, blocksize,
                        CBLAS_SADDR( mzone ), tmp1, lda,
                        CBLAS_SADDR(  zone ), tmp2, lda);
        }
    }
}
 
/**
 *******************************************************************************
 *
 * @brief Compute the LL^t factorization of the diagonal block in a panel.
 *
 * @warning This routine will fail if it discovers a null or negative value on
 *          the diagonal during factorization.
 *
 *******************************************************************************
 *
 * @param[in] solvmtx
 *          Solver Matrix structure of the problem
 *
 * @param[in] cblk
 *          Pointer to the structure representing the panel to factorize in the
 *          cblktab array.  Next column blok must be accessible through cblk[1].
 *
 * @param[inout] dataL
 *          The pointer to the correct representation of the lower part of the data.
 *          - coeftab if the block is in full rank. Must be of size cblk.stride -by- cblk.width.
 *          - pastix_lr_block if the block is compressed.
 *
 *******************************************************************************
 *
 * @return The number of static pivoting performed during the diagonal block
 *         factorization.
 *
 *******************************************************************************/
int
cpucblk_zpxtrfsp1d_pxtrf( SolverMatrix *solvmtx,
                          SolverCblk   *cblk,
                          void         *dataL )
{
    pastix_int_t  ncols, stride;
    pastix_int_t  nbpivots = 0;
    pastix_fixdbl_t time, flops;
    pastix_complex64_t *L;
    pastix_lrblock_t *lrL;
    double criterion = solvmtx->diagthreshold;
 
    time = kernel_trace_start( PastixKernelPXTRF );
 
    ncols   = cblk->lcolnum - cblk->fcolnum + 1;
    stride  = (cblk->cblktype & CBLK_LAYOUT_2D) ? ncols : cblk->stride;
 
    /* check if diagonal column block */
    assert( cblk->fcolnum == cblk->fblokptr->frownum );
    assert( cblk->lcolnum == cblk->fblokptr->lrownum );
 
    if ( cblk->cblktype & CBLK_COMPRESSED ) {
        /* dataL is a LRblock */
        lrL = (pastix_lrblock_t *)dataL;
        L   = lrL->u;
        stride = ncols;
 
        assert( lrL->rk == -1 );
        assert( stride == lrL->rkmax );
    } else {
        L = (pastix_complex64_t *)dataL;
    }
 
    /* Factorize diagonal block */
    flops = FLOPS_ZPOTRF( ncols );
    kernel_trace_start_lvl2( PastixKernelLvl2PXTRF );
    core_zpxtrfsp(ncols, L, stride, &nbpivots, criterion );
    kernel_trace_stop_lvl2( flops );
 
    kernel_trace_stop( cblk->fblokptr->inlast, PastixKernelPXTRF, ncols, 0, 0, flops, time );
 
    if ( nbpivots ) {
        pastix_atomic_add_32b( &(solvmtx->nbpivots), nbpivots );
    }
    return nbpivots;
}
 
/**
 *******************************************************************************
 *
 * @brief Compute the LL^t factorization of one panel.
 *
 *******************************************************************************
 *
 * @param[in] solvmtx
 *          Solver Matrix structure of the problem
 *
 * @param[in] cblk
 *          Pointer to the structure representing the panel to factorize in the
 *          cblktab array.  Next column blok must be accessible through cblk[1].
 *
 * @param[inout] L
 *          The pointer to the correct representation of the lower part of the data.
 *          - coeftab if the block is in full rank. Must be of size cblk.stride -by- cblk.width.
 *          - pastix_lr_block if the block is compressed.
 *
 *******************************************************************************
 *
 * @return The number of static pivoting during factorization of the diagonal
 * block.
 *
 *******************************************************************************/
int
cpucblk_zpxtrfsp1d_panel( SolverMatrix *solvmtx,
                          SolverCblk   *cblk,
                          void         *L )
{
    pastix_int_t nbpivots;
    nbpivots = cpucblk_zpxtrfsp1d_pxtrf( solvmtx, cblk, L );
 
    cpucblk_ztrsmsp( PastixRight, PastixLower,
                     PastixTrans, PastixNonUnit,
                     cblk, L, L, &(solvmtx->lowrank) );
    return nbpivots;
}
 
 
/**
 *******************************************************************************
 *
 * @brief Perform the LL^t factorization of a given panel and apply all its
 * updates.
 *
 *******************************************************************************
 *
 * @param[in] solvmtx
 *          Solver Matrix structure of the problem
 *
 * @param[in] cblk
 *          Pointer to the structure representing the panel to factorize in the
 *          cblktab array.  Next column blok must be accessible through cblk[1].
 *
 * @param[in] work
 *          Temporary memory buffer.
 *
 * @param[in] lwork
 *          Temporary workspace dimension.
 *
 *******************************************************************************
 *
 * @return The number of static pivoting during factorization of the diagonal
 * block.
 *
 *******************************************************************************/
int
cpucblk_zpxtrfsp1d( SolverMatrix       *solvmtx,
                    SolverCblk         *cblk,
                    pastix_complex64_t *work,
                    pastix_int_t        lwork )
{
    void        *L = cblk_getdataL( cblk );
    SolverCblk  *fcblk;
    SolverBlok  *blok, *lblk;
    pastix_int_t nbpivots;
 
    nbpivots = cpucblk_zpxtrfsp1d_panel( solvmtx, cblk, L );
 
    blok = cblk->fblokptr + 1; /* First off-diagonal block */
    lblk = cblk[1].fblokptr;   /* Next diagonal block      */
 
    /* If there are off-diagonal blocks, perform the updates */
    for( ; blok < lblk; blok++ )
    {
        fcblk = solvmtx->cblktab + blok->fcblknm;
 
        if ( fcblk->cblktype & CBLK_FANIN ) {
            cpucblk_zalloc( PastixLCoef, fcblk );
        }
 
        cpucblk_zgemmsp( PastixLCoef, PastixTrans,
                         cblk, blok, fcblk,
                         L, L, cblk_getdataL( fcblk ),
                         work, lwork, &(solvmtx->lowrank) );
 
        cpucblk_zrelease_deps( PastixLCoef, solvmtx, cblk, fcblk );
   }
 
    return nbpivots;
}
 
/**
 *******************************************************************************
 *
 * @brief Perform the LL^t factorization of a given panel.
 *
 *******************************************************************************
 *
 * @param[in] solvmtx
 *          Solver Matrix structure of the problem
 *
 * @param[in] cblk
 *          Pointer to the structure representing the panel to factorize in the
 *          cblktab array. Next column blok must be accessible through cblk[1].
 *
 *******************************************************************************
 *
 * @return The number of static pivoting during factorization of the diagonal
 * block.
 *
 *******************************************************************************/
int
cpucblk_zpxtrfsp1dplus( SolverMatrix *solvmtx,
                        SolverCblk   *cblk )
{
    void        *L = cblk_getdataL( cblk );
    SolverCblk  *fcblk;
    SolverBlok  *blok, *lblk;
    pastix_int_t i, nbpivots;
    pastix_queue_t *queue = solvmtx->computeQueue[ cblk->threadid ];
 
    assert( cblk->cblktype & CBLK_TASKS_2D );
    nbpivots = cpucblk_zpxtrfsp1d_panel( solvmtx, cblk, L );
 
    blok = cblk->fblokptr + 1; /* this diagonal block */
    lblk = cblk[1].fblokptr;   /* the next diagonal block */
 
    /* if there are off-diagonal supernodes in the column */
    for( i=0; blok < lblk; i++, blok++ )
    {
        fcblk = solvmtx->cblktab + blok->fcblknm;
 
        assert( !(fcblk->cblktype & CBLK_RECV) );
        pqueuePush1( queue, - (blok - solvmtx->bloktab) - 1, cblk->priority + i );
 
        /* Skip blocks facing the same cblk */
        while ( ( blok < lblk ) &&
                ( blok[0].fcblknm == blok[1].fcblknm ) &&
                ( blok[0].lcblknm == blok[1].lcblknm ) )
        {
            blok++;
        }
    }
 
    return nbpivots;
}
 
/**
 *******************************************************************************
 *
 * @brief Apply the updates of the LL^t factorisation of a given panel.
 *
 *******************************************************************************
 *
 * @param[in] solvmtx
 *          Solver Matrix structure of the problem
 *
 * @param[in] blok
 *          Pointer to the blok where the update start.
 *
 * @param[in] work
 *          Temporary memory buffer.
 *
 * @param[in] lwork
 *          Temporary workspace dimension.
 *
 *******************************************************************************/
void
cpucblk_zpxtrfsp1dplus_update( SolverMatrix       *solvmtx,
                               SolverBlok         *blok,
                               pastix_complex64_t *work,
                               pastix_int_t        lwork )
{
    SolverCblk *cblk = solvmtx->cblktab + blok->lcblknm;
    SolverCblk *fcbk = solvmtx->cblktab + blok->fcblknm;
    SolverBlok *lblk = cblk[1].fblokptr;   /* the next diagonal block */
    void       *L    = cblk_getdataL( cblk );
 
    if ( fcbk->cblktype & CBLK_FANIN ) {
        cpucblk_zalloc( PastixLCoef, fcbk );
    }
 
    do
    {
        /* Update on L */
        cpucblk_zgemmsp( PastixLCoef, PastixTrans,
                         cblk, blok, fcbk,
                         L, L, cblk_getdataL( fcbk ),
                         work, lwork, &(solvmtx->lowrank) );
 
        cpucblk_zrelease_deps( PastixLCoef, solvmtx, cblk, fcbk );
        blok++;
    }
    while ( ( blok < lblk ) &&
            ( blok[-1].fcblknm == blok[0].fcblknm ) &&
            ( blok[-1].lcblknm == blok[0].lcblknm ) );
}