core_zgetrfsp.c

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/**
 *
 * @file core_zgetrfsp.c
 *
 * PaStiX kernel routines for LU factorization.
 *
 * @copyright 2011-2023 Bordeaux INP, CNRS (LaBRI UMR 5800), Inria,
 *                      Univ. Bordeaux. All rights reserved.
 *
 * @version 6.3.0
 * @author Mathieu Faverge
 * @author Pierre Ramet
 * @author Xavier Lacoste
 * @author Gregoire Pichon
 * @date 2023-01-13
 * @generated from /builds/solverstack/pastix/kernels/core_zgetrfsp.c, normal z -> z, Mon Aug 28 13:40:36 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 LU factorization of the matrix
 * m-by-n A = L * U.
 *
 *******************************************************************************
 *
 * @param[in] m
 *          The number of rows and columns of the matrix A.
 *
 * @param[in] n
 *          The number of rows and columns of the matrix A.
 *
 * @param[inout] A
 *          The matrix A to factorize with LU 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.
 *
 *******************************************************************************/
static inline void
core_zgetf2sp( pastix_int_t        m,
               pastix_int_t        n,
               pastix_complex64_t *A,
               pastix_int_t        lda,
               pastix_int_t       *nbpivots,
               double              criterion )
{
    pastix_int_t k, minMN;
    pastix_complex64_t *Akk, *Aik, alpha;
 
    minMN = pastix_imin( m, n );
 
    Akk = A;
    for (k=0; k<minMN; k++) {
        Aik = Akk + 1;
 
        if ( cabs(*Akk) < criterion ) {
            if ( creal(*Akk) < 0. ) {
                *Akk = (pastix_complex64_t)(-criterion);
            }
            else {
                *Akk = (pastix_complex64_t)criterion;
            }
            (*nbpivots)++;
        }
 
        /* A_ik = A_ik / A_kk, i = k+1 .. n */
        alpha = 1.0 / (*Akk);
        cblas_zscal(m-k-1, CBLAS_SADDR( alpha ), Aik, 1 );
 
        if ( k+1 < minMN ) {
 
            /* A_ij = A_ij - A_ik * A_kj, i,j = k+1..n */
            cblas_zgeru(CblasColMajor, m-k-1, n-k-1,
                        CBLAS_SADDR(mzone),
                        Aik,        1,
                        Akk+lda, lda,
                        Aik+lda, lda);
        }
 
        Akk += lda+1;
    }
}
 
/**
 *******************************************************************************
 *
 * @brief Compute the block static pivoting LU factorization of the matrix
 * m-by-n A = L * U.
 *
 *******************************************************************************
 *
 * @param[in] n
 *          The number of rows and columns of the matrix A.
 *
 * @param[inout] A
 *          The matrix A to factorize with LU 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.
 *
 *******************************************************************************/
void
core_zgetrfsp( 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, tempm;
    pastix_complex64_t *Akk, *Lik, *Ukj, *Aij;
 
    blocknbr = pastix_iceil( n, MAXSIZEOFBLOCKS );
 
    Akk = A; /* Lk,k     */
 
    for (k=0; k<blocknbr; k++) {
 
        tempm = n - k * MAXSIZEOFBLOCKS;
        blocksize = pastix_imin(MAXSIZEOFBLOCKS, tempm);
        Lik = Akk + blocksize;
        Ukj = Akk + blocksize*lda;
        Aij = Ukj + blocksize;
 
        /* Factorize the diagonal block Akk*/
        core_zgetf2sp( tempm, blocksize, Akk, lda, nbpivots, criterion );
 
        matrixsize = tempm - blocksize;
        if ( matrixsize > 0 ) {
 
            /* Compute the column Ukk+1 */
            cblas_ztrsm(CblasColMajor,
                        CblasLeft, CblasLower,
                        CblasNoTrans, CblasUnit,
                        blocksize, matrixsize,
                        CBLAS_SADDR(zone), Akk, lda,
                                           Ukj, lda);
 
            /* Update Ak+1,k+1 = Ak+1,k+1 - Lk+1,k*Uk,k+1 */
            cblas_zgemm(CblasColMajor,
                        CblasNoTrans, CblasNoTrans,
                        matrixsize, matrixsize, blocksize,
                        CBLAS_SADDR(mzone), Lik, lda,
                                            Ukj, lda,
                        CBLAS_SADDR(zone),  Aij, lda);
        }
 
        Akk += blocksize * (lda+1);
    }
}
 
/**
 *******************************************************************************
 *
 * @brief Compute the LU factorization of the diagonal block in a 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] 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.
 *
 * @param[inout] dataU
 *          The pointer to the correct representation of the upper 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_zgetrfsp1d_getrf( SolverMatrix *solvmtx,
                          SolverCblk   *cblk,
                          void         *dataL,
                          void         *dataU )
{
    pastix_int_t ncols, stride;
    pastix_int_t nbpivots = 0;
    pastix_fixdbl_t time, flops;
    pastix_lrblock_t *lrL, *lrU;
    pastix_complex64_t *L, *U;
 
    double criterion = solvmtx->diagthreshold;
 
    time = kernel_trace_start( PastixKernelGETRF );
 
    ncols  = cblk->lcolnum - cblk->fcolnum + 1;
    stride = (cblk->cblktype & CBLK_LAYOUT_2D) ? ncols : cblk->stride;
 
    if ( cblk->cblktype & CBLK_COMPRESSED ) {
        /* dataL and dataU are LRblock */
 
        lrL = (pastix_lrblock_t *)dataL;
        lrU = (pastix_lrblock_t *)dataU;
        assert( (lrL->rk == -1) && (lrU->rk == -1) );
 
        L = lrL->u;
        U = lrU->u;
        stride = ncols;
 
        assert( stride == lrL->rkmax );
        assert( stride == lrU->rkmax );
    } else {
        L = (pastix_complex64_t *)dataL;
        U = (pastix_complex64_t *)dataU;
    }
 
    core_zgeadd( PastixTrans, ncols, ncols,
                 1.0, U, stride,
                 1.0, L, stride );
 
    /* Factorize diagonal block */
    flops = FLOPS_ZGETRF( ncols, ncols );
    kernel_trace_start_lvl2( PastixKernelLvl2GETRF );
    core_zgetrfsp(ncols, L, stride, &nbpivots, criterion);
    kernel_trace_stop_lvl2( flops );
 
    /* Transpose Akk in ucoeftab */
    core_zgetmo( ncols, ncols, L, stride, U, stride );
 
    kernel_trace_stop( cblk->fblokptr->inlast, PastixKernelGETRF, ncols, 0, 0, flops, time );
 
    if ( nbpivots ) {
        pastix_atomic_add_32b( &(solvmtx->nbpivots), nbpivots );
    }
    return nbpivots;
}
 
/**
 *******************************************************************************
 *
 * @brief Compute the LU 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.
 *
 * @param[inout] U
 *          The pointer to the correct representation of the upper 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_zgetrfsp1d_panel( SolverMatrix *solvmtx,
                          SolverCblk   *cblk,
                          void         *L,
                          void         *U )
{
    pastix_int_t nbpivots;
    nbpivots = cpucblk_zgetrfsp1d_getrf( solvmtx, cblk, L, U );
 
    /*
     * We exploit the fact that the upper triangle is stored at the top of the L
     * column, and by transposition the L part of the diagonal block is
     * similarly stored in the U panel
     */
    cpucblk_ztrsmsp( PastixRight, PastixUpper,
                     PastixNoTrans, PastixNonUnit,
                     cblk, L, L, &(solvmtx->lowrank) );
    cpucblk_ztrsmsp( PastixRight, PastixUpper,
                     PastixNoTrans, PastixUnit,
                     cblk, U, U, &(solvmtx->lowrank) );
    return nbpivots;
}
 
/**
 *******************************************************************************
 *
 * @brief Perform the LU 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_zgetrfsp1d( SolverMatrix       *solvmtx,
                    SolverCblk         *cblk,
                    pastix_complex64_t *work,
                    pastix_int_t        lwork )
{
    void        *L = cblk_getdataL( cblk );
    void        *U = cblk_getdataU( cblk );
    SolverCblk  *fcblk;
    SolverBlok  *blok, *lblk;
    pastix_int_t nbpivots;
 
    nbpivots = cpucblk_zgetrfsp1d_panel( solvmtx, cblk, L, U );
 
    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( ; blok < lblk; blok++ )
    {
        fcblk = solvmtx->cblktab + blok->fcblknm;
 
        if ( fcblk->cblktype & CBLK_FANIN ) {
            cpucblk_zalloc( PastixLUCoef, fcblk );
        }
 
        /* Update on L */
        cpucblk_zgemmsp( PastixLCoef, PastixTrans,
                         cblk, blok, fcblk,
                         L, U, cblk_getdataL( fcblk ),
                         work, lwork, &(solvmtx->lowrank) );
 
        /* Update on U */
        if ( blok+1 < lblk ) {
            cpucblk_zgemmsp( PastixUCoef, PastixTrans,
                             cblk, blok, fcblk,
                             U, L, cblk_getdataU( fcblk ),
                             work, lwork, &(solvmtx->lowrank) );
        }
        cpucblk_zrelease_deps( PastixLUCoef, solvmtx, cblk, fcblk );
    }
 
    return nbpivots;
}