dgstrsl.c

LU矩阵分解单机版最新版本

/*
 * -- SuperLU routine (version 2.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * September 15, 2003
 *
 */
/*
  Copyright (c) 1994 by Xerox Corporation.  All rights reserved.
 
  THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
  EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
 
  Permission is hereby granted to use or copy this program for any
  purpose, provided the above notices are retained on all copies.
  Permission to modify the code and to distribute modified code is
  granted, provided the above notices are retained, and a notice that
  the code was modified is included with the above copyright notice.
*/

#include "slu_ddefs.h"
#include "slu_util.h"


/* 
 * Function prototypes 
 */
void dusolve(int, int, double*, double*);
void dlsolve(int, int, double*, double*);
void dmatvec(int, int, int, double*, double*, double*);


void
dgstrsL(char *trans, SuperMatrix *L, int *perm_r, SuperMatrix *B, int *info)
{
/*
 * Purpose
 * =======
 *
 * DGSTRSL only performs the L-solve using the LU factorization computed
 * by DGSTRF.
 *
 * See supermatrix.h for the definition of 'SuperMatrix' structure.
 *
 * Arguments
 * =========
 *
 * trans   (input) char*
 *          Specifies the form of the system of equations:
 *          = 'N':  A * X = B  (No transpose)
 *          = 'T':  A'* X = B  (Transpose)
 *          = 'C':  A**H * X = B  (Conjugate transpose)
 *
 * L       (input) SuperMatrix*
 *         The factor L from the factorization Pr*A*Pc=L*U as computed by
 *         dgstrf(). Use compressed row subscripts storage for supernodes,
 *         i.e., L has types: Stype = SLU_SC, Dtype = SLU_D, Mtype = SLU_TRLU.
 *
 * U       (input) SuperMatrix*
 *         The factor U from the factorization Pr*A*Pc=L*U as computed by
 *         dgstrf(). Use column-wise storage scheme, i.e., U has types:
 *         Stype = SLU_NC, Dtype = SLU_D, Mtype = SLU_TRU.
 *
 * perm_r  (input) int*, dimension (L->nrow)
 *         Row permutation vector, which defines the permutation matrix Pr; 
 *         perm_r[i] = j means row i of A is in position j in Pr*A.
 *
 * B       (input/output) SuperMatrix*
 *         B has types: Stype = SLU_DN, Dtype = SLU_D, Mtype = SLU_GE.
 *         On entry, the right hand side matrix.
 *         On exit, the solution matrix if info = 0;
 *
 * info    (output) int*
 * 	   = 0: successful exit
 *	   < 0: if info = -i, the i-th argument had an illegal value
 *
 */
#ifdef _CRAY
    _fcd ftcs1, ftcs2, ftcs3, ftcs4;
#endif
    int      incx = 1, incy = 1;
    double   alpha = 1.0, beta = 1.0;
    DNformat *Bstore;
    double   *Bmat;
    SCformat *Lstore;
    double   *Lval, *Uval;
    int      nrow, notran;
    int      fsupc, nsupr, nsupc, luptr, istart, irow;
    int      i, j, k, iptr, jcol, n, ldb, nrhs;
    double   *work, *work_col, *rhs_work, *soln;
    flops_t  solve_ops;
    extern SuperLUStat_t SuperLUStat;
    void dprint_soln();

    /* Test input parameters ... */
    *info = 0;
    Bstore = B->Store;
    ldb = Bstore->lda;
    nrhs = B->ncol;
    notran = lsame_(trans, "N");
    if ( !notran && !lsame_(trans, "T") && !lsame_(trans, "C") ) *info = -1;
    else if ( L->nrow != L->ncol || L->nrow < 0 ||
	      L->Stype != SLU_SC || L->Dtype != SLU_D || L->Mtype != SLU_TRLU )
	*info = -2;
    else if ( ldb < SUPERLU_MAX(0, L->nrow) ||
	      B->Stype != SLU_DN || B->Dtype != SLU_D || B->Mtype != SLU_GE )
	*info = -4;
    if ( *info ) {
	i = -(*info);
	xerbla_("dgstrsL", &i);
	return;
    }

    n = L->nrow;
    work = doubleCalloc(n * nrhs);
    if ( !work ) ABORT("Malloc fails for local work[].");
    soln = doubleMalloc(n);
    if ( !soln ) ABORT("Malloc fails for local soln[].");

    Bmat = Bstore->nzval;
    Lstore = L->Store;
    Lval = Lstore->nzval;
    solve_ops = 0;
    
    if ( notran ) {
	/* Permute right hand sides to form Pr*B */
	for (i = 0; i < nrhs; i++) {
	    rhs_work = &Bmat[i*ldb];
	    for (k = 0; k < n; k++) soln[perm_r[k]] = rhs_work[k];
	    for (k = 0; k < n; k++) rhs_work[k] = soln[k];
	}
	
	/* Forward solve PLy=Pb. */
	for (k = 0; k <= Lstore->nsuper; k++) {
	    fsupc = L_FST_SUPC(k);
	    istart = L_SUB_START(fsupc);
	    nsupr = L_SUB_START(fsupc+1) - istart;
	    nsupc = L_FST_SUPC(k+1) - fsupc;
	    nrow = nsupr - nsupc;

	    solve_ops += nsupc * (nsupc - 1) * nrhs;
	    solve_ops += 2 * nrow * nsupc * nrhs;
	    
	    if ( nsupc == 1 ) {
		for (j = 0; j < nrhs; j++) {
		    rhs_work = &Bmat[j*ldb];
	    	    luptr = L_NZ_START(fsupc);
		    for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); iptr++){
			irow = L_SUB(iptr);
			++luptr;
			rhs_work[irow] -= rhs_work[fsupc] * Lval[luptr];
		    }
		}
	    } else {
	    	luptr = L_NZ_START(fsupc);
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
		ftcs1 = _cptofcd("L", strlen("L"));
		ftcs2 = _cptofcd("N", strlen("N"));
		ftcs3 = _cptofcd("U", strlen("U"));
		STRSM( ftcs1, ftcs1, ftcs2, ftcs3, &nsupc, &nrhs, &alpha,
		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
		
		SGEMM( ftcs2, ftcs2, &nrow, &nrhs, &nsupc, &alpha, 
			&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb, 
			&beta, &work[0], &n );
#else
		dtrsm_("L", "L", "N", "U", &nsupc, &nrhs, &alpha,
		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
		
		dgemm_( "N", "N", &nrow, &nrhs, &nsupc, &alpha, 
			&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb, 
			&beta, &work[0], &n );
#endif
		for (j = 0; j < nrhs; j++) {
		    rhs_work = &Bmat[j*ldb];
		    work_col = &work[j*n];
		    iptr = istart + nsupc;
		    for (i = 0; i < nrow; i++) {
			irow = L_SUB(iptr);
			rhs_work[irow] -= work_col[i]; /* Scatter */
			work_col[i] = 0.0;
			iptr++;
		    }
		}
#else		
		for (j = 0; j < nrhs; j++) {
		    rhs_work = &Bmat[j*ldb];
		    dlsolve (nsupr, nsupc, &Lval[luptr], &rhs_work[fsupc]);
		    dmatvec (nsupr, nrow, nsupc, &Lval[luptr+nsupc],
			    &rhs_work[fsupc], &work[0] );

		    iptr = istart + nsupc;
		    for (i = 0; i < nrow; i++) {
			irow = L_SUB(iptr);
			rhs_work[irow] -= work[i];
			work[i] = 0.0;
			iptr++;
		    }
		}
#endif		    
	    } /* else ... */
	} /* for L-solve */

#ifdef DEBUG
  	printf("After L-solve: y=\n");
	dprint_soln(n, nrhs, Bmat);
#endif
	
        SuperLUStat.ops[SOLVE] = solve_ops;

    } else { 
      printf("Transposed solve not implemented.\n");
      exit(0);
    }

    SUPERLU_FREE(work);
    SUPERLU_FREE(soln);
}

/*
 * Diagnostic print of the solution vector 
 */
void
dprint_soln(int n, int nrhs, double *soln)
{
    int i;

    for (i = 0; i < n; i++) 
  	printf("\t%d: %.4f\n", i, soln[i]);
}