int
sp_ztrsv(char *uplo, char *trans, char *diag, SuperMatrix *L, 
	 SuperMatrix *U, doublecomplex *x, int *info)
{
/*
 *   Purpose
 *   =======
 *
 *   sp_ztrsv() solves one of the systems of equations   
 *       A*x = b,   or   A'*x = b,
 *   where b and x are n element vectors and A is a sparse unit , or   
 *   non-unit, upper or lower triangular matrix.   
 *   No test for singularity or near-singularity is included in this   
 *   routine. Such tests must be performed before calling this routine.   
 *
 *   Parameters   
 *   ==========   
 *
 *   uplo   - (input) char*
 *            On entry, uplo specifies whether the matrix is an upper or   
 *             lower triangular matrix as follows:   
 *                uplo = 'U' or 'u'   A is an upper triangular matrix.   
 *                uplo = 'L' or 'l'   A is a lower triangular matrix.   
 *
 *   trans  - (input) char*
 *             On entry, trans specifies the equations to be solved as   
 *             follows:   
 *                trans = 'N' or 'n'   A*x = b.   
 *                trans = 'T' or 't'   A'*x = b.   
 *                trans = 'C' or 'c'   A'*x = b.   
 *
 *   diag   - (input) char*
 *             On entry, diag specifies whether or not A is unit   
 *             triangular as follows:   
 *                diag = 'U' or 'u'   A is assumed to be unit triangular.   
 *                diag = 'N' or 'n'   A is not assumed to be unit   
 *                                    triangular.   
 *	     
 *   L       - (input) SuperMatrix*
 *	       The factor L from the factorization Pr*A*Pc=L*U. Use
 *             compressed row subscripts storage for supernodes,
 *             i.e., L has types: Stype = SC, Dtype = SLU_Z, Mtype = TRLU.
 *
 *   U       - (input) SuperMatrix*
 *	        The factor U from the factorization Pr*A*Pc=L*U.
 *	        U has types: Stype = NC, Dtype = SLU_Z, Mtype = TRU.
 *    
 *   x       - (input/output) doublecomplex*
 *             Before entry, the incremented array X must contain the n   
 *             element right-hand side vector b. On exit, X is overwritten 
 *             with the solution vector x.
 *
 *   info    - (output) int*
 *             If *info = -i, the i-th argument had an illegal value.
 *
 */
#ifdef _CRAY
    _fcd ftcs1 = _cptofcd("L", strlen("L")),
	 ftcs2 = _cptofcd("N", strlen("N")),
	 ftcs3 = _cptofcd("U", strlen("U"));
#endif
    SCformat *Lstore;
    NCformat *Ustore;
    doublecomplex   *Lval, *Uval;
    int incx = 1, incy = 1;
    doublecomplex alpha = {1.0, 0.0}, beta = {1.0, 0.0};
    doublecomplex comp_zero = {0.0, 0.0};
    int nrow;
    int fsupc, nsupr, nsupc, luptr, istart, irow;
    int i, k, iptr, jcol;
    doublecomplex *work;
    flops_t solve_ops;
    extern SuperLUStat_t SuperLUStat;

    /* Test the input parameters */
    *info = 0;
    if ( !lsame_(uplo,"L") && !lsame_(uplo, "U") ) *info = -1;
    else if ( !lsame_(trans, "N") && !lsame_(trans, "T") ) *info = -2;
    else if ( !lsame_(diag, "U") && !lsame_(diag, "N") ) *info = -3;
    else if ( L->nrow != L->ncol || L->nrow < 0 ) *info = -4;
    else if ( U->nrow != U->ncol || U->nrow < 0 ) *info = -5;
    if ( *info ) {
	i = -(*info);
	xerbla_("sp_ztrsv", &i);
	return 0;
    }

    Lstore = L->Store;
    Lval = Lstore->nzval;
    Ustore = U->Store;
    Uval = Ustore->nzval;
    solve_ops = 0;

    if ( !(work = doublecomplexCalloc(L->nrow)) )
	ABORT("Malloc fails for work in sp_ztrsv().");
    
    if ( lsame_(trans, "N") ) {	/* Form x := inv(A)*x. */
	
	if ( lsame_(uplo, "L") ) {
	    /* Form x := inv(L)*x */
    	    if ( L->nrow == 0 ) return 0; /* Quick return */
	    
	    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;
		luptr = L_NZ_START(fsupc);
		nrow = nsupr - nsupc;

	        solve_ops += 4 * nsupc * (nsupc - 1);
	        solve_ops += 8 * nrow * nsupc;

		if ( nsupc == 1 ) {
		    for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); ++iptr) {
			irow = L_SUB(iptr);
			++luptr;
			zz_mult(&comp_zero, &x[fsupc], &Lval[luptr]);
			z_sub(&x[irow], &x[irow], &comp_zero);
		    }
		} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
		    CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
		       	&x[fsupc], &incx);
		
		    CGEMV(ftcs2, &nrow, &nsupc, &alpha, &Lval[luptr+nsupc], 
		       	&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#else
		    ztrsv_("L", "N", "U", &nsupc, &Lval[luptr], &nsupr,
		       	&x[fsupc], &incx);
		
		    zgemv_("N", &nrow, &nsupc, &alpha, &Lval[luptr+nsupc], 
		       	&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#endif
#else
		    zlsolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc]);
		
		    zmatvec ( nsupr, nsupr-nsupc, nsupc, &Lval[luptr+nsupc],
			&x[fsupc], &work[0] );
#endif		
		
		    iptr = istart + nsupc;
		    for (i = 0; i < nrow; ++i, ++iptr) {
			irow = L_SUB(iptr);
			z_sub(&x[irow], &x[irow], &work[i]); /* Scatter */
			work[i] = comp_zero;

		    }
	 	}
	    } /* for k ... */
	    
	} else {
	    /* Form x := inv(U)*x */
	    
	    if ( U->nrow == 0 ) return 0; /* Quick return */
	    
	    for (k = Lstore->nsuper; k >= 0; k--) {
	    	fsupc = L_FST_SUPC(k);
	    	nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
	    	nsupc = L_FST_SUPC(k+1) - fsupc;
	    	luptr = L_NZ_START(fsupc);
		
    	        solve_ops += 4 * nsupc * (nsupc + 1);

		if ( nsupc == 1 ) {
		    z_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
		    for (i = U_NZ_START(fsupc); i < U_NZ_START(fsupc+1); ++i) {
			irow = U_SUB(i);
			zz_mult(&comp_zero, &x[fsupc], &Uval[i]);
			z_sub(&x[irow], &x[irow], &comp_zero);
		    }
		} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
		    CTRSV(ftcs3, ftcs2, ftcs2, &nsupc, &Lval[luptr], &nsupr,
		       &x[fsupc], &incx);
#else
		    ztrsv_("U", "N", "N", &nsupc, &Lval[luptr], &nsupr,
		       &x[fsupc], &incx);
#endif
#else		
		    zusolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc] );
#endif		

		    for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
		        solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
		    	for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); 
				i++) {
			    irow = U_SUB(i);
			zz_mult(&comp_zero, &x[jcol], &Uval[i]);
			z_sub(&x[irow], &x[irow], &comp_zero);
		    	}
                    }
		}
	    } /* for k ... */
	    
	}
    } else { /* Form x := inv(A')*x */
	
	if ( lsame_(uplo, "L") ) {
	    /* Form x := inv(L')*x */
    	    if ( L->nrow == 0 ) return 0; /* Quick return */
	    
	    for (k = Lstore->nsuper; k >= 0; --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;
	    	luptr = L_NZ_START(fsupc);

		solve_ops += 8 * (nsupr - nsupc) * nsupc;

		for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
		    iptr = istart + nsupc;
		    for (i = L_NZ_START(jcol) + nsupc; 
				i < L_NZ_START(jcol+1); i++) {
			irow = L_SUB(iptr);
			zz_mult(&comp_zero, &x[irow], &Lval[i]);
		    	z_sub(&x[jcol], &x[jcol], &comp_zero);
			iptr++;
		    }
		}
		
		if ( nsupc > 1 ) {
		    solve_ops += 4 * nsupc * (nsupc - 1);
#ifdef _CRAY
                    ftcs1 = _cptofcd("L", strlen("L"));
                    ftcs2 = _cptofcd("T", strlen("T"));
                    ftcs3 = _cptofcd("U", strlen("U"));
		    CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
			&x[fsupc], &incx);
#else
		    ztrsv_("L", "T", "U", &nsupc, &Lval[luptr], &nsupr,
			&x[fsupc], &incx);
#endif
		}
	    }
	} else {
	    /* Form x := inv(U')*x */
	    if ( U->nrow == 0 ) return 0; /* Quick return */
	    
	    for (k = 0; k <= Lstore->nsuper; k++) {
	    	fsupc = L_FST_SUPC(k);
	    	nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
	    	nsupc = L_FST_SUPC(k+1) - fsupc;
	    	luptr = L_NZ_START(fsupc);

		for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
		    solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
		    for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
			irow = U_SUB(i);
			zz_mult(&comp_zero, &x[irow], &Uval[i]);
		    	z_sub(&x[jcol], &x[jcol], &comp_zero);
		    }
		}

		solve_ops += 4 * nsupc * (nsupc + 1);

		if ( nsupc == 1 ) {
		    z_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
		} else {
#ifdef _CRAY
                    ftcs1 = _cptofcd("U", strlen("U"));
                    ftcs2 = _cptofcd("T", strlen("T"));
                    ftcs3 = _cptofcd("N", strlen("N"));
		    CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
			    &x[fsupc], &incx);
#else
		    ztrsv_("U", "T", "N", &nsupc, &Lval[luptr], &nsupr,
			    &x[fsupc], &incx);
#endif
		}
	    } /* for k ... */
	}
    }

    SuperLUStat.ops[SOLVE] += solve_ops;
    SUPERLU_FREE(work);
    return 0;
}
Пример #2
0
/*! \brief Solves one of the systems of equations A*x = b,   or   A'*x = b
 *
 * <pre>
 *   Purpose
 *   =======
 *
 *   sp_ztrsv() solves one of the systems of equations
 *       A*x = b,   or   A'*x = b,
 *   where b and x are n element vectors and A is a sparse unit , or
 *   non-unit, upper or lower triangular matrix.
 *   No test for singularity or near-singularity is included in this
 *   routine. Such tests must be performed before calling this routine.
 *
 *   Parameters
 *   ==========
 *
 *   uplo   - (input) char*
 *            On entry, uplo specifies whether the matrix is an upper or
 *             lower triangular matrix as follows:
 *                uplo = 'U' or 'u'   A is an upper triangular matrix.
 *                uplo = 'L' or 'l'   A is a lower triangular matrix.
 *
 *   trans  - (input) char*
 *             On entry, trans specifies the equations to be solved as
 *             follows:
 *                trans = 'N' or 'n'   A*x = b.
 *                trans = 'T' or 't'   A'*x = b.
 *                trans = 'C' or 'c'   A^H*x = b.
 *
 *   diag   - (input) char*
 *             On entry, diag specifies whether or not A is unit
 *             triangular as follows:
 *                diag = 'U' or 'u'   A is assumed to be unit triangular.
 *                diag = 'N' or 'n'   A is not assumed to be unit
 *                                    triangular.
 *
 *   L       - (input) SuperMatrix*
 *             The factor L from the factorization Pr*A*Pc=L*U. Use
 *             compressed row subscripts storage for supernodes,
 *             i.e., L has types: Stype = SC, Dtype = SLU_Z, Mtype = TRLU.
 *
 *   U       - (input) SuperMatrix*
 *              The factor U from the factorization Pr*A*Pc=L*U.
 *              U has types: Stype = NC, Dtype = SLU_Z, Mtype = TRU.
 *
 *   x       - (input/output) doublecomplex*
 *             Before entry, the incremented array X must contain the n
 *             element right-hand side vector b. On exit, X is overwritten
 *             with the solution vector x.
 *
 *   info    - (output) int*
 *             If *info = -i, the i-th argument had an illegal value.
 * </pre>
 */
int
sp_ztrsv(char *uplo, char *trans, char *diag, SuperMatrix *L,
         SuperMatrix *U, doublecomplex *x, SuperLUStat_t *stat, int *info)
{
#ifdef _CRAY
    _fcd ftcs1 = _cptofcd("L", strlen("L")),
         ftcs2 = _cptofcd("N", strlen("N")),
         ftcs3 = _cptofcd("U", strlen("U"));
#endif
    SCformat *Lstore;
    NCformat *Ustore;
    doublecomplex   *Lval, *Uval;
    int incx = 1, incy = 1;
    doublecomplex temp;
    doublecomplex alpha = {1.0, 0.0}, beta = {1.0, 0.0};
    doublecomplex comp_zero = {0.0, 0.0};
    int nrow;
    int fsupc, nsupr, nsupc, luptr, istart, irow;
    int i, k, iptr, jcol;
    doublecomplex *work;
    flops_t solve_ops;

    /* Test the input parameters */
    *info = 0;
    if ( !lsame_(uplo,"L") && !lsame_(uplo, "U") ) *info = -1;
    else if ( !lsame_(trans, "N") && !lsame_(trans, "T") &&
              !lsame_(trans, "C")) *info = -2;
    else if ( !lsame_(diag, "U") && !lsame_(diag, "N") ) *info = -3;
    else if ( L->nrow != L->ncol || L->nrow < 0 ) *info = -4;
    else if ( U->nrow != U->ncol || U->nrow < 0 ) *info = -5;
    if ( *info ) {
        i = -(*info);
        xerbla_("sp_ztrsv", &i);
        return 0;
    }

    Lstore = L->Store;
    Lval = Lstore->nzval;
    Ustore = U->Store;
    Uval = Ustore->nzval;
    solve_ops = 0;

    if ( !(work = doublecomplexCalloc(L->nrow)) )
        ABORT("Malloc fails for work in sp_ztrsv().");

    if ( lsame_(trans, "N") ) { /* Form x := inv(A)*x. */

        if ( lsame_(uplo, "L") ) {
            /* Form x := inv(L)*x */
            if ( L->nrow == 0 ) return 0; /* Quick return */

            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;
                luptr = L_NZ_START(fsupc);
                nrow = nsupr - nsupc;

                /* 1 z_div costs 10 flops */
                solve_ops += 4 * nsupc * (nsupc - 1) + 10 * nsupc;
                solve_ops += 8 * nrow * nsupc;

                if ( nsupc == 1 ) {
                    for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); ++iptr) {
                        irow = L_SUB(iptr);
                        ++luptr;
                        zz_mult(&comp_zero, &x[fsupc], &Lval[luptr]);
                        z_sub(&x[irow], &x[irow], &comp_zero);
                    }
                } else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
                    CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
                        &x[fsupc], &incx);

                    CGEMV(ftcs2, &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
                        &nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#else
                    ztrsv_("L", "N", "U", &nsupc, &Lval[luptr], &nsupr,
                        &x[fsupc], &incx);

                    zgemv_("N", &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
                        &nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#endif
#else
                    zlsolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc]);

                    zmatvec ( nsupr, nsupr-nsupc, nsupc, &Lval[luptr+nsupc],
                             &x[fsupc], &work[0] );
#endif

                    iptr = istart + nsupc;
                    for (i = 0; i < nrow; ++i, ++iptr) {
                        irow = L_SUB(iptr);
                        z_sub(&x[irow], &x[irow], &work[i]); /* Scatter */
                        work[i] = comp_zero;

                    }
                }
            } /* for k ... */

        } else {
            /* Form x := inv(U)*x */

            if ( U->nrow == 0 ) return 0; /* Quick return */

            for (k = Lstore->nsuper; k >= 0; k--) {
                fsupc = L_FST_SUPC(k);
                nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
                nsupc = L_FST_SUPC(k+1) - fsupc;
                luptr = L_NZ_START(fsupc);

                /* 1 z_div costs 10 flops */
                solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;

                if ( nsupc == 1 ) {
                    z_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
                    for (i = U_NZ_START(fsupc); i < U_NZ_START(fsupc+1); ++i) {
                        irow = U_SUB(i);
                        zz_mult(&comp_zero, &x[fsupc], &Uval[i]);
                        z_sub(&x[irow], &x[irow], &comp_zero);
                    }
                } else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
                    CTRSV(ftcs3, ftcs2, ftcs2, &nsupc, &Lval[luptr], &nsupr,
                       &x[fsupc], &incx);
#else
                    ztrsv_("U", "N", "N", &nsupc, &Lval[luptr], &nsupr,
                           &x[fsupc], &incx);
#endif
#else
                    zusolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc] );
#endif

                    for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
                        solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
                        for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1);
                                i++) {
                            irow = U_SUB(i);
                        zz_mult(&comp_zero, &x[jcol], &Uval[i]);
                        z_sub(&x[irow], &x[irow], &comp_zero);
                        }
                    }
                }
            } /* for k ... */

        }
    } else if ( lsame_(trans, "T") ) { /* Form x := inv(A')*x */

        if ( lsame_(uplo, "L") ) {
            /* Form x := inv(L')*x */
            if ( L->nrow == 0 ) return 0; /* Quick return */

            for (k = Lstore->nsuper; k >= 0; --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;
                luptr = L_NZ_START(fsupc);

                solve_ops += 8 * (nsupr - nsupc) * nsupc;

                for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
                    iptr = istart + nsupc;
                    for (i = L_NZ_START(jcol) + nsupc;
                                i < L_NZ_START(jcol+1); i++) {
                        irow = L_SUB(iptr);
                        zz_mult(&comp_zero, &x[irow], &Lval[i]);
                        z_sub(&x[jcol], &x[jcol], &comp_zero);
                        iptr++;
                    }
                }

                if ( nsupc > 1 ) {
                    solve_ops += 4 * nsupc * (nsupc - 1);
#ifdef _CRAY
                    ftcs1 = _cptofcd("L", strlen("L"));
                    ftcs2 = _cptofcd("T", strlen("T"));
                    ftcs3 = _cptofcd("U", strlen("U"));
                    CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
                        &x[fsupc], &incx);
#else
                    ztrsv_("L", "T", "U", &nsupc, &Lval[luptr], &nsupr,
                        &x[fsupc], &incx);
#endif
                }
            }
        } else {
            /* Form x := inv(U')*x */
            if ( U->nrow == 0 ) return 0; /* Quick return */

            for (k = 0; k <= Lstore->nsuper; k++) {
                fsupc = L_FST_SUPC(k);
                nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
                nsupc = L_FST_SUPC(k+1) - fsupc;
                luptr = L_NZ_START(fsupc);

                for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
                    solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
                    for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
                        irow = U_SUB(i);
                        zz_mult(&comp_zero, &x[irow], &Uval[i]);
                        z_sub(&x[jcol], &x[jcol], &comp_zero);
                    }
                }

                /* 1 z_div costs 10 flops */
                solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;

                if ( nsupc == 1 ) {
                    z_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
                } else {
#ifdef _CRAY
                    ftcs1 = _cptofcd("U", strlen("U"));
                    ftcs2 = _cptofcd("T", strlen("T"));
                    ftcs3 = _cptofcd("N", strlen("N"));
                    CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
                            &x[fsupc], &incx);
#else
                    ztrsv_("U", "T", "N", &nsupc, &Lval[luptr], &nsupr,
                            &x[fsupc], &incx);
#endif
                }
            } /* for k ... */
        }
    } else { /* Form x := conj(inv(A'))*x */

        if ( lsame_(uplo, "L") ) {
            /* Form x := conj(inv(L'))*x */
            if ( L->nrow == 0 ) return 0; /* Quick return */

            for (k = Lstore->nsuper; k >= 0; --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;
                luptr = L_NZ_START(fsupc);

                solve_ops += 8 * (nsupr - nsupc) * nsupc;

                for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
                    iptr = istart + nsupc;
                    for (i = L_NZ_START(jcol) + nsupc;
                                i < L_NZ_START(jcol+1); i++) {
                        irow = L_SUB(iptr);
                        zz_conj(&temp, &Lval[i]);
                        zz_mult(&comp_zero, &x[irow], &temp);
                        z_sub(&x[jcol], &x[jcol], &comp_zero);
                        iptr++;
                    }
                }

                if ( nsupc > 1 ) {
                    solve_ops += 4 * nsupc * (nsupc - 1);
#ifdef _CRAY
                    ftcs1 = _cptofcd("L", strlen("L"));
                    ftcs2 = _cptofcd(trans, strlen("T"));
                    ftcs3 = _cptofcd("U", strlen("U"));
                    ZTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
                        &x[fsupc], &incx);
#else
                    ztrsv_("L", trans, "U", &nsupc, &Lval[luptr], &nsupr,
                           &x[fsupc], &incx);
#endif
                }
            }
        } else {
            /* Form x := conj(inv(U'))*x */
            if ( U->nrow == 0 ) return 0; /* Quick return */

            for (k = 0; k <= Lstore->nsuper; k++) {
                fsupc = L_FST_SUPC(k);
                nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
                nsupc = L_FST_SUPC(k+1) - fsupc;
                luptr = L_NZ_START(fsupc);

                for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
                    solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
                    for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
                        irow = U_SUB(i);
                        zz_conj(&temp, &Uval[i]);
                        zz_mult(&comp_zero, &x[irow], &temp);
                        z_sub(&x[jcol], &x[jcol], &comp_zero);
                    }
                }

                /* 1 z_div costs 10 flops */
                solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;

                if ( nsupc == 1 ) {
                    zz_conj(&temp, &Lval[luptr]);
                    z_div(&x[fsupc], &x[fsupc], &temp);
                } else {
#ifdef _CRAY
                    ftcs1 = _cptofcd("U", strlen("U"));
                    ftcs2 = _cptofcd(trans, strlen("T"));
                    ftcs3 = _cptofcd("N", strlen("N"));
                    ZTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
                            &x[fsupc], &incx);
#else
                    ztrsv_("U", trans, "N", &nsupc, &Lval[luptr], &nsupr,
                               &x[fsupc], &incx);
#endif
                }
            } /* for k ... */
        }
    }

    stat->ops[SOLVE] += solve_ops;
    SUPERLU_FREE(work);
    return 0;
}
Пример #3
0
void
zgstrs (trans_t trans, SuperMatrix *L, SuperMatrix *U,
        int *perm_c, int *perm_r, SuperMatrix *B,
        SuperLUStat_t *stat, int *info)
{
/*
 * Purpose
 * =======
 *
 * ZGSTRS solves a system of linear equations A*X=B or A'*X=B
 * with A sparse and B dense, using the LU factorization computed by
 * ZGSTRF.
 *
 * See supermatrix.h for the definition of 'SuperMatrix' structure.
 *
 * Arguments
 * =========
 *
 * trans   (input) trans_t
 *          Specifies the form of the system of equations:
 *          = NOTRANS: A * X = B  (No transpose)
 *          = TRANS:   A'* X = B  (Transpose)
 *          = CONJ:    A**H * X = B  (Conjugate transpose)
 *
 * L       (input) SuperMatrix*
 *         The factor L from the factorization Pr*A*Pc=L*U as computed by
 *         zgstrf(). Use compressed row subscripts storage for supernodes,
 *         i.e., L has types: Stype = SLU_SC, Dtype = SLU_Z, Mtype = SLU_TRLU.
 *
 * U       (input) SuperMatrix*
 *         The factor U from the factorization Pr*A*Pc=L*U as computed by
 *         zgstrf(). Use column-wise storage scheme, i.e., U has types:
 *         Stype = SLU_NC, Dtype = SLU_Z, Mtype = SLU_TRU.
 *
 * perm_c  (input) int*, dimension (L->ncol)
 *	   Column permutation vector, which defines the 
 *         permutation matrix Pc; perm_c[i] = j means column i of A is 
 *         in position j in A*Pc.
 *
 * 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_Z, Mtype = SLU_GE.
 *         On entry, the right hand side matrix.
 *         On exit, the solution matrix if info = 0;
 *
 * stat     (output) SuperLUStat_t*
 *          Record the statistics on runtime and floating-point operation count.
 *          See util.h for the definition of 'SuperLUStat_t'.
 *
 * 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;
#ifdef USE_VENDOR_BLAS
    doublecomplex   alpha = {1.0, 0.0}, beta = {1.0, 0.0};
    doublecomplex   *work_col;
#endif
    doublecomplex   temp_comp;
    DNformat *Bstore;
    doublecomplex   *Bmat;
    SCformat *Lstore;
    NCformat *Ustore;
    doublecomplex   *Lval, *Uval;
    int      fsupc, nrow, nsupr, nsupc, luptr, istart, irow;
    int      i, j, k, iptr, jcol, n, ldb, nrhs;
    doublecomplex   *work, *rhs_work, *soln;
    flops_t  solve_ops;
    void zprint_soln();

    /* Test input parameters ... */
    *info = 0;
    Bstore = B->Store;
    ldb = Bstore->lda;
    nrhs = B->ncol;
    if ( trans != NOTRANS && trans != TRANS && trans != CONJ ) *info = -1;
    else if ( L->nrow != L->ncol || L->nrow < 0 ||
	      L->Stype != SLU_SC || L->Dtype != SLU_Z || L->Mtype != SLU_TRLU )
	*info = -2;
    else if ( U->nrow != U->ncol || U->nrow < 0 ||
	      U->Stype != SLU_NC || U->Dtype != SLU_Z || U->Mtype != SLU_TRU )
	*info = -3;
    else if ( ldb < SUPERLU_MAX(0, L->nrow) ||
	      B->Stype != SLU_DN || B->Dtype != SLU_Z || B->Mtype != SLU_GE )
	*info = -6;
    if ( *info ) {
	i = -(*info);
	xerbla_("zgstrs", &i);
	return;
    }

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

    Bmat = Bstore->nzval;
    Lstore = L->Store;
    Lval = Lstore->nzval;
    Ustore = U->Store;
    Uval = Ustore->nzval;
    solve_ops = 0;
    
    if ( trans == NOTRANS ) {
	/* 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 += 4 * nsupc * (nsupc - 1) * nrhs;
	    solve_ops += 8 * 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;
			zz_mult(&temp_comp, &rhs_work[fsupc], &Lval[luptr]);
			z_sub(&rhs_work[irow], &rhs_work[irow], &temp_comp);
		    }
		}
	    } 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"));
		CTRSM( ftcs1, ftcs1, ftcs2, ftcs3, &nsupc, &nrhs, &alpha,
		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
		
		CGEMM( ftcs2, ftcs2, &nrow, &nrhs, &nsupc, &alpha, 
			&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb, 
			&beta, &work[0], &n );
#else
		ztrsm_("L", "L", "N", "U", &nsupc, &nrhs, &alpha,
		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
		
		zgemm_( "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);
			z_sub(&rhs_work[irow], &rhs_work[irow], &work_col[i]);
			work_col[i].r = 0.0;
	                work_col[i].i = 0.0;
			iptr++;
		    }
		}
#else		
		for (j = 0; j < nrhs; j++) {
		    rhs_work = &Bmat[j*ldb];
		    zlsolve (nsupr, nsupc, &Lval[luptr], &rhs_work[fsupc]);
		    zmatvec (nsupr, nrow, nsupc, &Lval[luptr+nsupc],
			    &rhs_work[fsupc], &work[0] );

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

#ifdef DEBUG
  	printf("After L-solve: y=\n");
	zprint_soln(n, nrhs, Bmat);
#endif

	/*
	 * Back solve Ux=y.
	 */
	for (k = Lstore->nsuper; k >= 0; 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;
	    luptr = L_NZ_START(fsupc);

	    solve_ops += 4 * nsupc * (nsupc + 1) * nrhs;

	    if ( nsupc == 1 ) {
		rhs_work = &Bmat[0];
		for (j = 0; j < nrhs; j++) {
		    z_div(&rhs_work[fsupc], &rhs_work[fsupc], &Lval[luptr]);
		    rhs_work += ldb;
		}
	    } else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
		ftcs1 = _cptofcd("L", strlen("L"));
		ftcs2 = _cptofcd("U", strlen("U"));
		ftcs3 = _cptofcd("N", strlen("N"));
		CTRSM( ftcs1, ftcs2, ftcs3, ftcs3, &nsupc, &nrhs, &alpha,
		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
#else
		ztrsm_("L", "U", "N", "N", &nsupc, &nrhs, &alpha,
		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
#endif
#else		
		for (j = 0; j < nrhs; j++)
		    zusolve ( nsupr, nsupc, &Lval[luptr], &Bmat[fsupc+j*ldb] );
#endif		
	    }

	    for (j = 0; j < nrhs; ++j) {
		rhs_work = &Bmat[j*ldb];
		for (jcol = fsupc; jcol < fsupc + nsupc; jcol++) {
		    solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
		    for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++ ){
			irow = U_SUB(i);
			zz_mult(&temp_comp, &rhs_work[jcol], &Uval[i]);
			z_sub(&rhs_work[irow], &rhs_work[irow], &temp_comp);
		    }
		}
	    }
	    
	} /* for U-solve */

#ifdef DEBUG
  	printf("After U-solve: x=\n");
	zprint_soln(n, nrhs, Bmat);
#endif

	/* Compute the final solution X := Pc*X. */
	for (i = 0; i < nrhs; i++) {
	    rhs_work = &Bmat[i*ldb];
	    for (k = 0; k < n; k++) soln[k] = rhs_work[perm_c[k]];
	    for (k = 0; k < n; k++) rhs_work[k] = soln[k];
	}
	
        stat->ops[SOLVE] = solve_ops;

    } else { /* Solve A'*X=B */
	/* Permute right hand sides to form Pc'*B. */
	for (i = 0; i < nrhs; i++) {
	    rhs_work = &Bmat[i*ldb];
	    for (k = 0; k < n; k++) soln[perm_c[k]] = rhs_work[k];
	    for (k = 0; k < n; k++) rhs_work[k] = soln[k];
	}

	stat->ops[SOLVE] = 0;
        
        if (trans == TRANS) {
	
            for (k = 0; k < nrhs; ++k) {
                
                /* Multiply by inv(U'). */
                sp_ztrsv("U", "T", "N", L, U, &Bmat[k*ldb], stat, info);
                
                /* Multiply by inv(L'). */
                sp_ztrsv("L", "T", "U", L, U, &Bmat[k*ldb], stat, info);
                
            }
        }
        else {
            for (k = 0; k < nrhs; ++k) {
                /* Multiply by inv(U'). */
                sp_ztrsv("U", "C", "N", L, U, &Bmat[k*ldb], stat, info);
                
                /* Multiply by inv(L'). */
                sp_ztrsv("L", "C", "U", L, U, &Bmat[k*ldb], stat, info);
                
            }
        }
	
	/* Compute the final solution X := Pr'*X (=inv(Pr)*X) */
	for (i = 0; i < nrhs; i++) {
	    rhs_work = &Bmat[i*ldb];
	    for (k = 0; k < n; k++) soln[k] = rhs_work[perm_r[k]];
	    for (k = 0; k < n; k++) rhs_work[k] = soln[k];
	}

    }

    SUPERLU_FREE(work);
    SUPERLU_FREE(soln);
}
Пример #4
0
void
zgstrs (trans_t trans, SuperMatrix *L, SuperMatrix *U,
        int *perm_c, int *perm_r, SuperMatrix *B,
        SuperLUStat_t *stat, int *info)
{

#ifdef _CRAY
    _fcd ftcs1, ftcs2, ftcs3, ftcs4;
#endif
    int      incx = 1, incy = 1;
#ifdef USE_VENDOR_BLAS
    doublecomplex   alpha = {1.0, 0.0}, beta = {1.0, 0.0};
    doublecomplex   *work_col;
#endif
    doublecomplex   temp_comp;
    DNformat *Bstore;
    doublecomplex   *Bmat;
    SCformat *Lstore;
    NCformat *Ustore;
    doublecomplex   *Lval, *Uval;
    int      fsupc, nrow, nsupr, nsupc, luptr, istart, irow;
    int      i, j, k, iptr, jcol, n, ldb, nrhs;
    doublecomplex   *work, *rhs_work, *soln;
    flops_t  solve_ops;
    void zprint_soln();

    /* Test input parameters ... */
    *info = 0;
    Bstore = B->Store;
    ldb = Bstore->lda;
    nrhs = B->ncol;
    if ( trans != NOTRANS && trans != TRANS && trans != CONJ ) *info = -1;
    else if ( L->nrow != L->ncol || L->nrow < 0 ||
	      L->Stype != SLU_SC || L->Dtype != SLU_Z || L->Mtype != SLU_TRLU )
	*info = -2;
    else if ( U->nrow != U->ncol || U->nrow < 0 ||
	      U->Stype != SLU_NC || U->Dtype != SLU_Z || U->Mtype != SLU_TRU )
	*info = -3;
    else if ( ldb < SUPERLU_MAX(0, L->nrow) ||
	      B->Stype != SLU_DN || B->Dtype != SLU_Z || B->Mtype != SLU_GE )
	*info = -6;
    if ( *info ) {
	i = -(*info);
	input_error("zgstrs", &i);
	return;
    }

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

    Bmat = Bstore->nzval;
    Lstore = L->Store;
    Lval = Lstore->nzval;
    Ustore = U->Store;
    Uval = Ustore->nzval;
    solve_ops = 0;
    
    if ( trans == NOTRANS ) {
	/* 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 += 4 * nsupc * (nsupc - 1) * nrhs;
	    solve_ops += 8 * 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;
			zz_mult(&temp_comp, &rhs_work[fsupc], &Lval[luptr]);
			z_sub(&rhs_work[irow], &rhs_work[irow], &temp_comp);
		    }
		}
	    } 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"));
		CTRSM( ftcs1, ftcs1, ftcs2, ftcs3, &nsupc, &nrhs, &alpha,
		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
		
		CGEMM( ftcs2, ftcs2, &nrow, &nrhs, &nsupc, &alpha, 
			&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb, 
			&beta, &work[0], &n );
#else
		ztrsm_("L", "L", "N", "U", &nsupc, &nrhs, &alpha,
		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
		
		zgemm_( "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);
			z_sub(&rhs_work[irow], &rhs_work[irow], &work_col[i]);
			work_col[i].r = 0.0;
	                work_col[i].i = 0.0;
			iptr++;
		    }
		}
#else		
		for (j = 0; j < nrhs; j++) {
		    rhs_work = &Bmat[j*ldb];
		    zlsolve (nsupr, nsupc, &Lval[luptr], &rhs_work[fsupc]);
		    zmatvec (nsupr, nrow, nsupc, &Lval[luptr+nsupc],
			    &rhs_work[fsupc], &work[0] );

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

#ifdef DEBUG
  	printf("After L-solve: y=\n");
	zprint_soln(n, nrhs, Bmat);
#endif

	/*
	 * Back solve Ux=y.
	 */
	for (k = Lstore->nsuper; k >= 0; 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;
	    luptr = L_NZ_START(fsupc);

	    solve_ops += 4 * nsupc * (nsupc + 1) * nrhs;

	    if ( nsupc == 1 ) {
		rhs_work = &Bmat[0];
		for (j = 0; j < nrhs; j++) {
		    z_div(&rhs_work[fsupc], &rhs_work[fsupc], &Lval[luptr]);
		    rhs_work += ldb;
		}
	    } else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
		ftcs1 = _cptofcd("L", strlen("L"));
		ftcs2 = _cptofcd("U", strlen("U"));
		ftcs3 = _cptofcd("N", strlen("N"));
		CTRSM( ftcs1, ftcs2, ftcs3, ftcs3, &nsupc, &nrhs, &alpha,
		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
#else
		ztrsm_("L", "U", "N", "N", &nsupc, &nrhs, &alpha,
		       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
#endif
#else		
		for (j = 0; j < nrhs; j++)
		    zusolve ( nsupr, nsupc, &Lval[luptr], &Bmat[fsupc+j*ldb] );
#endif		
	    }

	    for (j = 0; j < nrhs; ++j) {
		rhs_work = &Bmat[j*ldb];
		for (jcol = fsupc; jcol < fsupc + nsupc; jcol++) {
		    solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
		    for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++ ){
			irow = U_SUB(i);
			zz_mult(&temp_comp, &rhs_work[jcol], &Uval[i]);
			z_sub(&rhs_work[irow], &rhs_work[irow], &temp_comp);
		    }
		}
	    }
	    
	} /* for U-solve */

#ifdef DEBUG
  	printf("After U-solve: x=\n");
	zprint_soln(n, nrhs, Bmat);
#endif

	/* Compute the final solution X := Pc*X. */
	for (i = 0; i < nrhs; i++) {
	    rhs_work = &Bmat[i*ldb];
	    for (k = 0; k < n; k++) soln[k] = rhs_work[perm_c[k]];
	    for (k = 0; k < n; k++) rhs_work[k] = soln[k];
	}
	
        stat->ops[SOLVE] = solve_ops;

    } else { /* Solve A'*X=B or CONJ(A)*X=B */
	/* Permute right hand sides to form Pc'*B. */
	for (i = 0; i < nrhs; i++) {
	    rhs_work = &Bmat[i*ldb];
	    for (k = 0; k < n; k++) soln[perm_c[k]] = rhs_work[k];
	    for (k = 0; k < n; k++) rhs_work[k] = soln[k];
	}

	stat->ops[SOLVE] = 0;
        if (trans == TRANS) {
	    for (k = 0; k < nrhs; ++k) {
	        /* Multiply by inv(U'). */
	        sp_ztrsv("U", "T", "N", L, U, &Bmat[k*ldb], stat, info);
	    
	        /* Multiply by inv(L'). */
	        sp_ztrsv("L", "T", "U", L, U, &Bmat[k*ldb], stat, info);
	    }
         } else { /* trans == CONJ */
            for (k = 0; k < nrhs; ++k) {                
                /* Multiply by conj(inv(U')). */
                sp_ztrsv("U", "C", "N", L, U, &Bmat[k*ldb], stat, info);
                
                /* Multiply by conj(inv(L')). */
                sp_ztrsv("L", "C", "U", L, U, &Bmat[k*ldb], stat, info);
	    }
         }
	/* Compute the final solution X := Pr'*X (=inv(Pr)*X) */
	for (i = 0; i < nrhs; i++) {
	    rhs_work = &Bmat[i*ldb];
	    for (k = 0; k < n; k++) soln[k] = rhs_work[perm_r[k]];
	    for (k = 0; k < n; k++) rhs_work[k] = soln[k];
	}

    }

    SUPERLU_FREE(work);
    SUPERLU_FREE(soln);
}