예제 #1
0
int
pzgstrf_column_bmod(
		    const int  pnum,   /* process number */
		    const int  jcol,   /* current column in the panel */
		    const int  fpanelc,/* first column in the panel */
		    const int  nseg,   /* number of s-nodes to update jcol */
		    int        *segrep,/* in */
		    int        *repfnz,/* in */
		    doublecomplex     *dense, /* modified */
		    doublecomplex     *tempv, /* working array */
		    pxgstrf_shared_t *pxgstrf_shared, /* modified */
		    Gstat_t *Gstat     /* modified */
		    )
{
/*
 * -- SuperLU MT routine (version 2.0) --
 * Lawrence Berkeley National Lab, Univ. of California Berkeley,
 * and Xerox Palo Alto Research Center.
 * September 10, 2007
 *
 * Purpose:
 * ========
 *    Performs numeric block updates (sup-col) in topological order.
 *    It features: col-col, 2cols-col, 3cols-col, and sup-col updates.
 *    Special processing on the supernodal portion of L\U[*,j].
 *
 * Return value:
 * =============
 *      0 - successful return
 *    > 0 - number of bytes allocated when run out of space
 *
 */
#if ( MACH==CRAY_PVP )
    _fcd ftcs1 = _cptofcd("L", strlen("L")),
         ftcs2 = _cptofcd("N", strlen("N")),
         ftcs3 = _cptofcd("U", strlen("U"));
#endif
    
#ifdef USE_VENDOR_BLAS    
    int         incx = 1, incy = 1;
    doublecomplex      alpha, beta;
#endif
    GlobalLU_t *Glu = pxgstrf_shared->Glu;   /* modified */
    
    /* krep = representative of current k-th supernode
     * fsupc = first supernodal column
     * nsupc = no of columns in supernode
     * nsupr = no of rows in supernode (used as leading dimension)
     * luptr = location of supernodal LU-block in storage
     * kfnz = first nonz in the k-th supernodal segment
     * no_zeros = no of leading zeros in a supernodal U-segment
     */
    doublecomplex	  ukj, ukj1, ukj2;
    register int lptr, kfnz, isub, irow, i, no_zeros;
    register int luptr, luptr1, luptr2;
    int          fsupc, nsupc, nsupr, segsze;
    int          nrow;	  /* No of rows in the matrix of matrix-vector */
    int          jsupno, k, ksub, krep, krep_ind, ksupno;
    int          ufirst, nextlu;
    int          fst_col; /* First column within small LU update */
    int          d_fsupc; /* Distance between the first column of the current
			     panel and the first column of the current snode.*/
    int          *xsup, *supno;
    int          *lsub, *xlsub, *xlsub_end;
    doublecomplex       *lusup;
    int          *xlusup, *xlusup_end;
    doublecomplex       *tempv1;
    int          mem_error;
    register float flopcnt;

    doublecomplex      zero = {0.0, 0.0};
    doublecomplex      one = {1.0, 0.0};
    doublecomplex      none = {-1.0, 0.0};
    doublecomplex      comp_temp, comp_temp1;

    xsup       = Glu->xsup;
    supno      = Glu->supno;
    lsub       = Glu->lsub;
    xlsub      = Glu->xlsub;
    xlsub_end  = Glu->xlsub_end;
    lusup      = Glu->lusup;
    xlusup     = Glu->xlusup;
    xlusup_end = Glu->xlusup_end;
    jsupno     = supno[jcol];

    /* 
     * For each nonz supernode segment of U[*,j] in topological order 
     */
    k = nseg - 1;
    for (ksub = 0; ksub < nseg; ksub++) {

	krep = segrep[k];
	k--;
	ksupno = supno[krep];
#if ( DEBUGlvel>=2 )
if (jcol==BADCOL)
printf("(%d) pzgstrf_column_bmod[1]: %d, nseg %d, krep %d, jsupno %d, ksupno %d\n",
       pnum, jcol, nseg, krep, jsupno, ksupno);
#endif    
	if ( jsupno != ksupno ) { /* Outside the rectangular supernode */

	    fsupc = xsup[ksupno];
	    fst_col = SUPERLU_MAX ( fsupc, fpanelc );

  	    /* Distance from the current supernode to the current panel; 
	       d_fsupc=0 if fsupc >= fpanelc. */
  	    d_fsupc = fst_col - fsupc; 

	    luptr = xlusup[fst_col] + d_fsupc;
	    lptr = xlsub[fsupc] + d_fsupc;
	    kfnz = repfnz[krep];
	    kfnz = SUPERLU_MAX ( kfnz, fpanelc );
	    segsze = krep - kfnz + 1;
	    nsupc = krep - fst_col + 1;
	    nsupr = xlsub_end[fsupc] - xlsub[fsupc]; /* Leading dimension */
	    nrow = nsupr - d_fsupc - nsupc;
	    krep_ind = lptr + nsupc - 1;

            flopcnt = 4 * segsze * (segsze - 1) + 8 * nrow * segsze;
	    Gstat->procstat[pnum].fcops += flopcnt;

#if ( DEBUGlevel>=2 )
if (jcol==BADCOL)	    
printf("(%d) pzgstrf_column_bmod[2]: %d, krep %d, kfnz %d, segsze %d, d_fsupc %d,\
fsupc %d, nsupr %d, nsupc %d\n",
       pnum, jcol, krep, kfnz, segsze, d_fsupc, fsupc, nsupr, nsupc);

#endif



            /*
             * Case 1: Update U-segment of size 1 -- col-col update
             */
            if ( segsze == 1 ) {
                ukj = dense[lsub[krep_ind]];
                luptr += nsupr*(nsupc-1) + nsupc;

                for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
                    irow = lsub[i];
                    zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                    z_sub(&dense[irow], &dense[irow], &comp_temp);
                    luptr++;
                }

            } else if ( segsze <= 3 ) {
                ukj = dense[lsub[krep_ind]];
                luptr += nsupr*(nsupc-1) + nsupc-1;
                ukj1 = dense[lsub[krep_ind - 1]];
                luptr1 = luptr - nsupr;

                if ( segsze == 2 ) { /* Case 2: 2cols-col update */
                    zz_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                    z_sub(&ukj, &ukj, &comp_temp);
                    dense[lsub[krep_ind]] = ukj;
                    for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
                        irow = lsub[i];
                        luptr++;
                        luptr1++;
                        zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                        zz_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                        z_add(&comp_temp, &comp_temp, &comp_temp1);
                        z_sub(&dense[irow], &dense[irow], &comp_temp);
                    }
                } else { /* Case 3: 3cols-col update */
                    ukj2 = dense[lsub[krep_ind - 2]];
                    luptr2 = luptr1 - nsupr;
                    zz_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
                    z_sub(&ukj1, &ukj1, &comp_temp);

                    zz_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                    zz_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                    z_add(&comp_temp, &comp_temp, &comp_temp1);
                    z_sub(&ukj, &ukj, &comp_temp);

                    dense[lsub[krep_ind]] = ukj;
                    dense[lsub[krep_ind-1]] = ukj1;
                    for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
                        irow = lsub[i];
                        luptr++;
                        luptr1++;
                        luptr2++;
                        zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                        zz_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                        z_add(&comp_temp, &comp_temp, &comp_temp1);
                        zz_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                        z_add(&comp_temp, &comp_temp, &comp_temp1);
                        z_sub(&dense[irow], &dense[irow], &comp_temp);
                    }
                }


	    } else {
	  	/*
		 * Case: sup-col update
		 * Perform a triangular solve and block update,
		 * then scatter the result of sup-col update to dense
		 */
		no_zeros = kfnz - fst_col;

	        /* Copy U[*,j] segment from dense[*] to tempv[*] */
	        isub = lptr + no_zeros;
	        for (i = 0; i < segsze; i++) {
	  	    irow = lsub[isub];
		    tempv[i] = dense[irow];
		    ++isub; 
	        }

	        /* Dense triangular solve -- start effective triangle */
		luptr += nsupr * no_zeros + no_zeros; 
#ifdef USE_VENDOR_BLAS
#if ( MACH==CRAY_PVP )
		CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr], 
		       &nsupr, tempv, &incx );
#else
		ztrsv_( "L", "N", "U", &segsze, &lusup[luptr], 
		       &nsupr, tempv, &incx );
#endif
		
 		luptr += segsze;  /* Dense matrix-vector */
		tempv1 = &tempv[segsze];
		alpha = one;
		beta = zero;
#if ( MACH==CRAY_PVP )
		CGEMV( ftcs2, &nrow, &segsze, &alpha, &lusup[luptr], 
		       &nsupr, tempv, &incx, &beta, tempv1, &incy );
#else
		zgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr], 
		       &nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif
#else
		zlsolve ( nsupr, segsze, &lusup[luptr], tempv );

 		luptr += segsze;  /* Dense matrix-vector */
		tempv1 = &tempv[segsze];
		zmatvec (nsupr, nrow , segsze, &lusup[luptr], tempv, tempv1);
#endif
                /* Scatter tempv[] into SPA dense[*] */
                isub = lptr + no_zeros;
                for (i = 0; i < segsze; i++) {
                    irow = lsub[isub];
                    dense[irow] = tempv[i]; /* Scatter */
                    tempv[i] = zero;
                    isub++;
                }

		/* Scatter tempv1[] into SPA dense[*] */
		for (i = 0; i < nrow; i++) {
		    irow = lsub[isub];
                    z_sub(&dense[irow], &dense[irow], &tempv1[i]);
		    tempv1[i] = zero;
		    ++isub;
		}
	    } /* else segsze >= 4 */
	    
	} /* if jsupno ... */

    } /* for each segment... */

    
    /* ------------------------------------------
       Process the supernodal portion of L\U[*,j]
       ------------------------------------------ */
    
    fsupc = SUPER_FSUPC (jsupno);
    nsupr = xlsub_end[fsupc] - xlsub[fsupc];
    if ( (mem_error = Glu_alloc(pnum, jcol, nsupr, LUSUP, &nextlu, 
			       pxgstrf_shared)) )
	return mem_error;
    xlusup[jcol] = nextlu;
    lusup = Glu->lusup;
    
    /* Gather the nonzeros from SPA dense[*,j] into L\U[*,j] */
    for (isub = xlsub[fsupc]; isub < xlsub_end[fsupc]; ++isub) {
  	irow = lsub[isub];
	lusup[nextlu] = dense[irow];
	dense[irow] = zero;
#ifdef DEBUG
if (jcol == -1)
    printf("(%d) pzgstrf_column_bmod[lusup] jcol %d, irow %d, lusup %.10e\n",
	   pnum, jcol, irow, lusup[nextlu]);
#endif	
	++nextlu;
    }
    xlusup_end[jcol] = nextlu; /* close L\U[*,jcol] */

#if ( DEBUGlevel>=2 )
if (jcol == -1) {
    nrow = xlusup_end[jcol] - xlusup[jcol];
    print_double_vec("before sup-col update", nrow, &lsub[xlsub[fsupc]],
		     &lusup[xlusup[jcol]]);
}
#endif    
    
    /*
     * For more updates within the panel (also within the current supernode), 
     * should start from the first column of the panel, or the first column 
     * of the supernode, whichever is bigger. There are 2 cases:
     *    (1) fsupc < fpanelc,  then fst_col := fpanelc
     *    (2) fsupc >= fpanelc, then fst_col := fsupc
     */
    fst_col = SUPERLU_MAX ( fsupc, fpanelc );

    if ( fst_col < jcol ) {

  	/* distance between the current supernode and the current panel;
	   d_fsupc=0 if fsupc >= fpanelc. */
  	d_fsupc = fst_col - fsupc;

	lptr = xlsub[fsupc] + d_fsupc;
	luptr = xlusup[fst_col] + d_fsupc;
	nsupr = xlsub_end[fsupc] - xlsub[fsupc]; /* Leading dimension */
	nsupc = jcol - fst_col;	/* Excluding jcol */
	nrow = nsupr - d_fsupc - nsupc;

	/* points to the beginning of jcol in supernode L\U[*,jsupno] */
	ufirst = xlusup[jcol] + d_fsupc;	

#if ( DEBUGlevel>=2 )
if (jcol==BADCOL)
printf("(%d) pzgstrf_column_bmod[3] jcol %d, fsupc %d, nsupr %d, nsupc %d, nrow %d\n",
       pnum, jcol, fsupc, nsupr, nsupc, nrow);
#endif    

        flopcnt = 4 * nsupc * (nsupc - 1) + 8 * nrow * nsupc;
	Gstat->procstat[pnum].fcops += flopcnt;

/*	ops[TRSV] += nsupc * (nsupc - 1);
	ops[GEMV] += 2 * nrow * nsupc;    */
	
#ifdef USE_VENDOR_BLAS
	alpha = none; beta = one; /* y := beta*y + alpha*A*x */
#if ( MACH==CRAY_PVP )
	CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &lusup[luptr], 
	       &nsupr, &lusup[ufirst], &incx );
	CGEMV( ftcs2, &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
	       &lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#else
	ztrsv_( "L", "N", "U", &nsupc, &lusup[luptr], 
	       &nsupr, &lusup[ufirst], &incx );
	zgemv_( "N", &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
	       &lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#endif
#else
	zlsolve ( nsupr, nsupc, &lusup[luptr], &lusup[ufirst] );

	zmatvec ( nsupr, nrow, nsupc, &lusup[luptr+nsupc],
		 &lusup[ufirst], tempv );
	
        /* Copy updates from tempv[*] into lusup[*] */
	isub = ufirst + nsupc;
	for (i = 0; i < nrow; i++) {
            z_sub(&lusup[isub], &lusup[isub], &tempv[i]);
            tempv[i] = zero;
	    ++isub;
	}
#endif
    } /* if fst_col < jcol ... */ 

    return 0;
}
예제 #2
0
파일: zgstrs.c 프로젝트: huard/scipy-work
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);
}
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;
}
예제 #4
0
void
zpanel_bmod (
            const int  m,          /* in - number of rows in the matrix */
            const int  w,          /* in */
            const int  jcol,       /* in */
            const int  nseg,       /* in */
            doublecomplex     *dense,     /* out, of size n by w */
            doublecomplex     *tempv,     /* working array */
            int        *segrep,    /* in */
            int        *repfnz,    /* in, of size n by w */
            GlobalLU_t *Glu,       /* modified */
            SuperLUStat_t *stat    /* output */
            )
{


#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
    _fcd ftcs1 = _cptofcd("L", strlen("L")),
         ftcs2 = _cptofcd("N", strlen("N")),
         ftcs3 = _cptofcd("U", strlen("U"));
#endif
    int          incx = 1, incy = 1;
    doublecomplex       alpha, beta;
#endif

    register int k, ksub;
    int          fsupc, nsupc, nsupr, nrow;
    int          krep, krep_ind;
    doublecomplex       ukj, ukj1, ukj2;
    int          luptr, luptr1, luptr2;
    int          segsze;
    int          block_nrow;  /* no of rows in a block row */
    register int lptr;        /* Points to the row subscripts of a supernode */
    int          kfnz, irow, no_zeros;
    register int isub, isub1, i;
    register int jj;          /* Index through each column in the panel */
    int          *xsup, *supno;
    int          *lsub, *xlsub;
    doublecomplex       *lusup;
    int          *xlusup;
    int          *repfnz_col; /* repfnz[] for a column in the panel */
    doublecomplex       *dense_col;  /* dense[] for a column in the panel */
    doublecomplex       *tempv1;             /* Used in 1-D update */
    doublecomplex       *TriTmp, *MatvecTmp; /* used in 2-D update */
    doublecomplex      zero = {0.0, 0.0};
    doublecomplex      one = {1.0, 0.0};
    doublecomplex      comp_temp, comp_temp1;
    register int ldaTmp;
    register int r_ind, r_hi;
    static   int first = 1, maxsuper, rowblk, colblk;
    flops_t  *ops = stat->ops;

    xsup    = Glu->xsup;
    supno   = Glu->supno;
    lsub    = Glu->lsub;
    xlsub   = Glu->xlsub;
    lusup   = Glu->lusup;
    xlusup  = Glu->xlusup;

    if ( first ) {
        maxsuper = SUPERLU_MAX( sp_ienv(3), sp_ienv(7) );
        rowblk   = sp_ienv(4);
        colblk   = sp_ienv(5);
        first = 0;
    }
    ldaTmp = maxsuper + rowblk;

    /*
     * For each nonz supernode segment of U[*,j] in topological order
     */
    k = nseg - 1;
    for (ksub = 0; ksub < nseg; ksub++) { /* for each updating supernode */

        /* krep = representative of current k-th supernode
         * fsupc = first supernodal column
         * nsupc = no of columns in a supernode
         * nsupr = no of rows in a supernode
         */
        krep = segrep[k--];
        fsupc = xsup[supno[krep]];
        nsupc = krep - fsupc + 1;
        nsupr = xlsub[fsupc+1] - xlsub[fsupc];
        nrow = nsupr - nsupc;
        lptr = xlsub[fsupc];
        krep_ind = lptr + nsupc - 1;

        repfnz_col = repfnz;
        dense_col = dense;

        if ( nsupc >= colblk && nrow > rowblk ) { /* 2-D block update */

            TriTmp = tempv;

            /* Sequence through each column in panel -- triangular solves */
            for (jj = jcol; jj < jcol + w; jj++,
                 repfnz_col += m, dense_col += m, TriTmp += ldaTmp ) {

                kfnz = repfnz_col[krep];
                if ( kfnz == EMPTY ) continue;  /* Skip any zero segment */

                segsze = krep - kfnz + 1;
                luptr = xlusup[fsupc];

                ops[TRSV] += 4 * segsze * (segsze - 1);
                ops[GEMV] += 8 * nrow * segsze;

                /* Case 1: Update U-segment of size 1 -- col-col update */
                if ( segsze == 1 ) {
                    ukj = dense_col[lsub[krep_ind]];
                    luptr += nsupr*(nsupc-1) + nsupc;

                    for (i = lptr + nsupc; i < xlsub[fsupc+1]; i++) {
                        irow = lsub[i];
                        zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                        z_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
                        ++luptr;
                    }

                } else if ( segsze <= 3 ) {
                    ukj = dense_col[lsub[krep_ind]];
                    ukj1 = dense_col[lsub[krep_ind - 1]];
                    luptr += nsupr*(nsupc-1) + nsupc-1;
                    luptr1 = luptr - nsupr;

                    if ( segsze == 2 ) {
                        zz_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                        z_sub(&ukj, &ukj, &comp_temp);
                        dense_col[lsub[krep_ind]] = ukj;
                        for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
                            irow = lsub[i];
                            luptr++; luptr1++;
                            zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                            zz_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                            z_add(&comp_temp, &comp_temp, &comp_temp1);
                            z_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
                        }
                    } else {
                        ukj2 = dense_col[lsub[krep_ind - 2]];
                        luptr2 = luptr1 - nsupr;
                        zz_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
                        z_sub(&ukj1, &ukj1, &comp_temp);

                        zz_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                        zz_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                        z_add(&comp_temp, &comp_temp, &comp_temp1);
                        z_sub(&ukj, &ukj, &comp_temp);
                        dense_col[lsub[krep_ind]] = ukj;
                        dense_col[lsub[krep_ind-1]] = ukj1;
                        for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
                            irow = lsub[i];
                            luptr++; luptr1++; luptr2++;
                            zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                            zz_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                            z_add(&comp_temp, &comp_temp, &comp_temp1);
                            zz_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                            z_add(&comp_temp, &comp_temp, &comp_temp1);
                            z_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
                        }
                    }

                } else  {       /* segsze >= 4 */

                    /* Copy U[*,j] segment from dense[*] to TriTmp[*], which
                       holds the result of triangular solves.    */
                    no_zeros = kfnz - fsupc;
                    isub = lptr + no_zeros;
                    for (i = 0; i < segsze; ++i) {
                        irow = lsub[isub];
                        TriTmp[i] = dense_col[irow]; /* Gather */
                        ++isub;
                    }

                    /* start effective triangle */
                    luptr += nsupr * no_zeros + no_zeros;

#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
                    CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr],
                           &nsupr, TriTmp, &incx );
#else
                    ztrsv_( "L", "N", "U", &segsze, &lusup[luptr],
                           &nsupr, TriTmp, &incx );
#endif
#else
                    zlsolve ( nsupr, segsze, &lusup[luptr], TriTmp );
#endif


                } /* else ... */

            }  /* for jj ... end tri-solves */

            /* Block row updates; push all the way into dense[*] block */
            for ( r_ind = 0; r_ind < nrow; r_ind += rowblk ) {

                r_hi = SUPERLU_MIN(nrow, r_ind + rowblk);
                block_nrow = SUPERLU_MIN(rowblk, r_hi - r_ind);
                luptr = xlusup[fsupc] + nsupc + r_ind;
                isub1 = lptr + nsupc + r_ind;

                repfnz_col = repfnz;
                TriTmp = tempv;
                dense_col = dense;

                /* Sequence through each column in panel -- matrix-vector */
                for (jj = jcol; jj < jcol + w; jj++,
                     repfnz_col += m, dense_col += m, TriTmp += ldaTmp) {

                    kfnz = repfnz_col[krep];
                    if ( kfnz == EMPTY ) continue; /* Skip any zero segment */

                    segsze = krep - kfnz + 1;
                    if ( segsze <= 3 ) continue;   /* skip unrolled cases */

                    /* Perform a block update, and scatter the result of
                       matrix-vector to dense[].                 */
                    no_zeros = kfnz - fsupc;
                    luptr1 = luptr + nsupr * no_zeros;
                    MatvecTmp = &TriTmp[maxsuper];

#ifdef USE_VENDOR_BLAS
                    alpha = one;
                    beta = zero;
#ifdef _CRAY
                    CGEMV(ftcs2, &block_nrow, &segsze, &alpha, &lusup[luptr1],
                           &nsupr, TriTmp, &incx, &beta, MatvecTmp, &incy);
#else
                    zgemv_("N", &block_nrow, &segsze, &alpha, &lusup[luptr1],
                           &nsupr, TriTmp, &incx, &beta, MatvecTmp, &incy);
#endif
#else
                    zmatvec(nsupr, block_nrow, segsze, &lusup[luptr1],
                           TriTmp, MatvecTmp);
#endif

                    /* Scatter MatvecTmp[*] into SPA dense[*] temporarily
                     * such that MatvecTmp[*] can be re-used for the
                     * the next blok row update. dense[] will be copied into
                     * global store after the whole panel has been finished.
                     */
                    isub = isub1;
                    for (i = 0; i < block_nrow; i++) {
                        irow = lsub[isub];
                        z_sub(&dense_col[irow], &dense_col[irow],
                              &MatvecTmp[i]);
                        MatvecTmp[i] = zero;
                        ++isub;
                    }

                } /* for jj ... */

            } /* for each block row ... */

            /* Scatter the triangular solves into SPA dense[*] */
            repfnz_col = repfnz;
            TriTmp = tempv;
            dense_col = dense;

            for (jj = jcol; jj < jcol + w; jj++,
                 repfnz_col += m, dense_col += m, TriTmp += ldaTmp) {
                kfnz = repfnz_col[krep];
                if ( kfnz == EMPTY ) continue; /* Skip any zero segment */

                segsze = krep - kfnz + 1;
                if ( segsze <= 3 ) continue; /* skip unrolled cases */

                no_zeros = kfnz - fsupc;
                isub = lptr + no_zeros;
                for (i = 0; i < segsze; i++) {
                    irow = lsub[isub];
                    dense_col[irow] = TriTmp[i];
                    TriTmp[i] = zero;
                    ++isub;
                }

            } /* for jj ... */

        } else { /* 1-D block modification */


            /* Sequence through each column in the panel */
            for (jj = jcol; jj < jcol + w; jj++,
                 repfnz_col += m, dense_col += m) {

                kfnz = repfnz_col[krep];
                if ( kfnz == EMPTY ) continue;  /* Skip any zero segment */

                segsze = krep - kfnz + 1;
                luptr = xlusup[fsupc];

                ops[TRSV] += 4 * segsze * (segsze - 1);
                ops[GEMV] += 8 * nrow * segsze;

                /* Case 1: Update U-segment of size 1 -- col-col update */
                if ( segsze == 1 ) {
                    ukj = dense_col[lsub[krep_ind]];
                    luptr += nsupr*(nsupc-1) + nsupc;

                    for (i = lptr + nsupc; i < xlsub[fsupc+1]; i++) {
                        irow = lsub[i];
                        zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                        z_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
                        ++luptr;
                    }

                } else if ( segsze <= 3 ) {
                    ukj = dense_col[lsub[krep_ind]];
                    luptr += nsupr*(nsupc-1) + nsupc-1;
                    ukj1 = dense_col[lsub[krep_ind - 1]];
                    luptr1 = luptr - nsupr;

                    if ( segsze == 2 ) {
                        zz_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                        z_sub(&ukj, &ukj, &comp_temp);
                        dense_col[lsub[krep_ind]] = ukj;
                        for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
                            irow = lsub[i];
                            ++luptr;  ++luptr1;
                            zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                            zz_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                            z_add(&comp_temp, &comp_temp, &comp_temp1);
                            z_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
                        }
                    } else {
                        ukj2 = dense_col[lsub[krep_ind - 2]];
                        luptr2 = luptr1 - nsupr;
                        zz_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
                        z_sub(&ukj1, &ukj1, &comp_temp);

                        zz_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                        zz_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                        z_add(&comp_temp, &comp_temp, &comp_temp1);
                        z_sub(&ukj, &ukj, &comp_temp);
                        dense_col[lsub[krep_ind]] = ukj;
                        dense_col[lsub[krep_ind-1]] = ukj1;
                        for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
                            irow = lsub[i];
                            ++luptr; ++luptr1; ++luptr2;
                            zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                            zz_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                            z_add(&comp_temp, &comp_temp, &comp_temp1);
                            zz_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                            z_add(&comp_temp, &comp_temp, &comp_temp1);
                            z_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
                        }
                    }

                } else  { /* segsze >= 4 */
                    /*
                     * Perform a triangular solve and block update,
                     * then scatter the result of sup-col update to dense[].
                     */
                    no_zeros = kfnz - fsupc;

                    /* Copy U[*,j] segment from dense[*] to tempv[*]:
                     *    The result of triangular solve is in tempv[*];
                     *    The result of matrix vector update is in dense_col[*]
                     */
                    isub = lptr + no_zeros;
                    for (i = 0; i < segsze; ++i) {
                        irow = lsub[isub];
                        tempv[i] = dense_col[irow]; /* Gather */
                        ++isub;
                    }

                    /* start effective triangle */
                    luptr += nsupr * no_zeros + no_zeros;

#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
                    CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr],
                           &nsupr, tempv, &incx );
#else
                    ztrsv_( "L", "N", "U", &segsze, &lusup[luptr],
                           &nsupr, tempv, &incx );
#endif

                    luptr += segsze;    /* Dense matrix-vector */
                    tempv1 = &tempv[segsze];
                    alpha = one;
                    beta = zero;
#ifdef _CRAY
                    CGEMV( ftcs2, &nrow, &segsze, &alpha, &lusup[luptr],
                           &nsupr, tempv, &incx, &beta, tempv1, &incy );
#else
                    zgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr],
                           &nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif
#else
                    zlsolve ( nsupr, segsze, &lusup[luptr], tempv );

                    luptr += segsze;        /* Dense matrix-vector */
                    tempv1 = &tempv[segsze];
                    zmatvec (nsupr, nrow, segsze, &lusup[luptr], tempv, tempv1);
#endif

                    /* Scatter tempv[*] into SPA dense[*] temporarily, such
                     * that tempv[*] can be used for the triangular solve of
                     * the next column of the panel. They will be copied into
                     * ucol[*] after the whole panel has been finished.
                     */
                    isub = lptr + no_zeros;
                    for (i = 0; i < segsze; i++) {
                        irow = lsub[isub];
                        dense_col[irow] = tempv[i];
                        tempv[i] = zero;
                        isub++;
                    }

                    /* Scatter the update from tempv1[*] into SPA dense[*] */
                    /* Start dense rectangular L */
                    for (i = 0; i < nrow; i++) {
                        irow = lsub[isub];
                        z_sub(&dense_col[irow], &dense_col[irow], &tempv1[i]);
                        tempv1[i] = zero;
                        ++isub;
                    }

                } /* else segsze>=4 ... */

            } /* for each column in the panel... */

        } /* else 1-D update ... */

    } /* for each updating supernode ... */

}
예제 #5
0
/* Return value:   0 - successful return
 *               > 0 - number of bytes allocated when run out of space
 */
int
zcolumn_bmod (
	     const int  jcol,	  /* in */
	     const int  nseg,	  /* in */
	     doublecomplex     *dense,	  /* in */
	     doublecomplex     *tempv,	  /* working array */
	     int        *segrep,  /* in */
	     int        *repfnz,  /* in */
	     int        fpanelc,  /* in -- first column in the current panel */
	     GlobalLU_t *Glu,     /* modified */
	     SuperLUStat_t *stat  /* output */
	     )
{
/*
 * Purpose:
 * ========
 *    Performs numeric block updates (sup-col) in topological order.
 *    It features: col-col, 2cols-col, 3cols-col, and sup-col updates.
 *    Special processing on the supernodal portion of L\U[*,j]
 *
 */
#ifdef _CRAY
    _fcd ftcs1 = _cptofcd("L", strlen("L")),
         ftcs2 = _cptofcd("N", strlen("N")),
         ftcs3 = _cptofcd("U", strlen("U"));
#endif
    int         incx = 1, incy = 1;
    doublecomplex      alpha, beta;
    
    /* krep = representative of current k-th supernode
     * fsupc = first supernodal column
     * nsupc = no of columns in supernode
     * nsupr = no of rows in supernode (used as leading dimension)
     * luptr = location of supernodal LU-block in storage
     * kfnz = first nonz in the k-th supernodal segment
     * no_zeros = no of leading zeros in a supernodal U-segment
     */
    doublecomplex       ukj, ukj1, ukj2;
    int          luptr, luptr1, luptr2;
    int          fsupc, nsupc, nsupr, segsze;
    int          nrow;	  /* No of rows in the matrix of matrix-vector */
    int          jcolp1, jsupno, k, ksub, krep, krep_ind, ksupno;
    register int lptr, kfnz, isub, irow, i;
    register int no_zeros, new_next; 
    int          ufirst, nextlu;
    int          fst_col; /* First column within small LU update */
    int          d_fsupc; /* Distance between the first column of the current
			     panel and the first column of the current snode. */
    int          *xsup, *supno;
    int          *lsub, *xlsub;
    doublecomplex       *lusup;
    int          *xlusup;
    int          nzlumax;
    doublecomplex       *tempv1;
    doublecomplex      zero = {0.0, 0.0};
    doublecomplex      one = {1.0, 0.0};
    doublecomplex      none = {-1.0, 0.0};
    doublecomplex	 comp_temp, comp_temp1;
    int          mem_error;
    flops_t      *ops = stat->ops;

    xsup    = Glu->xsup;
    supno   = Glu->supno;
    lsub    = Glu->lsub;
    xlsub   = Glu->xlsub;
    lusup   = Glu->lusup;
    xlusup  = Glu->xlusup;
    nzlumax = Glu->nzlumax;
    jcolp1 = jcol + 1;
    jsupno = supno[jcol];
    
    /* 
     * For each nonz supernode segment of U[*,j] in topological order 
     */
    k = nseg - 1;
    for (ksub = 0; ksub < nseg; ksub++) {

	krep = segrep[k];
	k--;
	ksupno = supno[krep];
	if ( jsupno != ksupno ) { /* Outside the rectangular supernode */

	    fsupc = xsup[ksupno];
	    fst_col = SUPERLU_MAX ( fsupc, fpanelc );

  	    /* Distance from the current supernode to the current panel; 
	       d_fsupc=0 if fsupc > fpanelc. */
  	    d_fsupc = fst_col - fsupc; 

	    luptr = xlusup[fst_col] + d_fsupc;
	    lptr = xlsub[fsupc] + d_fsupc;

	    kfnz = repfnz[krep];
	    kfnz = SUPERLU_MAX ( kfnz, fpanelc );

	    segsze = krep - kfnz + 1;
	    nsupc = krep - fst_col + 1;
	    nsupr = xlsub[fsupc+1] - xlsub[fsupc];	/* Leading dimension */
	    nrow = nsupr - d_fsupc - nsupc;
	    krep_ind = lptr + nsupc - 1;

	    ops[TRSV] += 4 * segsze * (segsze - 1);
	    ops[GEMV] += 8 * nrow * segsze;



	    /* 
	     * Case 1: Update U-segment of size 1 -- col-col update 
	     */
	    if ( segsze == 1 ) {
	  	ukj = dense[lsub[krep_ind]];
		luptr += nsupr*(nsupc-1) + nsupc;

		for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
		    irow = lsub[i];
		    zz_mult(&comp_temp, &ukj, &lusup[luptr]);
		    z_sub(&dense[irow], &dense[irow], &comp_temp);
		    luptr++;
		}

	    } else if ( segsze <= 3 ) {
		ukj = dense[lsub[krep_ind]];
		luptr += nsupr*(nsupc-1) + nsupc-1;
		ukj1 = dense[lsub[krep_ind - 1]];
		luptr1 = luptr - nsupr;

		if ( segsze == 2 ) { /* Case 2: 2cols-col update */
		    zz_mult(&comp_temp, &ukj1, &lusup[luptr1]);
		    z_sub(&ukj, &ukj, &comp_temp);
		    dense[lsub[krep_ind]] = ukj;
		    for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
		    	irow = lsub[i];
		    	luptr++;
		    	luptr1++;
			zz_mult(&comp_temp, &ukj, &lusup[luptr]);
			zz_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
			z_add(&comp_temp, &comp_temp, &comp_temp1);
			z_sub(&dense[irow], &dense[irow], &comp_temp);
		    }
		} else { /* Case 3: 3cols-col update */
		    ukj2 = dense[lsub[krep_ind - 2]];
		    luptr2 = luptr1 - nsupr;
  		    zz_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
		    z_sub(&ukj1, &ukj1, &comp_temp);

		    zz_mult(&comp_temp, &ukj1, &lusup[luptr1]);
		    zz_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
		    z_add(&comp_temp, &comp_temp, &comp_temp1);
		    z_sub(&ukj, &ukj, &comp_temp);

		    dense[lsub[krep_ind]] = ukj;
		    dense[lsub[krep_ind-1]] = ukj1;
		    for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
		    	irow = lsub[i];
		    	luptr++;
		    	luptr1++;
			luptr2++;
			zz_mult(&comp_temp, &ukj, &lusup[luptr]);
			zz_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
			z_add(&comp_temp, &comp_temp, &comp_temp1);
			zz_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
			z_add(&comp_temp, &comp_temp, &comp_temp1);
			z_sub(&dense[irow], &dense[irow], &comp_temp);
		    }
		}


	    } else {
	  	/*
		 * Case: sup-col update
		 * Perform a triangular solve and block update,
		 * then scatter the result of sup-col update to dense
		 */

		no_zeros = kfnz - fst_col;

	        /* Copy U[*,j] segment from dense[*] to tempv[*] */
	        isub = lptr + no_zeros;
	        for (i = 0; i < segsze; i++) {
	  	    irow = lsub[isub];
		    tempv[i] = dense[irow];
		    ++isub; 
	        }

	        /* Dense triangular solve -- start effective triangle */
		luptr += nsupr * no_zeros + no_zeros; 
		
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
		CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr], 
		       &nsupr, tempv, &incx );
#else		
		ztrsv_( "L", "N", "U", &segsze, &lusup[luptr], 
		       &nsupr, tempv, &incx );
#endif		
 		luptr += segsze;  /* Dense matrix-vector */
		tempv1 = &tempv[segsze];
                alpha = one;
                beta = zero;
#ifdef _CRAY
		CGEMV( ftcs2, &nrow, &segsze, &alpha, &lusup[luptr], 
		       &nsupr, tempv, &incx, &beta, tempv1, &incy );
#else
		zgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr], 
		       &nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif
#else
		zlsolve ( nsupr, segsze, &lusup[luptr], tempv );

 		luptr += segsze;  /* Dense matrix-vector */
		tempv1 = &tempv[segsze];
		zmatvec (nsupr, nrow , segsze, &lusup[luptr], tempv, tempv1);
#endif
		
		
                /* Scatter tempv[] into SPA dense[] as a temporary storage */
                isub = lptr + no_zeros;
                for (i = 0; i < segsze; i++) {
                    irow = lsub[isub];
                    dense[irow] = tempv[i];
                    tempv[i] = zero;
                    ++isub;
                }

		/* Scatter tempv1[] into SPA dense[] */
		for (i = 0; i < nrow; i++) {
		    irow = lsub[isub];
		    z_sub(&dense[irow], &dense[irow], &tempv1[i]);
		    tempv1[i] = zero;
		    ++isub;
		}
	    }
	    
	} /* if jsupno ... */

    } /* for each segment... */

    /*
     *	Process the supernodal portion of L\U[*,j]
     */
    nextlu = xlusup[jcol];
    fsupc = xsup[jsupno];

    /* Copy the SPA dense into L\U[*,j] */
    new_next = nextlu + xlsub[fsupc+1] - xlsub[fsupc];
    while ( new_next > nzlumax ) {
	if (mem_error = zLUMemXpand(jcol, nextlu, LUSUP, &nzlumax, Glu))
	    return (mem_error);
	lusup = Glu->lusup;
	lsub = Glu->lsub;
    }

    for (isub = xlsub[fsupc]; isub < xlsub[fsupc+1]; isub++) {
  	irow = lsub[isub];
	lusup[nextlu] = dense[irow];
        dense[irow] = zero;
	++nextlu;
    }

    xlusup[jcolp1] = nextlu;	/* Close L\U[*,jcol] */

    /* For more updates within the panel (also within the current supernode), 
     * should start from the first column of the panel, or the first column 
     * of the supernode, whichever is bigger. There are 2 cases:
     *    1) fsupc < fpanelc, then fst_col := fpanelc
     *    2) fsupc >= fpanelc, then fst_col := fsupc
     */
    fst_col = SUPERLU_MAX ( fsupc, fpanelc );

    if ( fst_col < jcol ) {

  	/* Distance between the current supernode and the current panel.
	   d_fsupc=0 if fsupc >= fpanelc. */
  	d_fsupc = fst_col - fsupc;

	lptr = xlsub[fsupc] + d_fsupc;
	luptr = xlusup[fst_col] + d_fsupc;
	nsupr = xlsub[fsupc+1] - xlsub[fsupc];	/* Leading dimension */
	nsupc = jcol - fst_col;	/* Excluding jcol */
	nrow = nsupr - d_fsupc - nsupc;

	/* Points to the beginning of jcol in snode L\U(jsupno) */
	ufirst = xlusup[jcol] + d_fsupc;	

	ops[TRSV] += 4 * nsupc * (nsupc - 1);
	ops[GEMV] += 8 * nrow * nsupc;
	
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
	CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &lusup[luptr], 
	       &nsupr, &lusup[ufirst], &incx );
#else
	ztrsv_( "L", "N", "U", &nsupc, &lusup[luptr], 
	       &nsupr, &lusup[ufirst], &incx );
#endif
	
	alpha = none; beta = one; /* y := beta*y + alpha*A*x */

#ifdef _CRAY
	CGEMV( ftcs2, &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
	       &lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#else
	zgemv_( "N", &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
	       &lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#endif
#else
	zlsolve ( nsupr, nsupc, &lusup[luptr], &lusup[ufirst] );

	zmatvec ( nsupr, nrow, nsupc, &lusup[luptr+nsupc],
		&lusup[ufirst], tempv );
	
        /* Copy updates from tempv[*] into lusup[*] */
	isub = ufirst + nsupc;
	for (i = 0; i < nrow; i++) {
	    z_sub(&lusup[isub], &lusup[isub], &tempv[i]);
	    tempv[i] = zero;
	    ++isub;
	}

#endif
	
	
    } /* if fst_col < jcol ... */ 

    return 0;
}
예제 #6
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;
}
예제 #7
0
파일: zsnode_bmod.c 프로젝트: 7924102/scipy
/*! \brief Performs numeric block updates within the relaxed snode. 
 */
int
zsnode_bmod (
	    const int  jcol,	  /* in */
	    const int  jsupno,    /* in */
	    const int  fsupc,     /* in */
	    doublecomplex     *dense,    /* in */
	    doublecomplex     *tempv,    /* working array */
	    GlobalLU_t *Glu,      /* modified */
	    SuperLUStat_t *stat   /* output */
	    )
{
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
    _fcd ftcs1 = _cptofcd("L", strlen("L")),
	 ftcs2 = _cptofcd("N", strlen("N")),
	 ftcs3 = _cptofcd("U", strlen("U"));
#endif
    int            incx = 1, incy = 1;
    doublecomplex         alpha = {-1.0, 0.0},  beta = {1.0, 0.0};
#endif

    doublecomplex   comp_zero = {0.0, 0.0};
    int            luptr, nsupc, nsupr, nrow;
    int            isub, irow, i, iptr; 
    register int   ufirst, nextlu;
    int            *lsub, *xlsub;
    doublecomplex         *lusup;
    int            *xlusup;
    flops_t *ops = stat->ops;

    lsub    = Glu->lsub;
    xlsub   = Glu->xlsub;
    lusup   = Glu->lusup;
    xlusup  = Glu->xlusup;

    nextlu = xlusup[jcol];
    
    /*
     *	Process the supernodal portion of L\U[*,j]
     */
    for (isub = xlsub[fsupc]; isub < xlsub[fsupc+1]; isub++) {
  	irow = lsub[isub];
	lusup[nextlu] = dense[irow];
        dense[irow] = comp_zero;
	++nextlu;
    }

    xlusup[jcol + 1] = nextlu;	/* Initialize xlusup for next column */
    
    if ( fsupc < jcol ) {

	luptr = xlusup[fsupc];
	nsupr = xlsub[fsupc+1] - xlsub[fsupc];
	nsupc = jcol - fsupc;	/* Excluding jcol */
	ufirst = xlusup[jcol];	/* Points to the beginning of column
				   jcol in supernode L\U(jsupno). */
	nrow = nsupr - nsupc;

	ops[TRSV] += 4 * nsupc * (nsupc - 1);
	ops[GEMV] += 8 * nrow * nsupc;

#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
	CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &lusup[luptr], &nsupr, 
	      &lusup[ufirst], &incx );
	CGEMV( ftcs2, &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr, 
		&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#else
#if SCIPY_FIX
	if (nsupr < nsupc) {
	    /* Invalid input to LAPACK: fail more gracefully */
	    ABORT("superlu failure (singular matrix?)");
	}
#endif
	ztrsv_( "L", "N", "U", &nsupc, &lusup[luptr], &nsupr, 
	      &lusup[ufirst], &incx );
	zgemv_( "N", &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr, 
		&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#endif
#else
	zlsolve ( nsupr, nsupc, &lusup[luptr], &lusup[ufirst] );
	zmatvec ( nsupr, nrow, nsupc, &lusup[luptr+nsupc], 
			&lusup[ufirst], &tempv[0] );

        /* Scatter tempv[*] into lusup[*] */
	iptr = ufirst + nsupc;
	for (i = 0; i < nrow; i++) {
	    z_sub(&lusup[iptr], &lusup[iptr], &tempv[i]);
            ++iptr;
	    tempv[i] = comp_zero;
	}
#endif

    }

    return 0;
}
예제 #8
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);
}
int
pzgstrf_snode_bmod(
		   const int  pnum,   /* process number */
		   const int  jcol,   /* in - current column in the s-node */
		   const int  jsupno, /* in */
		   const int  fsupc,  /* in - first column in the s-node */
		   doublecomplex     *dense, /* in */
		   doublecomplex     *tempv, /* working array */
		   GlobalLU_t *Glu,   /* modified */
		   Gstat_t *Gstat     /* modified */
		   )
{
/*
 * -- SuperLU MT routine (version 2.0) --
 * Lawrence Berkeley National Lab, Univ. of California Berkeley,
 * and Xerox Palo Alto Research Center.
 * September 10, 2007
 *
 * Performs numeric block updates within the relaxed supernode. 
 */

    doublecomplex      zero = {0.0, 0.0};
    doublecomplex      one = {1.0, 0.0};
    doublecomplex      none = {-1.0, 0.0};

#if ( MACH==CRAY_PVP )
    _fcd ftcs1, ftcs2, ftcs3;
#endif
#ifdef USE_VENDOR_BLAS    
    int            incx = 1, incy = 1;
    doublecomplex         alpha = none, beta = one;
#endif
    
    int            luptr, nsupc, nsupr, nrow;
    int            isub, irow, i, iptr; 
    register int   ufirst, nextlu;
    doublecomplex         *lusup;
    int            *lsub, *xlsub, *xlsub_end, *xlusup, *xlusup_end;
    register float flopcnt;

    lsub       = Glu->lsub;
    xlsub      = Glu->xlsub;
    xlsub_end  = Glu->xlsub_end;
    lusup      = Glu->lusup;
    xlusup     = Glu->xlusup;
    xlusup_end = Glu->xlusup_end;

    nextlu = xlusup[jcol];
    
    /*
     *	Process the supernodal portion of L\U[*,j]
     */
    for (isub = xlsub[fsupc]; isub < xlsub_end[fsupc]; isub++) {
  	irow = lsub[isub];
	lusup[nextlu] = dense[irow];
	dense[irow] = zero;
	++nextlu;
    }

    xlusup_end[jcol] = nextlu;
    
    if ( fsupc < jcol ) {

	luptr = xlusup[fsupc];
	nsupr = xlsub_end[fsupc] - xlsub[fsupc];
	nsupc = jcol - fsupc;	/* Excluding jcol */
	ufirst = xlusup[jcol];	/* Points to the beginning of column
				   jcol in supernode L\U(jsupno). */
	nrow = nsupr - nsupc;
	
        flopcnt = 4 * nsupc * (nsupc - 1) + 8 * nrow * nsupc;
	Gstat->procstat[pnum].fcops += flopcnt;

/*	ops[TRSV] += nsupc * (nsupc - 1);
	ops[GEMV] += 2 * nrow * nsupc;    */

#ifdef USE_VENDOR_BLAS
#if ( MACH==CRAY_PVP )
	ftcs1 = _cptofcd("L", strlen("L"));
	ftcs2 = _cptofcd("N", strlen("N"));
	ftcs3 = _cptofcd("U", strlen("U"));
	CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &lusup[luptr], &nsupr, 
	      &lusup[ufirst], &incx );
	CGEMV( ftcs2, &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr, 
	      &lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#else
	ztrsv_( "L", "N", "U", &nsupc, &lusup[luptr], &nsupr, 
	      &lusup[ufirst], &incx );
	zgemv_( "N", &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr, 
		&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#endif
#else
	zlsolve ( nsupr, nsupc, &lusup[luptr], &lusup[ufirst] );
	zmatvec ( nsupr, nrow, nsupc, &lusup[luptr+nsupc], 
		 &lusup[ufirst], &tempv[0] );

        /* Scatter tempv[*] into lusup[*] */
	iptr = ufirst + nsupc;
	for (i = 0; i < nrow; i++) {
            z_sub(&lusup[iptr], &lusup[iptr], &tempv[i]);
            ++iptr;
            tempv[i] = zero;
	}
#endif

    }

    return 0;
}
예제 #10
0
void
pzgstrf_bmod2D(
	       const int pnum,   /* process number */
	       const int m,      /* number of columns in the matrix */
	       const int w,      /* current panel width */
	       const int jcol,   /* leading column of the current panel */
	       const int fsupc,  /* leading column of the updating supernode */
	       const int krep,   /* last column of the updating supernode */
	       const int nsupc,  /* number of columns in the updating s-node */
	       int nsupr,        /* number of rows in the updating s-node */
	       int nrow,         /* number of rows below the diagonal block of
				    the updating supernode */
	       int *repfnz,      /* in */
	       int *panel_lsub,  /* modified */
	       int *w_lsub_end,  /* modified */
	       int *spa_marker,  /* modified; size n-by-w */
	       doublecomplex *dense,    /* modified */
	       doublecomplex *tempv,    /* working array - zeros on entry/exit */
	       GlobalLU_t *Glu,  /* modified */
	       Gstat_t *Gstat    /* modified */
	       )
{
/*
 * -- SuperLU MT routine (version 2.0) --
 * Lawrence Berkeley National Lab, Univ. of California Berkeley,
 * and Xerox Palo Alto Research Center.
 * September 10, 2007
 *
 * Purpose
 * =======
 *
 *    Performs numeric 2-D block updates (sup-panel) in topological order.
 *    Results are returned in SPA dense[*,w].
 *
 */
#if ( MACH==CRAY_PVP )
    _fcd ftcs1 = _cptofcd("L", strlen("L")),
         ftcs2 = _cptofcd("N", strlen("N")),
         ftcs3 = _cptofcd("U", strlen("U"));
#endif
#ifdef USE_VENDOR_BLAS
    int          incx = 1, incy = 1;
    doublecomplex      alpha, beta;
#endif
    doublecomplex      zero = {0.0, 0.0};
    doublecomplex      one = {1.0, 0.0};
    doublecomplex      comp_temp, comp_temp1;

    doublecomplex       ukj, ukj1, ukj2;
    int          luptr, luptr1, luptr2;
    int          segsze;
    int          block_nrow;  /* no of rows in a block row */
    register int lptr;	      /* points to the row subscripts of a supernode */
    int          kfnz, irow, no_zeros; 
    register int isub, isub1, i;
    register int jj;	      /* index through each column in the panel */
    int          krep_ind;
    int          *repfnz_col; /* repfnz[] for a column in the panel */
    int          *col_marker; /* each column of the spa_marker[*,w] */
    int          *col_lsub;   /* each column of the panel_lsub[*,w] */
    doublecomplex       *dense_col;  /* dense[] for a column in the panel */
    doublecomplex       *TriTmp, *MatvecTmp;
    register int ldaTmp;
    register int r_ind, r_hi;
    static   int first = 1, maxsuper, rowblk;
    int          *lsub, *xlsub_end;
    doublecomplex       *lusup;
    int          *xlusup;
    register float flopcnt;
    
#ifdef TIMING    
    double *utime = Gstat->utime;
    double f_time;
#endif    
    
    if ( first ) {
	maxsuper = sp_ienv(3);
	rowblk   = sp_ienv(4);
	first = 0;
    }
    ldaTmp = maxsuper + rowblk;

    lsub      = Glu->lsub;
    xlsub_end = Glu->xlsub_end;
    lusup     = Glu->lusup;
    xlusup    = Glu->xlusup;
    lptr      = Glu->xlsub[fsupc];
    krep_ind  = lptr + nsupc - 1;
    repfnz_col= repfnz;
    dense_col = dense;
    TriTmp    = tempv;
    col_marker= spa_marker;
    col_lsub  = panel_lsub;
	
	
    /* ---------------------------------------------------------------
     * Sequence through each column in the panel -- triangular solves.
     * The results of the triangular solves of all columns in the
     * panel are temporaroly stored in TriTemp array.
     * For the unrolled small supernodes of size <= 3, we also perform
     * matrix-vector updates from below the diagonal block.
     * ---------------------------------------------------------------
     */
    for (jj = jcol; jj < jcol + w; ++jj, col_marker += m, col_lsub += m,
	 repfnz_col += m, dense_col += m, TriTmp += ldaTmp ) {

	kfnz = repfnz_col[krep];
	if ( kfnz == EMPTY ) continue;	/* Skip any zero segment */
	    
	segsze = krep - kfnz + 1;
	luptr = xlusup[fsupc];

        flopcnt = 4 * segsze * (segsze - 1) + 8 * nrow * segsze;
	Gstat->procstat[pnum].fcops += flopcnt;

/*	ops[TRSV] += segsze * (segsze - 1);
	ops[GEMV] += 2 * nrow * segsze;        */
	
#ifdef TIMING	    
	f_time = SuperLU_timer_();
#endif
	
	/* Case 1: Update U-segment of size 1 -- col-col update */
	if ( segsze == 1 ) {
	    ukj = dense_col[lsub[krep_ind]];
	    luptr += nsupr*(nsupc-1) + nsupc;
	    for (i = lptr + nsupc; i < xlsub_end[fsupc]; i++) {
		irow = lsub[i];
                zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                z_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
		++luptr;
#ifdef SCATTER_FOUND		
		if ( col_marker[irow] != jj ) {
		    col_marker[irow] = jj;
		    col_lsub[w_lsub_end[jj-jcol]++] = irow;
		}
#endif		
	    }
#ifdef TIMING
	    utime[FLOAT] += SuperLU_timer_() - f_time;
#endif	    
	} else if ( segsze <= 3 ) {
	    ukj = dense_col[lsub[krep_ind]];
	    ukj1 = dense_col[lsub[krep_ind - 1]];
	    luptr += nsupr*(nsupc-1) + nsupc-1;
	    luptr1 = luptr - nsupr;
	    if ( segsze == 2 ) {
                zz_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                z_sub(&ukj, &ukj, &comp_temp);
		dense_col[lsub[krep_ind]] = ukj;
		for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
		    irow = lsub[i];
		    luptr++; luptr1++;
                    zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                    zz_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                    z_add(&comp_temp, &comp_temp, &comp_temp1);
                    z_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
#ifdef SCATTER_FOUND		
		    if ( col_marker[irow] != jj ) {
			col_marker[irow] = jj;
			col_lsub[w_lsub_end[jj-jcol]++] = irow;
		    }
#endif		
		}
#ifdef TIMING
		utime[FLOAT] += SuperLU_timer_() - f_time;
#endif	    
	    } else {
		ukj2 = dense_col[lsub[krep_ind - 2]];
		luptr2 = luptr1 - nsupr;
                zz_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
                z_sub(&ukj1, &ukj1, &comp_temp);

                zz_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                zz_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                z_add(&comp_temp, &comp_temp, &comp_temp1);
                z_sub(&ukj, &ukj, &comp_temp);
		dense_col[lsub[krep_ind]] = ukj;
		dense_col[lsub[krep_ind-1]] = ukj1;
		for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
		    irow = lsub[i];
		    luptr++; luptr1++; luptr2++;
                    zz_mult(&comp_temp, &ukj, &lusup[luptr]);
                    zz_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                    z_add(&comp_temp, &comp_temp, &comp_temp1);
                    zz_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                    z_add(&comp_temp, &comp_temp, &comp_temp1);
                    z_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
#ifdef SCATTER_FOUND		
		    if ( col_marker[irow] != jj ) {
			col_marker[irow] = jj;
			col_lsub[w_lsub_end[jj-jcol]++] = irow;
		    }
#endif		
		}
	    }
#ifdef TIMING
	    utime[FLOAT] += SuperLU_timer_() - f_time;
#endif
	} else  { /* segsze >= 4 */
	    /* Copy A[*,j] segment from dense[*] to TriTmp[*], which
	       holds the result of triangular solve.    */
	    no_zeros = kfnz - fsupc;
	    isub = lptr + no_zeros;
	    for (i = 0; i < segsze; ++i) {
		irow = lsub[isub];
		TriTmp[i] = dense_col[irow]; /* Gather */
		++isub;
	    }

	    /* start effective triangle */
	    luptr += nsupr * no_zeros + no_zeros;
	    
#ifdef TIMING	    
	    f_time = SuperLU_timer_();
#endif
	    
#ifdef USE_VENDOR_BLAS
#if ( MACH==CRAY_PVP )
	    CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr], 
		   &nsupr, TriTmp, &incx );
#else
	    ztrsv_( "L", "N", "U", &segsze, &lusup[luptr], 
		   &nsupr, TriTmp, &incx );
#endif
#else		
	    zlsolve ( nsupr, segsze, &lusup[luptr], TriTmp );
#endif
		
#ifdef TIMING	    
	    utime[FLOAT] += SuperLU_timer_() - f_time;
#endif	    
	} /* else ... */
	    
    }  /* for jj ... end tri-solves */

    /* --------------------------------------------------------
     * Perform block row updates from below the diagonal block.
     * Push each block all the way into SPA dense[*].
     * --------------------------------------------------------
     */
    for ( r_ind = 0; r_ind < nrow; r_ind += rowblk ) {
	    
	r_hi = SUPERLU_MIN(nrow, r_ind + rowblk);
	block_nrow = SUPERLU_MIN(rowblk, r_hi - r_ind);
	luptr = xlusup[fsupc] + nsupc + r_ind;
	isub1 = lptr + nsupc + r_ind;
	    
	repfnz_col = repfnz;
	TriTmp = tempv;
	dense_col = dense;
	col_marker= spa_marker;
	col_lsub  = panel_lsub;
	
	/* Sequence through each column in the panel -- matrix-vector */
	for (jj = jcol; jj < jcol + w; ++jj, col_marker += m, col_lsub += m,
	     repfnz_col += m, dense_col += m, TriTmp += ldaTmp) {

	    kfnz = repfnz_col[krep];
	    if ( kfnz == EMPTY ) continue; /* skip any zero segment */
	    
	    segsze = krep - kfnz + 1;
	    if ( segsze <= 3 ) continue;   /* skip unrolled cases */
		
	    /* Perform a block update, and scatter the result of
	       matrix-vector into SPA dense[*].		 */
	    no_zeros = kfnz - fsupc;
	    luptr1 = luptr + nsupr * no_zeros;
	    MatvecTmp = &TriTmp[maxsuper];
	    
#ifdef TIMING
	    f_time = SuperLU_timer_();
#endif	    
	    
#ifdef USE_VENDOR_BLAS
            alpha = one;
            beta = zero;
#if ( MACH==CRAY_PVP )
	    CGEMV( ftcs2, &block_nrow, &segsze, &alpha, &lusup[luptr], 
		  &nsupr, TriTmp, &incx, &beta, MatvecTmp, &incy );
#else
	    zgemv_( "N", &block_nrow, &segsze, &alpha, &lusup[luptr1], 
		   &nsupr, TriTmp, &incx, &beta, MatvecTmp, &incy );
#endif /* _CRAY_PVP */
#else
	    zmatvec(nsupr, block_nrow, segsze, &lusup[luptr1],
		    TriTmp, MatvecTmp);
#endif
		
#ifdef TIMING
	    utime[FLOAT] += SuperLU_timer_() - f_time;
#endif	    

	    /* Scatter MatvecTmp[*] into SPA dense[*] temporarily,
	     * such that MatvecTmp[*] can be re-used for the
	     * the next block row update. dense[] will be copied into 
	     * global store after the whole panel has been finished.
	     */
	    isub = isub1;
	    for (i = 0; i < block_nrow; i++) {
		irow = lsub[isub];
                z_sub(&dense_col[irow], &dense_col[irow],
                              &MatvecTmp[i]); /* Scatter-add */
#ifdef SCATTER_FOUND		
		if ( col_marker[irow] != jj ) {
		    col_marker[irow] = jj;
		    col_lsub[w_lsub_end[jj-jcol]++] = irow;
		}
#endif		
		MatvecTmp[i] = zero;
		++isub;
	    }
	    
	} /* for jj ... */

    } /* for each block row ... */

    
    /* ------------------------------------------------
       Scatter the triangular solves into SPA dense[*].
       ------------------------------------------------ */
    repfnz_col = repfnz;
    TriTmp = tempv;
    dense_col = dense;
    
    for (jj = 0; jj < w; ++jj, repfnz_col += m, dense_col += m, 
	 TriTmp += ldaTmp) {
	kfnz = repfnz_col[krep];
	if ( kfnz == EMPTY ) continue; /* skip any zero segment */
	
	segsze = krep - kfnz + 1;
	if ( segsze <= 3 ) continue; /* skip unrolled cases */
	
	no_zeros = kfnz - fsupc;		
	isub = lptr + no_zeros;
	for (i = 0; i < segsze; i++) {
	    irow = lsub[isub];
	    dense_col[irow] = TriTmp[i]; /* Scatter */
	    TriTmp[i] = zero;
	    ++isub;
	}
    } /* for jj ... */
	
}