int
pcgstrf_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 */
		    complex     *dense, /* modified */
		    complex     *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;
    complex      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
     */
    complex	  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;
    complex       *lusup;
    int          *xlusup, *xlusup_end;
    complex       *tempv1;
    int          mem_error;
    register float flopcnt;

    complex      zero = {0.0, 0.0};
    complex      one = {1.0, 0.0};
    complex      none = {-1.0, 0.0};
    complex      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) pcgstrf_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 = segsze * (segsze - 1) + 2 * nrow * segsze;//sj
		Gstat->procstat[pnum].fcops += flopcnt;

#if ( DEBUGlevel>=2 )
if (jcol==BADCOL)	    
printf("(%d) pcgstrf_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];
                    cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                    c_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 */
                    cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                    c_sub(&ukj, &ukj, &comp_temp);
                    dense[lsub[krep_ind]] = ukj;
                    for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
                        irow = lsub[i];
                        luptr++;
                        luptr1++;
                        cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                        cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                        c_add(&comp_temp, &comp_temp, &comp_temp1);
                        c_sub(&dense[irow], &dense[irow], &comp_temp);
                    }
                } else { /* Case 3: 3cols-col update */
                    ukj2 = dense[lsub[krep_ind - 2]];
                    luptr2 = luptr1 - nsupr;
                    cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
                    c_sub(&ukj1, &ukj1, &comp_temp);

                    cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                    cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                    c_add(&comp_temp, &comp_temp, &comp_temp1);
                    c_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++;
                        cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                        cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                        c_add(&comp_temp, &comp_temp, &comp_temp1);
                        cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                        c_add(&comp_temp, &comp_temp, &comp_temp1);
                        c_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
		ctrsv_( "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
		cgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr], 
		       &nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif
#else
		clsolve ( nsupr, segsze, &lusup[luptr], tempv );

 		luptr += segsze;  /* Dense matrix-vector */
		tempv1 = &tempv[segsze];
		cmatvec (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];
                    c_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) pcgstrf_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) pcgstrf_column_bmod[3] jcol %d, fsupc %d, nsupr %d, nsupc %d, nrow %d\n",
       pnum, jcol, fsupc, nsupr, nsupc, nrow);
#endif    

	flopcnt = nsupc * (nsupc - 1) + 2 * nrow * nsupc; //sj
	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
	ctrsv_( "L", "N", "U", &nsupc, &lusup[luptr], 
	       &nsupr, &lusup[ufirst], &incx );
	cgemv_( "N", &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
	       &lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#endif
#else
	clsolve ( nsupr, nsupc, &lusup[luptr], &lusup[ufirst] );

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

    return 0;
}
Beispiel #2
0
void
cpanel_bmod (
            const int  m,          /* in - number of rows in the matrix */
            const int  w,          /* in */
            const int  jcol,       /* in */
            const int  nseg,       /* in */
            complex     *dense,     /* out, of size n by w */
            complex     *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;
    complex       alpha, beta;
#endif

    register int k, ksub;
    int          fsupc, nsupc, nsupr, nrow;
    int          krep, krep_ind;
    complex       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;
    complex       *lusup;
    int          *xlusup;
    int          *repfnz_col; /* repfnz[] for a column in the panel */
    complex       *dense_col;  /* dense[] for a column in the panel */
    complex       *tempv1;             /* Used in 1-D update */
    complex       *TriTmp, *MatvecTmp; /* used in 2-D update */
    complex      zero = {0.0, 0.0};
    complex      one = {1.0, 0.0};
    complex      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];
                        cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                        c_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 ) {
                        cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                        c_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++;
                            cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                            cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                            c_add(&comp_temp, &comp_temp, &comp_temp1);
                            c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
                        }
                    } else {
                        ukj2 = dense_col[lsub[krep_ind - 2]];
                        luptr2 = luptr1 - nsupr;
                        cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
                        c_sub(&ukj1, &ukj1, &comp_temp);

                        cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                        cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                        c_add(&comp_temp, &comp_temp, &comp_temp1);
                        c_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++;
                            cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                            cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                            c_add(&comp_temp, &comp_temp, &comp_temp1);
                            cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                            c_add(&comp_temp, &comp_temp, &comp_temp1);
                            c_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
                    ctrsv_( "L", "N", "U", &segsze, &lusup[luptr],
                           &nsupr, TriTmp, &incx );
#endif
#else
                    clsolve ( 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
                    cgemv_("N", &block_nrow, &segsze, &alpha, &lusup[luptr1],
                           &nsupr, TriTmp, &incx, &beta, MatvecTmp, &incy);
#endif
#else
                    cmatvec(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];
                        c_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];
                        cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                        c_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 ) {
                        cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                        c_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;
                            cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                            cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                            c_add(&comp_temp, &comp_temp, &comp_temp1);
                            c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
                        }
                    } else {
                        ukj2 = dense_col[lsub[krep_ind - 2]];
                        luptr2 = luptr1 - nsupr;
                        cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
                        c_sub(&ukj1, &ukj1, &comp_temp);

                        cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                        cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                        c_add(&comp_temp, &comp_temp, &comp_temp1);
                        c_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;
                            cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                            cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                            c_add(&comp_temp, &comp_temp, &comp_temp1);
                            cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                            c_add(&comp_temp, &comp_temp, &comp_temp1);
                            c_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
                    ctrsv_( "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
                    cgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr],
                           &nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif
#else
                    clsolve ( nsupr, segsze, &lusup[luptr], tempv );

                    luptr += segsze;        /* Dense matrix-vector */
                    tempv1 = &tempv[segsze];
                    cmatvec (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];
                        c_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 ... */

}
Beispiel #3
0
int cgst01(int m, int n, SuperMatrix *A, SuperMatrix *L, 
		SuperMatrix *U, int *perm_c, int *perm_r, float *resid)
{
/* 
    Purpose   
    =======   

    CGST01 reconstructs a matrix A from its L*U factorization and   
    computes the residual   
       norm(L*U - A) / ( N * norm(A) * EPS ),   
    where EPS is the machine epsilon.   

    Arguments   
    ==========   

    M       (input) INT   
            The number of rows of the matrix A.  M >= 0.   

    N       (input) INT   
            The number of columns of the matrix A.  N >= 0.   

    A       (input) SuperMatrix *, dimension (A->nrow, A->ncol)
            The original M x N matrix A.   

    L       (input) SuperMatrix *, dimension (L->nrow, L->ncol)
            The factor matrix L.

    U       (input) SuperMatrix *, dimension (U->nrow, U->ncol)
            The factor matrix U.

    perm_c (input) INT array, dimension (N)
            The column permutation from CGSTRF.   

    perm_r  (input) INT array, dimension (M)
            The pivot indices from CGSTRF.   

    RESID   (output) FLOAT*
            norm(L*U - A) / ( N * norm(A) * EPS )   

    ===================================================================== 
*/  

    /* Local variables */
    complex zero = {0.0, 0.0};
    int i, j, k, arow, lptr,isub,  urow, superno, fsupc, u_part;
    complex utemp, comp_temp;
    float anorm, tnorm, cnorm;
    float eps;
    complex *work;
    SCformat *Lstore;
    NCformat *Astore, *Ustore;
    complex *Aval, *Lval, *Uval;
    int *colbeg, *colend;

    /* Function prototypes */
    extern float clangs(char *, SuperMatrix *);

    /* Quick exit if M = 0 or N = 0. */

    if (m <= 0 || n <= 0) {
	*resid = 0.f;
	return 0;
    }

    work = (complex *)complexCalloc(m);

    Astore = A->Store;
    Aval = Astore->nzval;
    Lstore = L->Store;
    Lval = Lstore->nzval;
    Ustore = U->Store;
    Uval = Ustore->nzval;

    colbeg = intMalloc(n);
    colend = intMalloc(n);

        for (i = 0; i < n; i++) {
            colbeg[perm_c[i]] = Astore->colptr[i]; 
	    colend[perm_c[i]] = Astore->colptr[i+1];
        }
	
    /* Determine EPS and the norm of A. */
    eps = smach("Epsilon");
    anorm = clangs("1", A);
    cnorm = 0.;

    /* Compute the product L*U, one column at a time */
    for (k = 0; k < n; ++k) {

	/* The U part outside the rectangular supernode */
        for (i = U_NZ_START(k); i < U_NZ_START(k+1); ++i) {
	    urow = U_SUB(i);
	    utemp = Uval[i];
            superno = Lstore->col_to_sup[urow];
	    fsupc = L_FST_SUPC(superno);
	    u_part = urow - fsupc + 1;
	    lptr = L_SUB_START(fsupc) + u_part;
            work[L_SUB(lptr-1)].r -= utemp.r;
            work[L_SUB(lptr-1)].i -= utemp.i;
	    for (j = L_NZ_START(urow) + u_part; j < L_NZ_START(urow+1); ++j) {
                isub = L_SUB(lptr);
	        cc_mult(&comp_temp, &utemp, &Lval[j]);
		c_sub(&work[isub], &work[isub], &comp_temp);
	        ++lptr;
	    }
	}

	/* The U part inside the rectangular supernode */
	superno = Lstore->col_to_sup[k];
	fsupc = L_FST_SUPC(superno);
	urow = L_NZ_START(k);
	for (i = fsupc; i <= k; ++i) {
	    utemp = Lval[urow++];
	    u_part = i - fsupc + 1;
	    lptr = L_SUB_START(fsupc) + u_part;
            work[L_SUB(lptr-1)].r -= utemp.r;
            work[L_SUB(lptr-1)].i -= utemp.i;
	    for (j = L_NZ_START(i)+u_part; j < L_NZ_START(i+1); ++j) {
                isub = L_SUB(lptr);
	        cc_mult(&comp_temp, &utemp, &Lval[j]);
		c_sub(&work[isub], &work[isub], &comp_temp);
	        ++lptr;
	    }
	}

	/* Now compute A[k] - (L*U)[k] (Both matrices may be permuted.) */

	for (i = colbeg[k]; i < colend[k]; ++i) {
	    arow = Astore->rowind[i];
	    work[perm_r[arow]].r += Aval[i].r;
	    work[perm_r[arow]].i += Aval[i].i;
        }

	/* Now compute the 1-norm of the column vector work */
        tnorm = 0.;
	for (i = 0; i < m; ++i) {
            tnorm += fabs(work[i].r) + fabs(work[i].i);
	    work[i] = zero;
	}
	cnorm = SUPERLU_MAX(tnorm, cnorm);
    }

    *resid = cnorm;

    if (anorm <= 0.f) {
	if (*resid != 0.f) {
	    *resid = 1.f / eps;
	}
    } else {
	*resid = *resid / (float) n / anorm / eps;
    }

    SUPERLU_FREE(work);
    SUPERLU_FREE(colbeg);
    SUPERLU_FREE(colend);
    return 0;

/*     End of CGST01 */

} /* cgst01_ */
Beispiel #4
0
int
cpivotL(
        const int  jcol,     /* in */
        const float u,      /* in - diagonal pivoting threshold */
        int        *usepr,   /* re-use the pivot sequence given by perm_r/iperm_r */
        int        *perm_r,  /* may be modified */
        int        *iperm_r, /* in - inverse of perm_r */
        int        *iperm_c, /* in - used to find diagonal of Pc*A*Pc' */
        int        *pivrow,  /* out */
        GlobalLU_t *Glu,     /* modified - global LU data structures */
	SuperLUStat_t *stat  /* output */
       )
{

    complex one = {1.0, 0.0};
    int          fsupc;	    /* first column in the supernode */
    int          nsupc;	    /* no of columns in the supernode */
    int          nsupr;     /* no of rows in the supernode */
    int          lptr;	    /* points to the starting subscript of the supernode */
    int          pivptr, old_pivptr, diag, diagind;
    float       pivmax, rtemp, thresh;
    complex       temp;
    complex       *lu_sup_ptr; 
    complex       *lu_col_ptr;
    int          *lsub_ptr;
    int          isub, icol, k, itemp;
    int          *lsub, *xlsub;
    complex       *lusup;
    int          *xlusup;
    flops_t      *ops = stat->ops;

    /* Initialize pointers */
    lsub       = Glu->lsub;
    xlsub      = Glu->xlsub;
    lusup      = Glu->lusup;
    xlusup     = Glu->xlusup;
    fsupc      = (Glu->xsup)[(Glu->supno)[jcol]];
    nsupc      = jcol - fsupc;	        /* excluding jcol; nsupc >= 0 */
    lptr       = xlsub[fsupc];
    nsupr      = xlsub[fsupc+1] - lptr;
    lu_sup_ptr = &lusup[xlusup[fsupc]];	/* start of the current supernode */
    lu_col_ptr = &lusup[xlusup[jcol]];	/* start of jcol in the supernode */
    lsub_ptr   = &lsub[lptr];	/* start of row indices of the supernode */

#ifdef DEBUG
if ( jcol == MIN_COL ) {
    printf(_T("Before cdiv: col %d\n"), jcol);
    for (k = nsupc; k < nsupr; k++) 
	printf(_T("  lu[%d] %f\n"), lsub_ptr[k], lu_col_ptr[k]);
}
#endif
    
    /* Determine the largest abs numerical value for partial pivoting;
       Also search for user-specified pivot, and diagonal element. */
    if ( *usepr ) *pivrow = iperm_r[jcol];
    diagind = iperm_c[jcol];
    pivmax = 0.0;
    pivptr = nsupc;
    diag = EMPTY;
    old_pivptr = nsupc;
    for (isub = nsupc; isub < nsupr; ++isub) {
        rtemp = c_abs1 (&lu_col_ptr[isub]);
	if ( rtemp > pivmax ) {
	    pivmax = rtemp;
	    pivptr = isub;
	}
	if ( *usepr && lsub_ptr[isub] == *pivrow ) old_pivptr = isub;
	if ( lsub_ptr[isub] == diagind ) diag = isub;
    }

    /* Test for singularity */
    if ( pivmax == 0.0 ) {
	*pivrow = lsub_ptr[pivptr];
	perm_r[*pivrow] = jcol;
	*usepr = 0;
	return (jcol+1);
    }

    thresh = u * pivmax;
    
    /* Choose appropriate pivotal element by our policy. */
    if ( *usepr ) {
        rtemp = c_abs1 (&lu_col_ptr[old_pivptr]);
	if ( rtemp != 0.0 && rtemp >= thresh )
	    pivptr = old_pivptr;
	else
	    *usepr = 0;
    }
    if ( *usepr == 0 ) {
	/* Use diagonal pivot? */
	if ( diag >= 0 ) { /* diagonal exists */
            rtemp = c_abs1 (&lu_col_ptr[diag]);
	    if ( rtemp != 0.0 && rtemp >= thresh ) pivptr = diag;
        }
	*pivrow = lsub_ptr[pivptr];
    }
    
    /* Record pivot row */
    perm_r[*pivrow] = jcol;
    
    /* Interchange row subscripts */
    if ( pivptr != nsupc ) {
	itemp = lsub_ptr[pivptr];
	lsub_ptr[pivptr] = lsub_ptr[nsupc];
	lsub_ptr[nsupc] = itemp;

	/* Interchange numerical values as well, for the whole snode, such 
	 * that L is indexed the same way as A.
 	 */
	for (icol = 0; icol <= nsupc; icol++) {
	    itemp = pivptr + icol * nsupr;
	    temp = lu_sup_ptr[itemp];
	    lu_sup_ptr[itemp] = lu_sup_ptr[nsupc + icol*nsupr];
	    lu_sup_ptr[nsupc + icol*nsupr] = temp;
	}
    } /* if */

    /* cdiv operation */
    ops[FACT] += 10 * (nsupr - nsupc);

    c_div(&temp, &one, &lu_col_ptr[nsupc]);
    for (k = nsupc+1; k < nsupr; k++) 
	cc_mult(&lu_col_ptr[k], &lu_col_ptr[k], &temp);

    return 0;
}
Beispiel #5
0
int
ilu_cpivotL(
	const int  jcol,     /* in */
	const double u,      /* in - diagonal pivoting threshold */
	int	   *usepr,   /* re-use the pivot sequence given by
			      * perm_r/iperm_r */
	int	   *perm_r,  /* may be modified */
	int	   diagind,  /* diagonal of Pc*A*Pc' */
	int	   *swap,    /* in/out record the row permutation */
	int	   *iswap,   /* in/out inverse of swap, it is the same as
				perm_r after the factorization */
	int	   *marker,  /* in */
	int	   *pivrow,  /* in/out, as an input if *usepr!=0 */
	double	   fill_tol, /* in - fill tolerance of current column
			      * used for a singular column */
	milu_t	   milu,     /* in */
	complex	   drop_sum, /* in - computed in ilu_ccopy_to_ucol()
                                (MILU only) */
	GlobalLU_t *Glu,     /* modified - global LU data structures */
	SuperLUStat_t *stat  /* output */
       )
{

    int		 n;	 /* number of columns */
    int		 fsupc;  /* first column in the supernode */
    int		 nsupc;  /* no of columns in the supernode */
    int		 nsupr;  /* no of rows in the supernode */
    int		 lptr;	 /* points to the starting subscript of the supernode */
    register int	 pivptr;
    int		 old_pivptr, diag, ptr0;
    register float  pivmax, rtemp;
    float	 thresh;
    complex	 temp;
    complex	 *lu_sup_ptr;
    complex	 *lu_col_ptr;
    int		 *lsub_ptr;
    register int	 isub, icol, k, itemp;
    int		 *lsub, *xlsub;
    complex	 *lusup;
    int		 *xlusup;
    flops_t	 *ops = stat->ops;
    int		 info;
    complex one = {1.0, 0.0};

    /* Initialize pointers */
    n	       = Glu->n;
    lsub       = Glu->lsub;
    xlsub      = Glu->xlsub;
    lusup      = Glu->lusup;
    xlusup     = Glu->xlusup;
    fsupc      = (Glu->xsup)[(Glu->supno)[jcol]];
    nsupc      = jcol - fsupc;		/* excluding jcol; nsupc >= 0 */
    lptr       = xlsub[fsupc];
    nsupr      = xlsub[fsupc+1] - lptr;
    lu_sup_ptr = &lusup[xlusup[fsupc]]; /* start of the current supernode */
    lu_col_ptr = &lusup[xlusup[jcol]];	/* start of jcol in the supernode */
    lsub_ptr   = &lsub[lptr];	/* start of row indices of the supernode */

    /* Determine the largest abs numerical value for partial pivoting;
       Also search for user-specified pivot, and diagonal element. */
    pivmax = -1.0;
    pivptr = nsupc;
    diag = EMPTY;
    old_pivptr = nsupc;
    ptr0 = EMPTY;
    for (isub = nsupc; isub < nsupr; ++isub) {
        if (marker[lsub_ptr[isub]] > jcol)
            continue; /* do not overlap with a later relaxed supernode */

	switch (milu) {
	    case SMILU_1:
                c_add(&temp, &lu_col_ptr[isub], &drop_sum);
		rtemp = c_abs1(&temp);
		break;
	    case SMILU_2:
	    case SMILU_3:
                /* In this case, drop_sum contains the sum of the abs. value */
		rtemp = c_abs1(&lu_col_ptr[isub]);
		break;
	    case SILU:
	    default:
		rtemp = c_abs1(&lu_col_ptr[isub]);
		break;
	}
	if (rtemp > pivmax) { pivmax = rtemp; pivptr = isub; }
	if (*usepr && lsub_ptr[isub] == *pivrow) old_pivptr = isub;
	if (lsub_ptr[isub] == diagind) diag = isub;
	if (ptr0 == EMPTY) ptr0 = isub;
    }

    if (milu == SMILU_2 || milu == SMILU_3) pivmax += drop_sum.r;

    /* Test for singularity */
    if (pivmax < 0.0) {
	fprintf(stderr, "[0]: jcol=%d, SINGULAR!!!\n", jcol);
	fflush(stderr);
	exit(1);
    }
    if ( pivmax == 0.0 ) {
	if (diag != EMPTY)
	    *pivrow = lsub_ptr[pivptr = diag];
	else if (ptr0 != EMPTY)
	    *pivrow = lsub_ptr[pivptr = ptr0];
	else {
	    /* look for the first row which does not
	       belong to any later supernodes */
	    for (icol = jcol; icol < n; icol++)
		if (marker[swap[icol]] <= jcol) break;
	    if (icol >= n) {
		fprintf(stderr, "[1]: jcol=%d, SINGULAR!!!\n", jcol);
		fflush(stderr);
		exit(1);
	    }

	    *pivrow = swap[icol];

	    /* pick up the pivot row */
	    for (isub = nsupc; isub < nsupr; ++isub)
		if ( lsub_ptr[isub] == *pivrow ) { pivptr = isub; break; }
	}
	pivmax = fill_tol;
	lu_col_ptr[pivptr].r = pivmax;
	lu_col_ptr[pivptr].i = 0.0;
	*usepr = 0;
#ifdef DEBUG
	printf("[0] ZERO PIVOT: FILL (%d, %d).\n", *pivrow, jcol);
	fflush(stdout);
#endif
	info =jcol + 1;
    } /* if (*pivrow == 0.0) */
    else {
	thresh = u * pivmax;

	/* Choose appropriate pivotal element by our policy. */
	if ( *usepr ) {
	    switch (milu) {
		case SMILU_1:
                    c_add(&temp, &lu_col_ptr[old_pivptr], &drop_sum);
		    rtemp = c_abs1(&temp);
		    break;
		case SMILU_2:
		case SMILU_3:
		    rtemp = c_abs1(&lu_col_ptr[old_pivptr]) + drop_sum.r;
		    break;
		case SILU:
		default:
		    rtemp = c_abs1(&lu_col_ptr[old_pivptr]);
		    break;
	    }
	    if ( rtemp != 0.0 && rtemp >= thresh ) pivptr = old_pivptr;
	    else *usepr = 0;
	}
	if ( *usepr == 0 ) {
	    /* Use diagonal pivot? */
	    if ( diag >= 0 ) { /* diagonal exists */
		switch (milu) {
		    case SMILU_1:
                        c_add(&temp, &lu_col_ptr[diag], &drop_sum);
         	        rtemp = c_abs1(&temp);
			break;
		    case SMILU_2:
		    case SMILU_3:
			rtemp = c_abs1(&lu_col_ptr[diag]) + drop_sum.r;
			break;
		    case SILU:
		    default:
			rtemp = c_abs1(&lu_col_ptr[diag]);
			break;
		}
		if ( rtemp != 0.0 && rtemp >= thresh ) pivptr = diag;
	    }
	    *pivrow = lsub_ptr[pivptr];
	}
	info = 0;

	/* Reset the diagonal */
	switch (milu) {
	    case SMILU_1:
		c_add(&lu_col_ptr[pivptr], &lu_col_ptr[pivptr], &drop_sum);
		break;
	    case SMILU_2:
	    case SMILU_3:
                temp = c_sgn(&lu_col_ptr[pivptr]);
                cc_mult(&temp, &temp, &drop_sum);
                c_add(&lu_col_ptr[pivptr], &lu_col_ptr[pivptr], &drop_sum);
		break;
	    case SILU:
	    default:
		break;
	}

    } /* else */

    /* Record pivot row */
    perm_r[*pivrow] = jcol;
    if (jcol < n - 1) {
	register int t1, t2, t;
	t1 = iswap[*pivrow]; t2 = jcol;
	if (t1 != t2) {
	    t = swap[t1]; swap[t1] = swap[t2]; swap[t2] = t;
	    t1 = swap[t1]; t2 = t;
	    t = iswap[t1]; iswap[t1] = iswap[t2]; iswap[t2] = t;
	}
    } /* if (jcol < n - 1) */

    /* Interchange row subscripts */
    if ( pivptr != nsupc ) {
	itemp = lsub_ptr[pivptr];
	lsub_ptr[pivptr] = lsub_ptr[nsupc];
	lsub_ptr[nsupc] = itemp;

	/* Interchange numerical values as well, for the whole snode, such 
	 * that L is indexed the same way as A.
	 */
	for (icol = 0; icol <= nsupc; icol++) {
	    itemp = pivptr + icol * nsupr;
	    temp = lu_sup_ptr[itemp];
	    lu_sup_ptr[itemp] = lu_sup_ptr[nsupc + icol*nsupr];
	    lu_sup_ptr[nsupc + icol*nsupr] = temp;
	}
    } /* if */

    /* cdiv operation */
    ops[FACT] += 10 * (nsupr - nsupc);
    c_div(&temp, &one, &lu_col_ptr[nsupc]);
    for (k = nsupc+1; k < nsupr; k++) 
	cc_mult(&lu_col_ptr[k], &lu_col_ptr[k], &temp);

    return info;
}
Beispiel #6
0
/*! \brief
 * <pre>
 * Purpose
 * =======
 *    ilu_cdrop_row() - Drop some small rows from the previous 
 *    supernode (L-part only).
 * </pre>
 */
int ilu_cdrop_row(
	superlu_options_t *options, /* options */
	int    first,	    /* index of the first column in the supernode */
	int    last,	    /* index of the last column in the supernode */
	double drop_tol,    /* dropping parameter */
	int    quota,	    /* maximum nonzero entries allowed */
	int    *nnzLj,	    /* in/out number of nonzeros in L(:, 1:last) */
	double *fill_tol,   /* in/out - on exit, fill_tol=-num_zero_pivots,
			     * does not change if options->ILU_MILU != SMILU1 */
	GlobalLU_t *Glu,    /* modified */
	float swork[],   /* working space
	                     * the length of swork[] should be no less than
			     * the number of rows in the supernode */
	float swork2[], /* working space with the same size as swork[],
			     * used only by the second dropping rule */
	int    lastc	    /* if lastc == 0, there is nothing after the
			     * working supernode [first:last];
			     * if lastc == 1, there is one more column after
			     * the working supernode. */ )
{
    register int i, j, k, m1;
    register int nzlc; /* number of nonzeros in column last+1 */
    register int xlusup_first, xlsub_first;
    int m, n; /* m x n is the size of the supernode */
    int r = 0; /* number of dropped rows */
    register float *temp;
    register complex *lusup = (complex *) Glu->lusup;
    register int *lsub = Glu->lsub;
    register int *xlsub = Glu->xlsub;
    register int *xlusup = Glu->xlusup;
    register float d_max = 0.0, d_min = 1.0;
    int    drop_rule = options->ILU_DropRule;
    milu_t milu = options->ILU_MILU;
    norm_t nrm = options->ILU_Norm;
    complex zero = {0.0, 0.0};
    complex one = {1.0, 0.0};
    complex none = {-1.0, 0.0};
    int i_1 = 1;
    int inc_diag; /* inc_diag = m + 1 */
    int nzp = 0;  /* number of zero pivots */
    float alpha = pow((double)(Glu->n), -1.0 / options->ILU_MILU_Dim);

    xlusup_first = xlusup[first];
    xlsub_first = xlsub[first];
    m = xlusup[first + 1] - xlusup_first;
    n = last - first + 1;
    m1 = m - 1;
    inc_diag = m + 1;
    nzlc = lastc ? (xlusup[last + 2] - xlusup[last + 1]) : 0;
    temp = swork - n;

    /* Quick return if nothing to do. */
    if (m == 0 || m == n || drop_rule == NODROP)
    {
	*nnzLj += m * n;
	return 0;
    }

    /* basic dropping: ILU(tau) */
    for (i = n; i <= m1; )
    {
	/* the average abs value of ith row */
	switch (nrm)
	{
	    case ONE_NORM:
		temp[i] = scasum_(&n, &lusup[xlusup_first + i], &m) / (double)n;
		break;
	    case TWO_NORM:
		temp[i] = scnrm2_(&n, &lusup[xlusup_first + i], &m)
		    / sqrt((double)n);
		break;
	    case INF_NORM:
	    default:
		k = icamax_(&n, &lusup[xlusup_first + i], &m) - 1;
		temp[i] = c_abs1(&lusup[xlusup_first + i + m * k]);
		break;
	}

	/* drop small entries due to drop_tol */
	if (drop_rule & DROP_BASIC && temp[i] < drop_tol)
	{
	    r++;
	    /* drop the current row and move the last undropped row here */
	    if (r > 1) /* add to last row */
	    {
		/* accumulate the sum (for MILU) */
		switch (milu)
		{
		    case SMILU_1:
		    case SMILU_2:
			caxpy_(&n, &one, &lusup[xlusup_first + i], &m,
				&lusup[xlusup_first + m - 1], &m);
			break;
		    case SMILU_3:
			for (j = 0; j < n; j++)
			    lusup[xlusup_first + (m - 1) + j * m].r +=
				    c_abs1(&lusup[xlusup_first + i + j * m]);
			break;
		    case SILU:
		    default:
			break;
		}
		ccopy_(&n, &lusup[xlusup_first + m1], &m,
                       &lusup[xlusup_first + i], &m);
	    } /* if (r > 1) */
	    else /* move to last row */
	    {
		cswap_(&n, &lusup[xlusup_first + m1], &m,
			&lusup[xlusup_first + i], &m);
		if (milu == SMILU_3)
		    for (j = 0; j < n; j++) {
			lusup[xlusup_first + m1 + j * m].r =
				c_abs1(&lusup[xlusup_first + m1 + j * m]);
			lusup[xlusup_first + m1 + j * m].i = 0.0;
                    }
	    }
	    lsub[xlsub_first + i] = lsub[xlsub_first + m1];
	    m1--;
	    continue;
	} /* if dropping */
	else
	{
	    if (temp[i] > d_max) d_max = temp[i];
	    if (temp[i] < d_min) d_min = temp[i];
	}
	i++;
    } /* for */

    /* Secondary dropping: drop more rows according to the quota. */
    quota = ceil((double)quota / (double)n);
    if (drop_rule & DROP_SECONDARY && m - r > quota)
    {
	register double tol = d_max;

	/* Calculate the second dropping tolerance */
	if (quota > n)
	{
	    if (drop_rule & DROP_INTERP) /* by interpolation */
	    {
		d_max = 1.0 / d_max; d_min = 1.0 / d_min;
		tol = 1.0 / (d_max + (d_min - d_max) * quota / (m - n - r));
	    }
	    else /* by quick select */
	    {
		int len = m1 - n + 1;
		scopy_(&len, swork, &i_1, swork2, &i_1);
		tol = sqselect(len, swork2, quota - n);
#if 0
		register int *itemp = iwork - n;
		A = temp;
		for (i = n; i <= m1; i++) itemp[i] = i;
		qsort(iwork, m1 - n + 1, sizeof(int), _compare_);
		tol = temp[itemp[quota]];
#endif
	    }
	}

	for (i = n; i <= m1; )
	{
	    if (temp[i] <= tol)
	    {
		register int j;
		r++;
		/* drop the current row and move the last undropped row here */
		if (r > 1) /* add to last row */
		{
		    /* accumulate the sum (for MILU) */
		    switch (milu)
		    {
			case SMILU_1:
			case SMILU_2:
			    caxpy_(&n, &one, &lusup[xlusup_first + i], &m,
				    &lusup[xlusup_first + m - 1], &m);
			    break;
			case SMILU_3:
			    for (j = 0; j < n; j++)
				lusup[xlusup_first + (m - 1) + j * m].r +=
   				  c_abs1(&lusup[xlusup_first + i + j * m]);
			    break;
			case SILU:
			default:
			    break;
		    }
		    ccopy_(&n, &lusup[xlusup_first + m1], &m,
			    &lusup[xlusup_first + i], &m);
		} /* if (r > 1) */
		else /* move to last row */
		{
		    cswap_(&n, &lusup[xlusup_first + m1], &m,
			    &lusup[xlusup_first + i], &m);
		    if (milu == SMILU_3)
			for (j = 0; j < n; j++) {
			    lusup[xlusup_first + m1 + j * m].r =
				    c_abs1(&lusup[xlusup_first + m1 + j * m]);
			    lusup[xlusup_first + m1 + j * m].i = 0.0;
                        }
		}
		lsub[xlsub_first + i] = lsub[xlsub_first + m1];
		m1--;
		temp[i] = temp[m1];

		continue;
	    }
	    i++;

	} /* for */

    } /* if secondary dropping */

    for (i = n; i < m; i++) temp[i] = 0.0;

    if (r == 0)
    {
	*nnzLj += m * n;
	return 0;
    }

    /* add dropped entries to the diagnal */
    if (milu != SILU)
    {
	register int j;
	complex t;
	float omega;
	for (j = 0; j < n; j++)
	{
	    t = lusup[xlusup_first + (m - 1) + j * m];
            if (t.r == 0.0 && t.i == 0.0) continue;
            omega = SUPERLU_MIN(2.0 * (1.0 - alpha) / c_abs1(&t), 1.0);
	    cs_mult(&t, &t, omega);

 	    switch (milu)
	    {
		case SMILU_1:
		    if ( !(c_eq(&t, &none)) ) {
                        c_add(&t, &t, &one);
                        cc_mult(&lusup[xlusup_first + j * inc_diag],
			                  &lusup[xlusup_first + j * inc_diag],
                                          &t);
                    }
		    else
		    {
                        cs_mult(
                                &lusup[xlusup_first + j * inc_diag],
			        &lusup[xlusup_first + j * inc_diag],
                                *fill_tol);
#ifdef DEBUG
			printf("[1] ZERO PIVOT: FILL col %d.\n", first + j);
			fflush(stdout);
#endif
			nzp++;
		    }
		    break;
		case SMILU_2:
                    cs_mult(&lusup[xlusup_first + j * inc_diag],
                                          &lusup[xlusup_first + j * inc_diag],
                                          1.0 + c_abs1(&t));
		    break;
		case SMILU_3:
                    c_add(&t, &t, &one);
                    cc_mult(&lusup[xlusup_first + j * inc_diag],
	                              &lusup[xlusup_first + j * inc_diag],
                                      &t);
		    break;
		case SILU:
		default:
		    break;
	    }
	}
	if (nzp > 0) *fill_tol = -nzp;
    }

    /* Remove dropped entries from the memory and fix the pointers. */
    m1 = m - r;
    for (j = 1; j < n; j++)
    {
	register int tmp1, tmp2;
	tmp1 = xlusup_first + j * m1;
	tmp2 = xlusup_first + j * m;
	for (i = 0; i < m1; i++)
	    lusup[i + tmp1] = lusup[i + tmp2];
    }
    for (i = 0; i < nzlc; i++)
	lusup[xlusup_first + i + n * m1] = lusup[xlusup_first + i + n * m];
    for (i = 0; i < nzlc; i++)
	lsub[xlsub[last + 1] - r + i] = lsub[xlsub[last + 1] + i];
    for (i = first + 1; i <= last + 1; i++)
    {
	xlusup[i] -= r * (i - first);
	xlsub[i] -= r;
    }
    if (lastc)
    {
	xlusup[last + 2] -= r * n;
	xlsub[last + 2] -= r;
    }

    *nnzLj += (m - r) * n;
    return r;
}
Beispiel #7
0
/*! \brief Performs one of the matrix-vector operations y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y
 *
 * <pre>  
 *   Purpose   
 *   =======   
 *
 *   sp_cgemv()  performs one of the matrix-vector operations   
 *      y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,   
 *   where alpha and beta are scalars, x and y are vectors and A is a
 *   sparse A->nrow by A->ncol matrix.   
 *
 *   Parameters   
 *   ==========   
 *
 *   TRANS  - (input) char*
 *            On entry, TRANS specifies the operation to be performed as   
 *            follows:   
 *               TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.   
 *               TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.   
 *               TRANS = 'C' or 'c'   y := alpha*A^H*x + beta*y.   
 *
 *   ALPHA  - (input) complex
 *            On entry, ALPHA specifies the scalar alpha.   
 *
 *   A      - (input) SuperMatrix*
 *            Before entry, the leading m by n part of the array A must   
 *            contain the matrix of coefficients.   
 *
 *   X      - (input) complex*, array of DIMENSION at least   
 *            ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'   
 *           and at least   
 *            ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.   
 *            Before entry, the incremented array X must contain the   
 *            vector x.   
 * 
 *   INCX   - (input) int
 *            On entry, INCX specifies the increment for the elements of   
 *            X. INCX must not be zero.   
 *
 *   BETA   - (input) complex
 *            On entry, BETA specifies the scalar beta. When BETA is   
 *            supplied as zero then Y need not be set on input.   
 *
 *   Y      - (output) complex*,  array of DIMENSION at least   
 *            ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'   
 *            and at least   
 *            ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.   
 *            Before entry with BETA non-zero, the incremented array Y   
 *            must contain the vector y. On exit, Y is overwritten by the 
 *            updated vector y.
 *	      
 *   INCY   - (input) int
 *            On entry, INCY specifies the increment for the elements of   
 *            Y. INCY must not be zero.   
 *
 *    ==== Sparse Level 2 Blas routine.   
 * </pre>
*/
int
sp_cgemv(char *trans, complex alpha, SuperMatrix *A, complex *x, 
	 int incx, complex beta, complex *y, int incy)
{

    /* Local variables */
    NCformat *Astore;
    complex   *Aval;
    int info;
    complex temp, temp1;
    int lenx, leny, i, j, irow;
    int iy, jx, jy, kx, ky;
    int notran;
    complex comp_zero = {0.0, 0.0};
    complex comp_one = {1.0, 0.0};

    notran = ( strncmp(trans, "N", 1)==0 || strncmp(trans, "n", 1)==0 );
    Astore = A->Store;
    Aval = Astore->nzval;
    
    /* Test the input parameters */
    info = 0;
    if ( !notran && strncmp(trans, "T", 1)!=0 && strncmp(trans, "C", 1)!=0)
        info = 1;
    else if ( A->nrow < 0 || A->ncol < 0 ) info = 3;
    else if (incx == 0) info = 5;
    else if (incy == 0)	info = 8;
    if (info != 0) {
	input_error("sp_cgemv ", &info);
	return 0;
    }

    /* Quick return if possible. */
    if (A->nrow == 0 || A->ncol == 0 || 
	c_eq(&alpha, &comp_zero) && 
	c_eq(&beta, &comp_one))
	return 0;

    /* Set  LENX  and  LENY, the lengths of the vectors x and y, and set 
       up the start points in  X  and  Y. */
    if ( notran ) {
	lenx = A->ncol;
	leny = A->nrow;
    } else {
	lenx = A->nrow;
	leny = A->ncol;
    }
    if (incx > 0) kx = 0;
    else kx =  - (lenx - 1) * incx;
    if (incy > 0) ky = 0;
    else ky =  - (leny - 1) * incy;

    /* Start the operations. In this version the elements of A are   
       accessed sequentially with one pass through A. */
    /* First form  y := beta*y. */
    if ( !c_eq(&beta, &comp_one) ) {
	if (incy == 1) {
	    if ( c_eq(&beta, &comp_zero) )
		for (i = 0; i < leny; ++i) y[i] = comp_zero;
	    else
		for (i = 0; i < leny; ++i) 
		  cc_mult(&y[i], &beta, &y[i]);
	} else {
	    iy = ky;
	    if ( c_eq(&beta, &comp_zero) )
		for (i = 0; i < leny; ++i) {
		    y[iy] = comp_zero;
		    iy += incy;
		}
	    else
		for (i = 0; i < leny; ++i) {
		    cc_mult(&y[iy], &beta, &y[iy]);
		    iy += incy;
		}
	}
    }
    
    if ( c_eq(&alpha, &comp_zero) ) return 0;

    if ( notran ) {
	/* Form  y := alpha*A*x + y. */
	jx = kx;
	if (incy == 1) {
	    for (j = 0; j < A->ncol; ++j) {
		if ( !c_eq(&x[jx], &comp_zero) ) {
		    cc_mult(&temp, &alpha, &x[jx]);
		    for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
			irow = Astore->rowind[i];
			cc_mult(&temp1, &temp,  &Aval[i]);
			c_add(&y[irow], &y[irow], &temp1);
		    }
		}
		jx += incx;
	    }
	} else {
	    ABORT("Not implemented.");
	}
    } else if (strncmp(trans, "T", 1) == 0 || strncmp(trans, "t", 1) == 0) {
	/* Form  y := alpha*A'*x + y. */
	jy = ky;
	if (incx == 1) {
	    for (j = 0; j < A->ncol; ++j) {
		temp = comp_zero;
		for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
		    irow = Astore->rowind[i];
		    cc_mult(&temp1, &Aval[i], &x[irow]);
		    c_add(&temp, &temp, &temp1);
		}
		cc_mult(&temp1, &alpha, &temp);
		c_add(&y[jy], &y[jy], &temp1);
		jy += incy;
	    }
	} else {
	    ABORT("Not implemented.");
	}
    } else { /* trans == 'C' or 'c' */
	/* Form  y := alpha * conj(A) * x + y. */
	complex temp2;
	jy = ky;
	if (incx == 1) {
	    for (j = 0; j < A->ncol; ++j) {
		temp = comp_zero;
		for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
		    irow = Astore->rowind[i];
		    temp2.r = Aval[i].r;
		    temp2.i = -Aval[i].i;  /* conjugation */
		    cc_mult(&temp1, &temp2, &x[irow]);
		    c_add(&temp, &temp, &temp1);
		}
		cc_mult(&temp1, &alpha, &temp);
		c_add(&y[jy], &y[jy], &temp1);
		jy += incy;
	    }
	} else {
	    ABORT("Not implemented.");
	}
    }

    return 0;    
} /* sp_cgemv */
Beispiel #8
0
/*! \brief Solves one of the systems of equations A*x = b,   or   A'*x = b
 * 
 * <pre>
 *   Purpose
 *   =======
 *
 *   sp_ctrsv() 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_C, Mtype = TRLU.
 *
 *   U       - (input) SuperMatrix*
 *	        The factor U from the factorization Pr*A*Pc=L*U.
 *	        U has types: Stype = NC, Dtype = SLU_C, Mtype = TRU.
 *    
 *   x       - (input/output) complex*
 *             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_ctrsv(char *uplo, char *trans, char *diag, SuperMatrix *L, 
         SuperMatrix *U, complex *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;
    complex   *Lval, *Uval;
    int incx = 1, incy = 1;
    complex temp;
    complex alpha = {1.0, 0.0}, beta = {1.0, 0.0};
    complex comp_zero = {0.0, 0.0};
    int nrow;
    int fsupc, nsupr, nsupc, luptr, istart, irow;
    int i, k, iptr, jcol;
    complex *work;
    flops_t solve_ops;

    /* Test the input parameters */
    *info = 0;
    if ( strncmp(uplo,"L", 1)!=0 && strncmp(uplo, "U", 1)!=0 ) *info = -1;
    else if ( strncmp(trans, "N", 1)!=0 && strncmp(trans, "T", 1)!=0 && 
              strncmp(trans, "C", 1)!=0) *info = -2;
    else if ( strncmp(diag, "U", 1)!=0 && strncmp(diag, "N", 1)!=0 )
         *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);
	input_error("sp_ctrsv", &i);
	return 0;
    }

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

    if ( !(work = complexCalloc(L->nrow)) )
	ABORT("Malloc fails for work in sp_ctrsv().");
    
    if ( strncmp(trans, "N", 1)==0 ) {	/* Form x := inv(A)*x. */
	
	if ( strncmp(uplo, "L", 1)==0 ) {
	    /* 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 c_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;
			cc_mult(&comp_zero, &x[fsupc], &Lval[luptr]);
			c_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
		    ctrsv_("L", "N", "U", &nsupc, &Lval[luptr], &nsupr,
		       	&x[fsupc], &incx);
		
		    cgemv_("N", &nrow, &nsupc, &alpha, &Lval[luptr+nsupc], 
		       	&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#endif
#else
		    clsolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc]);
		
		    cmatvec ( 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);
			c_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 c_div costs 10 flops */
    	        solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;

		if ( nsupc == 1 ) {
		    c_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
		    for (i = U_NZ_START(fsupc); i < U_NZ_START(fsupc+1); ++i) {
			irow = U_SUB(i);
			cc_mult(&comp_zero, &x[fsupc], &Uval[i]);
			c_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
		    ctrsv_("U", "N", "N", &nsupc, &Lval[luptr], &nsupr,
                           &x[fsupc], &incx);
#endif
#else		
		    cusolve ( 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);
			cc_mult(&comp_zero, &x[jcol], &Uval[i]);
			c_sub(&x[irow], &x[irow], &comp_zero);
		    	}
                    }
		}
	    } /* for k ... */
	    
	}
    } else if ( strncmp(trans, "T", 1)==0 ) { /* Form x := inv(A')*x */
	
	if ( strncmp(uplo, "L", 1)==0 ) {
	    /* 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);
			cc_mult(&comp_zero, &x[irow], &Lval[i]);
		    	c_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
		    ctrsv_("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);
			cc_mult(&comp_zero, &x[irow], &Uval[i]);
		    	c_sub(&x[jcol], &x[jcol], &comp_zero);
		    }
		}

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

		if ( nsupc == 1 ) {
		    c_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
		    ctrsv_("U", "T", "N", &nsupc, &Lval[luptr], &nsupr,
			    &x[fsupc], &incx);
#endif
		}
	    } /* for k ... */
	}
    } else { /* Form x := conj(inv(A'))*x */
	
	if ( strncmp(uplo, "L", 1)==0 ) {
	    /* 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);
                        cc_conj(&temp, &Lval[i]);
			cc_mult(&comp_zero, &x[irow], &temp);
		    	c_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"));
		    CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
			&x[fsupc], &incx);
#else
                    ctrsv_("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);
                        cc_conj(&temp, &Uval[i]);
			cc_mult(&comp_zero, &x[irow], &temp);
		    	c_sub(&x[jcol], &x[jcol], &comp_zero);
		    }
		}

                /* 1 c_div costs 10 flops */
		solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
 
		if ( nsupc == 1 ) {
                    cc_conj(&temp, &Lval[luptr]);
		    c_div(&x[fsupc], &x[fsupc], &temp);
		} else {
#ifdef _CRAY
                    ftcs1 = _cptofcd("U", strlen("U"));
                    ftcs2 = _cptofcd(trans, strlen("T"));
                    ftcs3 = _cptofcd("N", strlen("N"));
		    CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
			    &x[fsupc], &incx);
#else
                    ctrsv_("U", trans, "N", &nsupc, &Lval[luptr], &nsupr,
                               &x[fsupc], &incx);
#endif
  		}
  	    } /* for k ... */
  	}
    }

    stat->ops[SOLVE] += solve_ops;
    SUPERLU_FREE(work);
    return 0;
}
Beispiel #9
0
void
pcgstrf_bmod1D(
	       const int pnum,  /* process number */
	       const int m,     /* number of rows 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 supernode */  
	       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 */
	       complex *dense,   /* modified */
	       complex *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 block updates (sup-panel) in topological order.
 *    It features: col-col, 2cols-col, 3cols-col, and sup-col updates.
 *    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;
    complex       alpha, beta;
#endif

    complex       ukj, ukj1, ukj2;
    int          luptr, luptr1, luptr2;
    int          segsze;
    register int lptr; /* start of row subscripts of the updating supernode */
    register int i, krep_ind, kfnz, isub, irow, no_zeros;
    register int jj;	      /* index through each column in the panel */
    int          *repfnz_col; /* repfnz[] for a column in the panel */
    complex       *dense_col;  /* dense[] for a column in the panel */
    complex      *tempv1;     /* used to store matrix-vector result */
    int          *col_marker; /* each column of the spa_marker[*,w] */
    int          *col_lsub;   /* each column of the panel_lsub[*,w] */
    int          *lsub, *xlsub_end;
    complex       *lusup;
    int          *xlusup;
    register float flopcnt;

    complex      zero = {0.0, 0.0};
    complex      one = {1.0, 0.0};
    complex      comp_temp, comp_temp1;
    
#ifdef TIMING
    double *utime = Gstat->utime;
    double f_time;
#endif    
    
    lsub      = Glu->lsub;
    xlsub_end = Glu->xlsub_end;
    lusup     = Glu->lusup;
    xlusup    = Glu->xlusup;
    lptr      = Glu->xlsub[fsupc];
    krep_ind  = lptr + nsupc - 1;

    /* Pointers to each column of the w-wide arrays. */
    repfnz_col= repfnz;
    dense_col = dense;
    col_marker= spa_marker;
    col_lsub  = panel_lsub;

#if ( DEBUGlevel>=2 )
if (jcol == BADPAN && krep == BADREP) {
    printf("(%d) pcgstrf_bmod1D[1] jcol %d, fsupc %d, krep %d, nsupc %d, nsupr %d, nrow %d\n",
	   pnum, jcol, fsupc, krep, nsupc, nsupr, nrow);
    PrintInt10("lsub[xlsub[2774]]", nsupr, &lsub[lptr]);
}    
#endif
    
    /*
     * Sequence through each column in the panel ...
     */
    for (jj = jcol; jj < jcol + w; ++jj, col_marker += m, col_lsub += m,
	 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];

	/* Calculate flops: tri-solve + mat-vector */
	Gstat->procstat[pnum].fcops += flopcnt;

	/* Case 1: Update U-segment of size 1 -- col-col update */
	if ( segsze == 1 ) {
#ifdef TIMING
	    f_time = SuperLU_timer_();
#endif	    
	    ukj = dense_col[lsub[krep_ind]];
	    luptr += nsupr*(nsupc-1) + nsupc;
#if ( DEBUGlevel>=2 )
if (krep == BADCOL && jj == -1) {
    printf("(%d) pcgstrf_bmod1D[segsze=1]: k %d, j %d, ukj %.10e\n",
	   pnum, lsub[krep_ind], jj, ukj);
    PrintInt10("segsze=1", nsupr, &lsub[lptr]);
}
#endif	    
	    for (i = lptr + nsupc; i < xlsub_end[fsupc]; i++) {
		irow = lsub[i];
                        cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                        c_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 ) {
#ifdef TIMING
	    f_time = SuperLU_timer_();
#endif	    
	    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 ) {
                cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                c_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;
                            cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                            cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                            c_add(&comp_temp, &comp_temp, &comp_temp1);
                            c_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		
		}
	    } else {
		ukj2 = dense_col[lsub[krep_ind - 2]];
		luptr2 = luptr1 - nsupr;
                cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
                c_sub(&ukj1, &ukj1, &comp_temp);

                cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
                cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                c_add(&comp_temp, &comp_temp, &comp_temp1);
                c_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;
                    cc_mult(&comp_temp, &ukj, &lusup[luptr]);
                    cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
                    c_add(&comp_temp, &comp_temp, &comp_temp1);
                    cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
                    c_add(&comp_temp, &comp_temp, &comp_temp1);
                    c_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 */
	    /* 
	     * Perform a triangular solve and matrix-vector update,
	     * then scatter the result of sup-col update to dense[*].
	     */
	    no_zeros = kfnz - fsupc;

	    /* Gather 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;
/*#pragma ivdep*/
	    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 TIMING
	    f_time = SuperLU_timer_();
#endif
		
#ifdef USE_VENDOR_BLAS
#if ( MACH==CRAY_PVP )
	    CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr], 
		  &nsupr, tempv, &incx );
#else
	    ctrsv_( "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
	    cgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr], 
		   &nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif /* _CRAY_PVP */
#else
	    clsolve ( nsupr, segsze, &lusup[luptr], tempv );
	    
	    luptr += segsze;        /* Dense matrix-vector */
	    tempv1 = &tempv[segsze];
	    cmatvec (nsupr, nrow, segsze, &lusup[luptr], tempv, tempv1);
#endif
		
#ifdef TIMING
	    utime[FLOAT] += SuperLU_timer_() - f_time;
#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;
/*#pragma ivdep*/
	    for (i = 0; i < segsze; i++) {
		irow = lsub[isub];
		dense_col[irow] = tempv[i]; /* Scatter */
		tempv[i] = zero;
		isub++;
#if ( DEBUGlevel>=2 )
	if (jj == -1 && krep == 3423)
	    printf("(%d) pcgstrf_bmod1D[scatter] jj %d, dense_col[%d] %e\n",
		   pnum, jj, irow, dense_col[irow]);
#endif
	    }
		
	    /* Scatter the update from tempv1[*] into SPA dense[*] */
/*#pragma ivdep*/
	    for (i = 0; i < nrow; i++) {
		irow = lsub[isub];
                c_sub(&dense_col[irow], &dense_col[irow],
                              &tempv1[i]); /* Scatter-add */
#ifdef SCATTER_FOUND		
		if ( col_marker[irow] != jj ) {
		    col_marker[irow] = jj;
		    col_lsub[w_lsub_end[jj-jcol]++] = irow;
		}
#endif		
		tempv1[i] = zero;
		isub++;
	    }
		
	} /* else segsze >= 4 ... */
	
    } /* for jj ... */

}
Beispiel #10
0
/* Return value:   0 - successful return
 *               > 0 - number of bytes allocated when run out of space
 */
int
ccolumn_bmod (
	     const int  jcol,	  /* in */
	     const int  nseg,	  /* in */
	     complex     *dense,	  /* in */
	     complex     *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;
    complex      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
     */
    complex       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;
    complex       *lusup;
    int          *xlusup;
    int          nzlumax;
    complex       *tempv1;
    complex      zero = {0.0, 0.0};
    complex      one = {1.0, 0.0};
    complex      none = {-1.0, 0.0};
    complex	 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;




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

		    cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
		    cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
		    c_add(&comp_temp, &comp_temp, &comp_temp1);
		    c_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++;
			cc_mult(&comp_temp, &ukj, &lusup[luptr]);
			cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
			c_add(&comp_temp, &comp_temp, &comp_temp1);
			cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
			c_add(&comp_temp, &comp_temp, &comp_temp1);
			c_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		
		ctrsv_( "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
		cgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr], 
		       &nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif
#else
		clsolve ( nsupr, segsze, &lusup[luptr], tempv );

 		luptr += segsze;  /* Dense matrix-vector */
		tempv1 = &tempv[segsze];
		cmatvec (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];
		    c_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 = cLUMemXpand(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
	ctrsv_( "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
	cgemv_( "N", &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
	       &lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#endif
#else
	clsolve ( nsupr, nsupc, &lusup[luptr], &lusup[ufirst] );

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

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

    return 0;
}
Beispiel #11
0
void
cgstrs (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
    complex   alpha = {1.0, 0.0}, beta = {1.0, 0.0};
    complex   *work_col;
#endif
    complex   temp_comp;
    DNformat *Bstore;
    complex   *Bmat;
    SCformat *Lstore;
    NCformat *Ustore;
    complex   *Lval, *Uval;
    int      fsupc, nrow, nsupr, nsupc, luptr, istart, irow;
    int      i, j, k, iptr, jcol, n, ldb, nrhs;
    complex   *work, *rhs_work, *soln;
    flops_t  solve_ops;
    void cprint_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_C || L->Mtype != SLU_TRLU )
        *info = -2;
    else if ( U->nrow != U->ncol || U->nrow < 0 ||
              U->Stype != SLU_NC || U->Dtype != SLU_C || U->Mtype != SLU_TRU )
        *info = -3;
    else if ( ldb < SUPERLU_MAX(0, L->nrow) ||
              B->Stype != SLU_DN || B->Dtype != SLU_C || B->Mtype != SLU_GE )
        *info = -6;
    if ( *info ) {
        i = -(*info);
        xerbla_("cgstrs", &i);
        return;
    }

    n = L->nrow;
    work = complexCalloc(n * nrhs);
    if ( !work ) ABORT("Malloc fails for local work[].");
    soln = complexMalloc(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;
                        cc_mult(&temp_comp, &rhs_work[fsupc], &Lval[luptr]);
                        c_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
                ctrsm_("L", "L", "N", "U", &nsupc, &nrhs, &alpha,
                       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);

                cgemm_( "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);
                        c_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];
                    clsolve (nsupr, nsupc, &Lval[luptr], &rhs_work[fsupc]);
                    cmatvec (nsupr, nrow, nsupc, &Lval[luptr+nsupc],
                            &rhs_work[fsupc], &work[0] );

                    iptr = istart + nsupc;
                    for (i = 0; i < nrow; i++) {
                        irow = L_SUB(iptr);
                        c_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");
        cprint_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++) {
                    c_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
                ctrsm_("L", "U", "N", "N", &nsupc, &nrhs, &alpha,
                       &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
#endif
#else
                for (j = 0; j < nrhs; j++)
                    cusolve ( 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);
                        cc_mult(&temp_comp, &rhs_work[jcol], &Uval[i]);
                        c_sub(&rhs_work[irow], &rhs_work[irow], &temp_comp);
                    }
                }
            }

        } /* for U-solve */

#ifdef DEBUG
        printf("After U-solve: x=\n");
        cprint_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_ctrsv("U", "T", "N", L, U, &Bmat[k*ldb], stat, info);

                /* Multiply by inv(L'). */
                sp_ctrsv("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_ctrsv("U", "C", "N", L, U, &Bmat[k*ldb], stat, info);

                /* Multiply by conj(inv(L')). */
                sp_ctrsv("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_cgemv(char *trans, complex alpha, SuperMatrix *A, complex *x, 
	 int incx, complex beta, complex *y, int incy)
{
/*  Purpose   
    =======   

    sp_cgemv()  performs one of the matrix-vector operations   
       y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,   
    where alpha and beta are scalars, x and y are vectors and A is a
    sparse A->nrow by A->ncol matrix.   

    Parameters   
    ==========   

    TRANS  - (input) char*
             On entry, TRANS specifies the operation to be performed as   
             follows:   
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.   
                TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.   
                TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.   

    ALPHA  - (input) complex
             On entry, ALPHA specifies the scalar alpha.   

    A      - (input) SuperMatrix*
             Before entry, the leading m by n part of the array A must   
             contain the matrix of coefficients.   

    X      - (input) complex*, array of DIMENSION at least   
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'   
             and at least   
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.   
             Before entry, the incremented array X must contain the   
             vector x.   

    INCX   - (input) int
             On entry, INCX specifies the increment for the elements of   
             X. INCX must not be zero.   

    BETA   - (input) complex
             On entry, BETA specifies the scalar beta. When BETA is   
             supplied as zero then Y need not be set on input.   

    Y      - (output) complex*,  array of DIMENSION at least   
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'   
             and at least   
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.   
             Before entry with BETA non-zero, the incremented array Y   
             must contain the vector y. On exit, Y is overwritten by the 
             updated vector y.
	     
    INCY   - (input) int
             On entry, INCY specifies the increment for the elements of   
             Y. INCY must not be zero.   

    ==== Sparse Level 2 Blas routine.   
*/

    /* Local variables */
    NCformat *Astore;
    complex   *Aval;
    int info;
    complex temp, temp1;
    int lenx, leny, i, j, irow;
    int iy, jx, jy, kx, ky;
    int notran;
    complex comp_zero = {0.0, 0.0};
    complex comp_one = {1.0, 0.0};

    notran = lsame_(trans, "N");
    Astore = A->Store;
    Aval = Astore->nzval;
    
    /* Test the input parameters */
    info = 0;
    if ( !notran && !lsame_(trans, "T") && !lsame_(trans, "C")) info = 1;
    else if ( A->nrow < 0 || A->ncol < 0 ) info = 3;
    else if (incx == 0) info = 5;
    else if (incy == 0)	info = 8;
    if (info != 0) {
	xerbla_("sp_cgemv ", &info);
	return 0;
    }

    /* Quick return if possible. */
    if (A->nrow == 0 || A->ncol == 0 || 
	c_eq(&alpha, &comp_zero) && 
	c_eq(&beta, &comp_one))
	return 0;


    /* Set  LENX  and  LENY, the lengths of the vectors x and y, and set 
       up the start points in  X  and  Y. */
    if (lsame_(trans, "N")) {
	lenx = A->ncol;
	leny = A->nrow;
    } else {
	lenx = A->nrow;
	leny = A->ncol;
    }
    if (incx > 0) kx = 0;
    else kx =  - (lenx - 1) * incx;
    if (incy > 0) ky = 0;
    else ky =  - (leny - 1) * incy;

    /* Start the operations. In this version the elements of A are   
       accessed sequentially with one pass through A. */
    /* First form  y := beta*y. */
    if ( !c_eq(&beta, &comp_one) ) {
	if (incy == 1) {
	    if ( c_eq(&beta, &comp_zero) )
		for (i = 0; i < leny; ++i) y[i] = comp_zero;
	    else
		for (i = 0; i < leny; ++i) 
		  cc_mult(&y[i], &beta, &y[i]);
	} else {
	    iy = ky;
	    if ( c_eq(&beta, &comp_zero) )
		for (i = 0; i < leny; ++i) {
		    y[iy] = comp_zero;
		    iy += incy;
		}
	    else
		for (i = 0; i < leny; ++i) {
		    cc_mult(&y[iy], &beta, &y[iy]);
		    iy += incy;
		}
	}
    }
    
    if ( c_eq(&alpha, &comp_zero) ) return 0;

    if ( notran ) {
	/* Form  y := alpha*A*x + y. */
	jx = kx;
	if (incy == 1) {
	    for (j = 0; j < A->ncol; ++j) {
		if ( !c_eq(&x[jx], &comp_zero) ) {
		    cc_mult(&temp, &alpha, &x[jx]);
		    for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
			irow = Astore->rowind[i];
			cc_mult(&temp1, &temp,  &Aval[i]);
			c_add(&y[irow], &y[irow], &temp1);
		    }
		}
		jx += incx;
	    }
	} else {
	    ABORT("Not implemented.");
	}
    } else {
	/* Form  y := alpha*A'*x + y. */
	jy = ky;
	if (incx == 1) {
	    for (j = 0; j < A->ncol; ++j) {
		temp = comp_zero;
		for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
		    irow = Astore->rowind[i];
		    cc_mult(&temp1, &Aval[i], &x[irow]);
		    c_add(&temp, &temp, &temp1);
		}
		cc_mult(&temp1, &alpha, &temp);
		c_add(&y[jy], &y[jy], &temp1);
		jy += incy;
	    }
	} else {
	    ABORT("Not implemented.");
	}
    }
    return 0;    
} /* sp_cgemv */
int
sp_ctrsv(char *uplo, char *trans, char *diag, SuperMatrix *L, 
	 SuperMatrix *U, complex *x, int *info)
{
/*
 *   Purpose
 *   =======
 *
 *   sp_ctrsv() 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_C, Mtype = TRLU.
 *
 *   U       - (input) SuperMatrix*
 *	        The factor U from the factorization Pr*A*Pc=L*U.
 *	        U has types: Stype = NC, Dtype = SLU_C, Mtype = TRU.
 *    
 *   x       - (input/output) complex*
 *             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;
    complex   *Lval, *Uval;
    int incx = 1, incy = 1;
    complex alpha = {1.0, 0.0}, beta = {1.0, 0.0};
    complex comp_zero = {0.0, 0.0};
    int nrow;
    int fsupc, nsupr, nsupc, luptr, istart, irow;
    int i, k, iptr, jcol;
    complex *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_ctrsv", &i);
	return 0;
    }

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

    if ( !(work = complexCalloc(L->nrow)) )
	ABORT("Malloc fails for work in sp_ctrsv().");
    
    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;
			cc_mult(&comp_zero, &x[fsupc], &Lval[luptr]);
			c_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
		    ctrsv_("L", "N", "U", &nsupc, &Lval[luptr], &nsupr,
		       	&x[fsupc], &incx);
		
		    cgemv_("N", &nrow, &nsupc, &alpha, &Lval[luptr+nsupc], 
		       	&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#endif
#else
		    clsolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc]);
		
		    cmatvec ( 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);
			c_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 ) {
		    c_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
		    for (i = U_NZ_START(fsupc); i < U_NZ_START(fsupc+1); ++i) {
			irow = U_SUB(i);
			cc_mult(&comp_zero, &x[fsupc], &Uval[i]);
			c_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
		    ctrsv_("U", "N", "N", &nsupc, &Lval[luptr], &nsupr,
		       &x[fsupc], &incx);
#endif
#else		
		    cusolve ( 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);
			cc_mult(&comp_zero, &x[jcol], &Uval[i]);
			c_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);
			cc_mult(&comp_zero, &x[irow], &Lval[i]);
		    	c_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
		    ctrsv_("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);
			cc_mult(&comp_zero, &x[irow], &Uval[i]);
		    	c_sub(&x[jcol], &x[jcol], &comp_zero);
		    }
		}

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

		if ( nsupc == 1 ) {
		    c_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
		    ctrsv_("U", "T", "N", &nsupc, &Lval[luptr], &nsupr,
			    &x[fsupc], &incx);
#endif
		}
	    } /* for k ... */
	}
    }

    SuperLUStat.ops[SOLVE] += solve_ops;
    SUPERLU_FREE(work);
    return 0;
}