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sgstrs.c

/*
 * -- SuperLU routine (version 3.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * October 15, 2003
 *
 */
/*
  Copyright (c) 1994 by Xerox Corporation.  All rights reserved.
 
  THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
  EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
 
  Permission is hereby granted to use or copy this program for any
  purpose, provided the above notices are retained on all copies.
  Permission to modify the code and to distribute modified code is
  granted, provided the above notices are retained, and a notice that
  the code was modified is included with the above copyright notice.
*/

#include "ssp_defs.h"


/* 
 * Function prototypes 
 */
void susolve(int, int, float*, float*);
void slsolve(int, int, float*, float*);
void smatvec(int, int, int, float*, float*, float*);


void
sgstrs (trans_t trans, SuperMatrix *L, SuperMatrix *U,
        int *perm_c, int *perm_r, SuperMatrix *B,
        SuperLUStat_t *stat, int *info)
{
/*
 * Purpose
 * =======
 *
 * SGSTRS solves a system of linear equations A*X=B or A'*X=B
 * with A sparse and B dense, using the LU factorization computed by
 * SGSTRF.
 *
 * See supermatrix.h for the definition of 'SuperMatrix' structure.
 *
 * Arguments
 * =========
 *
 * trans   (input) trans_t
 *          Specifies the form of the system of equations:
 *          = NOTRANS: A * X = B  (No transpose)
 *          = TRANS:   A'* X = B  (Transpose)
 *          = CONJ:    A**H * X = B  (Conjugate transpose)
 *
 * L       (input) SuperMatrix*
 *         The factor L from the factorization Pr*A*Pc=L*U as computed by
 *         sgstrf(). Use compressed row subscripts storage for supernodes,
 *         i.e., L has types: Stype = SLU_SC, Dtype = SLU_S, Mtype = SLU_TRLU.
 *
 * U       (input) SuperMatrix*
 *         The factor U from the factorization Pr*A*Pc=L*U as computed by
 *         sgstrf(). Use column-wise storage scheme, i.e., U has types:
 *         Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_TRU.
 *
 * perm_c  (input) int*, dimension (L->ncol)
 *       Column permutation vector, which defines the 
 *         permutation matrix Pc; perm_c[i] = j means column i of A is 
 *         in position j in A*Pc.
 *
 * perm_r  (input) int*, dimension (L->nrow)
 *         Row permutation vector, which defines the permutation matrix Pr; 
 *         perm_r[i] = j means row i of A is in position j in Pr*A.
 *
 * B       (input/output) SuperMatrix*
 *         B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
 *         On entry, the right hand side matrix.
 *         On exit, the solution matrix if info = 0;
 *
 * stat     (output) SuperLUStat_t*
 *          Record the statistics on runtime and floating-point operation count.
 *          See util.h for the definition of 'SuperLUStat_t'.
 *
 * info    (output) int*
 *       = 0: successful exit
 *       < 0: if info = -i, the i-th argument had an illegal value
 *
 */
#ifdef _CRAY
    _fcd ftcs1, ftcs2, ftcs3, ftcs4;
#endif
#ifdef USE_VENDOR_BLAS
    float   alpha = 1.0, beta = 1.0;
    float   *work_col;
#endif
    DNformat *Bstore;
    float   *Bmat;
    SCformat *Lstore;
    NCformat *Ustore;
    float   *Lval, *Uval;
    int      fsupc, nrow, nsupr, nsupc, luptr, istart, irow;
    int      i, j, k, iptr, jcol, n, ldb, nrhs;
    float   *work, *rhs_work, *soln;
    flops_t  solve_ops;
    void sprint_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_S || L->Mtype != SLU_TRLU )
      *info = -2;
    else if ( U->nrow != U->ncol || U->nrow < 0 ||
            U->Stype != SLU_NC || U->Dtype != SLU_S || U->Mtype != SLU_TRU )
      *info = -3;
    else if ( ldb < SUPERLU_MAX(0, L->nrow) ||
            B->Stype != SLU_DN || B->Dtype != SLU_S || B->Mtype != SLU_GE )
      *info = -6;
    if ( *info ) {
      i = -(*info);
      xerbla_("sgstrs", &i);
      return;
    }

    n = L->nrow;
    work = floatCalloc(n * nrhs);
    if ( !work ) ABORT("Malloc fails for local work[].");
    soln = floatMalloc(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 += nsupc * (nsupc - 1) * nrhs;
          solve_ops += 2 * nrow * nsupc * nrhs;
          
          if ( nsupc == 1 ) {
            for (j = 0; j < nrhs; j++) {
                rhs_work = &Bmat[j*ldb];
                luptr = L_NZ_START(fsupc);
                for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); iptr++){
                  irow = L_SUB(iptr);
                  ++luptr;
                  rhs_work[irow] -= rhs_work[fsupc] * Lval[luptr];
                }
            }
          } else {
            luptr = L_NZ_START(fsupc);
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
            ftcs1 = _cptofcd("L", strlen("L"));
            ftcs2 = _cptofcd("N", strlen("N"));
            ftcs3 = _cptofcd("U", strlen("U"));
            STRSM( ftcs1, ftcs1, ftcs2, ftcs3, &nsupc, &nrhs, &alpha,
                   &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
            
            SGEMM( ftcs2, ftcs2, &nrow, &nrhs, &nsupc, &alpha, 
                  &Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb, 
                  &beta, &work[0], &n );
#else
            strsm_("L", "L", "N", "U", &nsupc, &nrhs, &alpha,
                   &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
            
            sgemm_( "N", "N", &nrow, &nrhs, &nsupc, &alpha, 
                  &Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb, 
                  &beta, &work[0], &n );
#endif
            for (j = 0; j < nrhs; j++) {
                rhs_work = &Bmat[j*ldb];
                work_col = &work[j*n];
                iptr = istart + nsupc;
                for (i = 0; i < nrow; i++) {
                  irow = L_SUB(iptr);
                  rhs_work[irow] -= work_col[i]; /* Scatter */
                  work_col[i] = 0.0;
                  iptr++;
                }
            }
#else       
            for (j = 0; j < nrhs; j++) {
                rhs_work = &Bmat[j*ldb];
                slsolve (nsupr, nsupc, &Lval[luptr], &rhs_work[fsupc]);
                smatvec (nsupr, nrow, nsupc, &Lval[luptr+nsupc],
                      &rhs_work[fsupc], &work[0] );

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

#ifdef DEBUG
      printf("After L-solve: y=\n");
      sprint_soln(n, 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 += nsupc * (nsupc + 1) * nrhs;

          if ( nsupc == 1 ) {
            rhs_work = &Bmat[0];
            for (j = 0; j < nrhs; j++) {
                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"));
            STRSM( ftcs1, ftcs2, ftcs3, ftcs3, &nsupc, &nrhs, &alpha,
                   &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
#else
            strsm_("L", "U", "N", "N", &nsupc, &nrhs, &alpha,
                   &Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
#endif
#else       
            for (j = 0; j < nrhs; j++)
                susolve ( 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 += 2*(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);
                  rhs_work[irow] -= rhs_work[jcol] * Uval[i];
                }
            }
          }
          
      } /* for U-solve */

#ifdef DEBUG
      printf("After U-solve: x=\n");
      sprint_soln(n, 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;
      for (k = 0; k < nrhs; ++k) {
          
          /* Multiply by inv(U'). */
          sp_strsv("U", "T", "N", L, U, &Bmat[k*ldb], stat, info);
          
          /* Multiply by inv(L'). */
          sp_strsv("L", "T", "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);
}

/*
 * Diagnostic print of the solution vector 
 */
void
sprint_soln(int n, float *soln)
{
    int i;

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

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