pdgssvx.c

LU分解求解矩阵方程组的解

	    stat->utime[SYMBFAC] = SuperLU_timer_() - t;
	    if ( iinfo < 0 ) { /* Successful return */
		QuerySpace_dist(n, -iinfo, Glu_freeable, &symb_mem_usage);
#if ( PRNTlevel>=1 )
		if ( !iam ) {
		    printf("\tNo of supers %ld\n", Glu_persist->supno[n-1]+1);
		    printf("\tSize of G(L) %ld\n", Glu_freeable->xlsub[n]);
		    printf("\tSize of G(U) %ld\n", Glu_freeable->xusub[n]);
		    printf("\tint %d, short %d, float %d, double %d\n", 
			   sizeof(int_t), sizeof(short), sizeof(float),
			   sizeof(double));
		    printf("\tSYMBfact (MB):\tL\\U %.2f\ttotal %.2f\texpansions %d\n",
			   symb_mem_usage.for_lu*1e-6, 
			   symb_mem_usage.total*1e-6,
			   symb_mem_usage.expansions);
		}
#endif
	    } else {
		if ( !iam ) {
		    fprintf(stderr, "symbfact() error returns %d\n", iinfo);
		    exit(-1);
		}
	    }
	} /* end if Fact ... */

	/* Apply column permutation to the original distributed A */
	for (j = 0; j < nnz_loc; ++j) colind[j] = perm_c[colind[j]];

	/* Distribute Pc*Pr*diag(R)*A*diag(C)*Pc' into L and U storage. 
	   NOTE: the row permutation Pc*Pr is applied internally in the
	   distribution routine. */
	t = SuperLU_timer_();
	dist_mem_use = pddistribute(Fact, n, A, ScalePermstruct,
                                  Glu_freeable, LUstruct, grid);
	stat->utime[DIST] = SuperLU_timer_() - t;

	/* Deallocate storage used in symbolic factorization. */
	if ( Fact != SamePattern_SameRowPerm ) {
	    iinfo = symbfact_SubFree(Glu_freeable);
	    SUPERLU_FREE(Glu_freeable);
	}

	/* Perform numerical factorization in parallel. */
	t = SuperLU_timer_();
	pdgstrf(options, m, n, anorm, LUstruct, grid, stat, info);
	stat->utime[FACT] = SuperLU_timer_() - t;

#if ( PRNTlevel>=1 )
	{
	    int_t TinyPivots;
	    float for_lu, total, max, avg, temp;
	    dQuerySpace_dist(n, LUstruct, grid, &num_mem_usage);
	    MPI_Reduce( &num_mem_usage.for_lu, &for_lu,
		       1, MPI_FLOAT, MPI_SUM, 0, grid->comm );
	    MPI_Reduce( &num_mem_usage.total, &total,
		       1, MPI_FLOAT, MPI_SUM, 0, grid->comm );
	    temp = SUPERLU_MAX(symb_mem_usage.total,
			       symb_mem_usage.for_lu +
			       (float)dist_mem_use + num_mem_usage.for_lu);
	    temp = SUPERLU_MAX(temp, num_mem_usage.total);
	    MPI_Reduce( &temp, &max,
		       1, MPI_FLOAT, MPI_MAX, 0, grid->comm );
	    MPI_Reduce( &temp, &avg,
		       1, MPI_FLOAT, MPI_SUM, 0, grid->comm );
	    MPI_Allreduce( &stat->TinyPivots, &TinyPivots, 1, mpi_int_t,
			  MPI_SUM, grid->comm );
	    stat->TinyPivots = TinyPivots;
	    if ( !iam ) {
		printf("\tNUMfact (MB) all PEs:\tL\\U\t%.2f\tall\t%.2f\n",
		       for_lu*1e-6, total*1e-6);
		printf("\tAll space (MB):"
		       "\t\ttotal\t%.2f\tAvg\t%.2f\tMax\t%.2f\n",
		       avg*1e-6, avg/grid->nprow/grid->npcol*1e-6, max*1e-6);
		printf("\tNumber of tiny pivots: %10d\n", stat->TinyPivots);
	    }
	}
#endif
    
        /* Destroy GA */
        if ( Fact != SamePattern_SameRowPerm )
            Destroy_CompCol_Matrix_dist(&GA);
    } /* end if (!factored) */
	
    /* ------------------------------------------------------------
       Compute the solution matrix X.
       ------------------------------------------------------------*/
    if ( nrhs ) {

	if ( !(b_work = doubleMalloc_dist(n)) )
	    ABORT("Malloc fails for b_work[]");

	/* ------------------------------------------------------------
	   Scale the right-hand side if equilibration was performed. 
	   ------------------------------------------------------------*/
	if ( notran ) {
	    if ( rowequ ) {
		b_col = B;
		for (j = 0; j < nrhs; ++j) {
		    irow = fst_row;
		    for (i = 0; i < m_loc; ++i) {
		        b_col[i] *= R[irow];
		        ++irow;
		    }
		    b_col += ldb;
		}
	    }
	} else if ( colequ ) {
	    b_col = B;
	    for (j = 0; j < nrhs; ++j) {
	        irow = fst_row;
		for (i = 0; i < m_loc; ++i) {
		    b_col[i] *= C[irow];
		    ++irow;
		}
		b_col += ldb;
	    }
	}

	/* Save a copy of the right-hand side. */
	ldx = ldb;
	if ( !(X = doubleMalloc_dist(((size_t)ldx) * nrhs)) )
	    ABORT("Malloc fails for X[]");
	x_col = X;  b_col = B;
	for (j = 0; j < nrhs; ++j) {
	    for (i = 0; i < m_loc; ++i) x_col[i] = b_col[i];
	    x_col += ldx;  b_col += ldb;
	}

	/* ------------------------------------------------------------
	   Solve the linear system.
	   ------------------------------------------------------------*/
	if ( options->SolveInitialized == NO ) {
	    dSolveInit(options, A, perm_r, perm_c, nrhs, LUstruct, grid,
		       SOLVEstruct);
	}

	pdgstrs(n, LUstruct, ScalePermstruct, grid, X, m_loc, 
		fst_row, ldb, nrhs, SOLVEstruct, stat, info);

	/* ------------------------------------------------------------
	   Use iterative refinement to improve the computed solution and
	   compute error bounds and backward error estimates for it.
	   ------------------------------------------------------------*/
	if ( options->IterRefine ) {
	    /* Improve the solution by iterative refinement. */
	    int_t *it, *colind_gsmv = SOLVEstruct->A_colind_gsmv;
	    SOLVEstruct_t *SOLVEstruct1;  /* Used by refinement. */

	    t = SuperLU_timer_();
	    if ( options->RefineInitialized == NO || Fact == DOFACT ) {
	        /* All these cases need to re-initialize gsmv structure */
	        if ( options->RefineInitialized )
		    pdgsmv_finalize(SOLVEstruct->gsmv_comm);
	        pdgsmv_init(A, SOLVEstruct->row_to_proc, grid,
			    SOLVEstruct->gsmv_comm);
	       
                /* Save a copy of the transformed local col indices
		   in colind_gsmv[]. */
	        if ( colind_gsmv ) SUPERLU_FREE(colind_gsmv);
	        if ( !(it = intMalloc_dist(nnz_loc)) )
		    ABORT("Malloc fails for colind_gsmv[]");
	        colind_gsmv = SOLVEstruct->A_colind_gsmv = it;
	        for (i = 0; i < nnz_loc; ++i) colind_gsmv[i] = colind[i];
	        options->RefineInitialized = YES;
	    } else if ( Fact == SamePattern ||
			Fact == SamePattern_SameRowPerm ) {
	        double at;
	        int_t k, jcol, p;
	        /* Swap to beginning the part of A corresponding to the
		   local part of X, as was done in pdgsmv_init() */
	        for (i = 0; i < m_loc; ++i) { /* Loop through each row */
		    k = rowptr[i];
		    for (j = rowptr[i]; j < rowptr[i+1]; ++j) {
		        jcol = colind[j];
		        p = SOLVEstruct->row_to_proc[jcol];
		        if ( p == iam ) { /* Local */
		            at = a[k]; a[k] = a[j]; a[j] = at;
		            ++k;
		        }
		    }
	        }
	      
	        /* Re-use the local col indices of A obtained from the
		   previous call to pdgsmv_init() */
	        for (i = 0; i < nnz_loc; ++i) colind[i] = colind_gsmv[i];
	    }

	    if ( nrhs == 1 ) { /* Use the existing solve structure */
	        SOLVEstruct1 = SOLVEstruct;
	    } else { /* For nrhs > 1, since refinement is performed for RHS
			one at a time, the communication structure for pdgstrs
			is different than the solve with nrhs RHS. 
			So we use SOLVEstruct1 for the refinement step.
		     */
	        if ( !(SOLVEstruct1 = (SOLVEstruct_t *) 
		                       SUPERLU_MALLOC(sizeof(SOLVEstruct_t))) )
		    ABORT("Malloc fails for SOLVEstruct1");
	        /* Copy the same stuff */
	        SOLVEstruct1->row_to_proc = SOLVEstruct->row_to_proc;
	        SOLVEstruct1->inv_perm_c = SOLVEstruct->inv_perm_c;
	        SOLVEstruct1->num_diag_procs = SOLVEstruct->num_diag_procs;
	        SOLVEstruct1->diag_procs = SOLVEstruct->diag_procs;
	        SOLVEstruct1->diag_len = SOLVEstruct->diag_len;
	        SOLVEstruct1->gsmv_comm = SOLVEstruct->gsmv_comm;
	        SOLVEstruct1->A_colind_gsmv = SOLVEstruct->A_colind_gsmv;
		
		/* Initialize the *gstrs_comm for 1 RHS. */
		if ( !(SOLVEstruct1->gstrs_comm = (pxgstrs_comm_t *)
		       SUPERLU_MALLOC(sizeof(pxgstrs_comm_t))) )
		    ABORT("Malloc fails for gstrs_comm[]");
		pxgstrs_init(n, m_loc, 1, fst_row, perm_r, perm_c, grid, 
			     Glu_persist, SOLVEstruct1);
	    }

	    pdgsrfs(n, A, anorm, LUstruct, ScalePermstruct, grid,
		    B, ldb, X, ldx, nrhs, SOLVEstruct1, berr, stat, info);

            /* Deallocate the storage associated with SOLVEstruct1 */
	    if ( nrhs > 1 ) {
	        pxgstrs_finalize(SOLVEstruct1->gstrs_comm);
	        SUPERLU_FREE(SOLVEstruct1);
	    }

	    stat->utime[REFINE] = SuperLU_timer_() - t;
	}

	/* Permute the solution matrix B <= Pc'*X. */
	pdPermute_Dense_Matrix(fst_row, m_loc, SOLVEstruct->row_to_proc,
			       SOLVEstruct->inv_perm_c,
			       X, ldx, B, ldb, nrhs, grid);
#if ( DEBUGlevel>=2 )
	printf("\n (%d) .. After pdPermute_Dense_Matrix(): b =\n", iam);
	for (i = 0; i < m_loc; ++i)
	  printf("\t(%d)\t%4d\t%.10f\n", iam, i+fst_row, B[i]);
#endif
	
	/* Transform the solution matrix X to a solution of the original
	   system before the equilibration. */
	if ( notran ) {
	    if ( colequ ) {
		b_col = B;
		for (j = 0; j < nrhs; ++j) {
		    irow = fst_row;
		    for (i = 0; i < m_loc; ++i) {
		        b_col[i] *= C[irow];
		        ++irow;
		    }
		    b_col += ldb;
		}
	    }
	} else if ( rowequ ) {
	    b_col = B;
	    for (j = 0; j < nrhs; ++j) {
	        irow = fst_row;
		for (i = 0; i < m_loc; ++i) {
		    b_col[i] *= R[irow];
		    ++irow;
		}
		b_col += ldb;
	    }
	}

	SUPERLU_FREE(b_work);
	SUPERLU_FREE(X);

    } /* end if nrhs != 0 */

#if ( PRNTlevel>=1 )
    if ( !iam ) printf(".. DiagScale = %d\n", ScalePermstruct->DiagScale);
#endif

    /* Deallocate R and/or C if it was not used. */
    if ( Equil && Fact != SamePattern_SameRowPerm ) {
	switch ( ScalePermstruct->DiagScale ) {
	    case NOEQUIL:
	        SUPERLU_FREE(R);
		SUPERLU_FREE(C);
		break;
	    case ROW: 
		SUPERLU_FREE(C);
		break;
	    case COL: 
		SUPERLU_FREE(R);
		break;
	}
    }
    if ( !factored && Fact != SamePattern_SameRowPerm )
 	Destroy_CompCol_Permuted_dist(&GAC);

#if ( DEBUGlevel>=1 )
    CHECK_MALLOC(iam, "Exit pdgssvx()");
#endif

}