Example #1
0
int sfill_diag(int n, NCformat *Astore)
/* fill explicit zeros on the diagonal entries, so that the matrix is not
   structurally singular. */
{
    float *nzval = (float *)Astore->nzval;
    int *rowind = Astore->rowind;
    int *colptr = Astore->colptr;
    int nnz = colptr[n];
    int fill = 0;
    float *nzval_new;
    float zero = 0.0;
    int *rowind_new;
    int i, j, diag;

    for (i = 0; i < n; i++)
    {
	diag = -1;
	for (j = colptr[i]; j < colptr[i + 1]; j++)
	    if (rowind[j] == i) diag = j;
	if (diag < 0) fill++;
    }
    if (fill)
    {
	nzval_new = floatMalloc(nnz + fill);
	rowind_new = intMalloc(nnz + fill);
	fill = 0;
	for (i = 0; i < n; i++)
	{
	    diag = -1;
	    for (j = colptr[i] - fill; j < colptr[i + 1]; j++)
	    {
		if ((rowind_new[j + fill] = rowind[j]) == i) diag = j;
		nzval_new[j + fill] = nzval[j];
	    }
	    if (diag < 0)
	    {
		rowind_new[colptr[i + 1] + fill] = i;
		nzval_new[colptr[i + 1] + fill] = zero;
		fill++;
	    }
	    colptr[i + 1] += fill;
	}
	Astore->nzval = nzval_new;
	Astore->rowind = rowind_new;
	SUPERLU_FREE(nzval);
	SUPERLU_FREE(rowind);
    }
    Astore->nnz += fill;
    return fill;
}
Example #2
0
/*
 * Convert a row compressed storage into a column compressed storage.
 */
void
sCompRow_to_CompCol(int m, int n, int nnz, 
		    float *a, int *colind, int *rowptr,
		    float **at, int **rowind, int **colptr)
{
    register int i, j, col, relpos;
    int *marker;

    /* Allocate storage for another copy of the matrix. */
    *at = (float *) floatMalloc(nnz);
    *rowind = (int *) intMalloc(nnz);
    *colptr = (int *) intMalloc(n+1);
    marker = (int *) intCalloc(n);
    
    /* Get counts of each column of A, and set up column pointers */
    for (i = 0; i < m; ++i)
	for (j = rowptr[i]; j < rowptr[i+1]; ++j) ++marker[colind[j]];
    (*colptr)[0] = 0;
    for (j = 0; j < n; ++j) {
	(*colptr)[j+1] = (*colptr)[j] + marker[j];
	marker[j] = (*colptr)[j];
    }

    /* Transfer the matrix into the compressed column storage. */
    for (i = 0; i < m; ++i) {
	for (j = rowptr[i]; j < rowptr[i+1]; ++j) {
	    col = colind[j];
	    relpos = marker[col];
	    (*rowind)[relpos] = i;
	    (*at)[relpos] = a[j];
	    ++marker[col];
	}
    }

    SUPERLU_FREE(marker);
}
Example #3
0
int main(int argc, char *argv[])
{
    char           equed[1];
    yes_no_t       equil;
    trans_t        trans;
    SuperMatrix    A, L, U;
    SuperMatrix    B, X;
    NCformat       *Astore;
    NCformat       *Ustore;
    SCformat       *Lstore;
    float         *a;
    int            *asub, *xa;
    int            *perm_r; /* row permutations from partial pivoting */
    int            *perm_c; /* column permutation vector */
    int            *etree;
    void           *work;
    int            info, lwork, nrhs, ldx;
    int            i, m, n, nnz;
    float         *rhsb, *rhsx, *xact;
    float         *R, *C;
    float         *ferr, *berr;
    float         u, rpg, rcond;
    mem_usage_t    mem_usage;
    superlu_options_t options;
    SuperLUStat_t stat;
    extern void  parse_command_line();

#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Enter main()");
#endif

    /* Defaults */
    lwork = 0;
    nrhs  = 1;
    equil = YES;	
    u     = 1.0;
    trans = NOTRANS;
    
    /* Set the default input options:
	options.Fact = DOFACT;
        options.Equil = YES;
    	options.ColPerm = COLAMD;
	options.DiagPivotThresh = 1.0;
    	options.Trans = NOTRANS;
    	options.IterRefine = NOREFINE;
    	options.SymmetricMode = NO;
    	options.PivotGrowth = NO;
    	options.ConditionNumber = NO;
    	options.PrintStat = YES;
    */
    set_default_options(&options);

    /* Can use command line input to modify the defaults. */
    parse_command_line(argc, argv, &lwork, &u, &equil, &trans);
    options.Equil = equil;
    options.DiagPivotThresh = u;
    options.Trans = trans;

    /* Add more functionalities that the defaults. */
    options.PivotGrowth = YES;    /* Compute reciprocal pivot growth */
    options.ConditionNumber = YES;/* Compute reciprocal condition number */
    options.IterRefine = SLU_SINGLE;  /* Perform single-precision refinement */
    
    if ( lwork > 0 ) {
	work = SUPERLU_MALLOC(lwork);
	if ( !work ) {
	    ABORT("SLINSOLX: cannot allocate work[]");
	}
    }

    /* Read matrix A from a file in Harwell-Boeing format.*/
    sreadhb(&m, &n, &nnz, &a, &asub, &xa);
    
    sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
    Astore = A.Store;
    printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
    
    if ( !(rhsb = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
    if ( !(rhsx = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
    sCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE);
    sCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE);
    xact = floatMalloc(n * nrhs);
    ldx = n;
    sGenXtrue(n, nrhs, xact, ldx);
    sFillRHS(trans, nrhs, xact, ldx, &A, &B);
    
    if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
    if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
    if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
    if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) ) 
        ABORT("SUPERLU_MALLOC fails for R[].");
    if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
        ABORT("SUPERLU_MALLOC fails for C[].");
    if ( !(ferr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
        ABORT("SUPERLU_MALLOC fails for ferr[].");
    if ( !(berr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) ) 
        ABORT("SUPERLU_MALLOC fails for berr[].");

    
    /* Initialize the statistics variables. */
    StatInit(&stat);
    
    /* Solve the system and compute the condition number
       and error bounds using dgssvx.      */
    
    sgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
           &L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
           &mem_usage, &stat, &info);

    printf("sgssvx(): info %d\n", info);

    if ( info == 0 || info == n+1 ) {

        /* This is how you could access the solution matrix. */
        float *sol = (float*) ((DNformat*) X.Store)->nzval; 

	if ( options.PivotGrowth == YES )
            printf("Recip. pivot growth = %e\n", rpg);
	if ( options.ConditionNumber == YES )
	    printf("Recip. condition number = %e\n", rcond);
	if ( options.IterRefine != NOREFINE ) {
            printf("Iterative Refinement:\n");
	    printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
	    for (i = 0; i < nrhs; ++i)
	      printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
	}
        Lstore = (SCformat *) L.Store;
        Ustore = (NCformat *) U.Store;
	printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
    	printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
    	printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
    	printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);

	printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
	       mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
	     
	fflush(stdout);

    } else if ( info > 0 && lwork == -1 ) {
        printf("** Estimated memory: %d bytes\n", info - n);
    }

    if ( options.PrintStat ) StatPrint(&stat);
    StatFree(&stat);

    SUPERLU_FREE (rhsb);
    SUPERLU_FREE (rhsx);
    SUPERLU_FREE (xact);
    SUPERLU_FREE (etree);
    SUPERLU_FREE (perm_r);
    SUPERLU_FREE (perm_c);
    SUPERLU_FREE (R);
    SUPERLU_FREE (C);
    SUPERLU_FREE (ferr);
    SUPERLU_FREE (berr);
    Destroy_CompCol_Matrix(&A);
    Destroy_SuperMatrix_Store(&B);
    Destroy_SuperMatrix_Store(&X);
    if ( lwork == 0 ) {
        Destroy_SuperNode_Matrix(&L);
        Destroy_CompCol_Matrix(&U);
    } else if ( lwork > 0 ) {
        SUPERLU_FREE(work);
    }

#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Exit main()");
#endif
}
Example #4
0
void
cgsitrf(superlu_options_t *options, SuperMatrix *A, int relax, int panel_size,
        int *etree, void *work, int lwork, int *perm_c, int *perm_r,
        SuperMatrix *L, SuperMatrix *U, SuperLUStat_t *stat, int *info)
{
    /* Local working arrays */
    NCPformat *Astore;
    int       *iperm_r = NULL; /* inverse of perm_r; used when
                                  options->Fact == SamePattern_SameRowPerm */
    int       *iperm_c; /* inverse of perm_c */
    int       *swap, *iswap; /* swap is used to store the row permutation
                                during the factorization. Initially, it is set
                                to iperm_c (row indeces of Pc*A*Pc').
                                iswap is the inverse of swap. After the
                                factorization, it is equal to perm_r. */
    int       *iwork;
    complex   *cwork;
    int       *segrep, *repfnz, *parent, *xplore;
    int       *panel_lsub; /* dense[]/panel_lsub[] pair forms a w-wide SPA */
    int       *marker, *marker_relax;
    complex    *dense, *tempv;
    float *stempv;
    int       *relax_end, *relax_fsupc;
    complex    *a;
    int       *asub;
    int       *xa_begin, *xa_end;
    int       *xsup, *supno;
    int       *xlsub, *xlusup, *xusub;
    int       nzlumax;
    float    *amax;
    complex    drop_sum;
    float alpha, omega;  /* used in MILU, mimicing DRIC */
    static GlobalLU_t Glu; /* persistent to facilitate multiple factors. */
    float    *swork2;      /* used by the second dropping rule */

    /* Local scalars */
    fact_t    fact = options->Fact;
    double    diag_pivot_thresh = options->DiagPivotThresh;
    double    drop_tol = options->ILU_DropTol; /* tau */
    double    fill_ini = options->ILU_FillTol; /* tau^hat */
    double    gamma = options->ILU_FillFactor;
    int       drop_rule = options->ILU_DropRule;
    milu_t    milu = options->ILU_MILU;
    double    fill_tol;
    int       pivrow;   /* pivotal row number in the original matrix A */
    int       nseg1;    /* no of segments in U-column above panel row jcol */
    int       nseg;     /* no of segments in each U-column */
    register int jcol;
    register int kcol;  /* end column of a relaxed snode */
    register int icol;
    register int i, k, jj, new_next, iinfo;
    int       m, n, min_mn, jsupno, fsupc, nextlu, nextu;
    int       w_def;    /* upper bound on panel width */
    int       usepr, iperm_r_allocated = 0;
    int       nnzL, nnzU;
    int       *panel_histo = stat->panel_histo;
    flops_t   *ops = stat->ops;

    int       last_drop;/* the last column which the dropping rules applied */
    int       quota;
    int       nnzAj;    /* number of nonzeros in A(:,1:j) */
    int       nnzLj, nnzUj;
    double    tol_L = drop_tol, tol_U = drop_tol;
    complex zero = {0.0, 0.0};
    float one = 1.0;

    /* Executable */
    iinfo    = 0;
    m        = A->nrow;
    n        = A->ncol;
    min_mn   = SUPERLU_MIN(m, n);
    Astore   = A->Store;
    a        = Astore->nzval;
    asub     = Astore->rowind;
    xa_begin = Astore->colbeg;
    xa_end   = Astore->colend;

    /* Allocate storage common to the factor routines */
    *info = cLUMemInit(fact, work, lwork, m, n, Astore->nnz, panel_size,
                       gamma, L, U, &Glu, &iwork, &cwork);
    if ( *info ) return;

    xsup    = Glu.xsup;
    supno   = Glu.supno;
    xlsub   = Glu.xlsub;
    xlusup  = Glu.xlusup;
    xusub   = Glu.xusub;

    SetIWork(m, n, panel_size, iwork, &segrep, &parent, &xplore,
             &repfnz, &panel_lsub, &marker_relax, &marker);
    cSetRWork(m, panel_size, cwork, &dense, &tempv);

    usepr = (fact == SamePattern_SameRowPerm);
    if ( usepr ) {
        /* Compute the inverse of perm_r */
        iperm_r = (int *) intMalloc(m);
        for (k = 0; k < m; ++k) iperm_r[perm_r[k]] = k;
        iperm_r_allocated = 1;
    }

    iperm_c = (int *) intMalloc(n);
    for (k = 0; k < n; ++k) iperm_c[perm_c[k]] = k;
    swap = (int *)intMalloc(n);
    for (k = 0; k < n; k++) swap[k] = iperm_c[k];
    iswap = (int *)intMalloc(n);
    for (k = 0; k < n; k++) iswap[k] = perm_c[k];
    amax = (float *) floatMalloc(panel_size);
    if (drop_rule & DROP_SECONDARY)
        swork2 = (float *)floatMalloc(n);
    else
        swork2 = NULL;

    nnzAj = 0;
    nnzLj = 0;
    nnzUj = 0;
    last_drop = SUPERLU_MAX(min_mn - 2 * sp_ienv(7), (int)(min_mn * 0.95));
    alpha = pow((double)n, -1.0 / options->ILU_MILU_Dim);

    /* Identify relaxed snodes */
    relax_end = (int *) intMalloc(n);
    relax_fsupc = (int *) intMalloc(n);
    if ( options->SymmetricMode == YES )
        ilu_heap_relax_snode(n, etree, relax, marker, relax_end, relax_fsupc);
    else
        ilu_relax_snode(n, etree, relax, marker, relax_end, relax_fsupc);

    ifill (perm_r, m, EMPTY);
    ifill (marker, m * NO_MARKER, EMPTY);
    supno[0] = -1;
    xsup[0]  = xlsub[0] = xusub[0] = xlusup[0] = 0;
    w_def    = panel_size;

    /* Mark the rows used by relaxed supernodes */
    ifill (marker_relax, m, EMPTY);
    i = mark_relax(m, relax_end, relax_fsupc, xa_begin, xa_end,
                 asub, marker_relax);
#if ( PRNTlevel >= 1)
    printf("%d relaxed supernodes.\n", i);
#endif

    /*
     * Work on one "panel" at a time. A panel is one of the following:
     *     (a) a relaxed supernode at the bottom of the etree, or
     *     (b) panel_size contiguous columns, defined by the user
     */
    for (jcol = 0; jcol < min_mn; ) {

        if ( relax_end[jcol] != EMPTY ) { /* start of a relaxed snode */
            kcol = relax_end[jcol];       /* end of the relaxed snode */
            panel_histo[kcol-jcol+1]++;

            /* Drop small rows in the previous supernode. */
            if (jcol > 0 && jcol < last_drop) {
                int first = xsup[supno[jcol - 1]];
                int last = jcol - 1;
                int quota;

                /* Compute the quota */
                if (drop_rule & DROP_PROWS)
                    quota = gamma * Astore->nnz / m * (m - first) / m
                            * (last - first + 1);
                else if (drop_rule & DROP_COLUMN) {
                    int i;
                    quota = 0;
                    for (i = first; i <= last; i++)
                        quota += xa_end[i] - xa_begin[i];
                    quota = gamma * quota * (m - first) / m;
                } else if (drop_rule & DROP_AREA)
                    quota = gamma * nnzAj * (1.0 - 0.5 * (last + 1.0) / m)
                            - nnzLj;
                else
                    quota = m * n;
                fill_tol = pow(fill_ini, 1.0 - 0.5 * (first + last) / min_mn);

                /* Drop small rows */
                stempv = (float *) tempv;
                i = ilu_cdrop_row(options, first, last, tol_L, quota, &nnzLj,
                                  &fill_tol, &Glu, stempv, swork2, 0);
                /* Reset the parameters */
                if (drop_rule & DROP_DYNAMIC) {
                    if (gamma * nnzAj * (1.0 - 0.5 * (last + 1.0) / m)
                             < nnzLj)
                        tol_L = SUPERLU_MIN(1.0, tol_L * 2.0);
                    else
                        tol_L = SUPERLU_MAX(drop_tol, tol_L * 0.5);
                }
                if (fill_tol < 0) iinfo -= (int)fill_tol;
#ifdef DEBUG
                num_drop_L += i * (last - first + 1);
#endif
            }

            /* --------------------------------------
             * Factorize the relaxed supernode(jcol:kcol)
             * -------------------------------------- */
            /* Determine the union of the row structure of the snode */
            if ( (*info = ilu_csnode_dfs(jcol, kcol, asub, xa_begin, xa_end,
                                         marker, &Glu)) != 0 )
                return;

            nextu    = xusub[jcol];
            nextlu   = xlusup[jcol];
            jsupno   = supno[jcol];
            fsupc    = xsup[jsupno];
            new_next = nextlu + (xlsub[fsupc+1]-xlsub[fsupc])*(kcol-jcol+1);
            nzlumax = Glu.nzlumax;
            while ( new_next > nzlumax ) {
                if ((*info = cLUMemXpand(jcol, nextlu, LUSUP, &nzlumax, &Glu)))
                    return;
            }

            for (icol = jcol; icol <= kcol; icol++) {
                xusub[icol+1] = nextu;

                amax[0] = 0.0;
                /* Scatter into SPA dense[*] */
                for (k = xa_begin[icol]; k < xa_end[icol]; k++) {
                    register float tmp = c_abs1 (&a[k]);
                    if (tmp > amax[0]) amax[0] = tmp;
                    dense[asub[k]] = a[k];
                }
                nnzAj += xa_end[icol] - xa_begin[icol];
                if (amax[0] == 0.0) {
                    amax[0] = fill_ini;
#if ( PRNTlevel >= 1)
                    printf("Column %d is entirely zero!\n", icol);
                    fflush(stdout);
#endif
                }

                /* Numeric update within the snode */
                csnode_bmod(icol, jsupno, fsupc, dense, tempv, &Glu, stat);

                if (usepr) pivrow = iperm_r[icol];
                fill_tol = pow(fill_ini, 1.0 - (double)icol / (double)min_mn);
                if ( (*info = ilu_cpivotL(icol, diag_pivot_thresh, &usepr,
                                          perm_r, iperm_c[icol], swap, iswap,
                                          marker_relax, &pivrow,
                                          amax[0] * fill_tol, milu, zero,
                                          &Glu, stat)) ) {
                    iinfo++;
                    marker[pivrow] = kcol;
                }

            }

            jcol = kcol + 1;

        } else { /* Work on one panel of panel_size columns */

            /* Adjust panel_size so that a panel won't overlap with the next
             * relaxed snode.
             */
            panel_size = w_def;
            for (k = jcol + 1; k < SUPERLU_MIN(jcol+panel_size, min_mn); k++)
                if ( relax_end[k] != EMPTY ) {
                    panel_size = k - jcol;
                    break;
                }
            if ( k == min_mn ) panel_size = min_mn - jcol;
            panel_histo[panel_size]++;

            /* symbolic factor on a panel of columns */
            ilu_cpanel_dfs(m, panel_size, jcol, A, perm_r, &nseg1,
                          dense, amax, panel_lsub, segrep, repfnz,
                          marker, parent, xplore, &Glu);

            /* numeric sup-panel updates in topological order */
            cpanel_bmod(m, panel_size, jcol, nseg1, dense,
                        tempv, segrep, repfnz, &Glu, stat);

            /* Sparse LU within the panel, and below panel diagonal */
            for (jj = jcol; jj < jcol + panel_size; jj++) {

                k = (jj - jcol) * m; /* column index for w-wide arrays */

                nseg = nseg1;   /* Begin after all the panel segments */

                nnzAj += xa_end[jj] - xa_begin[jj];

                if ((*info = ilu_ccolumn_dfs(m, jj, perm_r, &nseg,
                                             &panel_lsub[k], segrep, &repfnz[k],
                                             marker, parent, xplore, &Glu)))
                    return;

                /* Numeric updates */
                if ((*info = ccolumn_bmod(jj, (nseg - nseg1), &dense[k],
                                          tempv, &segrep[nseg1], &repfnz[k],
                                          jcol, &Glu, stat)) != 0) return;

                /* Make a fill-in position if the column is entirely zero */
                if (xlsub[jj + 1] == xlsub[jj]) {
                    register int i, row;
                    int nextl;
                    int nzlmax = Glu.nzlmax;
                    int *lsub = Glu.lsub;
                    int *marker2 = marker + 2 * m;

                    /* Allocate memory */
                    nextl = xlsub[jj] + 1;
                    if (nextl >= nzlmax) {
                        int error = cLUMemXpand(jj, nextl, LSUB, &nzlmax, &Glu);
                        if (error) { *info = error; return; }
                        lsub = Glu.lsub;
                    }
                    xlsub[jj + 1]++;
                    assert(xlusup[jj]==xlusup[jj+1]);
                    xlusup[jj + 1]++;
                    Glu.lusup[xlusup[jj]] = zero;

                    /* Choose a row index (pivrow) for fill-in */
                    for (i = jj; i < n; i++)
                        if (marker_relax[swap[i]] <= jj) break;
                    row = swap[i];
                    marker2[row] = jj;
                    lsub[xlsub[jj]] = row;
#ifdef DEBUG
                    printf("Fill col %d.\n", jj);
                    fflush(stdout);
#endif
                }

                /* Computer the quota */
                if (drop_rule & DROP_PROWS)
                    quota = gamma * Astore->nnz / m * jj / m;
                else if (drop_rule & DROP_COLUMN)
                    quota = gamma * (xa_end[jj] - xa_begin[jj]) *
                            (jj + 1) / m;
                else if (drop_rule & DROP_AREA)
                    quota = gamma * 0.9 * nnzAj * 0.5 - nnzUj;
                else
                    quota = m;

                /* Copy the U-segments to ucol[*] and drop small entries */
                if ((*info = ilu_ccopy_to_ucol(jj, nseg, segrep, &repfnz[k],
                                               perm_r, &dense[k], drop_rule,
                                               milu, amax[jj - jcol] * tol_U,
                                               quota, &drop_sum, &nnzUj, &Glu,
                                               swork2)) != 0)
                    return;

                /* Reset the dropping threshold if required */
                if (drop_rule & DROP_DYNAMIC) {
                    if (gamma * 0.9 * nnzAj * 0.5 < nnzLj)
                        tol_U = SUPERLU_MIN(1.0, tol_U * 2.0);
                    else
                        tol_U = SUPERLU_MAX(drop_tol, tol_U * 0.5);
                }

                if (drop_sum.r != 0.0 && drop_sum.i != 0.0)
                {
                    omega = SUPERLU_MIN(2.0*(1.0-alpha)/c_abs1(&drop_sum), 1.0);
                    cs_mult(&drop_sum, &drop_sum, omega);
                }
                if (usepr) pivrow = iperm_r[jj];
                fill_tol = pow(fill_ini, 1.0 - (double)jj / (double)min_mn);
                if ( (*info = ilu_cpivotL(jj, diag_pivot_thresh, &usepr, perm_r,
                                          iperm_c[jj], swap, iswap,
                                          marker_relax, &pivrow,
                                          amax[jj - jcol] * fill_tol, milu,
                                          drop_sum, &Glu, stat)) ) {
                    iinfo++;
                    marker[m + pivrow] = jj;
                    marker[2 * m + pivrow] = jj;
                }

                /* Reset repfnz[] for this column */
                resetrep_col (nseg, segrep, &repfnz[k]);

                /* Start a new supernode, drop the previous one */
                if (jj > 0 && supno[jj] > supno[jj - 1] && jj < last_drop) {
                    int first = xsup[supno[jj - 1]];
                    int last = jj - 1;
                    int quota;

                    /* Compute the quota */
                    if (drop_rule & DROP_PROWS)
                        quota = gamma * Astore->nnz / m * (m - first) / m
                                * (last - first + 1);
                    else if (drop_rule & DROP_COLUMN) {
                        int i;
                        quota = 0;
                        for (i = first; i <= last; i++)
                            quota += xa_end[i] - xa_begin[i];
                        quota = gamma * quota * (m - first) / m;
                    } else if (drop_rule & DROP_AREA)
                        quota = gamma * nnzAj * (1.0 - 0.5 * (last + 1.0)
                                / m) - nnzLj;
                    else
                        quota = m * n;
                    fill_tol = pow(fill_ini, 1.0 - 0.5 * (first + last) /
                            (double)min_mn);

                    /* Drop small rows */
                    stempv = (float *) tempv;
                    i = ilu_cdrop_row(options, first, last, tol_L, quota,
                                      &nnzLj, &fill_tol, &Glu, stempv, swork2,
                                      1);

                    /* Reset the parameters */
                    if (drop_rule & DROP_DYNAMIC) {
                        if (gamma * nnzAj * (1.0 - 0.5 * (last + 1.0) / m)
                                < nnzLj)
                            tol_L = SUPERLU_MIN(1.0, tol_L * 2.0);
                        else
                            tol_L = SUPERLU_MAX(drop_tol, tol_L * 0.5);
                    }
                    if (fill_tol < 0) iinfo -= (int)fill_tol;
#ifdef DEBUG
                    num_drop_L += i * (last - first + 1);
#endif
                } /* if start a new supernode */

            } /* for */

            jcol += panel_size; /* Move to the next panel */

        } /* else */

    } /* for */

    *info = iinfo;

    if ( m > n ) {
        k = 0;
        for (i = 0; i < m; ++i)
            if ( perm_r[i] == EMPTY ) {
                perm_r[i] = n + k;
                ++k;
            }
    }

    ilu_countnz(min_mn, &nnzL, &nnzU, &Glu);
    fixupL(min_mn, perm_r, &Glu);

    cLUWorkFree(iwork, cwork, &Glu); /* Free work space and compress storage */

    if ( fact == SamePattern_SameRowPerm ) {
        /* L and U structures may have changed due to possibly different
           pivoting, even though the storage is available.
           There could also be memory expansions, so the array locations
           may have changed, */
        ((SCformat *)L->Store)->nnz = nnzL;
        ((SCformat *)L->Store)->nsuper = Glu.supno[n];
        ((SCformat *)L->Store)->nzval = Glu.lusup;
        ((SCformat *)L->Store)->nzval_colptr = Glu.xlusup;
        ((SCformat *)L->Store)->rowind = Glu.lsub;
        ((SCformat *)L->Store)->rowind_colptr = Glu.xlsub;
        ((NCformat *)U->Store)->nnz = nnzU;
        ((NCformat *)U->Store)->nzval = Glu.ucol;
        ((NCformat *)U->Store)->rowind = Glu.usub;
        ((NCformat *)U->Store)->colptr = Glu.xusub;
    } else {
        cCreate_SuperNode_Matrix(L, A->nrow, min_mn, nnzL, Glu.lusup,
                                 Glu.xlusup, Glu.lsub, Glu.xlsub, Glu.supno,
                                 Glu.xsup, SLU_SC, SLU_C, SLU_TRLU);
        cCreate_CompCol_Matrix(U, min_mn, min_mn, nnzU, Glu.ucol,
                               Glu.usub, Glu.xusub, SLU_NC, SLU_C, SLU_TRU);
    }

    ops[FACT] += ops[TRSV] + ops[GEMV];
    stat->expansions = --(Glu.num_expansions);

    if ( iperm_r_allocated ) SUPERLU_FREE (iperm_r);
    SUPERLU_FREE (iperm_c);
    SUPERLU_FREE (relax_end);
    SUPERLU_FREE (swap);
    SUPERLU_FREE (iswap);
    SUPERLU_FREE (relax_fsupc);
    SUPERLU_FREE (amax);
    if ( swork2 ) SUPERLU_FREE (swork2);

}
Example #5
0
main(int argc, char *argv[])
{
/* 
 * Purpose
 * =======
 *
 * SDRIVE is the main test program for the FLOAT linear 
 * equation driver routines SGSSV and SGSSVX.
 * 
 * The program is invoked by a shell script file -- stest.csh.
 * The output from the tests are written into a file -- stest.out.
 *
 * =====================================================================
 */
    float         *a, *a_save;
    int            *asub, *asub_save;
    int            *xa, *xa_save;
    SuperMatrix  A, B, X, L, U;
    SuperMatrix  ASAV, AC;
    GlobalLU_t   Glu; /* Not needed on return. */
    mem_usage_t    mem_usage;
    int            *perm_r; /* row permutation from partial pivoting */
    int            *perm_c, *pc_save; /* column permutation */
    int            *etree;
    float  zero = 0.0;
    float         *R, *C;
    float         *ferr, *berr;
    float         *rwork;
    float	   *wwork;
    void           *work;
    int            info, lwork, nrhs, panel_size, relax;
    int            m, n, nnz;
    float         *xact;
    float         *rhsb, *solx, *bsav;
    int            ldb, ldx;
    float         rpg, rcond;
    int            i, j, k1;
    float         rowcnd, colcnd, amax;
    int            maxsuper, rowblk, colblk;
    int            prefact, nofact, equil, iequed;
    int            nt, nrun, nfail, nerrs, imat, fimat, nimat;
    int            nfact, ifact, itran;
    int            kl, ku, mode, lda;
    int            zerot, izero, ioff;
    double         u;
    float         anorm, cndnum;
    float         *Afull;
    float         result[NTESTS];
    superlu_options_t options;
    fact_t         fact;
    trans_t        trans;
    SuperLUStat_t  stat;
    static char    matrix_type[8];
    static char    equed[1], path[4], sym[1], dist[1];
    FILE           *fp;

    /* Fixed set of parameters */
    int            iseed[]  = {1988, 1989, 1990, 1991};
    static char    equeds[]  = {'N', 'R', 'C', 'B'};
    static fact_t  facts[] = {FACTORED, DOFACT, SamePattern,
			      SamePattern_SameRowPerm};
    static trans_t transs[]  = {NOTRANS, TRANS, CONJ};

    /* Some function prototypes */ 
    extern int sgst01(int, int, SuperMatrix *, SuperMatrix *, 
		      SuperMatrix *, int *, int *, float *);
    extern int sgst02(trans_t, int, int, int, SuperMatrix *, float *,
                      int, float *, int, float *resid);
    extern int sgst04(int, int, float *, int, 
                      float *, int, float rcond, float *resid);
    extern int sgst07(trans_t, int, int, SuperMatrix *, float *, int,
                         float *, int, float *, int, 
                         float *, float *, float *);
    extern int slatb4_slu(char *, int *, int *, int *, char *, int *, int *, 
	               float *, int *, float *, char *);
    extern int slatms_slu(int *, int *, char *, int *, char *, float *d,
                       int *, float *, float *, int *, int *,
                       char *, float *, int *, float *, int *);
    extern int sp_sconvert(int, int, float *, int, int, int,
	                   float *a, int *, int *, int *);


    /* Executable statements */

    strcpy(path, "SGE");
    nrun  = 0;
    nfail = 0;
    nerrs = 0;

    /* Defaults */
    lwork      = 0;
    n          = 1;
    nrhs       = 1;
    panel_size = sp_ienv(1);
    relax      = sp_ienv(2);
    u          = 1.0;
    strcpy(matrix_type, "LA");
    parse_command_line(argc, argv, matrix_type, &n,
		       &panel_size, &relax, &nrhs, &maxsuper,
		       &rowblk, &colblk, &lwork, &u, &fp);
    if ( lwork > 0 ) {
	work = SUPERLU_MALLOC(lwork);
	if ( !work ) {
	    fprintf(stderr, "expert: cannot allocate %d bytes\n", lwork);
	    exit (-1);
	}
    }

    /* Set the default input options. */
    set_default_options(&options);
    options.DiagPivotThresh = u;
    options.PrintStat = NO;
    options.PivotGrowth = YES;
    options.ConditionNumber = YES;
    options.IterRefine = SLU_SINGLE;
    
    if ( strcmp(matrix_type, "LA") == 0 ) {
	/* Test LAPACK matrix suite. */
	m = n;
	lda = SUPERLU_MAX(n, 1);
	nnz = n * n;        /* upper bound */
	fimat = 1;
	nimat = NTYPES;
	Afull = floatCalloc(lda * n);
	sallocateA(n, nnz, &a, &asub, &xa);
    } else {
	/* Read a sparse matrix */
	fimat = nimat = 0;
	sreadhb(fp, &m, &n, &nnz, &a, &asub, &xa);
    }

    sallocateA(n, nnz, &a_save, &asub_save, &xa_save);
    rhsb = floatMalloc(m * nrhs);
    bsav = floatMalloc(m * nrhs);
    solx = floatMalloc(n * nrhs);
    ldb  = m;
    ldx  = n;
    sCreate_Dense_Matrix(&B, m, nrhs, rhsb, ldb, SLU_DN, SLU_S, SLU_GE);
    sCreate_Dense_Matrix(&X, n, nrhs, solx, ldx, SLU_DN, SLU_S, SLU_GE);
    xact = floatMalloc(n * nrhs);
    etree   = intMalloc(n);
    perm_r  = intMalloc(n);
    perm_c  = intMalloc(n);
    pc_save = intMalloc(n);
    R       = (float *) SUPERLU_MALLOC(m*sizeof(float));
    C       = (float *) SUPERLU_MALLOC(n*sizeof(float));
    ferr    = (float *) SUPERLU_MALLOC(nrhs*sizeof(float));
    berr    = (float *) SUPERLU_MALLOC(nrhs*sizeof(float));
    j = SUPERLU_MAX(m,n) * SUPERLU_MAX(4,nrhs);    
    rwork   = (float *) SUPERLU_MALLOC(j*sizeof(float));
    for (i = 0; i < j; ++i) rwork[i] = 0.;
    if ( !R ) ABORT("SUPERLU_MALLOC fails for R");
    if ( !C ) ABORT("SUPERLU_MALLOC fails for C");
    if ( !ferr ) ABORT("SUPERLU_MALLOC fails for ferr");
    if ( !berr ) ABORT("SUPERLU_MALLOC fails for berr");
    if ( !rwork ) ABORT("SUPERLU_MALLOC fails for rwork");
    wwork   = floatCalloc( SUPERLU_MAX(m,n) * SUPERLU_MAX(4,nrhs) );

    for (i = 0; i < n; ++i) perm_c[i] = pc_save[i] = i;
    options.ColPerm = MY_PERMC;

    for (imat = fimat; imat <= nimat; ++imat) { /* All matrix types */
	
	if ( imat ) {

	    /* Skip types 5, 6, or 7 if the matrix size is too small. */
	    zerot = (imat >= 5 && imat <= 7);
	    if ( zerot && n < imat-4 )
		continue;
	    
	    /* Set up parameters with SLATB4 and generate a test matrix
	       with SLATMS.  */
	    slatb4_slu(path, &imat, &n, &n, sym, &kl, &ku, &anorm, &mode,
		    &cndnum, dist);

	    slatms_slu(&n, &n, dist, iseed, sym, &rwork[0], &mode, &cndnum,
		    &anorm, &kl, &ku, "No packing", Afull, &lda,
		    &wwork[0], &info);

	    if ( info ) {
		printf(FMT3, "SLATMS", info, izero, n, nrhs, imat, nfail);
		continue;
	    }

	    /* For types 5-7, zero one or more columns of the matrix
	       to test that INFO is returned correctly.   */
	    if ( zerot ) {
		if ( imat == 5 ) izero = 1;
		else if ( imat == 6 ) izero = n;
		else izero = n / 2 + 1;
		ioff = (izero - 1) * lda;
		if ( imat < 7 ) {
		    for (i = 0; i < n; ++i) Afull[ioff + i] = zero;
		} else {
		    for (j = 0; j < n - izero + 1; ++j)
			for (i = 0; i < n; ++i)
			    Afull[ioff + i + j*lda] = zero;
		}
	    } else {
		izero = 0;
	    }

	    /* Convert to sparse representation. */
	    sp_sconvert(n, n, Afull, lda, kl, ku, a, asub, xa, &nnz);

	} else {
	    izero = 0;
	    zerot = 0;
	}
	
	sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);

	/* Save a copy of matrix A in ASAV */
	sCreate_CompCol_Matrix(&ASAV, m, n, nnz, a_save, asub_save, xa_save,
			      SLU_NC, SLU_S, SLU_GE);
	sCopy_CompCol_Matrix(&A, &ASAV);
	
	/* Form exact solution. */
	sGenXtrue(n, nrhs, xact, ldx);
	
	StatInit(&stat);

	for (iequed = 0; iequed < 4; ++iequed) {
	    *equed = equeds[iequed];
	    if (iequed == 0) nfact = 4;
	    else nfact = 1; /* Only test factored, pre-equilibrated matrix */

	    for (ifact = 0; ifact < nfact; ++ifact) {
		fact = facts[ifact];
		options.Fact = fact;

		for (equil = 0; equil < 2; ++equil) {
		    options.Equil = equil;
		    prefact   = ( options.Fact == FACTORED ||
				  options.Fact == SamePattern_SameRowPerm );
                                /* Need a first factor */
		    nofact    = (options.Fact != FACTORED);  /* Not factored */

		    /* Restore the matrix A. */
		    sCopy_CompCol_Matrix(&ASAV, &A);
			
		    if ( zerot ) {
                        if ( prefact ) continue;
		    } else if ( options.Fact == FACTORED ) {
                        if ( equil || iequed ) {
			    /* Compute row and column scale factors to
			       equilibrate matrix A.    */
			    sgsequ(&A, R, C, &rowcnd, &colcnd, &amax, &info);

			    /* Force equilibration. */
			    if ( !info && n > 0 ) {
				if ( strncmp(equed, "R", 1)==0 ) {
				    rowcnd = 0.;
				    colcnd = 1.;
				} else if ( strncmp(equed, "C", 1)==0 ) {
				    rowcnd = 1.;
				    colcnd = 0.;
				} else if ( strncmp(equed, "B", 1)==0 ) {
				    rowcnd = 0.;
				    colcnd = 0.;
				}
			    }
			
			    /* Equilibrate the matrix. */
			    slaqgs(&A, R, C, rowcnd, colcnd, amax, equed);
			}
		    }
		    
		    if ( prefact ) { /* Need a factor for the first time */
			
		        /* Save Fact option. */
		        fact = options.Fact;
			options.Fact = DOFACT;

			/* Preorder the matrix, obtain the column etree. */
			sp_preorder(&options, &A, perm_c, etree, &AC);

			/* Factor the matrix AC. */
			sgstrf(&options, &AC, relax, panel_size,
                               etree, work, lwork, perm_c, perm_r, &L, &U,
                               &Glu, &stat, &info);

			if ( info ) { 
                            printf("** First factor: info %d, equed %c\n",
				   info, *equed);
                            if ( lwork == -1 ) {
                                printf("** Estimated memory: %d bytes\n",
                                        info - n);
                                exit(0);
                            }
                        }
	
                        Destroy_CompCol_Permuted(&AC);
			
		        /* Restore Fact option. */
			options.Fact = fact;
		    } /* if .. first time factor */
		    
		    for (itran = 0; itran < NTRAN; ++itran) {
			trans = transs[itran];
                        options.Trans = trans;

			/* Restore the matrix A. */
			sCopy_CompCol_Matrix(&ASAV, &A);
			
 			/* Set the right hand side. */
			sFillRHS(trans, nrhs, xact, ldx, &A, &B);
			sCopy_Dense_Matrix(m, nrhs, rhsb, ldb, bsav, ldb);

			/*----------------
			 * Test sgssv
			 *----------------*/
			if ( options.Fact == DOFACT && itran == 0) {
                            /* Not yet factored, and untransposed */
	
			    sCopy_Dense_Matrix(m, nrhs, rhsb, ldb, solx, ldx);
			    sgssv(&options, &A, perm_c, perm_r, &L, &U, &X,
                                  &stat, &info);
			    
			    if ( info && info != izero ) {
                                printf(FMT3, "sgssv",
				       info, izero, n, nrhs, imat, nfail);
			    } else {
                                /* Reconstruct matrix from factors and
	                           compute residual. */
                                sgst01(m, n, &A, &L, &U, perm_c, perm_r,
                                         &result[0]);
				nt = 1;
				if ( izero == 0 ) {
				    /* Compute residual of the computed
				       solution. */
				    sCopy_Dense_Matrix(m, nrhs, rhsb, ldb,
						       wwork, ldb);
				    sgst02(trans, m, n, nrhs, &A, solx,
                                              ldx, wwork,ldb, &result[1]);
				    nt = 2;
				}
				
				/* Print information about the tests that
				   did not pass the threshold.      */
				for (i = 0; i < nt; ++i) {
				    if ( result[i] >= THRESH ) {
					printf(FMT1, "sgssv", n, i,
					       result[i]);
					++nfail;
				    }
				}
				nrun += nt;
			    } /* else .. info == 0 */

			    /* Restore perm_c. */
			    for (i = 0; i < n; ++i) perm_c[i] = pc_save[i];

		            if (lwork == 0) {
			        Destroy_SuperNode_Matrix(&L);
			        Destroy_CompCol_Matrix(&U);
			    }
			} /* if .. end of testing sgssv */
    
			/*----------------
			 * Test sgssvx
			 *----------------*/
    
			/* Equilibrate the matrix if fact = FACTORED and
			   equed = 'R', 'C', or 'B'.   */
			if ( options.Fact == FACTORED &&
			     (equil || iequed) && n > 0 ) {
			    slaqgs(&A, R, C, rowcnd, colcnd, amax, equed);
			}
			
			/* Solve the system and compute the condition number
			   and error bounds using sgssvx.      */
			sgssvx(&options, &A, perm_c, perm_r, etree,
                               equed, R, C, &L, &U, work, lwork, &B, &X, &rpg,
                               &rcond, ferr, berr, &Glu,
			       &mem_usage, &stat, &info);

			if ( info && info != izero ) {
			    printf(FMT3, "sgssvx",
				   info, izero, n, nrhs, imat, nfail);
                            if ( lwork == -1 ) {
                                printf("** Estimated memory: %.0f bytes\n",
                                        mem_usage.total_needed);
                                exit(0);
                            }
			} else {
			    if ( !prefact ) {
			    	/* Reconstruct matrix from factors and
	 			   compute residual. */
                                sgst01(m, n, &A, &L, &U, perm_c, perm_r,
                                         &result[0]);
				k1 = 0;
			    } else {
			   	k1 = 1;
			    }

			    if ( !info ) {
				/* Compute residual of the computed solution.*/
				sCopy_Dense_Matrix(m, nrhs, bsav, ldb,
						  wwork, ldb);
				sgst02(trans, m, n, nrhs, &ASAV, solx, ldx,
					  wwork, ldb, &result[1]);

				/* Check solution from generated exact
				   solution. */
				sgst04(n, nrhs, solx, ldx, xact, ldx, rcond,
					  &result[2]);

				/* Check the error bounds from iterative
				   refinement. */
				sgst07(trans, n, nrhs, &ASAV, bsav, ldb,
					  solx, ldx, xact, ldx, ferr, berr,
					  &result[3]);

				/* Print information about the tests that did
				   not pass the threshold.    */
				for (i = k1; i < NTESTS; ++i) {
				    if ( result[i] >= THRESH ) {
					printf(FMT2, "sgssvx",
					       options.Fact, trans, *equed,
					       n, imat, i, result[i]);
					++nfail;
				    }
				}
				nrun += NTESTS;
			    } /* if .. info == 0 */
			} /* else .. end of testing sgssvx */

		    } /* for itran ... */

		    if ( lwork == 0 ) {
			Destroy_SuperNode_Matrix(&L);
			Destroy_CompCol_Matrix(&U);
		    }

		} /* for equil ... */
	    } /* for ifact ... */
	} /* for iequed ... */
#if 0    
    if ( !info ) {
	PrintPerf(&L, &U, &mem_usage, rpg, rcond, ferr, berr, equed);
    }
#endif
        Destroy_SuperMatrix_Store(&A);
        Destroy_SuperMatrix_Store(&ASAV);
        StatFree(&stat);

    } /* for imat ... */

    /* Print a summary of the results. */
    PrintSumm("SGE", nfail, nrun, nerrs);

    if ( strcmp(matrix_type, "LA") == 0 ) SUPERLU_FREE (Afull);
    SUPERLU_FREE (rhsb);
    SUPERLU_FREE (bsav);
    SUPERLU_FREE (solx);    
    SUPERLU_FREE (xact);
    SUPERLU_FREE (etree);
    SUPERLU_FREE (perm_r);
    SUPERLU_FREE (perm_c);
    SUPERLU_FREE (pc_save);
    SUPERLU_FREE (R);
    SUPERLU_FREE (C);
    SUPERLU_FREE (ferr);
    SUPERLU_FREE (berr);
    SUPERLU_FREE (rwork);
    SUPERLU_FREE (wwork);
    Destroy_SuperMatrix_Store(&B);
    Destroy_SuperMatrix_Store(&X);
#if 0
    Destroy_CompCol_Matrix(&A);
    Destroy_CompCol_Matrix(&ASAV);
#else
    SUPERLU_FREE(a); SUPERLU_FREE(asub); SUPERLU_FREE(xa);
    SUPERLU_FREE(a_save); SUPERLU_FREE(asub_save); SUPERLU_FREE(xa_save);
#endif
    if ( lwork > 0 ) {
	SUPERLU_FREE (work);
	Destroy_SuperMatrix_Store(&L);
	Destroy_SuperMatrix_Store(&U);
    }

    return 0;
}
Example #6
0
int sfgmr(int n,
     void (*smatvec) (float, float[], float, float[]),
     void (*spsolve) (int, float[], float[]),
     float *rhs, float *sol, double tol, int im, int *itmax, FILE * fits)
{
/*----------------------------------------------------------------------
|                 *** Preconditioned FGMRES ***
+-----------------------------------------------------------------------
| This is a simple version of the ARMS preconditioned FGMRES algorithm.
+-----------------------------------------------------------------------
| Y. S. Dec. 2000. -- Apr. 2008
+-----------------------------------------------------------------------
| on entry:
|----------
|
| rhs     = real vector of length n containing the right hand side.
| sol     = real vector of length n containing an initial guess to the
|           solution on input.
| tol     = tolerance for stopping iteration
| im      = Krylov subspace dimension
| (itmax) = max number of iterations allowed.
| fits    = NULL: no output
|        != NULL: file handle to output " resid vs time and its"
|
| on return:
|----------
| fgmr      int =  0 --> successful return.
|           int =  1 --> convergence not achieved in itmax iterations.
| sol     = contains an approximate solution (upon successful return).
| itmax   = has changed. It now contains the number of steps required
|           to converge --
+-----------------------------------------------------------------------
| internal work arrays:
|----------
| vv      = work array of length [im+1][n] (used to store the Arnoldi
|           basis)
| hh      = work array of length [im][im+1] (Householder matrix)
| z       = work array of length [im][n] to store preconditioned vectors
+-----------------------------------------------------------------------
| subroutines called :
| matvec - matrix-vector multiplication operation
| psolve - (right) preconditionning operation
|	   psolve can be a NULL pointer (GMRES without preconditioner)
+---------------------------------------------------------------------*/

    int maxits = *itmax;
    int i, i1, ii, j, k, k1, its, retval, i_1 = 1, i_2 = 2;
    float beta, eps1 = 0.0, t, t0, gam;
    float **hh, *c, *s, *rs;
    float **vv, **z, tt;
    float zero = 0.0;
    float one = 1.0;

    its = 0;
    vv = (float **)SUPERLU_MALLOC((im + 1) * sizeof(float *));
    for (i = 0; i <= im; i++) vv[i] = floatMalloc(n);
    z = (float **)SUPERLU_MALLOC(im * sizeof(float *));
    hh = (float **)SUPERLU_MALLOC(im * sizeof(float *));
    for (i = 0; i < im; i++)
    {
	hh[i] = floatMalloc(i + 2);
	z[i] = floatMalloc(n);
    }
    c = floatMalloc(im);
    s = floatMalloc(im);
    rs = floatMalloc(im + 1);

    /*---- outer loop starts here ----*/
    do
    {
	/*---- compute initial residual vector ----*/
	smatvec(one, sol, zero, vv[0]);
	for (j = 0; j < n; j++)
	    vv[0][j] = rhs[j] - vv[0][j];	/* vv[0]= initial residual */
	beta = snrm2_(&n, vv[0], &i_1);

	/*---- print info if fits != null ----*/
	if (fits != NULL && its == 0)
	    fprintf(fits, "%8d   %10.2e\n", its, beta);
	/*if ( beta <= tol * dnrm2_(&n, rhs, &i_1) )*/
	if ( !(beta > tol * snrm2_(&n, rhs, &i_1)) )
	    break;
	t = 1.0 / beta;

	/*---- normalize: vv[0] = vv[0] / beta ----*/
	for (j = 0; j < n; j++)
	    vv[0][j] = vv[0][j] * t;
	if (its == 0)
	    eps1 = tol * beta;

	/*---- initialize 1-st term of rhs of hessenberg system ----*/
	rs[0] = beta;
	for (i = 0; i < im; i++)
	{
	    its++;
	    i1 = i + 1;

	    /*------------------------------------------------------------
	    |  (Right) Preconditioning Operation   z_{j} = M^{-1} v_{j}
	    +-----------------------------------------------------------*/
	    if (spsolve)
		spsolve(n, z[i], vv[i]);
	    else
		scopy_(&n, vv[i], &i_1, z[i], &i_1);

	    /*---- matvec operation w = A z_{j} = A M^{-1} v_{j} ----*/
	    smatvec(one, z[i], zero, vv[i1]);

	    /*------------------------------------------------------------
	    |     modified gram - schmidt...
	    |     h_{i,j} = (w,v_{i})
	    |     w  = w - h_{i,j} v_{i}
	    +------------------------------------------------------------*/
	    t0 = snrm2_(&n, vv[i1], &i_1);
	    for (j = 0; j <= i; j++)
	    {
		float negt;
		tt = sdot_(&n, vv[j], &i_1, vv[i1], &i_1);
		hh[i][j] = tt;
		negt = -tt;
		saxpy_(&n, &negt, vv[j], &i_1, vv[i1], &i_1);
	    }

	    /*---- h_{j+1,j} = ||w||_{2} ----*/
	    t = snrm2_(&n, vv[i1], &i_1);
	    while (t < 0.5 * t0)
	    {
		t0 = t;
		for (j = 0; j <= i; j++)
		{
		    float negt;
		    tt = sdot_(&n, vv[j], &i_1, vv[i1], &i_1);
		    hh[i][j] += tt;
		    negt = -tt;
		    saxpy_(&n, &negt, vv[j], &i_1, vv[i1], &i_1);
		}
		t = snrm2_(&n, vv[i1], &i_1);
	    }

	    hh[i][i1] = t;

	    if (t != 0.0)
	    {
		/*---- v_{j+1} = w / h_{j+1,j} ----*/
		t = 1.0 / t;
		for (k = 0; k < n; k++)
		    vv[i1][k] = vv[i1][k] * t;
	    }
	    /*---------------------------------------------------
	    |     done with modified gram schimdt and arnoldi step
	    |     now  update factorization of hh
	    +--------------------------------------------------*/

	    /*--------------------------------------------------------
	    |   perform previous transformations  on i-th column of h
	    +-------------------------------------------------------*/
	    for (k = 1; k <= i; k++)
	    {
		k1 = k - 1;
		tt = hh[i][k1];
		hh[i][k1] = c[k1] * tt + s[k1] * hh[i][k];
		hh[i][k] = -s[k1] * tt + c[k1] * hh[i][k];
	    }

	    gam = sqrt(pow(hh[i][i], 2) + pow(hh[i][i1], 2));

	    /*---------------------------------------------------
	    |     if gamma is zero then any small value will do
	    |     affect only residual estimate
	    +--------------------------------------------------*/
	    /* if (gam == 0.0) gam = epsmac; */

	    /*---- get next plane rotation ---*/
	    if (gam == 0.0)
	    {
		c[i] = one;
		s[i] = zero;
	    }
            else
	    {
		c[i] = hh[i][i] / gam;
		s[i] = hh[i][i1] / gam;
	    }

	    rs[i1] = -s[i] * rs[i];
	    rs[i] = c[i] * rs[i];

	    /*----------------------------------------------------
	    |   determine residual norm and test for convergence
	    +---------------------------------------------------*/
	    hh[i][i] = c[i] * hh[i][i] + s[i] * hh[i][i1];
	    beta = fabs(rs[i1]);
	    if (fits != NULL)
		fprintf(fits, "%8d   %10.2e\n", its, beta);
	    if (beta <= eps1 || its >= maxits)
		break;
	}

	if (i == im) i--;

	/*---- now compute solution. 1st, solve upper triangular system ----*/
	rs[i] = rs[i] / hh[i][i];

	for (ii = 1; ii <= i; ii++)
	{
	    k = i - ii;
	    k1 = k + 1;
	    tt = rs[k];
	    for (j = k1; j <= i; j++)
		tt = tt - hh[j][k] * rs[j];
	    rs[k] = tt / hh[k][k];
	}

	/*---- linear combination of v[i]'s to get sol. ----*/
	for (j = 0; j <= i; j++)
	{
	    tt = rs[j];
	    for (k = 0; k < n; k++)
		sol[k] += tt * z[j][k];
	}

	/* calculate the residual and output */
	smatvec(one, sol, zero, vv[0]);
	for (j = 0; j < n; j++)
	    vv[0][j] = rhs[j] - vv[0][j];	/* vv[0]= initial residual */

	/*---- print info if fits != null ----*/
	beta = snrm2_(&n, vv[0], &i_1);

	/*---- restart outer loop if needed ----*/
	/*if (beta >= eps1 / tol)*/
	if ( !(beta < eps1 / tol) )
	{
	    its = maxits + 10;
	    break;
	}
	if (beta <= eps1)
	    break;
    } while(its < maxits);

    retval = (its >= maxits);
    for (i = 0; i <= im; i++)
	SUPERLU_FREE(vv[i]);
    SUPERLU_FREE(vv);
    for (i = 0; i < im; i++)
    {
	SUPERLU_FREE(hh[i]);
	SUPERLU_FREE(z[i]);
    }
    SUPERLU_FREE(hh);
    SUPERLU_FREE(z);
    SUPERLU_FREE(c);
    SUPERLU_FREE(s);
    SUPERLU_FREE(rs);

    *itmax = its;

    return retval;
} /*----end of fgmr ----*/
Example #7
0
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
    int      incx = 1, incy = 1;
#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, 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 += 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, 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;
	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);
}
Example #8
0
int main ( int argc, char *argv[] )

/**********************************************************************/
/*
  Purpose:

    SUPER_LU_S3 solves a sparse system read from a file using SGSSVX.

  Discussion:

    The sparse matrix is stored in a file using the Harwell-Boeing
    sparse matrix format.  The file should be assigned to the standard
    input of this program.  For instance, if the matrix is stored
    in the file "g10_rua.txt", the execution command might be:

      super_lu_s3 < g10_rua.txt

  Modified:

    25 April 2004

  Reference:

    James Demmel, John Gilbert, Xiaoye Li,
    SuperLU Users's Guide,
    Sections 1 and 2.

  Local parameters:

    SuperMatrix L, the computed L factor.

    int *perm_c, the column permutation vector.

    int *perm_r, the row permutations from partial pivoting.

    SuperMatrix U, the computed U factor.
*/
{
  SuperMatrix A;
  NCformat *Astore;
  float *a;
  int *asub;
  SuperMatrix B;
  float *berr;
  float *C;
  char equed[1];
  yes_no_t equil;
  int *etree;
  float *ferr;
  int i;
  int info;
  SuperMatrix L;
  int ldx;
  SCformat *Lstore;
  int lwork;
  int m;
  mem_usage_t mem_usage;
  int n;
  int nnz;
  int nrhs;
  superlu_options_t options;
  int *perm_c;
  int *perm_r;
  float *R;
  float rcond;
  float *rhsb;
  float *rhsx;
  float rpg;
  float *sol;
  SuperLUStat_t stat;
  trans_t trans;
  SuperMatrix U;
  float u;
  NCformat *Ustore;
  void *work;
  SuperMatrix X;
  int *xa;
  float *xact;
/*
  Say hello.
*/
  printf ( "\n" );
  printf ( "SUPER_LU_S3:\n" );
  printf ( "  Read a sparse matrix A from standard input,\n");
  printf ( "  stored in Harwell-Boeing Sparse Matrix format.\n" );
  printf ( "\n" );
  printf ( "  Solve a linear system A * X = B using SGSSVX.\n" );
/* 
  Defaults 
*/
  lwork = 0;
  nrhs = 1;
  equil = YES;	
  u = 1.0;
  trans = NOTRANS;
/* 
  Set the default input options:
  options.Fact = DOFACT;
  options.Equil = YES;
  options.ColPerm = COLAMD;
  options.DiagPivotThresh = 1.0;
  options.Trans = NOTRANS;
  options.IterRefine = NOREFINE;
  options.SymmetricMode = NO;
  options.PivotGrowth = NO;
  options.ConditionNumber = NO;
  options.PrintStat = YES;
*/
  set_default_options ( &options );
/*
  Can use command line input to modify the defaults. 
*/
  parse_command_line ( argc, argv, &lwork, &u, &equil, &trans );

  options.Equil = equil;
  options.DiagPivotThresh = u;
  options.Trans = trans;

  printf ( "\n" );
  printf ( "  Length of work array LWORK = %d\n", lwork );
  printf ( "  Equilibration option EQUIL = %d\n", equil );
  printf ( "  Diagonal pivot threshhold value U = %f\n", u );
  printf ( "  Tranpose option TRANS = %d\n", trans );
/*
  Add more functionalities that the defaults. 

  Compute reciprocal pivot growth 
*/
  options.PivotGrowth = YES;    
/* 
  Compute reciprocal condition number 
*/
  options.ConditionNumber = YES;
/* 
  Perform single-precision refinement 
*/
  options.IterRefine = SINGLE;  
    
  if ( 0 < lwork ) 
  {
    work = SUPERLU_MALLOC(lwork);
    if ( !work ) 
    {
      ABORT ( "SUPERLU_MALLOC cannot allocate work[]" );
    }
  }
/* 
  Read matrix A from a file in Harwell-Boeing format.
*/
  sreadhb ( &m, &n, &nnz, &a, &asub, &xa );
/*
  Create storage for a compressed column matrix.
*/
  sCreate_CompCol_Matrix ( &A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE );
  Astore = A.Store;

  printf ( "\n" );
  printf ( "  Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz );
    
  rhsb = floatMalloc ( m * nrhs );
  if ( !rhsb ) 
  {
    ABORT ( "Malloc fails for rhsb[]." );
  }

  rhsx = floatMalloc ( m * nrhs );
  if ( !rhsx ) 
  {
    ABORT ( "Malloc fails for rhsx[]." );
  }

  sCreate_Dense_Matrix ( &B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE );

  sCreate_Dense_Matrix ( &X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE );

  xact = floatMalloc ( n * nrhs );
  if ( !xact ) 
  {
    ABORT ( "SUPERLU_MALLOC cannot allocate xact[]" );
  }
  ldx = n;
  sGenXtrue ( n, nrhs, xact, ldx );
  sFillRHS ( trans, nrhs, xact, ldx, &A, &B );
    
  etree = intMalloc ( n );
  if ( !etree )
  {
    ABORT ( "Malloc fails for etree[]." );
  }

  perm_c = intMalloc ( n );
  if ( !perm_c ) 
  {
    ABORT ( "Malloc fails for perm_c[]." );
  }

  perm_r = intMalloc ( m );
  if ( !perm_r )
  {
    ABORT ( "Malloc fails for perm_r[]." );
  }

  R = (float *) SUPERLU_MALLOC ( A.nrow * sizeof(float) );
  if ( !R ) 
  {
    ABORT ( "SUPERLU_MALLOC fails for R[]." );
  }

  C = (float *) SUPERLU_MALLOC ( A.ncol * sizeof(float) );
  if ( !C )
  {
    ABORT ( "SUPERLU_MALLOC fails for C[]." );
  }

  ferr = (float *) SUPERLU_MALLOC ( nrhs * sizeof(float) );
  if ( !ferr )
  {
    ABORT ( "SUPERLU_MALLOC fails for ferr[]." );
  }

  berr = (float *) SUPERLU_MALLOC ( nrhs * sizeof(float) );
  if ( !berr ) 
  {
    ABORT ( "SUPERLU_MALLOC fails for berr[]." );
  }
/* 
  Initialize the statistics variables. 
*/
  StatInit(&stat);
/* 
  Solve the system and compute the condition number and error bounds using SGSSVX.      
*/
  sgssvx ( &options, &A, perm_c, perm_r, etree, equed, R, C,
    &L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
    &mem_usage, &stat, &info );

  printf ( "\n" );
  printf ( "  SGSSVX returns INFO = %d\n", info );

  if ( info == 0 || info == n+1 )
  {
    sol = (float*) ((DNformat*) X.Store)->nzval; 

    if ( options.PivotGrowth == YES )
    {
      printf ( "\n" );
      printf ( "  Reciprocal pivot growth = %e\n", rpg);
    }

    if ( options.ConditionNumber == YES )
    {
      printf ( "\n" );
      printf ( "  Reciprocal condition number = %e\n", rcond);
    }

    if ( options.IterRefine != NOREFINE )
    {
      printf ( "\n" );
      printf ( "  Iterative Refinement:\n");
      printf ( "%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
      for ( i = 0; i < nrhs; i++ )
      {
        printf ( "%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
      }
    }

    Lstore = (SCformat *) L.Store;
    Ustore = (NCformat *) U.Store;

    printf ( "\n" );
    printf ( "  Number of nonzeros in factor L = %d\n", Lstore->nnz );
    printf ( "  Number of nonzeros in factor U = %d\n", Ustore->nnz );
    printf ( "  Number of nonzeros in L+U = %d\n", 
      Lstore->nnz + Ustore->nnz - n );

    printf ( "\n" );
    printf ( "  L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n", 
      mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
      mem_usage.expansions );
	     
    fflush ( stdout );

  } 
  else if ( info > 0 && lwork == -1 )
  {
    printf ( "\n" );
    printf ( "  Estimated memory: %d bytes\n", info - n );
  }

  if ( options.PrintStat ) 
  {
    StatPrint ( &stat );
  }

  StatFree ( &stat );

  SUPERLU_FREE ( rhsb );
  SUPERLU_FREE ( rhsx );
  SUPERLU_FREE ( xact );
  SUPERLU_FREE ( etree );
  SUPERLU_FREE ( perm_r );
  SUPERLU_FREE ( perm_c );
  SUPERLU_FREE ( R );
  SUPERLU_FREE ( C );
  SUPERLU_FREE ( ferr );
  SUPERLU_FREE ( berr );
  Destroy_CompCol_Matrix ( &A );
  Destroy_SuperMatrix_Store ( &B );
  Destroy_SuperMatrix_Store ( &X );

  if ( 0 <= lwork )
  {
    Destroy_SuperNode_Matrix ( &L );
    Destroy_CompCol_Matrix ( &U );
  }
/*
  Say goodbye.
*/
  printf ( "\n" );
  printf ( "SUPER_LU_S3:\n" );
  printf ( "  Normal end of execution.\n");

  return 0;
}
Example #9
0
int main(int argc, char *argv[])
{
    SuperMatrix A;
    NCformat *Astore;
    float   *a;
    int      *asub, *xa;
    int      *perm_c; /* column permutation vector */
    int      *perm_r; /* row permutations from partial pivoting */
    SuperMatrix L;      /* factor L */
    SCformat *Lstore;
    SuperMatrix U;      /* factor U */
    NCformat *Ustore;
    SuperMatrix B;
    int      nrhs, ldx, info, m, n, nnz;
    float   *xact, *rhs;
    mem_usage_t   mem_usage;
    superlu_options_t options;
    SuperLUStat_t stat;
    FILE      *fp = stdin;
    
#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Enter main()");
#endif

    /* Set the default input options:
	options.Fact = DOFACT;
        options.Equil = YES;
    	options.ColPerm = COLAMD;
	options.DiagPivotThresh = 1.0;
    	options.Trans = NOTRANS;
    	options.IterRefine = NOREFINE;
    	options.SymmetricMode = NO;
    	options.PivotGrowth = NO;
    	options.ConditionNumber = NO;
    	options.PrintStat = YES;
     */
    set_default_options(&options);

    /* Read the matrix in Harwell-Boeing format. */
    sreadhb(fp, &m, &n, &nnz, &a, &asub, &xa);

    sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
    Astore = A.Store;
    printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
    
    nrhs   = 1;
    if ( !(rhs = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhs[].");
    sCreate_Dense_Matrix(&B, m, nrhs, rhs, m, SLU_DN, SLU_S, SLU_GE);
    xact = floatMalloc(n * nrhs);
    ldx = n;
    sGenXtrue(n, nrhs, xact, ldx);
    sFillRHS(options.Trans, nrhs, xact, ldx, &A, &B);

    if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
    if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");

    /* Initialize the statistics variables. */
    StatInit(&stat);
    
    sgssv(&options, &A, perm_c, perm_r, &L, &U, &B, &stat, &info);
    
    if ( info == 0 ) {

	/* This is how you could access the solution matrix. */
        float *sol = (float*) ((DNformat*) B.Store)->nzval; 

	 /* Compute the infinity norm of the error. */
	sinf_norm_error(nrhs, &B, xact);

	Lstore = (SCformat *) L.Store;
	Ustore = (NCformat *) U.Store;
    	printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
    	printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
    	printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
    	printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);
	
	sQuerySpace(&L, &U, &mem_usage);
	printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
	       mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
	
    } else {
	printf("sgssv() error returns INFO= %d\n", info);
	if ( info <= n ) { /* factorization completes */
	    sQuerySpace(&L, &U, &mem_usage);
	    printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
		   mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
	}
    }

    if ( options.PrintStat ) StatPrint(&stat);
    StatFree(&stat);

    SUPERLU_FREE (rhs);
    SUPERLU_FREE (xact);
    SUPERLU_FREE (perm_r);
    SUPERLU_FREE (perm_c);
    Destroy_CompCol_Matrix(&A);
    Destroy_SuperMatrix_Store(&B);
    Destroy_SuperNode_Matrix(&L);
    Destroy_CompCol_Matrix(&U);

#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Exit main()");
#endif
}
Example #10
0
int sdominate(int n, NCformat *Astore)
/* make the matrix diagonally dominant */
{
    float *nzval = (float *)Astore->nzval;
    int *rowind = Astore->rowind;
    int *colptr = Astore->colptr;
    int nnz = colptr[n];
    int fill = 0;
    float *nzval_new;
    int *rowind_new;
    int i, j, diag;
    double s;

    for (i = 0; i < n; i++)
    {
	diag = -1;
	for (j = colptr[i]; j < colptr[i + 1]; j++)
	    if (rowind[j] == i) diag = j;
	if (diag < 0) fill++;
    }
    if (fill)
    {
	nzval_new = floatMalloc(nnz + fill);
	rowind_new = intMalloc(nnz+ fill);
	fill = 0;
	for (i = 0; i < n; i++)
	{
	    s = 1e-6;
	    diag = -1;
	    for (j = colptr[i] - fill; j < colptr[i + 1]; j++)
	    {
		if ((rowind_new[j + fill] = rowind[j]) == i) diag = j;
		s += fabs(nzval_new[j + fill] = nzval[j]);
	    }
	    if (diag >= 0) {
		nzval_new[diag+fill] = s * 3.0;
	    } else {
		rowind_new[colptr[i + 1] + fill] = i;
		nzval_new[colptr[i + 1] + fill] = s * 3.0;
		fill++;
	    }
	    colptr[i + 1] += fill;
	}
	Astore->nzval = nzval_new;
	Astore->rowind = rowind_new;
	SUPERLU_FREE(nzval);
	SUPERLU_FREE(rowind);
    }
    else
    {
	for (i = 0; i < n; i++)
	{
	    s = 1e-6;
	    diag = -1;
	    for (j = colptr[i]; j < colptr[i + 1]; j++)
	    {
		if (rowind[j] == i) diag = j;
		s += fabs(nzval[j]);
	    }
	    nzval[diag] = s * 3.0;
	}
    }
    Astore->nnz += fill;
    return fill;
}
Example #11
0
main(int argc, char *argv[])
{
/*
 * Purpose
 * =======
 *
 * The driver program SLINSOLX1.
 *
 * This example illustrates how to use SGSSVX to solve systems with the same
 * A but different right-hand side.
 * In this case, we factorize A only once in the first call to DGSSVX,
 * and reuse the following data structures in the subsequent call to SGSSVX:
 *     perm_c, perm_r, R, C, L, U.
 * 
 */
    char           equed[1];
    yes_no_t       equil;
    trans_t        trans;
    SuperMatrix    A, L, U;
    SuperMatrix    B, X;
    NCformat       *Astore;
    NCformat       *Ustore;
    SCformat       *Lstore;
    float         *a;
    int            *asub, *xa;
    int            *perm_c; /* column permutation vector */
    int            *perm_r; /* row permutations from partial pivoting */
    int            *etree;
    void           *work;
    int            info, lwork, nrhs, ldx;
    int            i, m, n, nnz;
    float         *rhsb, *rhsx, *xact;
    float         *R, *C;
    float         *ferr, *berr;
    float         u, rpg, rcond;
    mem_usage_t    mem_usage;
    superlu_options_t options;
    SuperLUStat_t stat;
    extern void    parse_command_line();

#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Enter main()");
#endif

    /* Defaults */
    lwork = 0;
    nrhs  = 1;
    equil = YES;	
    u     = 1.0;
    trans = NOTRANS;

    /* Set the default values for options argument:
	options.Fact = DOFACT;
        options.Equil = YES;
    	options.ColPerm = COLAMD;
	options.DiagPivotThresh = 1.0;
    	options.Trans = NOTRANS;
    	options.IterRefine = NOREFINE;
    	options.SymmetricMode = NO;
    	options.PivotGrowth = NO;
    	options.ConditionNumber = NO;
    	options.PrintStat = YES;
    */
    set_default_options(&options);

    /* Can use command line input to modify the defaults. */
    parse_command_line(argc, argv, &lwork, &u, &equil, &trans);
    options.Equil = equil;
    options.DiagPivotThresh = u;
    options.Trans = trans;
    
    if ( lwork > 0 ) {
	work = SUPERLU_MALLOC(lwork);
	if ( !work ) {
	    ABORT("SLINSOLX: cannot allocate work[]");
	}
    }

    /* Read matrix A from a file in Harwell-Boeing format.*/
    sreadhb(&m, &n, &nnz, &a, &asub, &xa);
    
    sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
    Astore = A.Store;
    printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
    
    if ( !(rhsb = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
    if ( !(rhsx = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
    sCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE);
    sCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE);
    xact = floatMalloc(n * nrhs);
    ldx = n;
    sGenXtrue(n, nrhs, xact, ldx);
    sFillRHS(trans, nrhs, xact, ldx, &A, &B);
    
    if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
    if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
    if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
    if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) ) 
        ABORT("SUPERLU_MALLOC fails for R[].");
    if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
        ABORT("SUPERLU_MALLOC fails for C[].");
    if ( !(ferr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
        ABORT("SUPERLU_MALLOC fails for ferr[].");
    if ( !(berr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) ) 
        ABORT("SUPERLU_MALLOC fails for berr[].");

    /* Initialize the statistics variables. */
    StatInit(&stat);
    
    /* ONLY PERFORM THE LU DECOMPOSITION */
    B.ncol = 0;  /* Indicate not to solve the system */
    sgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
           &L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
           &mem_usage, &stat, &info);

    printf("LU factorization: sgssvx() returns info %d\n", info);

    if ( info == 0 || info == n+1 ) {

	if ( options.PivotGrowth ) printf("Recip. pivot growth = %e\n", rpg);
	if ( options.ConditionNumber )
	    printf("Recip. condition number = %e\n", rcond);
        Lstore = (SCformat *) L.Store;
        Ustore = (NCformat *) U.Store;
	printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
    	printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
    	printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
    	printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);

	printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
	       mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
	fflush(stdout);

    } else if ( info > 0 && lwork == -1 ) {
        printf("** Estimated memory: %d bytes\n", info - n);
    }

    if ( options.PrintStat ) StatPrint(&stat);
    StatFree(&stat);

    /* ------------------------------------------------------------
       NOW WE SOLVE THE LINEAR SYSTEM USING THE FACTORED FORM OF A.
       ------------------------------------------------------------*/
    options.Fact = FACTORED; /* Indicate the factored form of A is supplied. */
    B.ncol = nrhs;  /* Set the number of right-hand side */

    /* Initialize the statistics variables. */
    StatInit(&stat);

    sgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
           &L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
           &mem_usage, &stat, &info);

    printf("Triangular solve: sgssvx() returns info %d\n", info);

    if ( info == 0 || info == n+1 ) {

        /* This is how you could access the solution matrix. */
        float *sol = (float*) ((DNformat*) X.Store)->nzval; 

	if ( options.IterRefine ) {
            printf("Iterative Refinement:\n");
	    printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
	    for (i = 0; i < nrhs; ++i)
	      printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
	}
	fflush(stdout);
    } else if ( info > 0 && lwork == -1 ) {
        printf("** Estimated memory: %d bytes\n", info - n);
    }

    if ( options.PrintStat ) StatPrint(&stat);
    StatFree(&stat);

    SUPERLU_FREE (rhsb);
    SUPERLU_FREE (rhsx);
    SUPERLU_FREE (xact);
    SUPERLU_FREE (etree);
    SUPERLU_FREE (perm_r);
    SUPERLU_FREE (perm_c);
    SUPERLU_FREE (R);
    SUPERLU_FREE (C);
    SUPERLU_FREE (ferr);
    SUPERLU_FREE (berr);
    Destroy_CompCol_Matrix(&A);
    Destroy_SuperMatrix_Store(&B);
    Destroy_SuperMatrix_Store(&X);
    if ( lwork >= 0 ) {
        Destroy_SuperNode_Matrix(&L);
        Destroy_CompCol_Matrix(&U);
    }

#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Exit main()");
#endif
}
Example #12
0
void
sgsisx(superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r,
       int *etree, char *equed, float *R, float *C,
       SuperMatrix *L, SuperMatrix *U, void *work, int lwork,
       SuperMatrix *B, SuperMatrix *X,
       float *recip_pivot_growth, float *rcond,
       mem_usage_t *mem_usage, SuperLUStat_t *stat, int *info)
{

    DNformat  *Bstore, *Xstore;
    float    *Bmat, *Xmat;
    int       ldb, ldx, nrhs;
    SuperMatrix *AA;/* A in SLU_NC format used by the factorization routine.*/
    SuperMatrix AC; /* Matrix postmultiplied by Pc */
    int       colequ, equil, nofact, notran, rowequ, permc_spec, mc64;
    trans_t   trant;
    char      norm[1];
    int       i, j, info1;
    float    amax, anorm, bignum, smlnum, colcnd, rowcnd, rcmax, rcmin;
    int       relax, panel_size;
    float    diag_pivot_thresh;
    double    t0;      /* temporary time */
    double    *utime;

    int *perm = NULL;

    /* External functions */
    extern float slangs(char *, SuperMatrix *);

    Bstore = B->Store;
    Xstore = X->Store;
    Bmat   = Bstore->nzval;
    Xmat   = Xstore->nzval;
    ldb    = Bstore->lda;
    ldx    = Xstore->lda;
    nrhs   = B->ncol;

    *info = 0;
    nofact = (options->Fact != FACTORED);
    equil = (options->Equil == YES);
    notran = (options->Trans == NOTRANS);
    mc64 = (options->RowPerm == LargeDiag);
    if ( nofact ) {
        *(unsigned char *)equed = 'N';
        rowequ = FALSE;
        colequ = FALSE;
    } else {
        rowequ = lsame_(equed, "R") || lsame_(equed, "B");
        colequ = lsame_(equed, "C") || lsame_(equed, "B");
        smlnum = slamch_("Safe minimum");
        bignum = 1. / smlnum;
    }

    /* Test the input parameters */
    if (!nofact && options->Fact != DOFACT && options->Fact != SamePattern &&
        options->Fact != SamePattern_SameRowPerm &&
        !notran && options->Trans != TRANS && options->Trans != CONJ &&
        !equil && options->Equil != NO)
        *info = -1;
    else if ( A->nrow != A->ncol || A->nrow < 0 ||
              (A->Stype != SLU_NC && A->Stype != SLU_NR) ||
              A->Dtype != SLU_S || A->Mtype != SLU_GE )
        *info = -2;
    else if (options->Fact == FACTORED &&
             !(rowequ || colequ || lsame_(equed, "N")))
        *info = -6;
    else {
        if (rowequ) {
            rcmin = bignum;
            rcmax = 0.;
            for (j = 0; j < A->nrow; ++j) {
                rcmin = SUPERLU_MIN(rcmin, R[j]);
                rcmax = SUPERLU_MAX(rcmax, R[j]);
            }
            if (rcmin <= 0.) *info = -7;
            else if ( A->nrow > 0)
                rowcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
            else rowcnd = 1.;
        }
        if (colequ && *info == 0) {
            rcmin = bignum;
            rcmax = 0.;
            for (j = 0; j < A->nrow; ++j) {
                rcmin = SUPERLU_MIN(rcmin, C[j]);
                rcmax = SUPERLU_MAX(rcmax, C[j]);
            }
            if (rcmin <= 0.) *info = -8;
            else if (A->nrow > 0)
                colcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
            else colcnd = 1.;
        }
        if (*info == 0) {
            if ( lwork < -1 ) *info = -12;
            else if ( B->ncol < 0 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
                      B->Stype != SLU_DN || B->Dtype != SLU_S ||
                      B->Mtype != SLU_GE )
                *info = -13;
            else if ( X->ncol < 0 || Xstore->lda < SUPERLU_MAX(0, A->nrow) ||
                      (B->ncol != 0 && B->ncol != X->ncol) ||
                      X->Stype != SLU_DN ||
                      X->Dtype != SLU_S || X->Mtype != SLU_GE )
                *info = -14;
        }
    }
    if (*info != 0) {
        i = -(*info);
        xerbla_("sgsisx", &i);
        return;
    }

    /* Initialization for factor parameters */
    panel_size = sp_ienv(1);
    relax      = sp_ienv(2);
    diag_pivot_thresh = options->DiagPivotThresh;

    utime = stat->utime;

    /* Convert A to SLU_NC format when necessary. */
    if ( A->Stype == SLU_NR ) {
        NRformat *Astore = A->Store;
        AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
        sCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz,
                               Astore->nzval, Astore->colind, Astore->rowptr,
                               SLU_NC, A->Dtype, A->Mtype);
        if ( notran ) { /* Reverse the transpose argument. */
            trant = TRANS;
            notran = 0;
        } else {
            trant = NOTRANS;
            notran = 1;
        }
    } else { /* A->Stype == SLU_NC */
        trant = options->Trans;
        AA = A;
    }

    if ( nofact ) {
        register int i, j;
        NCformat *Astore = AA->Store;
        int nnz = Astore->nnz;
        int *colptr = Astore->colptr;
        int *rowind = Astore->rowind;
        float *nzval = (float *)Astore->nzval;
        int n = AA->nrow;

        if ( mc64 ) {
            *equed = 'B';
            /*rowequ = colequ = 1;*/
            t0 = SuperLU_timer_();
            if ((perm = intMalloc(n)) == NULL)
                ABORT("SUPERLU_MALLOC fails for perm[]");

            info1 = sldperm(5, n, nnz, colptr, rowind, nzval, perm, R, C);

            if (info1 > 0) { /* MC64 fails, call sgsequ() later */
                mc64 = 0;
                SUPERLU_FREE(perm);
                perm = NULL;
            } else {
                rowequ = colequ = 1;
                for (i = 0; i < n; i++) {
                    R[i] = exp(R[i]);
                    C[i] = exp(C[i]);
                }
                /* permute and scale the matrix */
                for (j = 0; j < n; j++) {
                    for (i = colptr[j]; i < colptr[j + 1]; i++) {
                        nzval[i] *= R[rowind[i]] * C[j];
                        rowind[i] = perm[rowind[i]];
                    }
                }
            }
            utime[EQUIL] = SuperLU_timer_() - t0;
        }
        if ( !mc64 & equil ) {
            t0 = SuperLU_timer_();
            /* Compute row and column scalings to equilibrate the matrix A. */
            sgsequ(AA, R, C, &rowcnd, &colcnd, &amax, &info1);

            if ( info1 == 0 ) {
                /* Equilibrate matrix A. */
                slaqgs(AA, R, C, rowcnd, colcnd, amax, equed);
                rowequ = lsame_(equed, "R") || lsame_(equed, "B");
                colequ = lsame_(equed, "C") || lsame_(equed, "B");
            }
            utime[EQUIL] = SuperLU_timer_() - t0;
        }
    }


    if ( nofact ) {

        t0 = SuperLU_timer_();
        /*
         * Gnet column permutation vector perm_c[], according to permc_spec:
         *   permc_spec = NATURAL:  natural ordering
         *   permc_spec = MMD_AT_PLUS_A: minimum degree on structure of A'+A
         *   permc_spec = MMD_ATA:  minimum degree on structure of A'*A
         *   permc_spec = COLAMD:   approximate minimum degree column ordering
         *   permc_spec = MY_PERMC: the ordering already supplied in perm_c[]
         */
        permc_spec = options->ColPerm;
        if ( permc_spec != MY_PERMC && options->Fact == DOFACT )
            get_perm_c(permc_spec, AA, perm_c);
        utime[COLPERM] = SuperLU_timer_() - t0;

        t0 = SuperLU_timer_();
        sp_preorder(options, AA, perm_c, etree, &AC);
        utime[ETREE] = SuperLU_timer_() - t0;

        /* Compute the LU factorization of A*Pc. */
        t0 = SuperLU_timer_();
        sgsitrf(options, &AC, relax, panel_size, etree, work, lwork,
                perm_c, perm_r, L, U, stat, info);
        utime[FACT] = SuperLU_timer_() - t0;

        if ( lwork == -1 ) {
            mem_usage->total_needed = *info - A->ncol;
            return;
        }
    }

    if ( options->PivotGrowth ) {
        if ( *info > 0 ) return;

        /* Compute the reciprocal pivot growth factor *recip_pivot_growth. */
        *recip_pivot_growth = sPivotGrowth(A->ncol, AA, perm_c, L, U);
    }

    if ( options->ConditionNumber ) {
        /* Estimate the reciprocal of the condition number of A. */
        t0 = SuperLU_timer_();
        if ( notran ) {
            *(unsigned char *)norm = '1';
        } else {
            *(unsigned char *)norm = 'I';
        }
        anorm = slangs(norm, AA);
        sgscon(norm, L, U, anorm, rcond, stat, &info1);
        utime[RCOND] = SuperLU_timer_() - t0;
    }

    if ( nrhs > 0 ) { /* Solve the system */
        float *tmp, *rhs_work;
        int n = A->nrow;
        if ( mc64 ) {
            if ((tmp = floatMalloc(n)) == NULL)
                ABORT("SUPERLU_MALLOC fails for tmp[]");
        }

        /* Scale and permute the right-hand side if equilibration
           and permutation from MC64 were performed. */
        if ( notran ) {
            if ( rowequ ) {
                for (j = 0; j < nrhs; ++j)
                    for (i = 0; i < n; ++i)
                        Bmat[i + j*ldb] *= R[i];
            }
            if ( mc64 ) {
                for (j = 0; j < nrhs; ++j) {
                   rhs_work = &Bmat[j*ldb];
                   for (i = 0; i < n; i++) tmp[perm[i]] = rhs_work[i];
                   for (i = 0; i < n; i++) rhs_work[i] = tmp[i];
                }
            }
        } else if ( colequ ) {
            for (j = 0; j < nrhs; ++j)
                for (i = 0; i < n; ++i) {
                    Bmat[i + j*ldb] *= C[i];
                }
        }

        /* Compute the solution matrix X. */
        for (j = 0; j < nrhs; j++)  /* Save a copy of the right hand sides */
            for (i = 0; i < B->nrow; i++)
                Xmat[i + j*ldx] = Bmat[i + j*ldb];

        t0 = SuperLU_timer_();
        sgstrs (trant, L, U, perm_c, perm_r, X, stat, &info1);
        utime[SOLVE] = SuperLU_timer_() - t0;

        /* Transform the solution matrix X to a solution of the original
           system. */
        if ( notran ) {
            if ( colequ ) {
                for (j = 0; j < nrhs; ++j)
                    for (i = 0; i < n; ++i) {
                        Xmat[i + j*ldx] *= C[i];
                    }
            }
        } else { /* transposed system */
            if ( rowequ ) {
                if ( mc64 ) {
                    for (j = 0; j < nrhs; j++) {
                        for (i = 0; i < n; i++)
                            tmp[i] = Xmat[i + j * ldx]; /*dcopy*/
                        for (i = 0; i < n; i++)
                            Xmat[i + j * ldx] = R[i] * tmp[perm[i]];
                    }
                } else {
                    for (j = 0; j < nrhs; ++j)
                        for (i = 0; i < A->nrow; ++i) {
                            Xmat[i + j*ldx] *= R[i];
                        }
                }
            }
        }

        if ( mc64 ) SUPERLU_FREE(tmp);

    } /* end if nrhs > 0 */

    if ( options->ConditionNumber ) {
        /* Set INFO = A->ncol+1 if the matrix is singular to working precision. */
        if ( *rcond < slamch_("E") && *info == 0) *info = A->ncol + 1;
    }

    if (perm) SUPERLU_FREE(perm);

    if ( nofact ) {
        ilu_sQuerySpace(L, U, mem_usage);
        Destroy_CompCol_Permuted(&AC);
    }
    if ( A->Stype == SLU_NR ) {
        Destroy_SuperMatrix_Store(AA);
        SUPERLU_FREE(AA);
    }

}
Example #13
0
main(int argc, char *argv[])
{
/*
 * Purpose
 * =======
 *
 * The driver program SLINSOLX2.
 *
 * This example illustrates how to use SGSSVX to solve systems repeatedly
 * with the same sparsity pattern of matrix A.
 * In this case, the column permutation vector perm_c is computed once.
 * The following data structures will be reused in the subsequent call to
 * SGSSVX: perm_c, etree
 *
 */
    char           equed[1];
    yes_no_t       equil;
    trans_t        trans;
    SuperMatrix    A, A1, L, U;
    SuperMatrix    B, B1, X;
    NCformat       *Astore;
    NCformat       *Ustore;
    SCformat       *Lstore;
    float         *a, *a1;
    int            *asub, *xa, *asub1, *xa1;
    int            *perm_r; /* row permutations from partial pivoting */
    int            *perm_c; /* column permutation vector */
    int            *etree;
    void           *work;
    int            info, lwork, nrhs, ldx;
    int            i, j, m, n, nnz;
    float         *rhsb, *rhsb1, *rhsx, *xact;
    float         *R, *C;
    float         *ferr, *berr;
    float         u, rpg, rcond;
    mem_usage_t    mem_usage;
    superlu_options_t options;
    SuperLUStat_t stat;
    extern void    parse_command_line();

#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Enter main()");
#endif

    /* Defaults */
    lwork = 0;
    nrhs  = 1;
    equil = YES;
    u     = 1.0;
    trans = NOTRANS;

    /* Set the default input options:
        options.Fact = DOFACT;
        options.Equil = YES;
        options.ColPerm = COLAMD;
        options.DiagPivotThresh = 1.0;
        options.Trans = NOTRANS;
        options.IterRefine = NOREFINE;
        options.SymmetricMode = NO;
        options.PivotGrowth = NO;
        options.ConditionNumber = NO;
        options.PrintStat = YES;
     */
    set_default_options(&options);

    /* Can use command line input to modify the defaults. */
    parse_command_line(argc, argv, &lwork, &u, &equil, &trans);
    options.Equil = equil;
    options.DiagPivotThresh = u;
    options.Trans = trans;

    if ( lwork > 0 ) {
        work = SUPERLU_MALLOC(lwork);
        if ( !work ) {
            ABORT("DLINSOLX: cannot allocate work[]");
        }
    }

    /* Read matrix A from a file in Harwell-Boeing format.*/
    sreadhb(&m, &n, &nnz, &a, &asub, &xa);
    if ( !(a1 = floatMalloc(nnz)) ) ABORT("Malloc fails for a1[].");
    if ( !(asub1 = intMalloc(nnz)) ) ABORT("Malloc fails for asub1[].");
    if ( !(xa1 = intMalloc(n+1)) ) ABORT("Malloc fails for xa1[].");
    for (i = 0; i < nnz; ++i) {
        a1[i] = a[i];
        asub1[i] = asub[i];
    }
    for (i = 0; i < n+1; ++i) xa1[i] = xa[i];

    sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
    Astore = A.Store;
    printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);

    if ( !(rhsb = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
    if ( !(rhsb1 = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb1[].");
    if ( !(rhsx = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
    sCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE);
    sCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE);
    xact = floatMalloc(n * nrhs);
    ldx = n;
    sGenXtrue(n, nrhs, xact, ldx);
    sFillRHS(trans, nrhs, xact, ldx, &A, &B);
    for (j = 0; j < nrhs; ++j)
        for (i = 0; i < m; ++i) rhsb1[i+j*m] = rhsb[i+j*m];

    if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
    if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
    if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
    if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) )
        ABORT("SUPERLU_MALLOC fails for R[].");
    if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
        ABORT("SUPERLU_MALLOC fails for C[].");
    if ( !(ferr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
        ABORT("SUPERLU_MALLOC fails for ferr[].");
    if ( !(berr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
        ABORT("SUPERLU_MALLOC fails for berr[].");

    /* Initialize the statistics variables. */
    StatInit(&stat);

    /* ------------------------------------------------------------
       WE SOLVE THE LINEAR SYSTEM FOR THE FIRST TIME: AX = B
       ------------------------------------------------------------*/
    sgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
           &L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
           &mem_usage, &stat, &info);

    printf("First system: sgssvx() returns info %d\n", info);

    if ( info == 0 || info == n+1 ) {

        /* This is how you could access the solution matrix. */
        float *sol = (float*) ((DNformat*) X.Store)->nzval;

        if ( options.PivotGrowth ) printf("Recip. pivot growth = %e\n", rpg);
        if ( options.ConditionNumber )
            printf("Recip. condition number = %e\n", rcond);
        Lstore = (SCformat *) L.Store;
        Ustore = (NCformat *) U.Store;
        printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
        printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
        printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
        printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);

        printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
               mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
        if ( options.IterRefine ) {
            printf("Iterative Refinement:\n");
            printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
            for (i = 0; i < nrhs; ++i)
              printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
        }
        fflush(stdout);

    } else if ( info > 0 && lwork == -1 ) {
        printf("** Estimated memory: %d bytes\n", info - n);
    }

    if ( options.PrintStat ) StatPrint(&stat);
    StatFree(&stat);
    Destroy_CompCol_Matrix(&A);
    Destroy_Dense_Matrix(&B);
    if ( lwork >= 0 ) { /* Deallocate storage associated with L and U. */
        Destroy_SuperNode_Matrix(&L);
        Destroy_CompCol_Matrix(&U);
    }

    /* ------------------------------------------------------------
       NOW WE SOLVE ANOTHER LINEAR SYSTEM: A1*X = B1
       ONLY THE SPARSITY PATTERN OF A1 IS THE SAME AS THAT OF A.
       ------------------------------------------------------------*/
    options.Fact = SamePattern;
    StatInit(&stat); /* Initialize the statistics variables. */

    sCreate_CompCol_Matrix(&A1, m, n, nnz, a1, asub1, xa1,
                           SLU_NC, SLU_S, SLU_GE);
    sCreate_Dense_Matrix(&B1, m, nrhs, rhsb1, m, SLU_DN, SLU_S, SLU_GE);

    sgssvx(&options, &A1, perm_c, perm_r, etree, equed, R, C,
           &L, &U, work, lwork, &B1, &X, &rpg, &rcond, ferr, berr,
           &mem_usage, &stat, &info);

    printf("\nSecond system: sgssvx() returns info %d\n", info);

    if ( info == 0 || info == n+1 ) {

        /* This is how you could access the solution matrix. */
        float *sol = (float*) ((DNformat*) X.Store)->nzval;

        if ( options.PivotGrowth ) printf("Recip. pivot growth = %e\n", rpg);
        if ( options.ConditionNumber )
            printf("Recip. condition number = %e\n", rcond);
        Lstore = (SCformat *) L.Store;
        Ustore = (NCformat *) U.Store;
        printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
        printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
        printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
        printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
               mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
        if ( options.IterRefine ) {
            printf("Iterative Refinement:\n");
            printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
            for (i = 0; i < nrhs; ++i)
              printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
        }
        fflush(stdout);
    } else if ( info > 0 && lwork == -1 ) {
        printf("** Estimated memory: %d bytes\n", info - n);
    }

    if ( options.PrintStat ) StatPrint(&stat);
    StatFree(&stat);

    SUPERLU_FREE (xact);
    SUPERLU_FREE (etree);
    SUPERLU_FREE (perm_r);
    SUPERLU_FREE (perm_c);
    SUPERLU_FREE (R);
    SUPERLU_FREE (C);
    SUPERLU_FREE (ferr);
    SUPERLU_FREE (berr);
    Destroy_CompCol_Matrix(&A1);
    Destroy_Dense_Matrix(&B1);
    Destroy_Dense_Matrix(&X);
    if ( lwork == 0 ) {
        Destroy_SuperNode_Matrix(&L);
        Destroy_CompCol_Matrix(&U);
    } else if ( lwork > 0 ) {
        SUPERLU_FREE(work);
    }

#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Exit main()");
#endif
}
Example #14
0
void
sgsrfs(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix *U,
       int *perm_c, int *perm_r, char *equed, float *R, float *C,
       SuperMatrix *B, SuperMatrix *X, float *ferr, float *berr,
       SuperLUStat_t *stat, int *info)
{
/*
 *   Purpose   
 *   =======   
 *
 *   SGSRFS improves the computed solution to a system of linear   
 *   equations and provides error bounds and backward error estimates for 
 *   the solution.   
 *
 *   If equilibration was performed, the system becomes:
 *           (diag(R)*A_original*diag(C)) * X = diag(R)*B_original.
 *
 *   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)
 *   
 *   A       (input) SuperMatrix*
 *           The original matrix A in the system, or the scaled A if
 *           equilibration was done. The type of A can be:
 *           Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_GE.
 *    
 *   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 = 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 (A->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 (A->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.
 *
 *   equed   (input) Specifies the form of equilibration that was done.
 *           = 'N': No equilibration.
 *           = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
 *           = 'C': Column equilibration, i.e., A was postmultiplied by
 *                  diag(C).
 *           = 'B': Both row and column equilibration, i.e., A was replaced 
 *                  by diag(R)*A*diag(C).
 *
 *   R       (input) float*, dimension (A->nrow)
 *           The row scale factors for A.
 *           If equed = 'R' or 'B', A is premultiplied by diag(R).
 *           If equed = 'N' or 'C', R is not accessed.
 * 
 *   C       (input) float*, dimension (A->ncol)
 *           The column scale factors for A.
 *           If equed = 'C' or 'B', A is postmultiplied by diag(C).
 *           If equed = 'N' or 'R', C is not accessed.
 *
 *   B       (input) SuperMatrix*
 *           B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
 *           The right hand side matrix B.
 *           if equed = 'R' or 'B', B is premultiplied by diag(R).
 *
 *   X       (input/output) SuperMatrix*
 *           X has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
 *           On entry, the solution matrix X, as computed by sgstrs().
 *           On exit, the improved solution matrix X.
 *           if *equed = 'C' or 'B', X should be premultiplied by diag(C)
 *               in order to obtain the solution to the original system.
 *
 *   FERR    (output) float*, dimension (B->ncol)   
 *           The estimated forward error bound for each solution vector   
 *           X(j) (the j-th column of the solution matrix X).   
 *           If XTRUE is the true solution corresponding to X(j), FERR(j) 
 *           is an estimated upper bound for the magnitude of the largest 
 *           element in (X(j) - XTRUE) divided by the magnitude of the   
 *           largest element in X(j).  The estimate is as reliable as   
 *           the estimate for RCOND, and is almost always a slight   
 *           overestimate of the true error.
 *
 *   BERR    (output) float*, dimension (B->ncol)   
 *           The componentwise relative backward error of each solution   
 *           vector X(j) (i.e., the smallest relative change in   
 *           any element of A or B that makes X(j) an exact solution).
 *
 *   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   
 *
 *    Internal Parameters   
 *    ===================   
 *
 *    ITMAX is the maximum number of steps of iterative refinement.   
 *
 */  

#define ITMAX 5
    
    /* Table of constant values */
    int    ione = 1;
    float ndone = -1.;
    float done = 1.;
    
    /* Local variables */
    NCformat *Astore;
    float   *Aval;
    SuperMatrix Bjcol;
    DNformat *Bstore, *Xstore, *Bjcol_store;
    float   *Bmat, *Xmat, *Bptr, *Xptr;
    int      kase;
    float   safe1, safe2;
    int      i, j, k, irow, nz, count, notran, rowequ, colequ;
    int      ldb, ldx, nrhs;
    float   s, xk, lstres, eps, safmin;
    char     transc[1];
    trans_t  transt;
    float   *work;
    float   *rwork;
    int      *iwork;
    extern double slamch_(char *);
    extern int slacon_(int *, float *, float *, int *, float *, int *);
#ifdef _CRAY
    extern int SCOPY(int *, float *, int *, float *, int *);
    extern int SSAXPY(int *, float *, float *, int *, float *, int *);
#else
    extern int scopy_(int *, float *, int *, float *, int *);
    extern int saxpy_(int *, float *, float *, int *, float *, int *);
#endif

    Astore = A->Store;
    Aval   = Astore->nzval;
    Bstore = B->Store;
    Xstore = X->Store;
    Bmat   = Bstore->nzval;
    Xmat   = Xstore->nzval;
    ldb    = Bstore->lda;
    ldx    = Xstore->lda;
    nrhs   = B->ncol;
    
    /* Test the input parameters */
    *info = 0;
    notran = (trans == NOTRANS);
    if ( !notran && trans != TRANS && trans != CONJ ) *info = -1;
    else if ( A->nrow != A->ncol || A->nrow < 0 ||
	      A->Stype != SLU_NC || A->Dtype != SLU_S || A->Mtype != SLU_GE )
	*info = -2;
    else if ( L->nrow != L->ncol || L->nrow < 0 ||
 	      L->Stype != SLU_SC || L->Dtype != SLU_S || L->Mtype != SLU_TRLU )
	*info = -3;
    else if ( U->nrow != U->ncol || U->nrow < 0 ||
 	      U->Stype != SLU_NC || U->Dtype != SLU_S || U->Mtype != SLU_TRU )
	*info = -4;
    else if ( ldb < SUPERLU_MAX(0, A->nrow) ||
 	      B->Stype != SLU_DN || B->Dtype != SLU_S || B->Mtype != SLU_GE )
        *info = -10;
    else if ( ldx < SUPERLU_MAX(0, A->nrow) ||
 	      X->Stype != SLU_DN || X->Dtype != SLU_S || X->Mtype != SLU_GE )
	*info = -11;
    if (*info != 0) {
	i = -(*info);
	xerbla_("sgsrfs", &i);
	return;
    }

    /* Quick return if possible */
    if ( A->nrow == 0 || nrhs == 0) {
	for (j = 0; j < nrhs; ++j) {
	    ferr[j] = 0.;
	    berr[j] = 0.;
	}
	return;
    }

    rowequ = lsame_(equed, "R") || lsame_(equed, "B");
    colequ = lsame_(equed, "C") || lsame_(equed, "B");
    
    /* Allocate working space */
    work = floatMalloc(2*A->nrow);
    rwork = (float *) SUPERLU_MALLOC( A->nrow * sizeof(float) );
    iwork = intMalloc(2*A->nrow);
    if ( !work || !rwork || !iwork ) 
        ABORT("Malloc fails for work/rwork/iwork.");
    
    if ( notran ) {
	*(unsigned char *)transc = 'N';
        transt = TRANS;
    } else {
	*(unsigned char *)transc = 'T';
	transt = NOTRANS;
    }

    /* NZ = maximum number of nonzero elements in each row of A, plus 1 */
    nz     = A->ncol + 1;
    eps    = slamch_("Epsilon");
    safmin = slamch_("Safe minimum");
    safe1  = nz * safmin;
    safe2  = safe1 / eps;

    /* Compute the number of nonzeros in each row (or column) of A */
    for (i = 0; i < A->nrow; ++i) iwork[i] = 0;
    if ( notran ) {
	for (k = 0; k < A->ncol; ++k)
	    for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) 
		++iwork[Astore->rowind[i]];
    } else {
	for (k = 0; k < A->ncol; ++k)
	    iwork[k] = Astore->colptr[k+1] - Astore->colptr[k];
    }	

    /* Copy one column of RHS B into Bjcol. */
    Bjcol.Stype = B->Stype;
    Bjcol.Dtype = B->Dtype;
    Bjcol.Mtype = B->Mtype;
    Bjcol.nrow  = B->nrow;
    Bjcol.ncol  = 1;
    Bjcol.Store = (void *) SUPERLU_MALLOC( sizeof(DNformat) );
    if ( !Bjcol.Store ) ABORT("SUPERLU_MALLOC fails for Bjcol.Store");
    Bjcol_store = Bjcol.Store;
    Bjcol_store->lda = ldb;
    Bjcol_store->nzval = work; /* address aliasing */
	
    /* Do for each right hand side ... */
    for (j = 0; j < nrhs; ++j) {
	count = 0;
	lstres = 3.;
	Bptr = &Bmat[j*ldb];
	Xptr = &Xmat[j*ldx];

	while (1) { /* Loop until stopping criterion is satisfied. */

	    /* Compute residual R = B - op(A) * X,   
	       where op(A) = A, A**T, or A**H, depending on TRANS. */
	    
#ifdef _CRAY
	    SCOPY(&A->nrow, Bptr, &ione, work, &ione);
#else
	    scopy_(&A->nrow, Bptr, &ione, work, &ione);
#endif
	    sp_sgemv(transc, ndone, A, Xptr, ione, done, work, ione);

	    /* Compute componentwise relative backward error from formula 
	       max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) )   
	       where abs(Z) is the componentwise absolute value of the matrix
	       or vector Z.  If the i-th component of the denominator is less
	       than SAFE2, then SAFE1 is added to the i-th component of the   
	       numerator and denominator before dividing. */

	    for (i = 0; i < A->nrow; ++i) rwork[i] = fabs( Bptr[i] );
	    
	    /* Compute abs(op(A))*abs(X) + abs(B). */
	    if (notran) {
		for (k = 0; k < A->ncol; ++k) {
		    xk = fabs( Xptr[k] );
		    for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
			rwork[Astore->rowind[i]] += fabs(Aval[i]) * xk;
		}
	    } else {
		for (k = 0; k < A->ncol; ++k) {
		    s = 0.;
		    for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
			irow = Astore->rowind[i];
			s += fabs(Aval[i]) * fabs(Xptr[irow]);
		    }
		    rwork[k] += s;
		}
	    }
	    s = 0.;
	    for (i = 0; i < A->nrow; ++i) {
		if (rwork[i] > safe2)
		    s = SUPERLU_MAX( s, fabs(work[i]) / rwork[i] );
		else
		    s = SUPERLU_MAX( s, (fabs(work[i]) + safe1) / 
				(rwork[i] + safe1) );
	    }
	    berr[j] = s;

	    /* Test stopping criterion. Continue iterating if   
	       1) The residual BERR(J) is larger than machine epsilon, and   
	       2) BERR(J) decreased by at least a factor of 2 during the   
	          last iteration, and   
	       3) At most ITMAX iterations tried. */

	    if (berr[j] > eps && berr[j] * 2. <= lstres && count < ITMAX) {
		/* Update solution and try again. */
		sgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
		
#ifdef _CRAY
		SAXPY(&A->nrow, &done, work, &ione,
		       &Xmat[j*ldx], &ione);
#else
		saxpy_(&A->nrow, &done, work, &ione,
		       &Xmat[j*ldx], &ione);
#endif
		lstres = berr[j];
		++count;
	    } else {
		break;
	    }
        
	} /* end while */

	stat->RefineSteps = count;

	/* Bound error from formula:
	   norm(X - XTRUE) / norm(X) .le. FERR = norm( abs(inv(op(A)))*   
	   ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X)   
          where   
            norm(Z) is the magnitude of the largest component of Z   
            inv(op(A)) is the inverse of op(A)   
            abs(Z) is the componentwise absolute value of the matrix or
	       vector Z   
            NZ is the maximum number of nonzeros in any row of A, plus 1   
            EPS is machine epsilon   

          The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B))   
          is incremented by SAFE1 if the i-th component of   
          abs(op(A))*abs(X) + abs(B) is less than SAFE2.   

          Use SLACON to estimate the infinity-norm of the matrix   
             inv(op(A)) * diag(W),   
          where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
	
	for (i = 0; i < A->nrow; ++i) rwork[i] = fabs( Bptr[i] );
	
	/* Compute abs(op(A))*abs(X) + abs(B). */
	if ( notran ) {
	    for (k = 0; k < A->ncol; ++k) {
		xk = fabs( Xptr[k] );
		for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
		    rwork[Astore->rowind[i]] += fabs(Aval[i]) * xk;
	    }
	} else {
	    for (k = 0; k < A->ncol; ++k) {
		s = 0.;
		for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
		    irow = Astore->rowind[i];
		    xk = fabs( Xptr[irow] );
		    s += fabs(Aval[i]) * xk;
		}
		rwork[k] += s;
	    }
	}
	
	for (i = 0; i < A->nrow; ++i)
	    if (rwork[i] > safe2)
		rwork[i] = fabs(work[i]) + (iwork[i]+1)*eps*rwork[i];
	    else
		rwork[i] = fabs(work[i])+(iwork[i]+1)*eps*rwork[i]+safe1;

	kase = 0;

	do {
	    slacon_(&A->nrow, &work[A->nrow], work,
		    &iwork[A->nrow], &ferr[j], &kase);
	    if (kase == 0) break;

	    if (kase == 1) {
		/* Multiply by diag(W)*inv(op(A)**T)*(diag(C) or diag(R)). */
		if ( notran && colequ )
		    for (i = 0; i < A->ncol; ++i) work[i] *= C[i];
		else if ( !notran && rowequ )
		    for (i = 0; i < A->nrow; ++i) work[i] *= R[i];
		
		sgstrs (transt, L, U, perm_c, perm_r, &Bjcol, stat, info);
		
		for (i = 0; i < A->nrow; ++i) work[i] *= rwork[i];
	    } else {
		/* Multiply by (diag(C) or diag(R))*inv(op(A))*diag(W). */
		for (i = 0; i < A->nrow; ++i) work[i] *= rwork[i];
		
		sgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
		
		if ( notran && colequ )
		    for (i = 0; i < A->ncol; ++i) work[i] *= C[i];
		else if ( !notran && rowequ )
		    for (i = 0; i < A->ncol; ++i) work[i] *= R[i];  
	    }
	    
	} while ( kase != 0 );


	/* Normalize error. */
	lstres = 0.;
 	if ( notran && colequ ) {
	    for (i = 0; i < A->nrow; ++i)
	    	lstres = SUPERLU_MAX( lstres, C[i] * fabs( Xptr[i]) );
  	} else if ( !notran && rowequ ) {
	    for (i = 0; i < A->nrow; ++i)
	    	lstres = SUPERLU_MAX( lstres, R[i] * fabs( Xptr[i]) );
	} else {
	    for (i = 0; i < A->nrow; ++i)
	    	lstres = SUPERLU_MAX( lstres, fabs( Xptr[i]) );
	}
	if ( lstres != 0. )
	    ferr[j] /= lstres;

    } /* for each RHS j ... */
    
    SUPERLU_FREE(work);
    SUPERLU_FREE(rwork);
    SUPERLU_FREE(iwork);
    SUPERLU_FREE(Bjcol.Store);

    return;

} /* sgsrfs */
Example #15
0
/*! \brief
 *
 * <pre>
 *   Purpose   
 *   =======   
 *
 *   SGSRFS improves the computed solution to a system of linear   
 *   equations and provides error bounds and backward error estimates for 
 *   the solution.   
 *
 *   If equilibration was performed, the system becomes:
 *           (diag(R)*A_original*diag(C)) * X = diag(R)*B_original.
 *
 *   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)
 *   
 *   A       (input) SuperMatrix*
 *           The original matrix A in the system, or the scaled A if
 *           equilibration was done. The type of A can be:
 *           Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_GE.
 *    
 *   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 = 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 (A->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 (A->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.
 *
 *   equed   (input) Specifies the form of equilibration that was done.
 *           = 'N': No equilibration.
 *           = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
 *           = 'C': Column equilibration, i.e., A was postmultiplied by
 *                  diag(C).
 *           = 'B': Both row and column equilibration, i.e., A was replaced 
 *                  by diag(R)*A*diag(C).
 *
 *   R       (input) float*, dimension (A->nrow)
 *           The row scale factors for A.
 *           If equed = 'R' or 'B', A is premultiplied by diag(R).
 *           If equed = 'N' or 'C', R is not accessed.
 * 
 *   C       (input) float*, dimension (A->ncol)
 *           The column scale factors for A.
 *           If equed = 'C' or 'B', A is postmultiplied by diag(C).
 *           If equed = 'N' or 'R', C is not accessed.
 *
 *   B       (input) SuperMatrix*
 *           B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
 *           The right hand side matrix B.
 *           if equed = 'R' or 'B', B is premultiplied by diag(R).
 *
 *   X       (input/output) SuperMatrix*
 *           X has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
 *           On entry, the solution matrix X, as computed by sgstrs().
 *           On exit, the improved solution matrix X.
 *           if *equed = 'C' or 'B', X should be premultiplied by diag(C)
 *               in order to obtain the solution to the original system.
 *
 *   FERR    (output) float*, dimension (B->ncol)   
 *           The estimated forward error bound for each solution vector   
 *           X(j) (the j-th column of the solution matrix X).   
 *           If XTRUE is the true solution corresponding to X(j), FERR(j) 
 *           is an estimated upper bound for the magnitude of the largest 
 *           element in (X(j) - XTRUE) divided by the magnitude of the   
 *           largest element in X(j).  The estimate is as reliable as   
 *           the estimate for RCOND, and is almost always a slight   
 *           overestimate of the true error.
 *
 *   BERR    (output) float*, dimension (B->ncol)   
 *           The componentwise relative backward error of each solution   
 *           vector X(j) (i.e., the smallest relative change in   
 *           any element of A or B that makes X(j) an exact solution).
 *
 *   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   
 *
 *    Internal Parameters   
 *    ===================   
 *
 *    ITMAX is the maximum number of steps of iterative refinement.   
 *
 * </pre>
 */
void
sgsrfs(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix *U,
       int *perm_c, int *perm_r, char *equed, float *R, float *C,
       SuperMatrix *B, SuperMatrix *X, float *ferr, float *berr,
       SuperLUStat_t *stat, int *info)
{


#define ITMAX 5
    
    /* Table of constant values */
    int    ione = 1;
    float ndone = -1.;
    float done = 1.;
    
    /* Local variables */
    NCformat *Astore;
    float   *Aval;
    SuperMatrix Bjcol;
    DNformat *Bstore, *Xstore, *Bjcol_store;
    float   *Bmat, *Xmat, *Bptr, *Xptr;
    int      kase;
    float   safe1, safe2;
    int      i, j, k, irow, nz, count, notran, rowequ, colequ;
    int      ldb, ldx, nrhs;
    float   s, xk, lstres, eps, safmin;
    char     transc[1];
    trans_t  transt;
    float   *work;
    float   *rwork;
    int      *iwork;

    extern int slacon_(int *, float *, float *, int *, float *, int *);
#ifdef _CRAY
    extern int SCOPY(int *, float *, int *, float *, int *);
    extern int SSAXPY(int *, float *, float *, int *, float *, int *);
#else
    extern int scopy_(int *, float *, int *, float *, int *);
    extern int saxpy_(int *, float *, float *, int *, float *, int *);
#endif

    Astore = A->Store;
    Aval   = Astore->nzval;
    Bstore = B->Store;
    Xstore = X->Store;
    Bmat   = Bstore->nzval;
    Xmat   = Xstore->nzval;
    ldb    = Bstore->lda;
    ldx    = Xstore->lda;
    nrhs   = B->ncol;
    
    /* Test the input parameters */
    *info = 0;
    notran = (trans == NOTRANS);
    if ( !notran && trans != TRANS && trans != CONJ ) *info = -1;
    else if ( A->nrow != A->ncol || A->nrow < 0 ||
	      A->Stype != SLU_NC || A->Dtype != SLU_S || A->Mtype != SLU_GE )
	*info = -2;
    else if ( L->nrow != L->ncol || L->nrow < 0 ||
 	      L->Stype != SLU_SC || L->Dtype != SLU_S || L->Mtype != SLU_TRLU )
	*info = -3;
    else if ( U->nrow != U->ncol || U->nrow < 0 ||
 	      U->Stype != SLU_NC || U->Dtype != SLU_S || U->Mtype != SLU_TRU )
	*info = -4;
    else if ( ldb < SUPERLU_MAX(0, A->nrow) ||
 	      B->Stype != SLU_DN || B->Dtype != SLU_S || B->Mtype != SLU_GE )
        *info = -10;
    else if ( ldx < SUPERLU_MAX(0, A->nrow) ||
 	      X->Stype != SLU_DN || X->Dtype != SLU_S || X->Mtype != SLU_GE )
	*info = -11;
    if (*info != 0) {
	i = -(*info);
	xerbla_("sgsrfs", &i);
	return;
    }

    /* Quick return if possible */
    if ( A->nrow == 0 || nrhs == 0) {
	for (j = 0; j < nrhs; ++j) {
	    ferr[j] = 0.;
	    berr[j] = 0.;
	}
	return;
    }

    rowequ = lsame_(equed, "R") || lsame_(equed, "B");
    colequ = lsame_(equed, "C") || lsame_(equed, "B");
    
    /* Allocate working space */
    work = floatMalloc(2*A->nrow);
    rwork = (float *) SUPERLU_MALLOC( A->nrow * sizeof(float) );
    iwork = intMalloc(2*A->nrow);
    if ( !work || !rwork || !iwork ) 
        ABORT("Malloc fails for work/rwork/iwork.");
    
    if ( notran ) {
	*(unsigned char *)transc = 'N';
        transt = TRANS;
    } else {
	*(unsigned char *)transc = 'T';
	transt = NOTRANS;
    }

    /* NZ = maximum number of nonzero elements in each row of A, plus 1 */
    nz     = A->ncol + 1;
    eps    = slamch_("Epsilon");
    safmin = slamch_("Safe minimum");
    /* Set SAFE1 essentially to be the underflow threshold times the
       number of additions in each row. */
    safe1  = nz * safmin;
    safe2  = safe1 / eps;

    /* Compute the number of nonzeros in each row (or column) of A */
    for (i = 0; i < A->nrow; ++i) iwork[i] = 0;
    if ( notran ) {
	for (k = 0; k < A->ncol; ++k)
	    for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) 
		++iwork[Astore->rowind[i]];
    } else {
	for (k = 0; k < A->ncol; ++k)
	    iwork[k] = Astore->colptr[k+1] - Astore->colptr[k];
    }	

    /* Copy one column of RHS B into Bjcol. */
    Bjcol.Stype = B->Stype;
    Bjcol.Dtype = B->Dtype;
    Bjcol.Mtype = B->Mtype;
    Bjcol.nrow  = B->nrow;
    Bjcol.ncol  = 1;
    Bjcol.Store = (void *) SUPERLU_MALLOC( sizeof(DNformat) );
    if ( !Bjcol.Store ) ABORT("SUPERLU_MALLOC fails for Bjcol.Store");
    Bjcol_store = Bjcol.Store;
    Bjcol_store->lda = ldb;
    Bjcol_store->nzval = work; /* address aliasing */
	
    /* Do for each right hand side ... */
    for (j = 0; j < nrhs; ++j) {
	count = 0;
	lstres = 3.;
	Bptr = &Bmat[j*ldb];
	Xptr = &Xmat[j*ldx];

	while (1) { /* Loop until stopping criterion is satisfied. */

	    /* Compute residual R = B - op(A) * X,   
	       where op(A) = A, A**T, or A**H, depending on TRANS. */
	    
#ifdef _CRAY
	    SCOPY(&A->nrow, Bptr, &ione, work, &ione);
#else
	    scopy_(&A->nrow, Bptr, &ione, work, &ione);
#endif
	    sp_sgemv(transc, ndone, A, Xptr, ione, done, work, ione);

	    /* Compute componentwise relative backward error from formula 
	       max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) )   
	       where abs(Z) is the componentwise absolute value of the matrix
	       or vector Z.  If the i-th component of the denominator is less
	       than SAFE2, then SAFE1 is added to the i-th component of the   
	       numerator before dividing. */

	    for (i = 0; i < A->nrow; ++i) rwork[i] = fabs( Bptr[i] );
	    
	    /* Compute abs(op(A))*abs(X) + abs(B). */
	    if (notran) {
		for (k = 0; k < A->ncol; ++k) {
		    xk = fabs( Xptr[k] );
		    for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
			rwork[Astore->rowind[i]] += fabs(Aval[i]) * xk;
		}
	    } else {
		for (k = 0; k < A->ncol; ++k) {
		    s = 0.;
		    for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
			irow = Astore->rowind[i];
			s += fabs(Aval[i]) * fabs(Xptr[irow]);
		    }
		    rwork[k] += s;
		}
	    }
	    s = 0.;
	    for (i = 0; i < A->nrow; ++i) {
		if (rwork[i] > safe2) {
		    s = SUPERLU_MAX( s, fabs(work[i]) / rwork[i] );
		} else if ( rwork[i] != 0.0 ) {
                    /* Adding SAFE1 to the numerator guards against
                       spuriously zero residuals (underflow). */
		    s = SUPERLU_MAX( s, (safe1 + fabs(work[i])) / rwork[i] );
                }
                /* If rwork[i] is exactly 0.0, then we know the true 
                   residual also must be exactly 0.0. */
	    }
	    berr[j] = s;

	    /* Test stopping criterion. Continue iterating if   
	       1) The residual BERR(J) is larger than machine epsilon, and   
	       2) BERR(J) decreased by at least a factor of 2 during the   
	          last iteration, and   
	       3) At most ITMAX iterations tried. */

	    if (berr[j] > eps && berr[j] * 2. <= lstres && count < ITMAX) {
		/* Update solution and try again. */
		sgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
		
#ifdef _CRAY
		SAXPY(&A->nrow, &done, work, &ione,
		       &Xmat[j*ldx], &ione);
#else
		saxpy_(&A->nrow, &done, work, &ione,
		       &Xmat[j*ldx], &ione);
#endif
		lstres = berr[j];
		++count;
	    } else {
		break;
	    }
        
	} /* end while */

	stat->RefineSteps = count;

	/* Bound error from formula:
	   norm(X - XTRUE) / norm(X) .le. FERR = norm( abs(inv(op(A)))*   
	   ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X)   
          where   
            norm(Z) is the magnitude of the largest component of Z   
            inv(op(A)) is the inverse of op(A)   
            abs(Z) is the componentwise absolute value of the matrix or
	       vector Z   
            NZ is the maximum number of nonzeros in any row of A, plus 1   
            EPS is machine epsilon   

          The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B))   
          is incremented by SAFE1 if the i-th component of   
          abs(op(A))*abs(X) + abs(B) is less than SAFE2.   

          Use SLACON to estimate the infinity-norm of the matrix   
             inv(op(A)) * diag(W),   
          where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
	
	for (i = 0; i < A->nrow; ++i) rwork[i] = fabs( Bptr[i] );
	
	/* Compute abs(op(A))*abs(X) + abs(B). */
	if ( notran ) {
	    for (k = 0; k < A->ncol; ++k) {
		xk = fabs( Xptr[k] );
		for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
		    rwork[Astore->rowind[i]] += fabs(Aval[i]) * xk;
	    }
	} else {
	    for (k = 0; k < A->ncol; ++k) {
		s = 0.;
		for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
		    irow = Astore->rowind[i];
		    xk = fabs( Xptr[irow] );
		    s += fabs(Aval[i]) * xk;
		}
		rwork[k] += s;
	    }
	}
	
	for (i = 0; i < A->nrow; ++i)
	    if (rwork[i] > safe2)
		rwork[i] = fabs(work[i]) + (iwork[i]+1)*eps*rwork[i];
	    else
		rwork[i] = fabs(work[i])+(iwork[i]+1)*eps*rwork[i]+safe1;

	kase = 0;

	do {
	    slacon_(&A->nrow, &work[A->nrow], work,
		    &iwork[A->nrow], &ferr[j], &kase);
	    if (kase == 0) break;

	    if (kase == 1) {
		/* Multiply by diag(W)*inv(op(A)**T)*(diag(C) or diag(R)). */
		if ( notran && colequ )
		    for (i = 0; i < A->ncol; ++i) work[i] *= C[i];
		else if ( !notran && rowequ )
		    for (i = 0; i < A->nrow; ++i) work[i] *= R[i];
		
		sgstrs (transt, L, U, perm_c, perm_r, &Bjcol, stat, info);
		
		for (i = 0; i < A->nrow; ++i) work[i] *= rwork[i];
	    } else {
		/* Multiply by (diag(C) or diag(R))*inv(op(A))*diag(W). */
		for (i = 0; i < A->nrow; ++i) work[i] *= rwork[i];
		
		sgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
		
		if ( notran && colequ )
		    for (i = 0; i < A->ncol; ++i) work[i] *= C[i];
		else if ( !notran && rowequ )
		    for (i = 0; i < A->ncol; ++i) work[i] *= R[i];  
	    }
	    
	} while ( kase != 0 );


	/* Normalize error. */
	lstres = 0.;
 	if ( notran && colequ ) {
	    for (i = 0; i < A->nrow; ++i)
	    	lstres = SUPERLU_MAX( lstres, C[i] * fabs( Xptr[i]) );
  	} else if ( !notran && rowequ ) {
	    for (i = 0; i < A->nrow; ++i)
	    	lstres = SUPERLU_MAX( lstres, R[i] * fabs( Xptr[i]) );
	} else {
	    for (i = 0; i < A->nrow; ++i)
	    	lstres = SUPERLU_MAX( lstres, fabs( Xptr[i]) );
	}
	if ( lstres != 0. )
	    ferr[j] /= lstres;

    } /* for each RHS j ... */
    
    SUPERLU_FREE(work);
    SUPERLU_FREE(rwork);
    SUPERLU_FREE(iwork);
    SUPERLU_FREE(Bjcol.Store);

    return;

} /* sgsrfs */
Example #16
0
int main(int argc, char *argv[])
{
    void smatvec_mult(float alpha, float x[], float beta, float y[]);
    void spsolve(int n, float x[], float y[]);
    extern int sfgmr( int n,
	void (*matvec_mult)(float, float [], float, float []),
	void (*psolve)(int n, float [], float[]),
	float *rhs, float *sol, double tol, int restrt, int *itmax,
	FILE *fits);
    extern int sfill_diag(int n, NCformat *Astore);

    char     equed[1] = {'B'};
    yes_no_t equil;
    trans_t  trans;
    SuperMatrix A, L, U;
    SuperMatrix B, X;
    NCformat *Astore;
    NCformat *Ustore;
    SCformat *Lstore;
    GlobalLU_t	   Glu; /* facilitate multiple factorizations with 
                           SamePattern_SameRowPerm                  */
    float   *a;
    int      *asub, *xa;
    int      *etree;
    int      *perm_c; /* column permutation vector */
    int      *perm_r; /* row permutations from partial pivoting */
    int      nrhs, ldx, lwork, info, m, n, nnz;
    float   *rhsb, *rhsx, *xact;
    float   *work = NULL;
    float   *R, *C;
    float   u, rpg, rcond;
    float zero = 0.0;
    float one = 1.0;
    mem_usage_t   mem_usage;
    superlu_options_t options;
    SuperLUStat_t stat;
    FILE 	  *fp = stdin;

    int restrt, iter, maxit, i;
    double resid;
    float *x, *b;

#ifdef DEBUG
    extern int num_drop_L, num_drop_U;
#endif

#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Enter main()");
#endif

    /* Defaults */
    lwork = 0;
    nrhs  = 1;
    trans = NOTRANS;

    /* Set the default input options:
	options.Fact = DOFACT;
	options.Equil = YES;
	options.ColPerm = COLAMD;
	options.DiagPivotThresh = 0.1; //different from complete LU
	options.Trans = NOTRANS;
	options.IterRefine = NOREFINE;
	options.SymmetricMode = NO;
	options.PivotGrowth = NO;
	options.ConditionNumber = NO;
	options.PrintStat = YES;
	options.RowPerm = LargeDiag;
	options.ILU_DropTol = 1e-4;
	options.ILU_FillTol = 1e-2;
	options.ILU_FillFactor = 10.0;
	options.ILU_DropRule = DROP_BASIC | DROP_AREA;
	options.ILU_Norm = INF_NORM;
	options.ILU_MILU = SILU;
     */
    ilu_set_default_options(&options);

    /* Modify the defaults. */
    options.PivotGrowth = YES;	  /* Compute reciprocal pivot growth */
    options.ConditionNumber = YES;/* Compute reciprocal condition number */

    if ( lwork > 0 ) {
	work = SUPERLU_MALLOC(lwork);
	if ( !work ) ABORT("Malloc fails for work[].");
    }

    /* Read matrix A from a file in Harwell-Boeing format.*/
    if (argc < 2)
    {
	printf("Usage:\n%s [OPTION] < [INPUT] > [OUTPUT]\nOPTION:\n"
		"-h -hb:\n\t[INPUT] is a Harwell-Boeing format matrix.\n"
		"-r -rb:\n\t[INPUT] is a Rutherford-Boeing format matrix.\n"
		"-t -triplet:\n\t[INPUT] is a triplet format matrix.\n",
		argv[0]);
	return 0;
    }
    else
    {
	switch (argv[1][1])
	{
	    case 'H':
	    case 'h':
		printf("Input a Harwell-Boeing format matrix:\n");
		sreadhb(fp, &m, &n, &nnz, &a, &asub, &xa);
		break;
	    case 'R':
	    case 'r':
		printf("Input a Rutherford-Boeing format matrix:\n");
		sreadrb(&m, &n, &nnz, &a, &asub, &xa);
		break;
	    case 'T':
	    case 't':
		printf("Input a triplet format matrix:\n");
		sreadtriple(&m, &n, &nnz, &a, &asub, &xa);
		break;
	    default:
		printf("Unrecognized format.\n");
		return 0;
	}
    }

    sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa,
                                SLU_NC, SLU_S, SLU_GE);
    Astore = A.Store;
    sfill_diag(n, Astore);
    printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
    fflush(stdout);

    /* Generate the right-hand side */
    if ( !(rhsb = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
    if ( !(rhsx = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
    sCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE);
    sCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE);
    xact = floatMalloc(n * nrhs);
    ldx = n;
    sGenXtrue(n, nrhs, xact, ldx);
    sFillRHS(trans, nrhs, xact, ldx, &A, &B);

    if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
    if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
    if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
    if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) )
	ABORT("SUPERLU_MALLOC fails for R[].");
    if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
	ABORT("SUPERLU_MALLOC fails for C[].");

    info = 0;
#ifdef DEBUG
    num_drop_L = 0;
    num_drop_U = 0;
#endif

    /* Initialize the statistics variables. */
    StatInit(&stat);

    /* Compute the incomplete factorization and compute the condition number
       and pivot growth using dgsisx. */
    B.ncol = 0;  /* not to perform triangular solution */
    sgsisx(&options, &A, perm_c, perm_r, etree, equed, R, C, &L, &U, work,
	   lwork, &B, &X, &rpg, &rcond, &Glu, &mem_usage, &stat, &info);

    /* Set RHS for GMRES. */
    if (!(b = floatMalloc(m))) ABORT("Malloc fails for b[].");
    if (*equed == 'R' || *equed == 'B') {
	for (i = 0; i < n; ++i) b[i] = rhsb[i] * R[i];
    } else {
	for (i = 0; i < m; i++) b[i] = rhsb[i];
    }

    printf("sgsisx(): info %d, equed %c\n", info, equed[0]);
    if (info > 0 || rcond < 1e-8 || rpg > 1e8)
	printf("WARNING: This preconditioner might be unstable.\n");

    if ( info == 0 || info == n+1 ) {
	if ( options.PivotGrowth == YES )
	    printf("Recip. pivot growth = %e\n", rpg);
	if ( options.ConditionNumber == YES )
	    printf("Recip. condition number = %e\n", rcond);
    } else if ( info > 0 && lwork == -1 ) {
	printf("** Estimated memory: %d bytes\n", info - n);
    }

    Lstore = (SCformat *) L.Store;
    Ustore = (NCformat *) U.Store;
    printf("n(A) = %d, nnz(A) = %d\n", n, Astore->nnz);
    printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
    printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
    printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
    printf("Fill ratio: nnz(F)/nnz(A) = %.3f\n",
	    ((double)(Lstore->nnz) + (double)(Ustore->nnz) - (double)n)
	    / (double)Astore->nnz);
    printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
	   mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
    fflush(stdout);

    /* Set the global variables. */
    GLOBAL_A = &A;
    GLOBAL_L = &L;
    GLOBAL_U = &U;
    GLOBAL_STAT = &stat;
    GLOBAL_PERM_C = perm_c;
    GLOBAL_PERM_R = perm_r;
    GLOBAL_OPTIONS = &options;
    GLOBAL_R = R;
    GLOBAL_C = C;
    GLOBAL_MEM_USAGE = &mem_usage;

    /* Set the options to do solve-only. */
    options.Fact = FACTORED;
    options.PivotGrowth = NO;
    options.ConditionNumber = NO;

    /* Set the variables used by GMRES. */
    restrt = SUPERLU_MIN(n / 3 + 1, 50);
    maxit = 1000;
    iter = maxit;
    resid = 1e-8;
    if (!(x = floatMalloc(n))) ABORT("Malloc fails for x[].");

    if (info <= n + 1)
    {
	int i_1 = 1;
	double maxferr = 0.0, nrmA, nrmB, res, t;
        float temp;
	extern float snrm2_(int *, float [], int *);
	extern void saxpy_(int *, float *, float [], int *, float [], int *);

	/* Initial guess */
	for (i = 0; i < n; i++) x[i] = zero;

	t = SuperLU_timer_();

	/* Call GMRES */
	sfgmr(n, smatvec_mult, spsolve, b, x, resid, restrt, &iter, stdout);

	t = SuperLU_timer_() - t;

	/* Output the result. */
	nrmA = snrm2_(&(Astore->nnz), (float *)((DNformat *)A.Store)->nzval,
		&i_1);
	nrmB = snrm2_(&m, b, &i_1);
	sp_sgemv("N", -1.0, &A, x, 1, 1.0, b, 1);
	res = snrm2_(&m, b, &i_1);
	resid = res / nrmB;
	printf("||A||_F = %.1e, ||B||_2 = %.1e, ||B-A*X||_2 = %.1e, "
		"relres = %.1e\n", nrmA, nrmB, res, resid);

	if (iter >= maxit)
	{
	    if (resid >= 1.0) iter = -180;
	    else if (resid > 1e-8) iter = -111;
	}
	printf("iteration: %d\nresidual: %.1e\nGMRES time: %.2f seconds.\n",
		iter, resid, t);

	/* Scale the solution back if equilibration was performed. */
	if (*equed == 'C' || *equed == 'B') 
	    for (i = 0; i < n; i++) x[i] *= C[i];

	for (i = 0; i < m; i++) {
	    maxferr = SUPERLU_MAX(maxferr, fabs(x[i] - xact[i]));
        }
	printf("||X-X_true||_oo = %.1e\n", maxferr);
    }
#ifdef DEBUG
    printf("%d entries in L and %d entries in U dropped.\n",
	    num_drop_L, num_drop_U);
#endif
    fflush(stdout);

    if ( options.PrintStat ) StatPrint(&stat);
    StatFree(&stat);

    SUPERLU_FREE (rhsb);
    SUPERLU_FREE (rhsx);
    SUPERLU_FREE (xact);
    SUPERLU_FREE (etree);
    SUPERLU_FREE (perm_r);
    SUPERLU_FREE (perm_c);
    SUPERLU_FREE (R);
    SUPERLU_FREE (C);
    Destroy_CompCol_Matrix(&A);
    Destroy_SuperMatrix_Store(&B);
    Destroy_SuperMatrix_Store(&X);
    if ( lwork >= 0 ) {
	Destroy_SuperNode_Matrix(&L);
	Destroy_CompCol_Matrix(&U);
    }
    SUPERLU_FREE(b);
    SUPERLU_FREE(x);

#if ( DEBUGlevel>=1 )
    CHECK_MALLOC("Exit main()");
#endif

    return 0;
}
Example #17
0
int main ( int argc, char *argv[] )

/******************************************************************************/
/*
  Purpose:

    MAIN is the main program for PSLINSOL.

  Licensing:

    This code is distributed under the GNU LGPL license. 

  Modified:

    10 February 2014

  Author:

    Xiaoye Li
*/
{
  SuperMatrix   A;
  NCformat *Astore;
  float   *a;
  int      *asub, *xa;
  int      *perm_r; /* row permutations from partial pivoting */
  int      *perm_c; /* column permutation vector */
  SuperMatrix   L;       /* factor L */
  SCPformat *Lstore;
  SuperMatrix   U;       /* factor U */
  NCPformat *Ustore;
  SuperMatrix   B;
  int      nrhs, ldx, info, m, n, nnz, b;
  int      nprocs; /* maximum number of processors to use. */
  int      panel_size, relax, maxsup;
  int      permc_spec;
  trans_t  trans;
  float   *xact, *rhs;
  superlu_memusage_t   superlu_memusage;
  void   parse_command_line();

  timestamp ( );
  printf ( "\n" );
  printf ( "PSLINSOL:\n" );
  printf ( "  C/OpenMP version\n" );
  printf ( "  Call the OpenMP version of SuperLU to solve a linear system.\n" );

  nrhs              = 1;
  trans             = NOTRANS;
  nprocs             = 1;
  n                 = 1000;
  b                 = 1;
  panel_size        = sp_ienv(1);
  relax             = sp_ienv(2);
  maxsup            = sp_ienv(3);
/*
  Check for any commandline input.
*/  
  parse_command_line ( argc, argv, &nprocs, &n, &b, &panel_size, 
    &relax, &maxsup );

#if ( PRNTlevel>=1 || DEBUGlevel>=1 )
    cpp_defs();
#endif

#define HB
#if defined( DEN )
    m = n;
    nnz = n * n;
    sband(n, n, nnz, &a, &asub, &xa);
#elif defined( BAND )
    m = n;
    nnz = (2*b+1) * n;
    sband(n, b, nnz, &a, &asub, &xa);
#elif defined( BD )
    nb = 5;
    bs = 200;
    m = n = bs * nb;
    nnz = bs * bs * nb;
    sblockdiag(nb, bs, nnz, &a, &asub, &xa);
#elif defined( HB )
    sreadhb(&m, &n, &nnz, &a, &asub, &xa);
#else    
    sreadmt(&m, &n, &nnz, &a, &asub, &xa);
#endif

    sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
    Astore = A.Store;
    printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
    
    if (!(rhs = floatMalloc(m * nrhs))) SUPERLU_ABORT("Malloc fails for rhs[].");
    sCreate_Dense_Matrix(&B, m, nrhs, rhs, m, SLU_DN, SLU_S, SLU_GE);
    xact = floatMalloc(n * nrhs);
    ldx = n;
    sGenXtrue(n, nrhs, xact, ldx);
    sFillRHS(trans, nrhs, xact, ldx, &A, &B);

    if (!(perm_r = intMalloc(m))) SUPERLU_ABORT("Malloc fails for perm_r[].");
    if (!(perm_c = intMalloc(n))) SUPERLU_ABORT("Malloc fails for perm_c[].");

    /*
     * Get column permutation vector perm_c[], according to permc_spec:
     *   permc_spec = 0: natural ordering 
     *   permc_spec = 1: minimum degree ordering on structure of A'*A
     *   permc_spec = 2: minimum degree ordering on structure of A'+A
     *   permc_spec = 3: approximate minimum degree for unsymmetric matrices
     */    	
    permc_spec = 1;
    get_perm_c(permc_spec, &A, perm_c);

    psgssv(nprocs, &A, perm_c, perm_r, &L, &U, &B, &info);
    
    if ( info == 0 ) {
	sinf_norm_error(nrhs, &B, xact); /* Inf. norm of the error */

	Lstore = (SCPformat *) L.Store;
	Ustore = (NCPformat *) U.Store;
    	printf("#NZ in factor L = %d\n", Lstore->nnz);
    	printf("#NZ in factor U = %d\n", Ustore->nnz);
    	printf("#NZ in L+U = %d\n", Lstore->nnz + Ustore->nnz - L.ncol);
	
	superlu_sQuerySpace(nprocs, &L, &U, panel_size, &superlu_memusage);
	printf("L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
	       superlu_memusage.for_lu/1024/1024, 
	       superlu_memusage.total_needed/1024/1024,
	       superlu_memusage.expansions);

    }

    SUPERLU_FREE (rhs);
    SUPERLU_FREE (xact);
    SUPERLU_FREE (perm_r);
    SUPERLU_FREE (perm_c);
    Destroy_CompCol_Matrix(&A);
    Destroy_SuperMatrix_Store(&B);
    Destroy_SuperNode_SCP(&L);
    Destroy_CompCol_NCP(&U);
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "PSLINSOL:\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

  return 0;
}
Example #18
0
int main ( int argc, char *argv[] )

/**********************************************************************/
/*
  Purpose:

    SUPER_LU_S2 solves a symmetric sparse system read from a file.

  Discussion:

    The sparse matrix is stored in a file using the Harwell-Boeing
    sparse matrix format.  The file should be assigned to the standard
    input of this program.  For instance, if the matrix is stored
    in the file "g10_rua.txt", the execution command might be:

      super_lu_s2 < g10_rua.txt

  Modified:

    25 April 2004

  Reference:

    James Demmel, John Gilbert, Xiaoye Li,
    SuperLU Users's Guide,
    Sections 1 and 2.

  Local parameters:

    SuperMatrix L, the computed L factor.

    int *perm_c, the column permutation vector.

    int *perm_r, the row permutations from partial pivoting.

    SuperMatrix U, the computed U factor.
*/
{
  SuperMatrix A;
  NCformat *Astore;
  float *a;
  int *asub;
  SuperMatrix B;
  int info;
  SuperMatrix L;
  int ldx;
  SCformat *Lstore;
  int m;
  mem_usage_t mem_usage;
  int n;
  int nnz;
  int nrhs;
  superlu_options_t options;
  int *perm_c;
  int *perm_r;
  float *rhs;
  float *sol;
  SuperLUStat_t stat;
  SuperMatrix U;
  NCformat *Ustore;
  int *xa;
  float *xact;
/*
  Say hello.
*/
  printf ( "\n" );
  printf ( "SUPER_LU_S2:\n" );
  printf ( "  Read a symmetric sparse matrix A from standard input,\n");
  printf ( "  stored in Harwell-Boeing Sparse Matrix format.\n" );
  printf ( "\n" );
  printf ( "  Solve a linear system A * X = B.\n" );
/* 
  Set the default input options:
  options.Fact = DOFACT;
  options.Equil = YES;
  options.ColPerm = COLAMD;
  options.DiagPivotThresh = 1.0;
  options.Trans = NOTRANS;
  options.IterRefine = NOREFINE;
  options.SymmetricMode = NO;
  options.PivotGrowth = NO;
  options.ConditionNumber = NO;
  options.PrintStat = YES;
*/
  set_default_options ( &options );
/* 
  Now we modify the default options to use the symmetric mode. 
*/
  options.SymmetricMode = YES;
  options.ColPerm = MMD_AT_PLUS_A;
  options.DiagPivotThresh = 0.001;
/* 
  Read the matrix in Harwell-Boeing format. 
*/
  sreadhb ( &m, &n, &nnz, &a, &asub, &xa );
/*
  Create storage for a compressed column matrix.
*/
  sCreate_CompCol_Matrix ( &A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE );
  Astore = A.Store;

  printf ( "\n" );
  printf ( "  Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz );
/*
  Set up the right hand side.
*/  
  nrhs = 1;
  rhs = floatMalloc ( m * nrhs );
  if ( !rhs ) 
  {
    ABORT ( " Malloc fails for rhs[]." );
  }

  sCreate_Dense_Matrix ( &B, m, nrhs, rhs, m, SLU_DN, SLU_S, SLU_GE );
  xact = floatMalloc ( n * nrhs );
  if ( !xact ) 
  {
    ABORT ( " Malloc fails for rhs[]." );
  }
  ldx = n;
  sGenXtrue ( n, nrhs, xact, ldx );
  sFillRHS ( options.Trans, nrhs, xact, ldx, &A, &B );

  perm_c = intMalloc ( n );
  if ( !perm_c ) 
  {
    ABORT ( "Malloc fails for perm_c[]." );
  }

  perm_r = intMalloc ( m );
  if ( !perm_r )
  {
    ABORT ( "Malloc fails for perm_r[]." );
  }
/* 
  Initialize the statistics variables. 
*/
  StatInit ( &stat );
/*
  Call SGSSV to factor the matrix and solve the linear system.
*/
  sgssv ( &options, &A, perm_c, perm_r, &L, &U, &B, &stat, &info );
    
  if ( info == 0 )
  {
/* 
  To conveniently access the solution matrix, you need to get a pointer to it. 
*/
    sol = (float*) ((DNformat*) B.Store)->nzval; 

/* 
  Compute the infinity norm of the error. 
*/
    sinf_norm_error ( nrhs, &B, xact );

    Lstore = (SCformat *) L.Store;
    Ustore = (NCformat *) U.Store;

    printf ( "\n" );
    printf ( "  Number of nonzeros in factor L = %d\n", Lstore->nnz );
    printf ( "  Number of nonzeros in factor U = %d\n", Ustore->nnz );
    printf ( "  Number of nonzeros in L+U = %d\n", 
      Lstore->nnz + Ustore->nnz - n );
	
    sQuerySpace ( &L, &U, &mem_usage );

    printf ( "\n" );
    printf ( "  L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
      mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
      mem_usage.expansions);
  } 
  else
  {
    printf ( "\n" );
    printf ( "  SGSSV error returns INFO= %d\n", info );

    if ( info <= n ) 
    {
      sQuerySpace ( &L, &U, &mem_usage );

      printf ( "\n" );
      printf ("  L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
        mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
        mem_usage.expansions );
    }
  }

  if ( options.PrintStat ) 
  {
    StatPrint ( &stat );
  }
  StatFree ( &stat );
/*
  Free the memory.
*/
  SUPERLU_FREE ( rhs );
  SUPERLU_FREE ( xact );
  SUPERLU_FREE ( perm_r );
  SUPERLU_FREE ( perm_c );
  Destroy_CompCol_Matrix ( &A );
  Destroy_SuperMatrix_Store ( &B );
  Destroy_SuperNode_Matrix ( &L );
  Destroy_CompCol_Matrix ( &U );
/*
  Say goodbye.
*/
  printf ( "\n" );
  printf ( "SUPER_LU_S2:\n" );
  printf ( "  Normal end of execution.\n");

  return 0;
}