329 lines
8.5 KiB
C
329 lines
8.5 KiB
C
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/*! @file ilu_sdrop_row.c
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* \brief Drop small rows from L
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*
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* <pre>
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* -- SuperLU routine (version 4.1) --
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* Lawrence Berkeley National Laboratory.
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* June 30, 2009
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* </pre>
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*/
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#include <math.h>
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#include <stdlib.h>
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#include "slu_sdefs.h"
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extern void sswap_(int *, float [], int *, float [], int *);
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extern void saxpy_(int *, float *, float [], int *, float [], int *);
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extern void scopy_(int *, float [], int *, float [], int *);
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extern float sasum_(int *, float *, int *);
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extern float snrm2_(int *, float *, int *);
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extern double dnrm2_(int *, double [], int *);
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extern int isamax_(int *, float [], int *);
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static float *A; /* used in _compare_ only */
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static int _compare_(const void *a, const void *b)
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{
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register int *x = (int *)a, *y = (int *)b;
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if (A[*x] - A[*y] > 0.0) return -1;
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else if (A[*x] - A[*y] < 0.0) return 1;
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else return 0;
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}
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/*! \brief
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* <pre>
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* Purpose
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* =======
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* ilu_sdrop_row() - Drop some small rows from the previous
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* supernode (L-part only).
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* </pre>
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*/
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int ilu_sdrop_row(
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superlu_options_t *options, /* options */
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int first, /* index of the first column in the supernode */
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int last, /* index of the last column in the supernode */
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double drop_tol, /* dropping parameter */
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int quota, /* maximum nonzero entries allowed */
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int *nnzLj, /* in/out number of nonzeros in L(:, 1:last) */
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double *fill_tol, /* in/out - on exit, fill_tol=-num_zero_pivots,
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* does not change if options->ILU_MILU != SMILU1 */
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GlobalLU_t *Glu, /* modified */
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float swork[], /* working space
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* the length of swork[] should be no less than
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* the number of rows in the supernode */
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float swork2[], /* working space with the same size as swork[],
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* used only by the second dropping rule */
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int lastc /* if lastc == 0, there is nothing after the
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* working supernode [first:last];
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* if lastc == 1, there is one more column after
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* the working supernode. */ )
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{
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register int i, j, k, m1;
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register int nzlc; /* number of nonzeros in column last+1 */
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register int xlusup_first, xlsub_first;
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int m, n; /* m x n is the size of the supernode */
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int r = 0; /* number of dropped rows */
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register float *temp;
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register float *lusup = Glu->lusup;
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register int *lsub = Glu->lsub;
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register int *xlsub = Glu->xlsub;
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register int *xlusup = Glu->xlusup;
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register float d_max = 0.0, d_min = 1.0;
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int drop_rule = options->ILU_DropRule;
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milu_t milu = options->ILU_MILU;
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norm_t nrm = options->ILU_Norm;
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float zero = 0.0;
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float one = 1.0;
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float none = -1.0;
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int i_1 = 1;
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int inc_diag; /* inc_diag = m + 1 */
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int nzp = 0; /* number of zero pivots */
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float alpha = pow((double)(Glu->n), -1.0 / options->ILU_MILU_Dim);
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xlusup_first = xlusup[first];
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xlsub_first = xlsub[first];
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m = xlusup[first + 1] - xlusup_first;
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n = last - first + 1;
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m1 = m - 1;
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inc_diag = m + 1;
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nzlc = lastc ? (xlusup[last + 2] - xlusup[last + 1]) : 0;
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temp = swork - n;
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/* Quick return if nothing to do. */
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if (m == 0 || m == n || drop_rule == NODROP)
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{
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*nnzLj += m * n;
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return 0;
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}
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/* basic dropping: ILU(tau) */
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for (i = n; i <= m1; )
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{
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/* the average abs value of ith row */
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switch (nrm)
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{
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case ONE_NORM:
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temp[i] = sasum_(&n, &lusup[xlusup_first + i], &m) / (double)n;
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break;
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case TWO_NORM:
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temp[i] = snrm2_(&n, &lusup[xlusup_first + i], &m)
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/ sqrt((double)n);
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break;
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case INF_NORM:
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default:
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k = isamax_(&n, &lusup[xlusup_first + i], &m) - 1;
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temp[i] = fabs(lusup[xlusup_first + i + m * k]);
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break;
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}
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/* drop small entries due to drop_tol */
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if (drop_rule & DROP_BASIC && temp[i] < drop_tol)
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{
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r++;
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/* drop the current row and move the last undropped row here */
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if (r > 1) /* add to last row */
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{
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/* accumulate the sum (for MILU) */
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switch (milu)
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{
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case SMILU_1:
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case SMILU_2:
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saxpy_(&n, &one, &lusup[xlusup_first + i], &m,
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&lusup[xlusup_first + m - 1], &m);
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break;
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case SMILU_3:
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for (j = 0; j < n; j++)
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lusup[xlusup_first + (m - 1) + j * m] +=
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fabs(lusup[xlusup_first + i + j * m]);
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break;
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case SILU:
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default:
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break;
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}
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scopy_(&n, &lusup[xlusup_first + m1], &m,
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&lusup[xlusup_first + i], &m);
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} /* if (r > 1) */
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else /* move to last row */
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{
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sswap_(&n, &lusup[xlusup_first + m1], &m,
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&lusup[xlusup_first + i], &m);
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if (milu == SMILU_3)
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for (j = 0; j < n; j++) {
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lusup[xlusup_first + m1 + j * m] =
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fabs(lusup[xlusup_first + m1 + j * m]);
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}
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}
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lsub[xlsub_first + i] = lsub[xlsub_first + m1];
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m1--;
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continue;
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} /* if dropping */
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else
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{
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if (temp[i] > d_max) d_max = temp[i];
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if (temp[i] < d_min) d_min = temp[i];
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}
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i++;
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} /* for */
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/* Secondary dropping: drop more rows according to the quota. */
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quota = ceil((double)quota / (double)n);
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if (drop_rule & DROP_SECONDARY && m - r > quota)
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{
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register double tol = d_max;
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/* Calculate the second dropping tolerance */
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if (quota > n)
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{
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if (drop_rule & DROP_INTERP) /* by interpolation */
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{
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d_max = 1.0 / d_max; d_min = 1.0 / d_min;
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tol = 1.0 / (d_max + (d_min - d_max) * quota / (m - n - r));
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}
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else /* by quick select */
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{
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int len = m1 - n + 1;
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scopy_(&len, swork, &i_1, swork2, &i_1);
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tol = sqselect(len, swork2, quota - n);
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#if 0
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register int *itemp = iwork - n;
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A = temp;
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for (i = n; i <= m1; i++) itemp[i] = i;
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qsort(iwork, m1 - n + 1, sizeof(int), _compare_);
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tol = temp[itemp[quota]];
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#endif
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}
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}
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for (i = n; i <= m1; )
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{
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if (temp[i] <= tol)
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{
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register int j;
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r++;
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/* drop the current row and move the last undropped row here */
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if (r > 1) /* add to last row */
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{
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/* accumulate the sum (for MILU) */
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switch (milu)
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{
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case SMILU_1:
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case SMILU_2:
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saxpy_(&n, &one, &lusup[xlusup_first + i], &m,
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&lusup[xlusup_first + m - 1], &m);
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break;
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case SMILU_3:
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for (j = 0; j < n; j++)
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lusup[xlusup_first + (m - 1) + j * m] +=
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fabs(lusup[xlusup_first + i + j * m]);
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break;
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case SILU:
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default:
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break;
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}
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scopy_(&n, &lusup[xlusup_first + m1], &m,
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&lusup[xlusup_first + i], &m);
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} /* if (r > 1) */
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else /* move to last row */
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{
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sswap_(&n, &lusup[xlusup_first + m1], &m,
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&lusup[xlusup_first + i], &m);
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if (milu == SMILU_3)
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for (j = 0; j < n; j++) {
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lusup[xlusup_first + m1 + j * m] =
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fabs(lusup[xlusup_first + m1 + j * m]);
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}
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}
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lsub[xlsub_first + i] = lsub[xlsub_first + m1];
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m1--;
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temp[i] = temp[m1];
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continue;
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}
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i++;
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} /* for */
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} /* if secondary dropping */
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for (i = n; i < m; i++) temp[i] = 0.0;
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if (r == 0)
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{
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*nnzLj += m * n;
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return 0;
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}
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/* add dropped entries to the diagnal */
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if (milu != SILU)
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{
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register int j;
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float t;
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float omega;
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for (j = 0; j < n; j++)
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{
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t = lusup[xlusup_first + (m - 1) + j * m];
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if (t == zero) continue;
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if (t > zero)
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omega = SUPERLU_MIN(2.0 * (1.0 - alpha) / t, 1.0);
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else
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omega = SUPERLU_MAX(2.0 * (1.0 - alpha) / t, -1.0);
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t *= omega;
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switch (milu)
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{
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case SMILU_1:
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if (t != none) {
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lusup[xlusup_first + j * inc_diag] *= (one + t);
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}
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else
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{
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lusup[xlusup_first + j * inc_diag] *= *fill_tol;
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#ifdef DEBUG
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printf("[1] ZERO PIVOT: FILL col %d.\n", first + j);
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fflush(stdout);
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#endif
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nzp++;
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}
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break;
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case SMILU_2:
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lusup[xlusup_first + j * inc_diag] *= (1.0 + fabs(t));
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break;
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case SMILU_3:
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lusup[xlusup_first + j * inc_diag] *= (one + t);
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break;
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case SILU:
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default:
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break;
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}
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}
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if (nzp > 0) *fill_tol = -nzp;
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}
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/* Remove dropped entries from the memory and fix the pointers. */
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m1 = m - r;
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for (j = 1; j < n; j++)
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{
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register int tmp1, tmp2;
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tmp1 = xlusup_first + j * m1;
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tmp2 = xlusup_first + j * m;
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for (i = 0; i < m1; i++)
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lusup[i + tmp1] = lusup[i + tmp2];
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}
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for (i = 0; i < nzlc; i++)
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lusup[xlusup_first + i + n * m1] = lusup[xlusup_first + i + n * m];
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for (i = 0; i < nzlc; i++)
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lsub[xlsub[last + 1] - r + i] = lsub[xlsub[last + 1] + i];
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for (i = first + 1; i <= last + 1; i++)
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{
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xlusup[i] -= r * (i - first);
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xlsub[i] -= r;
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}
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if (lastc)
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{
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xlusup[last + 2] -= r * n;
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xlsub[last + 2] -= r;
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}
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*nnzLj += (m - r) * n;
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return r;
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}
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