/* ========================================================================== */
/* === UMF_local_search ===================================================== */
/* ========================================================================== */
/* -------------------------------------------------------------------------- */
/* UMFPACK Version 5.0, Copyright (c) 1995-2006 by Timothy A. Davis. CISE, */
/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
/* -------------------------------------------------------------------------- */
/*
Perform pivot search to find pivot row and pivot column.
The pivot column is selected from the candidate set. The candidate set
corresponds to a supercolumn from colamd or UMF_analyze. The pivot column
is then removed from that set. Constructs the pivot column pattern and
values. Called by umf_kernel. Returns UMFPACK_OK if successful, or
UMFPACK_WARNING_singular_matrix or UMFPACK_ERROR_different_pattern if not.
*/
#include "umf_internal.h"
#include "umf_row_search.h"
#include "umf_mem_free_tail_block.h"
/* relaxed amalgamation control parameters are fixed at compile time */
#define RELAX1 0.25
#define SYM_RELAX1 0.0
#define RELAX2 0.1
#define RELAX3 0.125
/* ========================================================================== */
/* === remove_candidate ===================================================== */
/* ========================================================================== */
/* Remove a column from the set of candidate pivot columns. */
PRIVATE void remove_candidate (Int jj, WorkType *Work, SymbolicType *Symbolic)
{
#ifndef NDEBUG
Int j ;
DEBUGm2 (("pivot column Candidates before remove: nCand "ID" ncand "ID
" lo "ID" hi "ID" jj "ID"\n", Work->nCandidates, Work->ncand,
Work->lo, Work->hi, jj)) ;
for (j = 0 ; j < Work->nCandidates ; j++)
{
Int col = Work->Candidates [j] ;
DEBUGm2 ((ID" ", col));
ASSERT (col >= 0 && col < Work->n_col) ;
/* ASSERT (NON_PIVOTAL_COL (col)) ; */
ASSERT (col >= Work->lo && col <= Work->hi) ;
}
DEBUGm2 (("\n")) ;
#endif
if (Symbolic->fixQ)
{
DEBUGm2 (("FixQ\n")) ;
/* do not modify the column ordering */
ASSERT (Work->nCandidates == 1) ;
ASSERT (jj == 0) ;
if (Work->ncand > 1)
{
Work->Candidates [0] = Work->nextcand++ ;
}
else
{
Work->nCandidates = 0 ;
}
}
else
{
/* place the next candidate in the set */
if (Work->ncand > MAX_CANDIDATES)
{
Work->Candidates [jj] = Work->nextcand++ ;
}
else
{
ASSERT (Work->nCandidates == Work->ncand) ;
Work->Candidates [jj] = Work->Candidates [Work->ncand - 1] ;
Work->Candidates [Work->ncand - 1] = EMPTY ;
Work->nCandidates-- ;
}
}
Work->ncand-- ;
#ifndef NDEBUG
DEBUGm2 (("pivot column Candidates after remove: nCand "ID" ncand "ID
" lo "ID" hi "ID" jj "ID"\n", Work->nCandidates, Work->ncand, Work->lo,
Work->hi, jj)) ;
for (j = 0 ; j < Work->nCandidates ; j++)
{
Int col = Work->Candidates [j] ;
DEBUGm2 ((ID" ", col));
ASSERT (col >= 0 && col < Work->n_col) ;
/* ASSERT (NON_PIVOTAL_COL (col)) ; */
ASSERT (col >= Work->lo && col <= Work->hi) ;
}
DEBUGm2 (("\n")) ;
ASSERT (Work->ncand >= 0) ;
ASSERT (Work->nCandidates <= Work->ncand) ;
#endif
}
/* ========================================================================== */
/* === UMF_local_search ===================================================== */
/* ========================================================================== */
GLOBAL Int UMF_local_search
(
NumericType *Numeric,
WorkType *Work,
SymbolicType *Symbolic
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
double relax1 ;
Entry *Flblock, *Fublock, *Fs, *Fcblock, *C, *Wx, *Wy, *Fu, *Flublock,
*Flu ;
Int pos, nrows, *Cols, *Rows, e, f, status, max_cdeg, fnzeros, nb, j, col,
i, row, cdeg_in, rdeg [2][2], fnpiv, nothing [2], new_LUsize,
pivrow [2][2], pivcol [2], *Wp, *Fcpos, *Frpos, new_fnzeros, cdeg_out,
*Wm, *Wio, *Woi, *Woo, *Frows, *Fcols, fnrows, fncols, *E, deg, nr_in,
nc, thiscost, bestcost, nr_out, do_update, extra_cols, extra_rows,
extra_zeros, relaxed_front, do_extend, fnr_curr, fnc_curr, tpi,
*Col_tuples, *Col_degree, *Col_tlen, jj, jcand [2], freebie [2],
did_rowmerge, fnrows_new [2][2], fncols_new [2][2], search_pivcol_out,
*Diagonal_map, *Diagonal_imap, row2, col2 ;
Unit *Memory, *p ;
Tuple *tp, *tpend, *tp1, *tp2 ;
Element *ep ;
#ifndef NBLAS
Int blas_ok = TRUE ;
#else
#define blas_ok FALSE
#endif
#ifndef NDEBUG
Int debug_ok, n_row, n_col, *Row_degree ;
Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro only */
#endif
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
Memory = Numeric->Memory ;
E = Work->E ;
Col_degree = Numeric->Cperm ;
Col_tuples = Numeric->Lip ;
Col_tlen = Numeric->Lilen ;
Wx = Work->Wx ;
Wy = Work->Wy ;
Wp = Work->Wp ;
Wm = Work->Wm ;
Woi = Work->Woi ;
Wio = Work->Wio ;
Woo = Work->Woo ;
Fcpos = Work->Fcpos ;
Frpos = Work->Frpos ;
Frows = Work->Frows ;
Fcols = Work->Fcols ;
fnrows = Work->fnrows ;
fncols = Work->fncols ;
nb = Work->nb ;
fnr_curr = Work->fnr_curr ;
fnc_curr = Work->fnc_curr ;
fnpiv = Work->fnpiv ;
nothing [0] = EMPTY ;
nothing [1] = EMPTY ;
relax1 = (Symbolic->prefer_diagonal) ? SYM_RELAX1 : RELAX1 ;
fnzeros = Work->fnzeros ;
new_fnzeros = fnzeros ;
jj = EMPTY ;
Fcblock = Work->Fcblock ; /* current contribution block */
Flblock = Work->Flblock ; /* current L block */
Fublock = Work->Fublock ; /* current U block */
Flublock = Work->Flublock ; /* current LU block */
/* The pivot column degree cannot exceed max_cdeg */
max_cdeg = Work->fnrows_max ;
ASSERT (Work->fnrows_max <= Symbolic->maxnrows) ;
ASSERT (Work->fncols_max <= Symbolic->maxncols) ;
if (fnrows == 0 && fncols == 0)
{
/* frontal matrix is empty */
Work->firstsuper = Work->ksuper ;
}
#ifndef NDEBUG
n_row = Work->n_row ;
n_col = Work->n_col ;
DEBUG2 (("\n========LOCAL SEARCH: current frontal matrix: ========= \n")) ;
UMF_dump_current_front (Numeric, Work, TRUE) ;
if (UMF_debug > 0 || MAX (n_row, n_col) < 1000)
{
for (i = 0 ; i < MAX (n_row, n_col) ; i++)
{
ASSERT (Wp [i] < 0) ;
}
}
DEBUGm2 ((ID" pivot column Candidates: lo "ID" hi "ID"\n",
Work->nCandidates, Work->lo, Work->hi)) ;
for (j = 0 ; j < Work->nCandidates ; j++)
{
col = Work->Candidates [j] ;
DEBUGm2 ((ID" ", col));
ASSERT (col >= 0 && col < n_col) ;
ASSERT (NON_PIVOTAL_COL (col)) ;
ASSERT (col >= Work->lo && col <= Work->hi) ;
}
DEBUGm2 (("\n")) ;
/* there are no 0-by-c or r-by-0 fronts, where c and r are > 0 */
/* a front is either 0-by-0, or r-by-c */
DEBUG2 (("\n\n::: "ID" : Npiv: "ID" + fnpiv "ID" = "ID". "
"size "ID"-by-"ID"\n", Work->frontid,
Work->npiv, Work->fnpiv, Work->npiv + Work->fnpiv, fnrows, fncols)) ;
ASSERT ((fnrows == 0 && fncols == 0) ||(fnrows != 0 && fncols != 0)) ;
#endif
/* ====================================================================== */
/* === PIVOT SEARCH ===================================================== */
/* ====================================================================== */
/* initialize */
pivcol [IN] = EMPTY ;
pivcol [OUT] = EMPTY ;
cdeg_in = Int_MAX ;
cdeg_out = Int_MAX ;
pivrow [IN][IN] = EMPTY ;
pivrow [IN][OUT] = EMPTY ;
pivrow [OUT][IN] = EMPTY ;
pivrow [OUT][OUT] = EMPTY ;
rdeg [IN][IN] = Int_MAX ;
rdeg [IN][OUT] = Int_MAX ;
rdeg [OUT][IN] = Int_MAX ;
rdeg [OUT][OUT] = Int_MAX ;
freebie [IN] = FALSE ;
freebie [OUT] = FALSE ;
Work->pivot_case = EMPTY ;
bestcost = EMPTY ;
nr_out = EMPTY ;
nr_in = EMPTY ;
jcand [IN] = EMPTY ;
jcand [OUT] = EMPTY ;
fnrows_new [IN][IN] = EMPTY ;
fnrows_new [IN][OUT] = EMPTY ;
fnrows_new [OUT][IN] = EMPTY ;
fnrows_new [OUT][OUT] = EMPTY ;
fncols_new [IN][IN] = EMPTY ;
fncols_new [IN][OUT] = EMPTY ;
fncols_new [OUT][IN] = EMPTY ;
fncols_new [OUT][OUT] = EMPTY ;
#ifndef NDEBUG
/* check Frpos */
DEBUG4 (("Check Frpos : fnrows "ID" col "ID" maxcdeg "ID"\n",
fnrows, pivcol [IN], max_cdeg)) ;
for (i = 0 ; i < fnrows ; i++)
{
row = Frows [i] ;
DEBUG4 ((" row: "ID"\n", row)) ;
ASSERT (row >= 0 && row < n_row) ;
ASSERT (Frpos [row] == i) ;
}
DEBUG4 (("All:\n")) ;
if (UMF_debug > 0 || n_row < 1000)
{
Int cnt = fnrows ;
for (row = 0 ; row < n_row ; row++)
{
if (Frpos [row] == EMPTY)
{
cnt++ ;
}
else
{
DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ;
}
}
ASSERT (cnt == n_row) ;
}
#endif
/* ---------------------------------------------------------------------- */
/* find shortest column in the front, and shortest column not in the */
/* front, from the candidate pivot column set */
/* ---------------------------------------------------------------------- */
/* If there are too many candidates, then only look at the first */
/* MAX_CANDIDATES of them. Otherwise, if there are O(n) candidates, */
/* this code could take O(n^2) time. */
/* ------------------------------------------------------------------ */
/* look in the candidate set for the best column */
/* ------------------------------------------------------------------ */
DEBUG2 (("Max candidates %d, Work->ncand "ID" jmax "ID"\n",
MAX_CANDIDATES, Work->ncand, Work->nCandidates)) ;
col = Work->Candidates [0] ;
ASSERT (Work->nCandidates > 0) ;
DEBUG3 (("Pivot column candidate: "ID" j = "ID"\n", col, j)) ;
ASSERT (col >= 0 && col < n_col) ;
/* there is no Col_degree if fixQ is true */
deg = Symbolic->fixQ ? EMPTY : Col_degree [col] ;
#ifndef NDEBUG
DEBUG3 (("Pivot column candidate: "ID" cost: "ID" Fcpos[col] "ID"\n",
col, deg, Fcpos [col])) ;
UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ;
if (Symbolic->fixQ)
{
DEBUG1 (("FIXQ: Candidates "ID" pivcol "ID" npiv "ID" fnpiv "ID
" ndiscard "ID "\n", Work->nCandidates, col, Work->npiv,
Work->fnpiv, Work->ndiscard)) ;
ASSERT (Work->nCandidates == 1) ;
ASSERT (col == Work->npiv + Work->fnpiv + Work->ndiscard) ;
}
#endif
if (Fcpos [col] >= 0)
{
/* best column in front, so far */
pivcol [IN] = col ;
cdeg_in = deg ; /* ignored, if fixQ is true */
jcand [IN] = 0 ;
}
else
{
/* best column not in front, so far */
pivcol [OUT] = col ;
cdeg_out = deg ; /* ignored, if fixQ is true */
jcand [OUT] = 0 ;
}
/* look at the rest of the candidates */
for (j = 1 ; j < Work->nCandidates ; j++)
{
col = Work->Candidates [j] ;
DEBUG3 (("Pivot col candidate: "ID" j = "ID"\n", col, j)) ;
ASSERT (col >= 0 && col < n_col) ;
ASSERT (!Symbolic->fixQ) ;
deg = Col_degree [col] ;
#ifndef NDEBUG
DEBUG3 (("Pivot col candidate: "ID" cost: "ID" Fcpos[col] "ID"\n",
col, deg, Fcpos [col])) ;
UMF_dump_rowcol (1, Numeric, Work, col, !Symbolic->fixQ) ;
#endif
if (Fcpos [col] >= 0)
{
#ifndef NDEBUG
Int fs ;
fs = Fcpos [col] / fnr_curr ;
ASSERT (fs >= 0 && fs < fncols) ;
#endif
if (deg < cdeg_in || (deg == cdeg_in && col < pivcol [IN]))
{
/* best column in front, so far */
pivcol [IN] = col ;
cdeg_in = deg ;
jcand [IN] = j ;
}
}
else
{
if (deg < cdeg_out || (deg == cdeg_out && col < pivcol [OUT]))
{
/* best column not in front, so far */
pivcol [OUT] = col ;
cdeg_out = deg ;
jcand [OUT] = j ;
}
}
}
DEBUG2 (("Pivcol in "ID" out "ID"\n", pivcol [IN], pivcol [OUT])) ;
ASSERT ((pivcol [IN] >= 0 && pivcol [IN] < n_col)
|| (pivcol [OUT] >= 0 && pivcol [OUT] < n_col)) ;
cdeg_in = EMPTY ;
cdeg_out = EMPTY ;
/* ---------------------------------------------------------------------- */
/* construct candidate column in front, and search for pivot rows */
/* ---------------------------------------------------------------------- */
#ifndef NDEBUG
/* check Frpos */
DEBUG4 (("Prior to col update: fnrows "ID" col "ID" maxcdeg "ID"\n",
fnrows, pivcol [IN], max_cdeg)) ;
for (i = 0 ; i < fnrows ; i++)
{
row = Frows [i] ;
DEBUG4 ((" row: "ID"\n", row)) ;
ASSERT (row >= 0 && row < n_row) ;
ASSERT (Frpos [row] == i) ;
}
DEBUG4 (("All:\n")) ;
if (UMF_debug > 0 || n_row < 1000)
{
Int cnt = fnrows ;
for (row = 0 ; row < n_row ; row++)
{
if (Frpos [row] == EMPTY)
{
cnt++ ;
}
else
{
DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ;
}
}
ASSERT (cnt == n_row) ;
}
#endif
if (pivcol [IN] != EMPTY)
{
#ifndef NDEBUG
DEBUG2 (("col[IN] column "ID" in front at position = "ID"\n",
pivcol [IN], Fcpos [pivcol [IN]])) ;
UMF_dump_rowcol (1, Numeric, Work, pivcol [IN], !Symbolic->fixQ) ;
#endif
/* the only way we can have a pivcol[IN] is if the front is not empty */
ASSERT (fnrows > 0 && fncols > 0) ;
DEBUG4 (("Update pivot column:\n")) ;
Fs = Fcblock + Fcpos [pivcol [IN]] ;
Fu = Fublock + (Fcpos [pivcol [IN]] / fnr_curr) ;
Flu = Flublock + fnpiv * nb ;
/* ------------------------------------------------------------------ */
/* copy the pivot column from the U block into the LU block */
/* ------------------------------------------------------------------ */
/* This copy is permanent if the pivcol [IN] is chosen. */
for (i = 0 ; i < fnpiv ; i++)
{
Flu [i] = Fu [i*fnc_curr] ;
}
/* ------------------------------------------------------------------ */
/* update the pivot column in the LU block using a triangular solve */
/* ------------------------------------------------------------------ */
/* This work will be discarded if the pivcol [OUT] is chosen instead.
* It is permanent if the pivcol [IN] is chosen. */
if (fnpiv > 1)
{
/* solve Lx=b, where b = U (:,k), stored in the LU block */
#ifndef NBLAS
BLAS_TRSV (fnpiv, Flublock, Flu, nb) ;
#endif
if (!blas_ok)
{
/* use plain C code if no BLAS, or on integer overflow */
Entry *Flub = Flublock ;
for (j = 0 ; j < fnpiv ; j++)
{
Entry Fuj = Flu [j] ;
#pragma ivdep
for (i = j+1 ; i < fnpiv ; i++)
{
/* Flu [i] -= Flublock [i + j*nb] * Flu [j] ; */
MULT_SUB (Flu [i], Flub [i], Fuj) ;
}
Flub += nb ;
}
}
}
/* ------------------------------------------------------------------ */
/* copy the pivot column from the C block into Wy */
/* ------------------------------------------------------------------ */
for (i = 0 ; i < fnrows ; i++)
{
Wy [i] = Fs [i] ;
}
/* ------------------------------------------------------------------ */
/* update the pivot column of L using a matrix-vector multiply */
/* ------------------------------------------------------------------ */
/* this work will be discarded if the pivcol [OUT] is chosen instead */
#ifdef NBLAS
/* no BLAS available - use plain C code instead */
for (j = 0 ; j < fnpiv ; j++)
{
Entry Fuj, *Flub = Flblock + j * fnr_curr ;
Fuj = Flu [j] ;
if (IS_NONZERO (Fuj))
{
#pragma ivdep
for (i = 0 ; i < fnrows ; i++)
{
/* Wy [i] -= Flblock [i+j*fnr_curr] * Fuj ; */
MULT_SUB (Wy [i], Flub [i], Fuj) ;
}
}
/* Flblock += fnr_curr ; */
}
#else
/* Using 1-based notation:
* Wy (1:fnrows) -= Flblock (1:fnrows,1:fnpiv) * Flu (1:fnpiv) */
BLAS_GEMV (fnrows, fnpiv, Flblock, Flu, Wy, fnr_curr) ;
#endif
/* ------------------------------------------------------------------ */
#ifndef NDEBUG
DEBUG2 (("Wy after update: fnrows="ID"\n", fnrows)) ;
DEBUG4 ((" fnpiv="ID" \n", fnpiv)) ;
for (i = 0 ; i < fnrows ; i++)
{
DEBUG4 ((ID" "ID" "ID, i, Frows [i], Frpos [Frows [i]])) ;
EDEBUG4 (Wy [i]) ;
DEBUG4 (("\n")) ;
}
#endif
/* ------------------------------------------------------------------ */
/* construct the candidate column */
/* ------------------------------------------------------------------ */
cdeg_in = fnrows ;
#ifndef NDEBUG
/* check Frpos */
DEBUG4 (("After col update: fnrows "ID" col "ID" maxcdeg "ID"\n",
fnrows, pivcol [IN], max_cdeg)) ;
for (i = 0 ; i < fnrows ; i++)
{
row = Frows [i] ;
DEBUG4 ((" row: "ID"\n", row)) ;
ASSERT (row >= 0 && row < n_row) ;
ASSERT (Frpos [row] == i) ;
}
DEBUG4 (("All:\n")) ;
if (UMF_debug > 0 || n_row < 1000)
{
Int cnt = fnrows ;
for (row = 0 ; row < n_row ; row++)
{
if (Frpos [row] == EMPTY)
{
cnt++ ;
}
else
{
DEBUG4 ((" row: "ID" pos "ID"\n", row, Frpos [row])) ;
}
}
ASSERT (cnt == n_row) ;
}
#endif
#ifndef NDEBUG
/* check Frpos */
DEBUG4 (("COL ASSEMBLE: cdeg "ID"\nREDUCE COL in "ID" max_cdeg "ID"\n",
cdeg_in, pivcol [IN], max_cdeg)) ;
for (i = 0 ; i < cdeg_in ; i++)
{
row = Frows [i] ;
ASSERT (row >= 0 && row < n_row) ;
ASSERT (Frpos [row] == i) ;
}
if (UMF_debug > 0 || n_row < 1000)
{
Int cnt = cdeg_in ;
for (row = 0 ; row < n_row ; row++)
{
if (Frpos [row] == EMPTY) cnt++ ;
}
ASSERT (cnt == n_row) ;
}
#endif
/* assemble column into Wy */
ASSERT (pivcol [IN] >= 0 && pivcol [IN] < n_col) ;
ASSERT (NON_PIVOTAL_COL (pivcol [IN])) ;
tpi = Col_tuples [pivcol [IN]] ;
if (tpi)
{
tp = (Tuple *) (Memory + tpi) ;
tp1 = tp ;
tp2 = tp ;
tpend = tp + Col_tlen [pivcol [IN]] ;
for ( ; tp < tpend ; tp++)
{
e = tp->e ;
ASSERT (e > 0 && e <= Work->nel) ;
if (!E [e]) continue ; /* element already deallocated */
f = tp->f ;
p = Memory + E [e] ;
ep = (Element *) p ;
p += UNITS (Element, 1) ;
Cols = (Int *) p ;
if (Cols [f] == EMPTY) continue ; /* column already assembled */
ASSERT (pivcol [IN] == Cols [f]) ;
Rows = Cols + ep->ncols ;
nrows = ep->nrows ;
p += UNITS (Int, ep->ncols + nrows) ;
C = ((Entry *) p) + f * nrows ;
for (i = 0 ; i < nrows ; i++)
{
row = Rows [i] ;
if (row >= 0) /* skip this if already gone from element */
{
ASSERT (row < n_row) ;
pos = Frpos [row] ;
if (pos < 0)
{
/* new entry in the pattern - save Frpos */
ASSERT (cdeg_in < n_row) ;
if (cdeg_in >= max_cdeg)
{
/* :: pattern change (cdeg in failure) :: */
DEBUGm4 (("cdeg_in failure\n")) ;
return (UMFPACK_ERROR_different_pattern) ;
}
Frpos [row] = cdeg_in ;
Frows [cdeg_in] = row ;
Wy [cdeg_in++] = C [i] ;
}
else
{
/* entry already in pattern - sum values in Wy */
/* Wy [pos] += C [i] ; */
ASSERT (pos < max_cdeg) ;
ASSEMBLE (Wy [pos], C [i]) ;
}
}
}
*tp2++ = *tp ; /* leave the tuple in the list */
}
Col_tlen [pivcol [IN]] = tp2 - tp1 ;
}
/* ------------------------------------------------------------------ */
#ifndef NDEBUG
/* check Frpos again */
DEBUG4 (("COL DONE: cdeg "ID"\nREDUCE COL in "ID" max_cdeg "ID"\n",
cdeg_in, pivcol [IN], max_cdeg)) ;
for (i = 0 ; i < cdeg_in ; i++)
{
row = Frows [i] ;
ASSERT (row >= 0 && row < n_row) ;
ASSERT (Frpos [row] == i) ;
}
if (UMF_debug > 0 || n_row < 1000)
{
Int cnt = cdeg_in ;
for (row = 0 ; row < n_row ; row++)
{
if (Frpos [row] == EMPTY) cnt++ ;
}
ASSERT (cnt == n_row) ;
}
#endif
#ifndef NDEBUG
DEBUG4 (("Reduced column: cdeg in "ID" fnrows_max "ID"\n",
cdeg_in, Work->fnrows_max)) ;
for (i = 0 ; i < cdeg_in ; i++)
{
DEBUG4 ((" "ID" "ID" "ID, i, Frows [i], Frpos [Frows [i]])) ;
EDEBUG4 (Wy [i]) ;
DEBUG4 (("\n")) ;
ASSERT (i == Frpos [Frows [i]]) ;
}
ASSERT (cdeg_in <= Work->fnrows_max) ;
#endif
/* ------------------------------------------------------------------ */
/* cdeg_in is now the exact degree of this column */
/* ------------------------------------------------------------------ */
nr_in = cdeg_in - fnrows ;
/* since there are no 0-by-x fronts, if there is a pivcol [IN] the */
/* front must have at least one row. */
ASSERT (cdeg_in > 0) ;
/* new degree of pivcol [IN], excluding current front is nr_in */
/* column expands by nr_in rows */
/* ------------------------------------------------------------------ */
/* search for two candidate pivot rows */
/* ------------------------------------------------------------------ */
/* for the IN_IN pivot row (if any), */
/* extend the pattern in place, using Fcols */
status = UMF_row_search (Numeric, Work, Symbolic,
fnrows, cdeg_in, Frows, Frpos, /* pattern of column to search */
pivrow [IN], rdeg [IN], Fcols, Wio, nothing, Wy,
pivcol [IN], freebie) ;
ASSERT (!freebie [IN] && !freebie [OUT]) ;
/* ------------------------------------------------------------------ */
/* fatal error if matrix pattern has changed since symbolic analysis */
/* ------------------------------------------------------------------ */
if (status == UMFPACK_ERROR_different_pattern)
{
/* :: pattern change (row search IN failure) :: */
DEBUGm4 (("row search IN failure\n")) ;
return (UMFPACK_ERROR_different_pattern) ;
}
/* ------------------------------------------------------------------ */
/* we now must have a structural pivot */
/* ------------------------------------------------------------------ */
/* Since the pivcol[IN] exists, there must be at least one row in the */
/* current frontal matrix, and so we must have found a structural */
/* pivot. The numerical value might be zero, of course. */
ASSERT (status != UMFPACK_WARNING_singular_matrix) ;
/* ------------------------------------------------------------------ */
/* evaluate IN_IN option */
/* ------------------------------------------------------------------ */
if (pivrow [IN][IN] != EMPTY)
{
/* The current front would become an (implicit) LUson.
* Both candidate pivot row and column are in the current front.
* Cost is how much the current front would expand */
/* pivrow[IN][IN] candidates are not found via row merge search */
ASSERT (fnrows >= 0 && fncols >= 0) ;
ASSERT (cdeg_in > 0) ;
nc = rdeg [IN][IN] - fncols ;
thiscost =
/* each column in front (except pivot column) grows by nr_in: */
(nr_in * (fncols - 1)) +
/* new columns not in old front: */
(nc * (cdeg_in - 1)) ;
/* no extra cost to relaxed amalgamation */
ASSERT (fnrows + nr_in == cdeg_in) ;
ASSERT (fncols + nc == rdeg [IN][IN]) ;
/* size of relaxed front (after pivot row column removed): */
fnrows_new [IN][IN] = (fnrows-1) + nr_in ;
fncols_new [IN][IN] = (fncols-1) + nc ;
/* relaxed_front = fnrows_new [IN][IN] * fncols_new [IN][IN] ; */
do_extend = TRUE ;
DEBUG2 (("Evaluating option IN-IN:\n")) ;
DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_in "ID" nc "ID"\n",
Work->fnzeros, fnpiv, nr_in, nc)) ;
DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
/* determine if BLAS-3 update should be applied before extending. */
/* update if too many zero entries accumulate in the LU block */
fnzeros = Work->fnzeros + fnpiv * (nr_in + nc) ;
DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
new_LUsize = (fnpiv+1) * (fnrows + nr_in + fncols + nc) ;
DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
/* There are fnpiv pivots currently in the front. This one
* will be the (fnpiv+1)st pivot, if it is extended. */
/* RELAX2 parameter uses a double relop, but ignore NaN case: */
do_update = fnpiv > 0 &&
(((double) fnzeros) / ((double) new_LUsize)) > RELAX2 ;
DEBUG2 (("do_update "ID"\n", do_update))
DEBUG2 (("option IN IN : nr "ID" nc "ID" cost "ID"(0) relax "ID
"\n", nr_in, nc, thiscost, do_extend)) ;
/* this is the best option seen so far */
Work->pivot_case = IN_IN ;
bestcost = thiscost ;
/* do the amalgamation and extend the front */
Work->do_extend = do_extend ;
Work->do_update = do_update ;
new_fnzeros = fnzeros ;
}
/* ------------------------------------------------------------------ */
/* evaluate IN_OUT option */
/* ------------------------------------------------------------------ */
if (pivrow [IN][OUT] != EMPTY)
{
/* The current front would become a Uson of the new front.
* Candidate pivot column is in the current front, but the
* candidate pivot row is not. */
ASSERT (fnrows >= 0 && fncols > 0) ;
ASSERT (cdeg_in > 0) ;
/* must be at least one row outside the front */
/* (the pivrow [IN][OUT] itself) */
ASSERT (nr_in >= 1) ;
/* count columns not in current front */
nc = 0 ;
#ifndef NDEBUG
debug_ok = FALSE ;
#endif
for (i = 0 ; i < rdeg [IN][OUT] ; i++)
{
col = Wio [i] ;
DEBUG4 (("counting col "ID" Fcpos[] = "ID"\n", col,
Fcpos [col])) ;
ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
if (Fcpos [col] < 0) nc++ ;
#ifndef NDEBUG
/* we must see the pivot column somewhere */
if (col == pivcol [IN])
{
ASSERT (Fcpos [col] >= 0) ;
debug_ok = TRUE ;
}
#endif
}
ASSERT (debug_ok) ;
thiscost =
/* each row in front grows by nc: */
(nc * fnrows) +
/* new rows not affected by front: */
((nr_in-1) * (rdeg [IN][OUT]-1)) ;
/* check the cost of relaxed IN_OUT amalgamation */
extra_cols = ((fncols-1) + nc ) - (rdeg [IN][OUT] - 1) ;
ASSERT (extra_cols >= 0) ;
ASSERT (fncols + nc == extra_cols + rdeg [IN][OUT]) ;
extra_zeros = (nr_in-1) * extra_cols ; /* symbolic fill-in */
ASSERT (fnrows + nr_in == cdeg_in) ;
ASSERT (fncols + nc == rdeg [IN][OUT] + extra_cols) ;
/* size of relaxed front (after pivot column removed): */
fnrows_new [IN][OUT] = fnrows + (nr_in-1) ;
fncols_new [IN][OUT] = (fncols-1) + nc ;
relaxed_front = fnrows_new [IN][OUT] * fncols_new [IN][OUT] ;
/* do relaxed amalgamation if the extra zeros are no more */
/* than a fraction (default 0.25) of the relaxed front */
/* if relax = 0: no extra zeros allowed */
/* if relax = +inf: always amalgamate */
/* relax parameter uses a double relop, but ignore NaN case: */
if (extra_zeros == 0)
{
do_extend = TRUE ;
}
else
{
do_extend = ((double) extra_zeros) <
(relax1 * (double) relaxed_front) ;
}
if (do_extend)
{
/* count the cost of relaxed amalgamation */
thiscost += extra_zeros ;
DEBUG2 (("Evaluating option IN-OUT:\n")) ;
DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_in "ID" nc "ID"\n",
Work->fnzeros, fnpiv, nr_in, nc)) ;
DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
/* determine if BLAS-3 update to be applied before extending. */
/* update if too many zero entries accumulate in the LU block */
fnzeros = Work->fnzeros + fnpiv * (nr_in + nc) ;
DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
new_LUsize = (fnpiv+1) * (fnrows + nr_in + fncols + nc) ;
DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
/* RELAX3 parameter uses a double relop, ignore NaN case: */
do_update = fnpiv > 0 &&
(((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ;
DEBUG2 (("do_update "ID"\n", do_update))
}
else
{
/* the current front would not be extended */
do_update = fnpiv > 0 ;
fnzeros = 0 ;
DEBUG2 (("IN-OUT do_update forced true: "ID"\n", do_update)) ;
/* The new front would be just big enough to hold the new
* pivot row and column. */
fnrows_new [IN][OUT] = cdeg_in - 1 ;
fncols_new [IN][OUT] = rdeg [IN][OUT] - 1 ;
}
DEBUG2 (("option IN OUT: nr "ID" nc "ID" cost "ID"("ID") relax "ID
"\n", nr_in, nc, thiscost, extra_zeros, do_extend)) ;
if (bestcost == EMPTY || thiscost < bestcost)
{
/* this is the best option seen so far */
Work->pivot_case = IN_OUT ;
bestcost = thiscost ;
Work->do_extend = do_extend ;
Work->do_update = do_update ;
new_fnzeros = fnzeros ;
}
}
}
/* ---------------------------------------------------------------------- */
/* construct candidate column not in front, and search for pivot rows */
/* ---------------------------------------------------------------------- */
search_pivcol_out = (bestcost != 0 && pivcol [OUT] != EMPTY) ;
if (Symbolic->prefer_diagonal)
{
search_pivcol_out = search_pivcol_out && (pivrow [IN][IN] == EMPTY) ;
}
if (search_pivcol_out)
{
#ifndef NDEBUG
DEBUG2 (("out_col column "ID" NOT in front at position = "ID"\n",
pivcol [OUT], Fcpos [pivcol [OUT]])) ;
UMF_dump_rowcol (1, Numeric, Work, pivcol [OUT], !Symbolic->fixQ) ;
DEBUG2 (("fncols "ID" fncols_max "ID"\n", fncols, Work->fncols_max)) ;
ASSERT (fncols < Work->fncols_max) ;
#endif
/* Use Wx as temporary workspace to construct the pivcol [OUT] */
/* ------------------------------------------------------------------ */
/* construct the candidate column (currently not in the front) */
/* ------------------------------------------------------------------ */
/* Construct the column in Wx, Wm, using Wp for the positions: */
/* Wm [0..cdeg_out-1] list of row indices in the column */
/* Wx [0..cdeg_out-1] list of corresponding numerical values */
/* Wp [0..n-1] starts as all negative, and ends that way too. */
cdeg_out = 0 ;
#ifndef NDEBUG
/* check Wp */
DEBUG4 (("COL ASSEMBLE: cdeg 0\nREDUCE COL out "ID"\n", pivcol [OUT])) ;
if (UMF_debug > 0 || MAX (n_row, n_col) < 1000)
{
for (i = 0 ; i < MAX (n_row, n_col) ; i++)
{
ASSERT (Wp [i] < 0) ;
}
}
DEBUG4 (("max_cdeg: "ID"\n", max_cdeg)) ;
#endif
ASSERT (pivcol [OUT] >= 0 && pivcol [OUT] < n_col) ;
ASSERT (NON_PIVOTAL_COL (pivcol [OUT])) ;
tpi = Col_tuples [pivcol [OUT]] ;
if (tpi)
{
tp = (Tuple *) (Memory + tpi) ;
tp1 = tp ;
tp2 = tp ;
tpend = tp + Col_tlen [pivcol [OUT]] ;
for ( ; tp < tpend ; tp++)
{
e = tp->e ;
ASSERT (e > 0 && e <= Work->nel) ;
if (!E [e]) continue ; /* element already deallocated */
f = tp->f ;
p = Memory + E [e] ;
ep = (Element *) p ;
p += UNITS (Element, 1) ;
Cols = (Int *) p ;
if (Cols [f] == EMPTY) continue ; /* column already assembled */
ASSERT (pivcol [OUT] == Cols [f]) ;
Rows = Cols + ep->ncols ;
nrows = ep->nrows ;
p += UNITS (Int, ep->ncols + nrows) ;
C = ((Entry *) p) + f * nrows ;
for (i = 0 ; i < nrows ; i++)
{
row = Rows [i] ;
if (row >= 0) /* skip this if already gone from element */
{
ASSERT (row < n_row) ;
pos = Wp [row] ;
if (pos < 0)
{
/* new entry in the pattern - save Wp */
ASSERT (cdeg_out < n_row) ;
if (cdeg_out >= max_cdeg)
{
/* :: pattern change (cdeg out failure) :: */
DEBUGm4 (("cdeg out failure\n")) ;
return (UMFPACK_ERROR_different_pattern) ;
}
Wp [row] = cdeg_out ;
Wm [cdeg_out] = row ;
Wx [cdeg_out++] = C [i] ;
}
else
{
/* entry already in pattern - sum the values */
/* Wx [pos] += C [i] ; */
ASSEMBLE (Wx [pos], C [i]) ;
}
}
}
*tp2++ = *tp ; /* leave the tuple in the list */
}
Col_tlen [pivcol [OUT]] = tp2 - tp1 ;
}
/* ------------------------------------------------------------------ */
#ifndef NDEBUG
DEBUG4 (("Reduced column: cdeg out "ID"\n", cdeg_out)) ;
for (i = 0 ; i < cdeg_out ; i++)
{
DEBUG4 ((" "ID" "ID" "ID, i, Wm [i], Wp [Wm [i]])) ;
EDEBUG4 (Wx [i]) ;
DEBUG4 (("\n")) ;
ASSERT (i == Wp [Wm [i]]) ;
}
#endif
/* ------------------------------------------------------------------ */
/* new degree of pivcol [OUT] is cdeg_out */
/* ------------------------------------------------------------------ */
/* search for two candidate pivot rows */
status = UMF_row_search (Numeric, Work, Symbolic,
0, cdeg_out, Wm, Wp, /* pattern of column to search */
pivrow [OUT], rdeg [OUT], Woi, Woo, pivrow [IN], Wx,
pivcol [OUT], freebie) ;
/* ------------------------------------------------------------------ */
/* fatal error if matrix pattern has changed since symbolic analysis */
/* ------------------------------------------------------------------ */
if (status == UMFPACK_ERROR_different_pattern)
{
/* :: pattern change detected in umf_local_search :: */
return (UMFPACK_ERROR_different_pattern) ;
}
/* ------------------------------------------------------------------ */
/* Clear Wp */
/* ------------------------------------------------------------------ */
for (i = 0 ; i < cdeg_out ; i++)
{
Wp [Wm [i]] = EMPTY ; /* clear Wp */
}
/* ------------------------------------------------------------------ */
/* check for rectangular, singular matrix */
/* ------------------------------------------------------------------ */
if (status == UMFPACK_WARNING_singular_matrix)
{
/* Pivot column is empty, and row-merge set is empty too. The
* matrix is structurally singular. The current frontal matrix must
* be empty, too. It it weren't, and pivcol [OUT] exists, then
* there would be at least one row that could be selected. Since
* the current front is empty, pivcol [IN] must also be EMPTY.
*/
DEBUGm4 (("Note: pivcol [OUT]: "ID" discard\n", pivcol [OUT])) ;
ASSERT ((Work->fnrows == 0 && Work->fncols == 0)) ;
ASSERT (pivcol [IN] == EMPTY) ;
/* remove the failed pivcol [OUT] from candidate set */
ASSERT (pivcol [OUT] == Work->Candidates [jcand [OUT]]) ;
remove_candidate (jcand [OUT], Work, Symbolic) ;
Work->ndiscard++ ;
/* delete all of the tuples, and all contributions to this column */
DEBUG1 (("Prune tuples of dead outcol: "ID"\n", pivcol [OUT])) ;
Col_tlen [pivcol [OUT]] = 0 ;
UMF_mem_free_tail_block (Numeric, Col_tuples [pivcol [OUT]]) ;
Col_tuples [pivcol [OUT]] = 0 ;
/* no pivot found at all */
return (UMFPACK_WARNING_singular_matrix) ;
}
/* ------------------------------------------------------------------ */
if (freebie [IN])
{
/* the "in" row is the same as the "in" row for the "in" column */
Woi = Fcols ;
rdeg [OUT][IN] = rdeg [IN][IN] ;
DEBUG4 (("Freebie in, row "ID"\n", pivrow [IN][IN])) ;
}
if (freebie [OUT])
{
/* the "out" row is the same as the "out" row for the "in" column */
Woo = Wio ;
rdeg [OUT][OUT] = rdeg [IN][OUT] ;
DEBUG4 (("Freebie out, row "ID"\n", pivrow [IN][OUT])) ;
}
/* ------------------------------------------------------------------ */
/* evaluate OUT_IN option */
/* ------------------------------------------------------------------ */
if (pivrow [OUT][IN] != EMPTY)
{
/* The current front would become an Lson of the new front.
* The candidate pivot row is in the current front, but the
* candidate pivot column is not. */
ASSERT (fnrows > 0 && fncols >= 0) ;
did_rowmerge = (cdeg_out == 0) ;
if (did_rowmerge)
{
/* pivrow [OUT][IN] was found via row merge search */
/* it is not (yet) in the pivot column pattern (add it now) */
DEBUGm4 (("did row merge OUT col, IN row\n")) ;
Wm [0] = pivrow [OUT][IN] ;
CLEAR (Wx [0]) ;
cdeg_out = 1 ;
ASSERT (nr_out == EMPTY) ;
}
nc = rdeg [OUT][IN] - fncols ;
ASSERT (nc >= 1) ;
/* count rows not in current front */
nr_out = 0 ;
#ifndef NDEBUG
debug_ok = FALSE ;
#endif
for (i = 0 ; i < cdeg_out ; i++)
{
row = Wm [i] ;
ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
if (Frpos [row] < 0 || Frpos [row] >= fnrows) nr_out++ ;
#ifndef NDEBUG
/* we must see the pivot row somewhere */
if (row == pivrow [OUT][IN])
{
ASSERT (Frpos [row] >= 0) ;
debug_ok = TRUE ;
}
#endif
}
ASSERT (debug_ok) ;
thiscost =
/* each column in front grows by nr_out: */
(nr_out * fncols) +
/* new cols not affected by front: */
((nc-1) * (cdeg_out-1)) ;
/* check the cost of relaxed OUT_IN amalgamation */
extra_rows = ((fnrows-1) + nr_out) - (cdeg_out - 1) ;
ASSERT (extra_rows >= 0) ;
ASSERT (fnrows + nr_out == extra_rows + cdeg_out) ;
extra_zeros = (nc-1) * extra_rows ; /* symbolic fill-in */
ASSERT (fnrows + nr_out == cdeg_out + extra_rows) ;
ASSERT (fncols + nc == rdeg [OUT][IN]) ;
/* size of relaxed front (after pivot row removed): */
fnrows_new [OUT][IN] = (fnrows-1) + nr_out ;
fncols_new [OUT][IN] = fncols + (nc-1) ;
relaxed_front = fnrows_new [OUT][IN] * fncols_new [OUT][IN] ;
/* do relaxed amalgamation if the extra zeros are no more */
/* than a fraction (default 0.25) of the relaxed front */
/* if relax = 0: no extra zeros allowed */
/* if relax = +inf: always amalgamate */
if (did_rowmerge)
{
do_extend = FALSE ;
}
else
{
/* relax parameter uses a double relop, but ignore NaN case: */
if (extra_zeros == 0)
{
do_extend = TRUE ;
}
else
{
do_extend = ((double) extra_zeros) <
(relax1 * (double) relaxed_front) ;
}
}
if (do_extend)
{
/* count the cost of relaxed amalgamation */
thiscost += extra_zeros ;
DEBUG2 (("Evaluating option OUT-IN:\n")) ;
DEBUG2 ((" Work->fnzeros "ID" fnpiv "ID" nr_out "ID" nc "ID"\n",
Work->fnzeros, fnpiv, nr_out, nc)) ;
DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
/* determine if BLAS-3 update to be applied before extending. */
/* update if too many zero entries accumulate in the LU block */
fnzeros = Work->fnzeros + fnpiv * (nr_out + nc) ;
DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
new_LUsize = (fnpiv+1) * (fnrows + nr_out + fncols + nc) ;
DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
/* RELAX3 parameter uses a double relop, ignore NaN case: */
do_update = fnpiv > 0 &&
(((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ;
DEBUG2 (("do_update "ID"\n", do_update))
}
else
{
/* the current front would not be extended */
do_update = fnpiv > 0 ;
fnzeros = 0 ;
DEBUG2 (("OUT-IN do_update forced true: "ID"\n", do_update)) ;
/* The new front would be just big enough to hold the new
* pivot row and column. */
fnrows_new [OUT][IN] = cdeg_out - 1 ;
fncols_new [OUT][IN] = rdeg [OUT][IN] - 1 ;
}
DEBUG2 (("option OUT IN : nr "ID" nc "ID" cost "ID"("ID") relax "ID
"\n", nr_out, nc, thiscost, extra_zeros, do_extend)) ;
if (bestcost == EMPTY || thiscost < bestcost)
{
/* this is the best option seen so far */
Work->pivot_case = OUT_IN ;
bestcost = thiscost ;
Work->do_extend = do_extend ;
Work->do_update = do_update ;
new_fnzeros = fnzeros ;
}
}
/* ------------------------------------------------------------------ */
/* evaluate OUT_OUT option */
/* ------------------------------------------------------------------ */
if (pivrow [OUT][OUT] != EMPTY)
{
/* Neither the candidate pivot row nor the candidate pivot column
* are in the current front. */
ASSERT (fnrows >= 0 && fncols >= 0) ;
did_rowmerge = (cdeg_out == 0) ;
if (did_rowmerge)
{
/* pivrow [OUT][OUT] was found via row merge search */
/* it is not (yet) in the pivot column pattern (add it now) */
DEBUGm4 (("did row merge OUT col, OUT row\n")) ;
Wm [0] = pivrow [OUT][OUT] ;
CLEAR (Wx [0]) ;
cdeg_out = 1 ;
ASSERT (nr_out == EMPTY) ;
nr_out = 1 ;
}
if (fnrows == 0 && fncols == 0)
{
/* the current front is completely empty */
ASSERT (fnpiv == 0) ;
nc = rdeg [OUT][OUT] ;
extra_cols = 0 ;
nr_out = cdeg_out ;
extra_rows = 0 ;
extra_zeros = 0 ;
thiscost = (nc-1) * (cdeg_out-1) ; /* new columns only */
/* size of new front: */
fnrows_new [OUT][OUT] = nr_out-1 ;
fncols_new [OUT][OUT] = nc-1 ;
relaxed_front = fnrows_new [OUT][OUT] * fncols_new [OUT][OUT] ;
}
else
{
/* count rows not in current front */
if (nr_out == EMPTY)
{
nr_out = 0 ;
#ifndef NDEBUG
debug_ok = FALSE ;
#endif
for (i = 0 ; i < cdeg_out ; i++)
{
row = Wm [i] ;
ASSERT (row >= 0 && row < n_row) ;
ASSERT (NON_PIVOTAL_ROW (row)) ;
if (Frpos [row] < 0 || Frpos [row] >= fnrows) nr_out++ ;
#ifndef NDEBUG
/* we must see the pivot row somewhere */
if (row == pivrow [OUT][OUT])
{
ASSERT (Frpos [row] < 0 || Frpos [row] >= fnrows) ;
debug_ok = TRUE ;
}
#endif
}
ASSERT (debug_ok) ;
}
/* count columns not in current front */
nc = 0 ;
#ifndef NDEBUG
debug_ok = FALSE ;
#endif
for (i = 0 ; i < rdeg [OUT][OUT] ; i++)
{
col = Woo [i] ;
ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
if (Fcpos [col] < 0) nc++ ;
#ifndef NDEBUG
/* we must see the pivot column somewhere */
if (col == pivcol [OUT])
{
ASSERT (Fcpos [col] < 0) ;
debug_ok = TRUE ;
}
#endif
}
ASSERT (debug_ok) ;
extra_cols = (fncols + (nc-1)) - (rdeg [OUT][OUT] - 1) ;
extra_rows = (fnrows + (nr_out-1)) - (cdeg_out - 1) ;
ASSERT (extra_rows >= 0) ;
ASSERT (extra_cols >= 0) ;
extra_zeros = ((nc-1) * extra_rows) + ((nr_out-1) * extra_cols);
ASSERT (fnrows + nr_out == cdeg_out + extra_rows) ;
ASSERT (fncols + nc == rdeg [OUT][OUT] + extra_cols) ;
thiscost =
/* new columns: */
((nc-1) * (cdeg_out-1)) +
/* old columns in front grow by nr_out-1: */
((nr_out-1) * (fncols - extra_cols)) ;
/* size of relaxed front: */
fnrows_new [OUT][OUT] = fnrows + (nr_out-1) ;
fncols_new [OUT][OUT] = fncols + (nc-1) ;
relaxed_front = fnrows_new [OUT][OUT] * fncols_new [OUT][OUT] ;
}
/* do relaxed amalgamation if the extra zeros are no more */
/* than a fraction (default 0.25) of the relaxed front */
/* if relax = 0: no extra zeros allowed */
/* if relax = +inf: always amalgamate */
if (did_rowmerge)
{
do_extend = FALSE ;
}
else
{
/* relax parameter uses a double relop, but ignore NaN case: */
if (extra_zeros == 0)
{
do_extend = TRUE ;
}
else
{
do_extend = ((double) extra_zeros) <
(relax1 * (double) relaxed_front) ;
}
}
if (do_extend)
{
/* count the cost of relaxed amalgamation */
thiscost += extra_zeros ;
DEBUG2 (("Evaluating option OUT-OUT:\n")) ;
DEBUG2 (("Work->fnzeros "ID" fnpiv "ID" nr_out "ID" nc "ID"\n",
Work->fnzeros, fnpiv, nr_out, nc)) ;
DEBUG2 (("fncols "ID" fnrows "ID"\n", fncols, fnrows)) ;
/* determine if BLAS-3 update to be applied before extending. */
/* update if too many zero entries accumulate in the LU block */
fnzeros = Work->fnzeros + fnpiv * (nr_out + nc) ;
DEBUG2 (("fnzeros "ID"\n", fnzeros)) ;
new_LUsize = (fnpiv+1) * (fnrows + nr_out + fncols + nc) ;
DEBUG2 (("new_LUsize "ID"\n", new_LUsize)) ;
/* RELAX3 parameter uses a double relop, ignore NaN case: */
do_update = fnpiv > 0 &&
(((double) fnzeros) / ((double) new_LUsize)) > RELAX3 ;
DEBUG2 (("do_update "ID"\n", do_update))
}
else
{
/* the current front would not be extended */
do_update = fnpiv > 0 ;
fnzeros = 0 ;
DEBUG2 (("OUT-OUT do_update forced true: "ID"\n", do_update)) ;
/* The new front would be just big enough to hold the new
* pivot row and column. */
fnrows_new [OUT][OUT] = cdeg_out - 1 ;
fncols_new [OUT][OUT] = rdeg [OUT][OUT] - 1 ;
}
DEBUG2 (("option OUT OUT: nr "ID" nc "ID" cost "ID"\n",
rdeg [OUT][OUT], cdeg_out, thiscost)) ;
if (bestcost == EMPTY || thiscost < bestcost)
{
/* this is the best option seen so far */
Work->pivot_case = OUT_OUT ;
bestcost = thiscost ;
Work->do_extend = do_extend ;
Work->do_update = do_update ;
new_fnzeros = fnzeros ;
}
}
}
/* At this point, a structural pivot has been found. */
/* It may be numerically zero, however. */
ASSERT (Work->pivot_case != EMPTY) ;
DEBUG2 (("local search, best option "ID", best cost "ID"\n",
Work->pivot_case, bestcost)) ;
/* ====================================================================== */
/* Pivot row and column, and extension, now determined */
/* ====================================================================== */
Work->fnzeros = new_fnzeros ;
/* ---------------------------------------------------------------------- */
/* finalize the pivot row and column */
/* ---------------------------------------------------------------------- */
switch (Work->pivot_case)
{
case IN_IN:
DEBUG2 (("IN-IN option selected\n")) ;
ASSERT (fnrows > 0 && fncols > 0) ;
Work->pivcol_in_front = TRUE ;
Work->pivrow_in_front = TRUE ;
Work->pivcol = pivcol [IN] ;
Work->pivrow = pivrow [IN][IN] ;
Work->ccdeg = nr_in ;
Work->Wrow = Fcols ;
Work->rrdeg = rdeg [IN][IN] ;
jj = jcand [IN] ;
Work->fnrows_new = fnrows_new [IN][IN] ;
Work->fncols_new = fncols_new [IN][IN] ;
break ;
case IN_OUT:
DEBUG2 (("IN-OUT option selected\n")) ;
ASSERT (fnrows >= 0 && fncols > 0) ;
Work->pivcol_in_front = TRUE ;
Work->pivrow_in_front = FALSE ;
Work->pivcol = pivcol [IN] ;
Work->pivrow = pivrow [IN][OUT] ;
Work->ccdeg = nr_in ;
Work->Wrow = Wio ;
Work->rrdeg = rdeg [IN][OUT] ;
jj = jcand [IN] ;
Work->fnrows_new = fnrows_new [IN][OUT] ;
Work->fncols_new = fncols_new [IN][OUT] ;
break ;
case OUT_IN:
DEBUG2 (("OUT-IN option selected\n")) ;
ASSERT (fnrows > 0 && fncols >= 0) ;
Work->pivcol_in_front = FALSE ;
Work->pivrow_in_front = TRUE ;
Work->pivcol = pivcol [OUT] ;
Work->pivrow = pivrow [OUT][IN] ;
Work->ccdeg = cdeg_out ;
/* Wrow might be equivalenced to Fcols (Freebie in): */
Work->Wrow = Woi ;
Work->rrdeg = rdeg [OUT][IN] ;
/* Work->Wrow[0..fncols-1] is not there. See Fcols instead */
jj = jcand [OUT] ;
Work->fnrows_new = fnrows_new [OUT][IN] ;
Work->fncols_new = fncols_new [OUT][IN] ;
break ;
case OUT_OUT:
DEBUG2 (("OUT-OUT option selected\n")) ;
ASSERT (fnrows >= 0 && fncols >= 0) ;
Work->pivcol_in_front = FALSE ;
Work->pivrow_in_front = FALSE ;
Work->pivcol = pivcol [OUT] ;
Work->pivrow = pivrow [OUT][OUT] ;
Work->ccdeg = cdeg_out ;
/* Wrow might be equivalenced to Wio (Freebie out): */
Work->Wrow = Woo ;
Work->rrdeg = rdeg [OUT][OUT] ;
jj = jcand [OUT] ;
Work->fnrows_new = fnrows_new [OUT][OUT] ;
Work->fncols_new = fncols_new [OUT][OUT] ;
break ;
}
ASSERT (IMPLIES (fnrows == 0 && fncols == 0, Work->pivot_case == OUT_OUT)) ;
if (!Work->pivcol_in_front && pivcol [IN] != EMPTY)
{
/* clear Frpos if pivcol [IN] was searched, but not selected */
for (i = fnrows ; i < cdeg_in ; i++)
{
Frpos [Frows [i]] = EMPTY;
}
}
/* ---------------------------------------------------------------------- */
/* Pivot row and column have been found */
/* ---------------------------------------------------------------------- */
/* ---------------------------------------------------------------------- */
/* remove pivot column from candidate pivot column set */
/* ---------------------------------------------------------------------- */
ASSERT (jj >= 0 && jj < Work->nCandidates) ;
ASSERT (Work->pivcol == Work->Candidates [jj]) ;
remove_candidate (jj, Work, Symbolic) ;
/* ---------------------------------------------------------------------- */
/* check for frontal matrix growth */
/* ---------------------------------------------------------------------- */
DEBUG1 (("Check frontal growth:\n")) ;
DEBUG1 (("fnrows_new "ID" + 1 = "ID", fnr_curr "ID"\n",
Work->fnrows_new, Work->fnrows_new + 1, fnr_curr)) ;
DEBUG1 (("fncols_new "ID" + 1 = "ID", fnc_curr "ID"\n",
Work->fncols_new, Work->fncols_new + 1, fnc_curr)) ;
Work->do_grow = (Work->fnrows_new + 1 > fnr_curr
|| Work->fncols_new + 1 > fnc_curr) ;
if (Work->do_grow)
{
DEBUG0 (("\nNeed to grow frontal matrix, force do_update true\n")) ;
/* If the front must grow, then apply the pending updates and remove
* the current pivot rows/columns from the front prior to growing the
* front. This frees up as much space as possible for the new front. */
if (!Work->do_update && fnpiv > 0)
{
/* This update would not have to be done if the current front
* was big enough. */
Work->nforced++ ;
Work->do_update = TRUE ;
}
}
/* ---------------------------------------------------------------------- */
/* current pivot column */
/* ---------------------------------------------------------------------- */
/*
c1) If pivot column index is in the current front:
The pivot column pattern is in Frows [0 .. fnrows-1] and
the extension is in Frows [fnrows ... fnrows+ccdeg-1].
Frpos [Frows [0 .. fnrows+ccdeg-1]] is
equal to 0 .. fnrows+ccdeg-1. Wm is not needed.
The values are in Wy [0 .. fnrows+ccdeg-1].
c2) Otherwise, if the pivot column index is not in the current front:
c2a) If the front is being extended, old row indices in the the
pivot column pattern are in Frows [0 .. fnrows-1].
All entries are in Wm [0 ... ccdeg-1], with values in
Wx [0 .. ccdeg-1]. These may include entries already in
Frows [0 .. fnrows-1].
Frpos [Frows [0 .. fnrows-1]] is equal to 0 .. fnrows-1.
Frpos [Wm [0 .. ccdeg-1]] for new entries is < 0.
c2b) If the front is not being extended, then the entire pivot
column pattern is in Wm [0 .. ccdeg-1]. It includes
the pivot row index. It is does not contain the pattern
Frows [0..fnrows-1]. The intersection of these two
sets may or may not be empty. The values are in Wx [0..ccdeg-1]
In both cases c1 and c2, Frpos [Frows [0 .. fnrows-1]] is equal
to 0 .. fnrows-1, which is the pattern of the current front.
Any entry of Frpos that is not specified above is < 0.
*/
#ifndef NDEBUG
DEBUG2 (("\n\nSEARCH DONE: Pivot col "ID" in: ("ID") pivot row "ID" in: ("ID
") extend: "ID"\n\n", Work->pivcol, Work->pivcol_in_front,
Work->pivrow, Work->pivrow_in_front, Work->do_extend)) ;
UMF_dump_rowcol (1, Numeric, Work, Work->pivcol, !Symbolic->fixQ) ;
DEBUG2 (("Pivot col "ID": fnrows "ID" ccdeg "ID"\n", Work->pivcol, fnrows,
Work->ccdeg)) ;
if (Work->pivcol_in_front) /* case c1 */
{
Int found = FALSE ;
DEBUG3 (("Pivcol in front\n")) ;
for (i = 0 ; i < fnrows ; i++)
{
row = Frows [i] ;
DEBUG3 ((ID": row:: "ID" in front ", i, row)) ;
ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
ASSERT (Frpos [row] == i) ;
EDEBUG3 (Wy [i]) ;
if (row == Work->pivrow)
{
DEBUG3 ((" <- pivrow")) ;
found = TRUE ;
}
DEBUG3 (("\n")) ;
}
ASSERT (found == Work->pivrow_in_front) ;
found = FALSE ;
for (i = fnrows ; i < fnrows + Work->ccdeg ; i++)
{
row = Frows [i] ;
DEBUG3 ((ID": row:: "ID" (new)", i, row)) ;
ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
ASSERT (Frpos [row] == i) ;
EDEBUG3 (Wy [i]) ;
if (row == Work->pivrow)
{
DEBUG3 ((" <- pivrow")) ;
found = TRUE ;
}
DEBUG3 (("\n")) ;
}
ASSERT (found == !Work->pivrow_in_front) ;
}
else
{
if (Work->do_extend)
{
Int found = FALSE ;
DEBUG3 (("Pivcol not in front (extend)\n")) ;
for (i = 0 ; i < fnrows ; i++)
{
row = Frows [i] ;
DEBUG3 ((ID": row:: "ID" in front ", i, row)) ;
ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
ASSERT (Frpos [row] == i) ;
if (row == Work->pivrow)
{
DEBUG3 ((" <- pivrow")) ;
found = TRUE ;
}
DEBUG3 (("\n")) ;
}
ASSERT (found == Work->pivrow_in_front) ;
found = FALSE ;
DEBUG3 (("----\n")) ;
for (i = 0 ; i < Work->ccdeg ; i++)
{
row = Wm [i] ;
ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
DEBUG3 ((ID": row:: "ID" ", i, row)) ;
EDEBUG3 (Wx [i]) ;
if (Frpos [row] < 0)
{
DEBUG3 ((" (new) ")) ;
}
if (row == Work->pivrow)
{
DEBUG3 ((" <- pivrow")) ;
found = TRUE ;
/* ... */
if (Work->pivrow_in_front) ASSERT (Frpos [row] >= 0) ;
else ASSERT (Frpos [row] < 0) ;
}
DEBUG3 (("\n")) ;
}
ASSERT (found) ;
}
else
{
Int found = FALSE ;
DEBUG3 (("Pivcol not in front (no extend)\n")) ;
for (i = 0 ; i < Work->ccdeg ; i++)
{
row = Wm [i] ;
ASSERT (row >= 0 && row < n_row && NON_PIVOTAL_ROW (row)) ;
DEBUG3 ((ID": row:: "ID" ", i, row)) ;
EDEBUG3 (Wx [i]) ;
DEBUG3 ((" (new) ")) ;
if (row == Work->pivrow)
{
DEBUG3 ((" <- pivrow")) ;
found = TRUE ;
}
DEBUG3 (("\n")) ;
}
ASSERT (found) ;
}
}
#endif
/* ---------------------------------------------------------------------- */
/* current pivot row */
/* ---------------------------------------------------------------------- */
/*
r1) If the pivot row index is in the current front:
The pivot row pattern is in Fcols [0..fncols-1] and the extenson is
in Wrow [fncols .. rrdeg-1]. If the pivot column is in the current
front, then Fcols and Wrow are equivalenced.
r2) If the pivot row index is not in the current front:
r2a) If the front is being extended, the pivot row pattern is in
Fcols [0 .. fncols-1]. New entries are in Wrow [0 .. rrdeg-1],
but these may include entries already in Fcols [0 .. fncols-1].
r2b) Otherwise, the pivot row pattern is Wrow [0 .. rrdeg-1].
Fcpos [Fcols [0..fncols-1]] is (0..fncols-1) * fnr_curr.
All other entries in Fcpos are < 0.
These conditions are asserted below.
------------------------------------------------------------------------
Other items in Work structure that are relevant:
pivcol: the pivot column index
pivrow: the pivot column index
rrdeg:
ccdeg:
fnrows: the number of rows in the currnt contribution block
fncols: the number of columns in the current contribution block
fnrows_new: the number of rows in the new contribution block
fncols_new: the number of rows in the new contribution block
------------------------------------------------------------------------
*/
#ifndef NDEBUG
UMF_dump_rowcol (0, Numeric, Work, Work->pivrow, TRUE) ;
DEBUG2 (("Pivot row "ID":\n", Work->pivrow)) ;
if (Work->pivrow_in_front)
{
Int found = FALSE ;
for (i = 0 ; i < fncols ; i++)
{
col = Fcols [i] ;
DEBUG3 ((" col:: "ID" in front\n", col)) ;
ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
ASSERT (Fcpos [col] == i * fnr_curr) ;
if (col == Work->pivcol) found = TRUE ;
}
ASSERT (found == Work->pivcol_in_front) ;
found = FALSE ;
ASSERT (IMPLIES (Work->pivcol_in_front, Fcols == Work->Wrow)) ;
for (i = fncols ; i < Work->rrdeg ; i++)
{
col = Work->Wrow [i] ;
ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
ASSERT (Fcpos [col] < 0) ;
if (col == Work->pivcol) found = TRUE ;
else DEBUG3 ((" col:: "ID" (new)\n", col)) ;
}
ASSERT (found == !Work->pivcol_in_front) ;
}
else
{
if (Work->do_extend)
{
Int found = FALSE ;
for (i = 0 ; i < fncols ; i++)
{
col = Fcols [i] ;
DEBUG3 ((" col:: "ID" in front\n", col)) ;
ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
ASSERT (Fcpos [col] == i * fnr_curr) ;
if (col == Work->pivcol) found = TRUE ;
}
ASSERT (found == Work->pivcol_in_front) ;
found = FALSE ;
for (i = 0 ; i < Work->rrdeg ; i++)
{
col = Work->Wrow [i] ;
ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
if (Fcpos [col] >= 0) continue ;
if (col == Work->pivcol) found = TRUE ;
else DEBUG3 ((" col:: "ID" (new, extend)\n", col)) ;
}
ASSERT (found == !Work->pivcol_in_front) ;
}
else
{
Int found = FALSE ;
for (i = 0 ; i < Work->rrdeg ; i++)
{
col = Work->Wrow [i] ;
ASSERT (col >= 0 && col < n_col && NON_PIVOTAL_COL (col)) ;
if (col == Work->pivcol) found = TRUE ;
else DEBUG3 ((" col:: "ID" (all new)\n", col)) ;
}
ASSERT (found) ;
}
}
#endif
/* ---------------------------------------------------------------------- */
/* determine whether to do scan2-row and scan2-col */
/* ---------------------------------------------------------------------- */
if (Work->do_extend)
{
Work->do_scan2row = (fncols > 0) ;
Work->do_scan2col = (fnrows > 0) ;
}
else
{
Work->do_scan2row = (fncols > 0) && Work->pivrow_in_front ;
Work->do_scan2col = (fnrows > 0) && Work->pivcol_in_front ;
}
/* ---------------------------------------------------------------------- */
DEBUG2 (("LOCAL SEARCH DONE: pivot column "ID" pivot row: "ID"\n",
Work->pivcol, Work->pivrow)) ;
DEBUG2 (("do_extend: "ID"\n", Work->do_extend)) ;
DEBUG2 (("do_update: "ID"\n", Work->do_update)) ;
DEBUG2 (("do_grow: "ID"\n", Work->do_grow)) ;
/* ---------------------------------------------------------------------- */
/* keep track of the diagonal */
/* ---------------------------------------------------------------------- */
if (Symbolic->prefer_diagonal
&& Work->pivcol < Work->n_col - Symbolic->nempty_col)
{
Diagonal_map = Work->Diagonal_map ;
Diagonal_imap = Work->Diagonal_imap ;
ASSERT (Diagonal_map != (Int *) NULL) ;
ASSERT (Diagonal_imap != (Int *) NULL) ;
row2 = Diagonal_map [Work->pivcol] ;
col2 = Diagonal_imap [Work->pivrow] ;
if (row2 < 0)
{
/* this was an off-diagonal pivot row */
Work->noff_diagonal++ ;
row2 = UNFLIP (row2) ;
}
ASSERT (Diagonal_imap [row2] == Work->pivcol) ;
ASSERT (UNFLIP (Diagonal_map [col2]) == Work->pivrow) ;
if (row2 != Work->pivrow)
{
/* swap the diagonal map to attempt to maintain symmetry later on.
* Also mark the map for col2 (via FLIP) to denote that the entry
* now on the diagonal is not the original entry on the diagonal. */
DEBUG0 (("Unsymmetric pivot\n")) ;
Diagonal_map [Work->pivcol] = FLIP (Work->pivrow) ;
Diagonal_imap [Work->pivrow] = Work->pivcol ;
Diagonal_map [col2] = FLIP (row2) ;
Diagonal_imap [row2] = col2 ;
}
ASSERT (n_row == n_col) ;
#ifndef NDEBUG
UMF_dump_diagonal_map (Diagonal_map, Diagonal_imap, Symbolic->n1,
Symbolic->n_col, Symbolic->nempty_col) ;
#endif
}
return (UMFPACK_OK) ;
}
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