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/* ========================================================================== */
/* === UMF_scale_column ===================================================== */
/* ========================================================================== */
/* -------------------------------------------------------------------------- */
/* UMFPACK Copyright (c) Timothy A. Davis, CISE, */
/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
/* -------------------------------------------------------------------------- */
/*
Scale the current pivot column, move the pivot row and column into place,
and log the permutation.
*/
#include "umf_internal.h"
#include "umf_mem_free_tail_block.h"
#include "umf_scale.h"
/* ========================================================================== */
/* === shift_pivot_row ====================================================== */
/* ========================================================================== */
/* Except for the BLAS, most of the time is typically spent in the following
* shift_pivot_row routine. It copies the pivot row into the U block, and
* then fills in the whole in the C block by shifting the last row of C into
* the row vacated by the pivot row.
*/
PRIVATE void shift_pivot_row (Entry *Fd, Entry *Fs, Entry *Fe, Int len, Int d)
{
Int j ;
#pragma ivdep
for (j = 0 ; j < len ; j++)
{
Fd [j] = Fs [j*d] ;
Fs [j*d] = Fe [j*d] ;
}
}
/* ========================================================================== */
/* === UMF_scale_column ===================================================== */
/* ========================================================================== */
GLOBAL void UMF_scale_column
(
NumericType *Numeric,
WorkType *Work
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Entry pivot_value ;
Entry *Fcol, *Flublock, *Flblock, *Fublock, *Fcblock ;
Int k, k1, fnr_curr, fnrows, fncols, *Frpos, *Fcpos, pivrow, pivcol,
*Frows, *Fcols, fnc_curr, fnpiv, *Row_tuples, nb,
*Col_tuples, *Rperm, *Cperm, fspos, col2, row2 ;
#ifndef NDEBUG
Int *Col_degree, *Row_degree ;
#endif
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
fnrows = Work->fnrows ;
fncols = Work->fncols ;
fnpiv = Work->fnpiv ;
/* ---------------------------------------------------------------------- */
Rperm = Numeric->Rperm ;
Cperm = Numeric->Cperm ;
/* ---------------------------------------------------------------------- */
Flublock = Work->Flublock ;
Flblock = Work->Flblock ;
Fublock = Work->Fublock ;
Fcblock = Work->Fcblock ;
fnr_curr = Work->fnr_curr ;
fnc_curr = Work->fnc_curr ;
Frpos = Work->Frpos ;
Fcpos = Work->Fcpos ;
Frows = Work->Frows ;
Fcols = Work->Fcols ;
pivrow = Work->pivrow ;
pivcol = Work->pivcol ;
ASSERT (pivrow >= 0 && pivrow < Work->n_row) ;
ASSERT (pivcol >= 0 && pivcol < Work->n_col) ;
#ifndef NDEBUG
Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
#endif
Row_tuples = Numeric->Uip ;
Col_tuples = Numeric->Lip ;
nb = Work->nb ;
#ifndef NDEBUG
ASSERT (fnrows == Work->fnrows_new + 1) ;
ASSERT (fncols == Work->fncols_new + 1) ;
DEBUG1 (("SCALE COL: fnrows "ID" fncols "ID"
", fnrows, fncols)) ;
DEBUG2 (("
Frontal matrix, including all space:
"
"fnr_curr "ID" fnc_curr "ID" nb "ID"
"
"fnrows "ID" fncols "ID" fnpiv "ID"
",
fnr_curr, fnc_curr, nb, fnrows, fncols, fnpiv)) ;
DEBUG2 (("
Just the active part:
")) ;
DEBUG7 (("C block: ")) ;
UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ;
DEBUG7 (("L block: ")) ;
UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv);
DEBUG7 (("U' block: ")) ;
UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv) ;
DEBUG7 (("LU block: ")) ;
UMF_dump_dense (Flublock, nb, fnpiv, fnpiv) ;
#endif
/* ====================================================================== */
/* === Shift pivot row and column ======================================= */
/* ====================================================================== */
/* ---------------------------------------------------------------------- */
/* move pivot column into place */
/* ---------------------------------------------------------------------- */
/* Note that the pivot column is already in place. Just shift the last
* column into the position vacated by the pivot column. */
fspos = Fcpos [pivcol] ;
/* one less column in the contribution block */
fncols = --(Work->fncols) ;
if (fspos != fncols * fnr_curr)
{
Int fs = fspos / fnr_curr ;
DEBUG6 (("Shift pivot column in front
")) ;
DEBUG6 (("fspos: "ID" flpos: "ID"
", fspos, fncols * fnr_curr)) ;
/* ------------------------------------------------------------------ */
/* move Fe => Fs */
/* ------------------------------------------------------------------ */
/* column of the contribution block: */
{
/* Fs: current position of pivot column in contribution block */
/* Fe: position of last column in contribution block */
Int i ;
Entry *Fs, *Fe ;
Fs = Fcblock + fspos ;
Fe = Fcblock + fncols * fnr_curr ;
#pragma ivdep
for (i = 0 ; i < fnrows ; i++)
{
Fs [i] = Fe [i] ;
}
}
/* column of the U2 block */
{
/* Fs: current position of pivot column in U block */
/* Fe: last column in U block */
Int i ;
Entry *Fs, *Fe ;
Fs = Fublock + fs ;
Fe = Fublock + fncols ;
#pragma ivdep
for (i = 0 ; i < fnpiv ; i++)
{
Fs [i * fnc_curr] = Fe [i * fnc_curr] ;
}
}
/* move column Fe to Fs in the Fcols pattern */
col2 = Fcols [fncols] ;
Fcols [fs] = col2 ;
Fcpos [col2] = fspos ;
}
/* pivot column is no longer in the frontal matrix */
Fcpos [pivcol] = EMPTY ;
#ifndef NDEBUG
DEBUG2 (("
Frontal matrix after col swap, including all space:
"
"fnr_curr "ID" fnc_curr "ID" nb "ID"
"
"fnrows "ID" fncols "ID" fnpiv "ID"
",
fnr_curr, fnc_curr, nb,
fnrows, fncols, fnpiv)) ;
DEBUG2 (("
Just the active part:
")) ;
DEBUG7 (("C block: ")) ;
UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ;
DEBUG7 (("L block: ")) ;
UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv+1);
DEBUG7 (("U' block: ")) ;
UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv) ;
DEBUG7 (("LU block: ")) ;
UMF_dump_dense (Flublock, nb, fnpiv, fnpiv+1) ;
#endif
/* ---------------------------------------------------------------------- */
/* move pivot row into place */
/* ---------------------------------------------------------------------- */
fspos = Frpos [pivrow] ;
/* one less row in the contribution block */
fnrows = --(Work->fnrows) ;
DEBUG6 (("Swap/shift pivot row in front:
")) ;
DEBUG6 (("fspos: "ID" flpos: "ID"
", fspos, fnrows)) ;
if (fspos == fnrows)
{
/* ------------------------------------------------------------------ */
/* move Fs => Fd */
/* ------------------------------------------------------------------ */
DEBUG6 (("row case 1
")) ;
/* row of the contribution block: */
{
Int j ;
Entry *Fd, *Fs ;
Fd = Fublock + fnpiv * fnc_curr ;
Fs = Fcblock + fspos ;
#pragma ivdep
for (j = 0 ; j < fncols ; j++)
{
Fd [j] = Fs [j * fnr_curr] ;
}
}
/* row of the L2 block: */
if (Work->pivrow_in_front)
{
Int j ;
Entry *Fd, *Fs ;
Fd = Flublock + fnpiv ;
Fs = Flblock + fspos ;
#pragma ivdep
for (j = 0 ; j <= fnpiv ; j++)
{
Fd [j * nb] = Fs [j * fnr_curr] ;
}
}
else
{
Int j ;
Entry *Fd, *Fs ;
Fd = Flublock + fnpiv ;
Fs = Flblock + fspos ;
#pragma ivdep
for (j = 0 ; j < fnpiv ; j++)
{
ASSERT (IS_ZERO (Fs [j * fnr_curr])) ;
CLEAR (Fd [j * nb]) ;
}
Fd [fnpiv * nb] = Fs [fnpiv * fnr_curr] ;
}
}
else
{
/* ------------------------------------------------------------------ */
/* move Fs => Fd */
/* move Fe => Fs */
/* ------------------------------------------------------------------ */
DEBUG6 (("row case 2
")) ;
/* this is the most common case, by far */
/* row of the contribution block: */
{
/* Fd: destination of pivot row on U block */
/* Fs: current position of pivot row in contribution block */
/* Fe: position of last row in contribution block */
Entry *Fd, *Fs, *Fe ;
Fd = Fublock + fnpiv * fnc_curr ;
Fs = Fcblock + fspos ;
Fe = Fcblock + fnrows ;
shift_pivot_row (Fd, Fs, Fe, fncols, fnr_curr) ;
}
/* row of the L2 block: */
if (Work->pivrow_in_front)
{
/* Fd: destination of pivot row in LU block */
/* Fs: current position of pivot row in L block */
/* Fe: last row in L block */
Int j ;
Entry *Fd, *Fs, *Fe ;
Fd = Flublock + fnpiv ;
Fs = Flblock + fspos ;
Fe = Flblock + fnrows ;
#pragma ivdep
for (j = 0 ; j <= fnpiv ; j++)
{
Fd [j * nb] = Fs [j * fnr_curr] ;
Fs [j * fnr_curr] = Fe [j * fnr_curr] ;
}
}
else
{
Int j ;
Entry *Fd, *Fs, *Fe ;
Fd = Flublock + fnpiv ;
Fs = Flblock + fspos ;
Fe = Flblock + fnrows ;
#pragma ivdep
for (j = 0 ; j < fnpiv ; j++)
{
ASSERT (IS_ZERO (Fs [j * fnr_curr])) ;
CLEAR (Fd [j * nb]) ;
Fs [j * fnr_curr] = Fe [j * fnr_curr] ;
}
Fd [fnpiv * nb] = Fs [fnpiv * fnr_curr] ;
Fs [fnpiv * fnr_curr] = Fe [fnpiv * fnr_curr] ;
}
/* move row Fe to Fs in the Frows pattern */
row2 = Frows [fnrows] ;
Frows [fspos] = row2 ;
Frpos [row2] = fspos ;
}
/* pivot row is no longer in the frontal matrix */
Frpos [pivrow] = EMPTY ;
#ifndef NDEBUG
DEBUG2 (("
Frontal matrix after row swap, including all space:
"
"fnr_curr "ID" fnc_curr "ID" nb "ID"
"
"fnrows "ID" fncols "ID" fnpiv "ID"
",
Work->fnr_curr, Work->fnc_curr, Work->nb,
Work->fnrows, Work->fncols, Work->fnpiv)) ;
DEBUG2 (("
Just the active part:
")) ;
DEBUG7 (("C block: ")) ;
UMF_dump_dense (Fcblock, fnr_curr, fnrows, fncols) ;
DEBUG7 (("L block: ")) ;
UMF_dump_dense (Flblock, fnr_curr, fnrows, fnpiv+1);
DEBUG7 (("U' block: ")) ;
UMF_dump_dense (Fublock, fnc_curr, fncols, fnpiv+1) ;
DEBUG7 (("LU block: ")) ;
UMF_dump_dense (Flublock, nb, fnpiv+1, fnpiv+1) ;
#endif
/* ---------------------------------------------------------------------- */
/* Frpos [row] >= 0 for each row in pivot column pattern. */
/* offset into pattern is given by: */
/* Frpos [row] == offset - 1 */
/* Frpos [pivrow] is EMPTY */
/* Fcpos [col] >= 0 for each col in pivot row pattern. */
/* Fcpos [col] == (offset - 1) * fnr_curr */
/* Fcpos [pivcol] is EMPTY */
/* Fcols [0..fncols-1] is the pivot row pattern (excl pivot cols) */
/* Frows [0..fnrows-1] is the pivot col pattern (excl pivot rows) */
/* ====================================================================== */
/* === scale pivot column =============================================== */
/* ====================================================================== */
/* pivot column (except for pivot entry itself) */
Fcol = Flblock + fnpiv * fnr_curr ;
/* fnpiv-th pivot in frontal matrix located in Flublock (fnpiv, fnpiv) */
pivot_value = Flublock [fnpiv + fnpiv * nb] ;
/* this is the kth global pivot */
k = Work->npiv + fnpiv ;
DEBUG4 (("Pivot value: ")) ;
EDEBUG4 (pivot_value) ;
DEBUG4 (("
")) ;
UMF_scale (fnrows, pivot_value, Fcol) ;
/* ---------------------------------------------------------------------- */
/* deallocate the pivot row and pivot column tuples */
/* ---------------------------------------------------------------------- */
UMF_mem_free_tail_block (Numeric, Row_tuples [pivrow]) ;
UMF_mem_free_tail_block (Numeric, Col_tuples [pivcol]) ;
Row_tuples [pivrow] = 0 ;
Col_tuples [pivcol] = 0 ;
DEBUG5 (("number of pivots prior to this one: "ID"
", k)) ;
ASSERT (NON_PIVOTAL_ROW (pivrow)) ;
ASSERT (NON_PIVOTAL_COL (pivcol)) ;
/* save row and column inverse permutation */
k1 = ONES_COMPLEMENT (k) ;
Rperm [pivrow] = k1 ; /* aliased with Row_degree */
Cperm [pivcol] = k1 ; /* aliased with Col_degree */
ASSERT (!NON_PIVOTAL_ROW (pivrow)) ;
ASSERT (!NON_PIVOTAL_COL (pivcol)) ;
/* ---------------------------------------------------------------------- */
/* Keep track of the pivot order. This is the kth pivot row and column. */
/* ---------------------------------------------------------------------- */
/* keep track of pivot rows and columns in the LU, L, and U blocks */
ASSERT (fnpiv < MAXNB) ;
Work->Pivrow [fnpiv] = pivrow ;
Work->Pivcol [fnpiv] = pivcol ;
/* ====================================================================== */
/* === one step in the factorization is done ============================ */
/* ====================================================================== */
/* One more step is done, except for pending updates to the U and C blocks
* of this frontal matrix. Those are saved up, and applied by
* UMF_blas3_update when enough pivots have accumulated. Also, the
* LU factors for these pending pivots have not yet been stored. */
Work->fnpiv++ ;
#ifndef NDEBUG
DEBUG7 (("Current frontal matrix: (after pivcol scale)
")) ;
UMF_dump_current_front (Numeric, Work, TRUE) ;
#endif
}
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