GLOBAL void UMF_garbage_collection
(
NumericType *Numeric,
WorkType *Work,
Int drnew, /* compact current front to drnew-by-dcnew */
Int dcnew,
Int do_Fcpos
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Int size, e, n_row, n_col, nrows, ncols, nrowsleft, ncolsleft, prevsize,
csize, size2, i2, j2, i, j, cdeg, rdeg, *E, row, col,
*Rows, *Cols, *Rows2, *Cols2, nel, e2, *Row_tuples, *Col_tuples,
*Row_degree, *Col_degree ;
Entry *C, *C1, *C3, *C2 ;
Unit *psrc, *pdest, *p, *pnext ;
Element *epsrc, *epdest ;
#ifndef NDEBUG
Int nmark ;
#endif
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
Col_degree = Numeric->Cperm ; /* for NON_PIVOTAL_COL macro */
Row_degree = Numeric->Rperm ; /* for NON_PIVOTAL_ROW macro */
Row_tuples = Numeric->Uip ;
Col_tuples = Numeric->Lip ;
E = Work->E ;
n_row = Work->n_row ;
n_col = Work->n_col ;
/* note that the tuple lengths (Col_tlen and Row_tlen) are updated, but */
/* the tuple lists themselves are stale and are about to be destroyed */
/* and recreated. Do not attempt to scan them until they are recreated. */
#ifndef NDEBUG
DEBUGm1 (("::::GARBAGE COLLECTION::::\n")) ;
UMF_dump_memory (Numeric) ;
#endif
Numeric->ngarbage++ ;
/* ---------------------------------------------------------------------- */
/* delete the tuple lists by marking the blocks as free */
/* ---------------------------------------------------------------------- */
/* do not modify Row_tlen and Col_tlen */
/* those are needed for UMF_build_tuples */
for (row = 0 ; row < n_row ; row++)
{
if (NON_PIVOTAL_ROW (row) && Row_tuples [row])
{
DEBUG2 (("row "ID" tuples "ID"\n", row, Row_tuples [row])) ;
p = Numeric->Memory + Row_tuples [row] - 1 ;
DEBUG2 (("Freeing tuple list row "ID", p-S "ID", size "ID"\n",
row, (Int) (p-Numeric->Memory), p->header.size)) ;
ASSERT (p->header.size > 0) ;
ASSERT (p >= Numeric->Memory + Numeric->itail) ;
ASSERT (p < Numeric->Memory + Numeric->size) ;
p->header.size = -p->header.size ;
Row_tuples [row] = 0 ;
}
}
for (col = 0 ; col < n_col ; col++)
{
if (NON_PIVOTAL_COL (col) && Col_tuples [col])
{
DEBUG2 (("col "ID" tuples "ID"\n", col, Col_tuples [col])) ;
p = Numeric->Memory + Col_tuples [col] - 1 ;
DEBUG2 (("Freeing tuple list col "ID", p-S "ID", size "ID"\n",
col, (Int) (p-Numeric->Memory), p->header.size)) ;
ASSERT (p->header.size > 0) ;
ASSERT (p >= Numeric->Memory + Numeric->itail) ;
ASSERT (p < Numeric->Memory + Numeric->size) ;
p->header.size = -p->header.size ;
Col_tuples [col] = 0 ;
}
}
/* ---------------------------------------------------------------------- */
/* mark the elements, and compress the name space */
/* ---------------------------------------------------------------------- */
nel = Work->nel ;
ASSERT (nel < Work->elen) ;
#ifndef NDEBUG
nmark = 0 ;
UMF_dump_current_front (Numeric, Work, FALSE) ;
DEBUGm1 (("E [0] "ID" \n", E [0])) ;
ASSERT (IMPLIES (E [0],
Work->Flublock == (Entry *) (Numeric->Memory + E [0]))) ;
ASSERT (IMPLIES (Work->Flublock,
Work->Flublock == (Entry *) (Numeric->Memory + E [0]))) ;
ASSERT ((E [0] != 0) == (Work->Flublock != (Entry *) NULL)) ;
#endif
e2 = 0 ;
for (e = 0 ; e <= nel ; e++) /* for all elements in order of creation */
{
if (E [e])
{
psrc = Numeric->Memory + E [e] ;
psrc-- ; /* get the header of this block */
if (e > 0)
{
e2++ ; /* do not renumber element zero */
}
ASSERT (psrc->header.size > 0) ;
psrc->header.size = e2 ; /* store the new name in the header */
#ifndef NDEBUG
nmark++ ;
#endif
DEBUG7 ((ID":: Mark e "ID" at psrc-S "ID", new e "ID"\n",
nmark, e, (Int) (psrc-Numeric->Memory), e2)) ;
E [e] = 0 ;
if (e == Work->prior_element)
{
Work->prior_element = e2 ;
}
}
}
/* all 1..e2 are now in use (element zero may or may not be in use) */
Work->nel = e2 ;
nel = Work->nel ;
#ifndef NDEBUG
for (e = 0 ; e < Work->elen ; e++)
{
ASSERT (!E [e]) ;
}
#endif
/* ---------------------------------------------------------------------- */
/* compress the elements */
/* ---------------------------------------------------------------------- */
/* point to tail marker block of size 1 + header */
psrc = Numeric->Memory + Numeric->size - 2 ;
pdest = psrc ;
prevsize = psrc->header.prevsize ;
DEBUG7 (("Starting the compression:\n")) ;
while (prevsize > 0)
{
/* ------------------------------------------------------------------ */
/* move up to the next element above the current header, and */
/* get the element name and size */
/* (if it is an element, the name will be positive) */
/* ------------------------------------------------------------------ */
size = prevsize ;
psrc -= (size + 1) ;
e = psrc->header.size ;
prevsize = psrc->header.prevsize ;
/* top block at tail has prevsize of 0 */
/* a free block will have a negative size, so skip it */
/* otherwise, if size >= 0, it holds the element name, not the size */
DEBUG8 (("psrc-S: "ID" prevsize: "ID" size: "ID,
(Int) (psrc-Numeric->Memory), prevsize, size)) ;
if (e == 0)
{
/* -------------------------------------------------------------- */
/* this is the current frontal matrix */
/* -------------------------------------------------------------- */
Entry *F1, *F2, *Fsrc, *Fdst ;
Int c, r, k, dr, dc, gap, gap1, gap2, nb ;
/* shift the frontal matrix down */
F1 = (Entry *) (psrc + 1) ;
/* get the size of the current front. r and c could be zero */
k = Work->fnpiv ;
dr = Work->fnr_curr ;
dc = Work->fnc_curr ;
r = Work->fnrows ;
c = Work->fncols ;
nb = Work->nb ;
ASSERT ((dr >= 0 && (dr % 2) == 1) || dr == 0) ;
ASSERT (drnew >= 0) ;
if (drnew % 2 == 0)
{
/* make sure leading frontal matrix dimension is always odd */
drnew++ ;
}
drnew = MIN (dr, drnew) ;
ASSERT ((drnew >= 0 && (drnew % 2) == 1) || drnew == 0) ;
pnext = pdest ;
#ifndef NDEBUG
DEBUGm2 (("move front: dr "ID" dc "ID" r "ID" drnew "ID" c "ID
" dcnew " ID" k "ID"\n", dr, dc, r, drnew, c, dcnew, k)) ;
DEBUG7 (("\n")) ;
DEBUG7 ((ID":: Move current frontal matrix from: psrc-S: "ID" \n",
nmark, (Int) (psrc-Numeric->Memory))) ;
nmark-- ;
ASSERT (E [e] == 0) ;
ASSERT (Work->Flublock == F1) ;
ASSERT (Work->Flblock == Work->Flublock + nb*nb) ;
ASSERT (Work->Fublock == Work->Flblock + dr*nb) ;
ASSERT (Work->Fcblock == Work->Fublock + nb*dc) ;
DEBUG7 (("C block: ")) ;
UMF_dump_dense (Work->Fcblock, dr, r, c) ;
DEBUG7 (("L block: ")) ;
UMF_dump_dense (Work->Flblock, dr, r, k);
DEBUG7 (("U' block: ")) ;
UMF_dump_dense (Work->Fublock, dc, c, k) ;
DEBUG7 (("LU block: ")) ;
UMF_dump_dense (Work->Flublock, nb, k, k) ;
ASSERT (r <= drnew && c <= dcnew && drnew <= dr && dcnew <= dc) ;
#endif
/* compact frontal matrix to drnew-by-dcnew before moving it */
/* do not compact the LU block (nb-by-nb) */
/* compact the columns of L (from dr-by-nb to drnew-by-nb) */
Fsrc = Work->Flblock ;
Fdst = Work->Flblock ;
ASSERT (Fdst == F1 + nb*nb) ;
gap1 = dr - r ;
gap2 = drnew - r ;
ASSERT (gap1 >= 0) ;
for (j = 0 ; j < k ; j++)
{
for (i = 0 ; i < r ; i++)
{
*Fdst++ = *Fsrc++ ;
}
Fsrc += gap1 ;
Fdst += gap2 ;
}
ASSERT (Fdst == F1 + nb*nb + drnew*k) ;
Fdst += drnew * (nb - k) ;
/* compact the rows of U (U' from dc-by-nb to dcnew-by-nb) */
Fsrc = Work->Fublock ;
ASSERT (Fdst == F1 + nb*nb + drnew*nb) ;
gap1 = dc - c ;
gap2 = dcnew - c ;
for (i = 0 ; i < k ; i++)
{
for (j = 0 ; j < c ; j++)
{
*Fdst++ = *Fsrc++ ;
}
Fsrc += gap1 ;
Fdst += gap2 ;
}
ASSERT (Fdst == F1 + nb*nb + drnew*nb + dcnew*k) ;
Fdst += dcnew * (nb - k) ;
/* compact the columns of C (from dr-by-dc to drnew-by-dcnew) */
Fsrc = Work->Fcblock ;
ASSERT (Fdst == F1 + nb*nb + drnew*nb + nb*dcnew) ;
gap1 = dr - r ;
gap2 = drnew - r ;
for (j = 0 ; j < c ; j++)
{
for (i = 0 ; i < r ; i++)
{
*Fdst++ = *Fsrc++ ;
}
Fsrc += gap1 ;
Fdst += gap2 ;
}
ASSERT (Fdst == F1 + nb*nb + drnew*nb + nb*dcnew + drnew*c) ;
/* recompute Fcpos, if necessary */
if (do_Fcpos)
{
Int *Fcols, *Fcpos ;
Fcols = Work->Fcols ;
Fcpos = Work->Fcpos ;
for (j = 0 ; j < c ; j++)
{
col = Fcols [j] ;
ASSERT (col >= 0 && col < Work->n_col) ;
ASSERT (Fcpos [col] == j * dr) ;
Fcpos [col] = j * drnew ;
}
#ifndef NDEBUG
{
Int cnt = 0 ;
for (j = 0 ; j < Work->n_col ; j++)
{
if (Fcpos [j] != EMPTY) cnt++ ;
}
DEBUGm2 (("Recompute Fcpos cnt "ID" c "ID"\n", cnt, c)) ;
ASSERT (cnt == c) ;
}
#endif
}
#ifndef NDEBUG
DEBUGm2 (("Compacted front, drnew "ID" dcnew "ID"\n", drnew, dcnew)) ;
DEBUG7 (("C block: ")) ;
UMF_dump_dense (F1 + nb*nb + drnew*nb + nb*dcnew, drnew, r, c) ;
DEBUG7 (("L block: ")) ;
UMF_dump_dense (F1 + nb*nb, drnew, r, k) ;
DEBUG7 (("U block: ")) ;
UMF_dump_dense (F1 + nb*nb + drnew*nb, nb, k, c) ;
DEBUG7 (("LU block: ")) ;
UMF_dump_dense (F1, nb, k, k) ;
#endif
/* Compacted dimensions of the new frontal matrix. */
Work->fnr_curr = drnew ;
Work->fnc_curr = dcnew ;
Work->fcurr_size = (drnew + nb) * (dcnew + nb) ;
size = UNITS (Entry, Work->fcurr_size) ;
/* make sure the object doesn't evaporate. The front can have
* zero size (Work->fcurr_size = 0), but the size of the memory
* block containing it cannot have zero size. */
size = MAX (1, size) ;
/* get the destination of frontal matrix */
pnext->header.prevsize = size ;
pdest -= (size + 1) ;
F2 = (Entry *) (pdest + 1) ;
ASSERT ((unsigned Int) psrc + 1 + size <= (unsigned Int) pnext) ;
ASSERT (psrc <= pdest) ;
ASSERT (F1 <= F2) ;
/* move the C block first */
Fsrc = F1 + nb*nb + drnew*nb + nb*dcnew + drnew*c ;
Fdst = F2 + nb*nb + drnew*nb + nb*dcnew + drnew*c ;
gap = drnew - r ;
for (j = c-1 ; j >= 0 ; j--)
{
Fsrc -= gap ;
Fdst -= gap ;
/* move column j of C */
for (i = r-1 ; i >= 0 ; i--)
{
*--Fdst = *--Fsrc ;
}
}
ASSERT (Fsrc == F1 + nb*nb + drnew*nb + nb*dcnew) ;
ASSERT (Fdst == F2 + nb*nb + drnew*nb + nb*dcnew) ;
/* move the U block */
Fsrc -= dcnew * (nb - k) ;
Fdst -= dcnew * (nb - k) ;
ASSERT (Fsrc == F1 + nb*nb + drnew*nb + dcnew*k) ;
ASSERT (Fdst == F2 + nb*nb + drnew*nb + dcnew*k) ;
gap = dcnew - c ;
for (i = k-1 ; i >= 0 ; i--)
{
Fsrc -= gap ;
Fdst -= gap ;
for (j = c-1 ; j >= 0 ; j--)
{
*--Fdst = *--Fsrc ;
}
}
ASSERT (Fsrc == F1 + nb*nb + drnew*nb) ;
ASSERT (Fdst == F2 + nb*nb + drnew*nb) ;
/* move the L block */
Fsrc -= drnew * (nb - k) ;
Fdst -= drnew * (nb - k) ;
ASSERT (Fsrc == F1 + nb*nb + drnew*k) ;
ASSERT (Fdst == F2 + nb*nb + drnew*k) ;
gap = drnew - r ;
for (j = k-1 ; j >= 0 ; j--)
{
Fsrc -= gap ;
Fdst -= gap ;
for (i = r-1 ; i >= 0 ; i--)
{
*--Fdst = *--Fsrc ;
}
}
ASSERT (Fsrc == F1 + nb*nb) ;
ASSERT (Fdst == F2 + nb*nb) ;
/* move the LU block */
Fsrc -= nb * (nb - k) ;
Fdst -= nb * (nb - k) ;
ASSERT (Fsrc == F1 + nb*k) ;
ASSERT (Fdst == F2 + nb*k) ;
gap = nb - k ;
for (j = k-1 ; j >= 0 ; j--)
{
Fsrc -= gap ;
Fdst -= gap ;
for (i = k-1 ; i >= 0 ; i--)
{
*--Fdst = *--Fsrc ;
}
}
ASSERT (Fsrc == F1) ;
ASSERT (Fdst == F2) ;
E [0] = (pdest + 1) - Numeric->Memory ;
Work->Flublock = (Entry *) (Numeric->Memory + E [0]) ;
ASSERT (Work->Flublock == F2) ;
Work->Flblock = Work->Flublock + nb * nb ;
Work->Fublock = Work->Flblock + drnew * nb ;
Work->Fcblock = Work->Fublock + nb * dcnew ;
pdest->header.prevsize = 0 ;
pdest->header.size = size ;
#ifndef NDEBUG
DEBUG7 (("After moving compressed current frontal matrix:\n")) ;
DEBUG7 (("C block: ")) ;
UMF_dump_dense (Work->Fcblock, drnew, r, c) ;
DEBUG7 (("L block: ")) ;
UMF_dump_dense (Work->Flblock, drnew, r, k);
DEBUG7 (("U' block: ")) ;
UMF_dump_dense (Work->Fublock, dcnew, c, k) ;
DEBUG7 (("LU block: ")) ;
UMF_dump_dense (Work->Flublock, nb, k, k) ;
#endif
}
else if (e > 0)
{
/* -------------------------------------------------------------- */
/* this is an element, compress and move from psrc down to pdest */
/* -------------------------------------------------------------- */
#ifndef NDEBUG
DEBUG7 (("\n")) ;
DEBUG7 ((ID":: Move element "ID": from: "ID" \n",
nmark, e, (Int) (psrc-Numeric->Memory))) ;
nmark-- ;
ASSERT (e <= nel) ;
ASSERT (E [e] == 0) ;
#endif
/* -------------------------------------------------------------- */
/* get the element scalars, and pointers to C, Rows, and Cols: */
/* -------------------------------------------------------------- */
p = psrc + 1 ;
GET_ELEMENT (epsrc, p, Cols, Rows, ncols, nrows, C) ;
nrowsleft = epsrc->nrowsleft ;
ncolsleft = epsrc->ncolsleft ;
cdeg = epsrc->cdeg ;
rdeg = epsrc->rdeg ;
#ifndef NDEBUG
DEBUG7 ((" nrows "ID" nrowsleft "ID"\n", nrows, nrowsleft)) ;
DEBUG7 ((" ncols "ID" ncolsleft "ID"\n", ncols, ncolsleft)) ;
DEBUG8 ((" Rows:")) ;
for (i = 0 ; i < nrows ; i++) DEBUG8 ((" "ID, Rows [i])) ;
DEBUG8 (("\n Cols:")) ;
for (j = 0 ; j < ncols ; j++) DEBUG8 ((" "ID, Cols [j])) ;
DEBUG8 (("\n")) ;
#endif
/* -------------------------------------------------------------- */
/* determine the layout of the new element */
/* -------------------------------------------------------------- */
csize = nrowsleft * ncolsleft ;
size2 = UNITS (Element, 1)
+ UNITS (Int, nrowsleft + ncolsleft)
+ UNITS (Entry, csize) ;
DEBUG7 (("Old size "ID" New size "ID"\n", size, size2)) ;
pnext = pdest ;
pnext->header.prevsize = size2 ;
pdest -= (size2 + 1) ;
ASSERT (size2 <= size) ;
ASSERT ((unsigned Int) psrc + 1 + size <= (unsigned Int) pnext) ;
ASSERT (psrc <= pdest) ;
p = pdest + 1 ;
epdest = (Element *) p ;
p += UNITS (Element, 1) ;
Cols2 = (Int *) p ;
Rows2 = Cols2 + ncolsleft ;
p += UNITS (Int, nrowsleft + ncolsleft) ;
C2 = (Entry *) p ;
ASSERT (epdest >= epsrc) ;
ASSERT (Rows2 >= Rows) ;
ASSERT (Cols2 >= Cols) ;
ASSERT (C2 >= C) ;
ASSERT (p + UNITS (Entry, csize) == pnext) ;
/* -------------------------------------------------------------- */
/* move the contribution block */
/* -------------------------------------------------------------- */
/* overlap = psrc + size + 1 > pdest ; */
if (nrowsleft < nrows || ncolsleft < ncols)
{
/* ---------------------------------------------------------- */
/* compress contribution block in place prior to moving it */
/* ---------------------------------------------------------- */
DEBUG7 (("Compress C in place prior to move:\n"));
#ifndef NDEBUG
UMF_dump_dense (C, nrows, nrows, ncols) ;
#endif
C1 = C ;
C3 = C ;
for (j = 0 ; j < ncols ; j++)
{
if (Cols [j] >= 0)
{
for (i = 0 ; i < nrows ; i++)
{
if (Rows [i] >= 0)
{
*C3++ = C1 [i] ;
}
}
}
C1 += nrows ;
}
ASSERT (C3-C == csize) ;
DEBUG8 (("Newly compressed contrib. block (all in use):\n")) ;
#ifndef NDEBUG
UMF_dump_dense (C, nrowsleft, nrowsleft, ncolsleft) ;
#endif
}
/* shift the contribution block down */
C += csize ;
C2 += csize ;
for (i = 0 ; i < csize ; i++)
{
*--C2 = *--C ;
}
/* -------------------------------------------------------------- */
/* move the row indices */
/* -------------------------------------------------------------- */
i2 = nrowsleft ;
for (i = nrows - 1 ; i >= 0 ; i--)
{
ASSERT (Rows2+i2 >= Rows+i) ;
if (Rows [i] >= 0)
{
Rows2 [--i2] = Rows [i] ;
}
}
ASSERT (i2 == 0) ;
j2 = ncolsleft ;
for (j = ncols - 1 ; j >= 0 ; j--)
{
ASSERT (Cols2+j2 >= Cols+j) ;
if (Cols [j] >= 0)
{
Cols2 [--j2] = Cols [j] ;
}
}
ASSERT (j2 == 0) ;
/* -------------------------------------------------------------- */
/* construct the new header */
/* -------------------------------------------------------------- */
/* E [0...e] is now valid */
E [e] = (pdest + 1) - Numeric->Memory ;
epdest = (Element *) (pdest + 1) ;
epdest->next = EMPTY ; /* destroys the son list */
epdest->ncols = ncolsleft ;
epdest->nrows = nrowsleft ;
epdest->ncolsleft = ncolsleft ;
epdest->nrowsleft = nrowsleft ;
epdest->rdeg = rdeg ;
epdest->cdeg = cdeg ;
ASSERT (size2 <= size) ;
pdest->header.prevsize = 0 ;
pdest->header.size = size2 ;
DEBUG7 (("After moving it:\n")) ;
#ifndef NDEBUG
UMF_dump_element (Numeric, Work, e, FALSE) ;
#endif
}
#ifndef NDEBUG
else
{
DEBUG8 ((" free\n")) ;
}
#endif
DEBUG7 (("psrc "ID" tail "ID"\n",
(Int) (psrc-Numeric->Memory), Numeric->itail)) ;
}
ASSERT (psrc == Numeric->Memory + Numeric->itail) ;
ASSERT (nmark == 0) ;
/* ---------------------------------------------------------------------- */
/* final tail pointer */
/* ---------------------------------------------------------------------- */
ASSERT (pdest >= Numeric->Memory + Numeric->itail) ;
Numeric->itail = pdest - Numeric->Memory ;
pdest->header.prevsize = 0 ;
Numeric->ibig = EMPTY ;
Numeric->tail_usage = Numeric->size - Numeric->itail ;
/* ---------------------------------------------------------------------- */
/* clear the unused E [nel+1 .. Work->elen - 1] */
/* ---------------------------------------------------------------------- */
for (e = nel+1 ; e < Work->elen ; e++)
{
E [e] = 0 ;
}
#ifndef NDEBUG
UMF_dump_packed_memory (Numeric, Work) ;
#endif
DEBUG8 (("::::GARBAGE COLLECTION DONE::::\n")) ;
}
PRIVATE Int two_by_two /* returns # unmatched weak diagonals */
(
/* input, not modified */
Int n2, /* C is n2-by-n2 */
Int Cp [ ], /* size n2+1, column pointers for C */
Int Ci [ ], /* size snz = Cp [n2], row indices for C */
Int Degree [ ], /* Degree [i] = degree of row i of C+C' */
/* input, not defined on output */
Int Next [ ], /* Next [k] == IS_WEAK if k is a weak diagonal */
Int Ri [ ], /* Ri [i] is the length of row i in C */
/* output, not defined on input */
Int P [ ],
/* workspace, not defined on input or output */
Int Rp [ ],
Int Head [ ]
)
{
Int deg, newcol, row, col, p, p2, unmatched, k, j, j2, j_best, best, jdiff,
jdiff_best, jdeg, jdeg_best, cp, cp1, cp2, rp, rp1, rp2, maxdeg,
mindeg ;
/* ---------------------------------------------------------------------- */
/* place weak diagonals in the degree lists */
/* ---------------------------------------------------------------------- */
for (deg = 0 ; deg < n2 ; deg++)
{
Head [deg] = EMPTY ;
}
maxdeg = 0 ;
mindeg = Int_MAX ;
for (newcol = n2-1 ; newcol >= 0 ; newcol--)
{
if (Next [newcol] == IS_WEAK)
{
/* add this column to the list of weak nodes */
DEBUGm1 ((" newcol "ID" has a weak diagonal deg "ID"\n",
newcol, deg)) ;
deg = Degree [newcol] ;
ASSERT (deg >= 0 && deg < n2) ;
Next [newcol] = Head [deg] ;
Head [deg] = newcol ;
maxdeg = MAX (maxdeg, deg) ;
mindeg = MIN (mindeg, deg) ;
}
}
/* ---------------------------------------------------------------------- */
/* construct R = C' (C = strong entries in pruned submatrix) */
/* ---------------------------------------------------------------------- */
/* Ri [0..n2-1] is the length of each row of R */
/* use P as temporary pointer into the row form of R [ */
Rp [0] = 0 ;
for (row = 0 ; row < n2 ; row++)
{
Rp [row+1] = Rp [row] + Ri [row] ;
P [row] = Rp [row] ;
}
/* Ri no longer needed for row counts */
/* all entries in C are strong */
for (col = 0 ; col < n2 ; col++)
{
p2 = Cp [col+1] ;
for (p = Cp [col] ; p < p2 ; p++)
{
/* place the column index in row = Ci [p] */
Ri [P [Ci [p]]++] = col ;
}
}
/* contents of P no longer needed ] */
#ifndef NDEBUG
DEBUG0 (("==================R: row form of strong entries in A:\n")) ;
UMF_dump_col_matrix ((double *) NULL,
#ifdef COMPLEX
(double *) NULL,
#endif
Ri, Rp, n2, n2, Rp [n2]) ;
#endif
ASSERT (AMD_valid (n2, n2, Rp, Ri) == AMD_OK) ;
/* ---------------------------------------------------------------------- */
/* for each weak diagonal, find a pair of strong off-diagonal entries */
/* ---------------------------------------------------------------------- */
for (row = 0 ; row < n2 ; row++)
{
P [row] = EMPTY ;
}
unmatched = 0 ;
best = EMPTY ;
jdiff = EMPTY ;
jdeg = EMPTY ;
for (deg = mindeg ; deg <= maxdeg ; deg++)
{
/* find the next weak diagonal of lowest degree */
DEBUGm2 (("---------------------------------- Deg: "ID"\n", deg)) ;
for (k = Head [deg] ; k != EMPTY ; k = Next [k])
{
DEBUGm2 (("k: "ID"\n", k)) ;
if (P [k] == EMPTY)
{
/* C (k,k) is a weak diagonal entry. Find an index j != k such
* that C (j,k) and C (k,j) are both strong, and also such
* that Degree [j] is minimized. In case of a tie, pick
* the smallest index j. C and R contain the pattern of
* strong entries only.
*
* Note that row k of R and column k of C are both sorted. */
DEBUGm4 (("===== Weak diagonal k = "ID"\n", k)) ;
DEBUG1 (("Column k of C:\n")) ;
for (p = Cp [k] ; p < Cp [k+1] ; p++)
{
DEBUG1 ((" "ID": deg "ID"\n", Ci [p], Degree [Ci [p]]));
}
DEBUG1 (("Row k of R (strong entries only):\n")) ;
for (p = Rp [k] ; p < Rp [k+1] ; p++)
{
DEBUG1 ((" "ID": deg "ID"\n", Ri [p], Degree [Ri [p]]));
}
/* no (C (k,j), C (j,k)) pair exists yet */
j_best = EMPTY ;
jdiff_best = Int_MAX ;
jdeg_best = Int_MAX ;
/* pointers into column k (including values) */
cp1 = Cp [k] ;
cp2 = Cp [k+1] ;
cp = cp1 ;
/* pointers into row k (strong entries only, no values) */
rp1 = Rp [k] ;
rp2 = Rp [k+1] ;
rp = rp1 ;
/* while entries searched in column k and row k */
while (TRUE)
{
if (cp >= cp2)
{
/* no more entries in this column */
break ;
}
/* get C (j,k), which is strong */
j = Ci [cp] ;
if (rp >= rp2)
{
/* no more entries in this column */
break ;
}
/* get R (k,j2), which is strong */
j2 = Ri [rp] ;
if (j < j2)
{
/* C (j,k) is strong, but R (k,j) is not strong */
cp++ ;
continue ;
}
if (j2 < j)
{
/* C (k,j2) is strong, but R (j2,k) is not strong */
rp++ ;
continue ;
}
/* j == j2: C (j,k) is strong and R (k,j) is strong */
best = FALSE ;
if (P [j] == EMPTY)
{
/* j has not yet been matched */
jdeg = Degree [j] ;
jdiff = SCALAR_ABS (k-j) ;
DEBUG1 (("Try candidate j "ID" deg "ID" diff "ID
"\n", j, jdeg, jdiff)) ;
if (j_best == EMPTY)
{
/* this is the first candidate seen */
DEBUG1 ((" first\n")) ;
best = TRUE ;
}
else
{
if (jdeg < jdeg_best)
{
/* the degree of j is best seen so far. */
DEBUG1 ((" least degree\n")) ;
best = TRUE ;
}
else if (jdeg == jdeg_best)
{
/* degree of j and j_best are the same */
/* tie break by nearest node number */
if (jdiff < jdiff_best)
{
DEBUG1 ((" tie degree, closer\n")) ;
best = TRUE ;
}
else if (jdiff == jdiff_best)
{
/* |j-k| = |j_best-k|. For any given k
* and j_best there is only one other j
* than can be just as close as j_best.
* Tie break by picking the smaller of
* j and j_best */
DEBUG1 ((" tie degree, as close\n"));
best = j < j_best ;
}
}
else
{
/* j has higher degree than best so far */
best = FALSE ;
}
}
}
if (best)
{
/* j is best match for k */
/* found a strong pair, A (j,k) and A (k,j) */
DEBUG1 ((" --- Found pair k: "ID" j: " ID
" jdeg: "ID" jdiff: "ID"\n",
k, j, jdeg, jdiff)) ;
ASSERT (jdiff != EMPTY) ;
ASSERT (jdeg != EMPTY) ;
j_best = j ;
jdeg_best = jdeg ;
jdiff_best = jdiff ;
}
/* get the next entries in column k and row k */
cp++ ;
rp++ ;
}
/* save the pair (j,k), if we found one */
if (j_best != EMPTY)
{
j = j_best ;
DEBUGm4 ((" --- best pair j: "ID" for k: "ID"\n", j, k)) ;
P [k] = j ;
P [j] = k ;
}
else
{
/* no match was found for k */
unmatched++ ;
}
}
}
}
/* ---------------------------------------------------------------------- */
/* finalize the row permutation, P */
/* ---------------------------------------------------------------------- */
for (k = 0 ; k < n2 ; k++)
{
if (P [k] == EMPTY)
{
P [k] = k ;
}
}
ASSERT (UMF_is_permutation (P, Rp, n2, n2)) ;
return (unmatched) ;
}
GLOBAL void UMF_2by2
(
/* input, not modified: */
Int n, /* A is n-by-n */
const Int Ap [ ], /* size n+1 */
const Int Ai [ ], /* size nz = Ap [n] */
const double Ax [ ], /* size nz if present */
#ifdef COMPLEX
const double Az [ ], /* size nz if present */
#endif
double tol, /* tolerance for determining whether or not an
* entry is numerically acceptable. If tol <= 0
* then all numerical values ignored. */
Int scale, /* scaling to perform (none, sum, or max) */
Int Cperm1 [ ], /* singleton permutations */
#ifndef NDEBUG
Int Rperm1 [ ], /* not needed, since Rperm1 = Cperm1 for submatrix S */
#endif
Int InvRperm1 [ ], /* inverse of Rperm1 */
Int n1, /* number of singletons */
Int nempty, /* number of empty rows/cols */
/* input, contents undefined on output: */
Int Degree [ ], /* Degree [j] is the number of off-diagonal
* entries in row/column j of S+S', where
* where S = A (Cperm1 [n1..], Rperm1 [n1..]).
* Note that S is not used, nor formed. */
/* output: */
Int P [ ], /* P [k] = i means original row i is kth row in S(P,:)
* where S = A (Cperm1 [n1..], Rperm1 [n1..]) */
Int *p_nweak,
Int *p_unmatched,
/* workspace (not defined on input or output): */
Int Ri [ ], /* of size >= max (nz, n) */
Int Rp [ ], /* of size n+1 */
double Rs [ ], /* of size n if present. Rs = sum (abs (A),2) or
* max (abs (A),2), the sum or max of each row. Unused
* if scale is equal to UMFPACK_SCALE_NONE. */
Int Head [ ], /* of size n. Head pointers for bucket sort */
Int Next [ ], /* of size n. Next pointers for bucket sort */
Int Ci [ ], /* size nz */
Int Cp [ ] /* size n+1 */
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Entry aij ;
double cmax, value, rs, ctol, dvalue ;
Int k, p, row, col, do_values, do_sum, do_max, do_scale, nweak, weak,
p1, p2, dfound, unmatched, n2, oldrow, newrow, oldcol, newcol, pp ;
#ifdef COMPLEX
Int split = SPLIT (Az) ;
#endif
#ifndef NRECIPROCAL
Int do_recip = FALSE ;
#endif
#ifndef NDEBUG
/* UMF_debug += 99 ; */
DEBUGm3 (("\n ==================================UMF_2by2: tol %g\n", tol)) ;
ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ;
for (k = n1 ; k < n - nempty ; k++)
{
ASSERT (Cperm1 [k] == Rperm1 [k]) ;
}
#endif
/* ---------------------------------------------------------------------- */
/* determine scaling options */
/* ---------------------------------------------------------------------- */
/* use the values, but only if they are present */
/* ignore the values if tol <= 0 */
do_values = (tol > 0) && (Ax != (double *) NULL) ;
if (do_values && (Rs != (double *) NULL))
{
do_sum = (scale == UMFPACK_SCALE_SUM) ;
do_max = (scale == UMFPACK_SCALE_MAX) ;
}
else
{
/* no scaling */
do_sum = FALSE ;
do_max = FALSE ;
}
do_scale = do_max || do_sum ;
DEBUGm3 (("do_values "ID" do_sum "ID" do_max "ID" do_scale "ID"\n",
do_values, do_sum, do_max, do_scale)) ;
/* ---------------------------------------------------------------------- */
/* compute the row scaling, if requested */
/* ---------------------------------------------------------------------- */
/* see also umf_kernel_init */
if (do_scale)
{
#ifndef NRECIPROCAL
double rsmin ;
#endif
for (row = 0 ; row < n ; row++)
{
Rs [row] = 0.0 ;
}
for (col = 0 ; col < n ; col++)
{
p2 = Ap [col+1] ;
for (p = Ap [col] ; p < p2 ; p++)
{
row = Ai [p] ;
ASSIGN (aij, Ax, Az, p, split) ;
APPROX_ABS (value, aij) ;
rs = Rs [row] ;
if (!SCALAR_IS_NAN (rs))
{
if (SCALAR_IS_NAN (value))
{
/* if any entry in a row is NaN, then the scale factor
* for the row is NaN. It will be set to 1 later. */
Rs [row] = value ;
}
else if (do_max)
{
Rs [row] = MAX (rs, value) ;
}
else
{
Rs [row] += value ;
}
}
}
}
#ifndef NRECIPROCAL
rsmin = Rs [0] ;
if (SCALAR_IS_ZERO (rsmin) || SCALAR_IS_NAN (rsmin))
{
rsmin = 1.0 ;
}
#endif
for (row = 0 ; row < n ; row++)
{
/* do not scale an empty row, or a row with a NaN */
rs = Rs [row] ;
if (SCALAR_IS_ZERO (rs) || SCALAR_IS_NAN (rs))
{
Rs [row] = 1.0 ;
}
#ifndef NRECIPROCAL
rsmin = MIN (rsmin, Rs [row]) ;
#endif
}
#ifndef NRECIPROCAL
/* multiply by the reciprocal if Rs is not too small */
do_recip = (rsmin >= RECIPROCAL_TOLERANCE) ;
if (do_recip)
{
/* invert the scale factors */
for (row = 0 ; row < n ; row++)
{
Rs [row] = 1.0 / Rs [row] ;
}
}
#endif
}
/* ---------------------------------------------------------------------- */
/* compute the max in each column and find diagonal */
/* ---------------------------------------------------------------------- */
nweak = 0 ;
#ifndef NDEBUG
for (k = 0 ; k < n ; k++)
{
ASSERT (Rperm1 [k] >= 0 && Rperm1 [k] < n) ;
ASSERT (InvRperm1 [Rperm1 [k]] == k) ;
}
#endif
n2 = n - n1 - nempty ;
/* use Ri to count the number of strong entries in each row */
for (row = 0 ; row < n2 ; row++)
{
Ri [row] = 0 ;
}
pp = 0 ;
ctol = 0 ;
dvalue = 1 ;
/* construct C = pruned submatrix, strong values only, column form */
for (k = n1 ; k < n - nempty ; k++)
{
oldcol = Cperm1 [k] ;
newcol = k - n1 ;
Next [newcol] = EMPTY ;
DEBUGm1 (("Column "ID" newcol "ID" oldcol "ID"\n", k, newcol, oldcol)) ;
Cp [newcol] = pp ;
dfound = FALSE ;
p1 = Ap [oldcol] ;
p2 = Ap [oldcol+1] ;
if (do_values)
{
cmax = 0 ;
dvalue = 0 ;
if (!do_scale)
{
/* no scaling */
for (p = p1 ; p < p2 ; p++)
{
oldrow = Ai [p] ;
ASSERT (oldrow >= 0 && oldrow < n) ;
newrow = InvRperm1 [oldrow] - n1 ;
ASSERT (newrow >= -n1 && newrow < n2) ;
if (newrow < 0) continue ;
ASSIGN (aij, Ax, Az, p, split) ;
APPROX_ABS (value, aij) ;
/* if either cmax or value is NaN, define cmax as NaN */
if (!SCALAR_IS_NAN (cmax))
{
if (SCALAR_IS_NAN (value))
{
cmax = value ;
}
else
{
cmax = MAX (cmax, value) ;
}
}
if (oldrow == oldcol)
{
/* we found the diagonal entry in this column */
dvalue = value ;
dfound = TRUE ;
ASSERT (newrow == newcol) ;
}
}
}
#ifndef NRECIPROCAL
else if (do_recip)
{
/* multiply by the reciprocal */
for (p = p1 ; p < p2 ; p++)
{
oldrow = Ai [p] ;
ASSERT (oldrow >= 0 && oldrow < n) ;
newrow = InvRperm1 [oldrow] - n1 ;
ASSERT (newrow >= -n1 && newrow < n2) ;
if (newrow < 0) continue ;
ASSIGN (aij, Ax, Az, p, split) ;
APPROX_ABS (value, aij) ;
value *= Rs [oldrow] ;
/* if either cmax or value is NaN, define cmax as NaN */
if (!SCALAR_IS_NAN (cmax))
{
if (SCALAR_IS_NAN (value))
{
cmax = value ;
}
else
{
cmax = MAX (cmax, value) ;
}
}
if (oldrow == oldcol)
{
/* we found the diagonal entry in this column */
dvalue = value ;
dfound = TRUE ;
ASSERT (newrow == newcol) ;
}
}
}
#endif
else
{
/* divide instead */
for (p = p1 ; p < p2 ; p++)
{
oldrow = Ai [p] ;
ASSERT (oldrow >= 0 && oldrow < n) ;
newrow = InvRperm1 [oldrow] - n1 ;
ASSERT (newrow >= -n1 && newrow < n2) ;
if (newrow < 0) continue ;
ASSIGN (aij, Ax, Az, p, split) ;
APPROX_ABS (value, aij) ;
value /= Rs [oldrow] ;
/* if either cmax or value is NaN, define cmax as NaN */
if (!SCALAR_IS_NAN (cmax))
{
if (SCALAR_IS_NAN (value))
{
cmax = value ;
}
else
{
cmax = MAX (cmax, value) ;
}
}
if (oldrow == oldcol)
{
/* we found the diagonal entry in this column */
dvalue = value ;
dfound = TRUE ;
ASSERT (newrow == newcol) ;
}
}
}
ctol = tol * cmax ;
DEBUGm1 ((" cmax col "ID" %g ctol %g\n", oldcol, cmax, ctol)) ;
}
else
{
for (p = p1 ; p < p2 ; p++)
{
oldrow = Ai [p] ;
ASSERT (oldrow >= 0 && oldrow < n) ;
newrow = InvRperm1 [oldrow] - n1 ;
ASSERT (newrow >= -n1 && newrow < n2) ;
if (newrow < 0) continue ;
Ci [pp++] = newrow ;
if (oldrow == oldcol)
{
/* we found the diagonal entry in this column */
ASSERT (newrow == newcol) ;
dfound = TRUE ;
}
/* count the entries in each column */
Ri [newrow]++ ;
}
}
/* ------------------------------------------------------------------ */
/* flag the weak diagonals */
/* ------------------------------------------------------------------ */
if (!dfound)
{
/* no diagonal entry present */
weak = TRUE ;
}
else
{
/* diagonal entry is present, check its value */
weak = (do_values) ? WEAK (dvalue, ctol) : FALSE ;
}
if (weak)
{
/* flag this column as weak */
DEBUG0 (("Weak!\n")) ;
Next [newcol] = IS_WEAK ;
nweak++ ;
}
/* ------------------------------------------------------------------ */
/* count entries in each row that are not numerically weak */
/* ------------------------------------------------------------------ */
if (do_values)
{
if (!do_scale)
{
/* no scaling */
for (p = p1 ; p < p2 ; p++)
{
oldrow = Ai [p] ;
newrow = InvRperm1 [oldrow] - n1 ;
if (newrow < 0) continue ;
ASSIGN (aij, Ax, Az, p, split) ;
APPROX_ABS (value, aij) ;
weak = WEAK (value, ctol) ;
if (!weak)
{
DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ;
Ci [pp++] = newrow ;
Ri [newrow]++ ;
}
}
}
#ifndef NRECIPROCAL
else if (do_recip)
{
/* multiply by the reciprocal */
for (p = p1 ; p < p2 ; p++)
{
oldrow = Ai [p] ;
newrow = InvRperm1 [oldrow] - n1 ;
if (newrow < 0) continue ;
ASSIGN (aij, Ax, Az, p, split) ;
APPROX_ABS (value, aij) ;
value *= Rs [oldrow] ;
weak = WEAK (value, ctol) ;
if (!weak)
{
DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ;
Ci [pp++] = newrow ;
Ri [newrow]++ ;
}
}
}
#endif
else
{
/* divide instead */
for (p = p1 ; p < p2 ; p++)
{
oldrow = Ai [p] ;
newrow = InvRperm1 [oldrow] - n1 ;
if (newrow < 0) continue ;
ASSIGN (aij, Ax, Az, p, split) ;
APPROX_ABS (value, aij) ;
value /= Rs [oldrow] ;
weak = WEAK (value, ctol) ;
if (!weak)
{
DEBUG0 ((" strong: row "ID": %g\n", oldrow, value)) ;
Ci [pp++] = newrow ;
Ri [newrow]++ ;
}
}
}
}
}
Cp [n2] = pp ;
ASSERT (AMD_valid (n2, n2, Cp, Ci) == AMD_OK) ;
if (nweak == 0)
{
/* nothing to do, quick return */
DEBUGm2 (("\n =============================UMF_2by2: quick return\n")) ;
for (k = 0 ; k < n ; k++)
{
P [k] = k ;
}
*p_nweak = 0 ;
*p_unmatched = 0 ;
return ;
}
#ifndef NDEBUG
for (k = 0 ; k < n2 ; k++)
{
P [k] = EMPTY ;
}
for (k = 0 ; k < n2 ; k++)
{
ASSERT (Degree [k] >= 0 && Degree [k] < n2) ;
}
#endif
/* ---------------------------------------------------------------------- */
/* find the 2-by-2 permutation */
/* ---------------------------------------------------------------------- */
/* The matrix S is now mapped to the index range 0 to n2-1. We have
* S = A (Rperm [n1 .. n-nempty-1], Cperm [n1 .. n-nempty-1]), and then
* C = pattern of strong entries in S. A weak diagonal k in S is marked
* with Next [k] = IS_WEAK. */
unmatched = two_by_two (n2, Cp, Ci, Degree, Next, Ri, P, Rp, Head) ;
/* ---------------------------------------------------------------------- */
*p_nweak = nweak ;
*p_unmatched = unmatched ;
#ifndef NDEBUG
DEBUGm4 (("UMF_2by2: weak "ID" unmatched "ID"\n", nweak, unmatched)) ;
for (row = 0 ; row < n ; row++)
{
DEBUGm2 (("P ["ID"] = "ID"\n", row, P [row])) ;
}
DEBUGm2 (("\n =============================UMF_2by2: done\n\n")) ;
#endif
}
GLOBAL Int UMF_init_front
(
NumericType *Numeric,
WorkType *Work
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Int i, j, fnr_curr, row, col, *Frows, *Fcols,
*Fcpos, *Frpos, fncols, fnrows, *Wrow, fnr2, fnc2, rrdeg, ccdeg, *Wm,
fnrows_extended ;
Entry *Fcblock, *Fl, *Wy, *Wx ;
/* ---------------------------------------------------------------------- */
/* get current frontal matrix and check for frontal growth */
/* ---------------------------------------------------------------------- */
#ifndef NDEBUG
DEBUG0 (("INIT FRONT\n")) ;
DEBUG1 (("CURR before init:\n")) ;
UMF_dump_current_front (Numeric, Work, FALSE) ;
#endif
if (Work->do_grow)
{
fnr2 = UMF_FRONTAL_GROWTH * Work->fnrows_new + 2 ;
fnc2 = UMF_FRONTAL_GROWTH * Work->fncols_new + 2 ;
if (!UMF_grow_front (Numeric, fnr2, fnc2, Work,
Work->pivrow_in_front ? 2 : 0))
{
/* :: out of memory in umf_init_front :: */
DEBUGm4 (("out of memory: init front\n")) ;
return (FALSE) ;
}
}
#ifndef NDEBUG
DEBUG1 (("CURR after grow:\n")) ;
UMF_dump_current_front (Numeric, Work, FALSE) ;
DEBUG1 (("fnrows new "ID" fncols new "ID"\n",
Work->fnrows_new, Work->fncols_new)) ;
#endif
ASSERT (Work->fnpiv == 0) ;
fnr_curr = Work->fnr_curr ;
ASSERT (Work->fnrows_new + 1 <= fnr_curr) ;
ASSERT (Work->fncols_new + 1 <= Work->fnc_curr) ;
ASSERT (fnr_curr >= 0) ;
ASSERT (fnr_curr % 2 == 1) ;
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
/* current front is defined by pivot row and column */
Frows = Work->Frows ;
Fcols = Work->Fcols ;
Frpos = Work->Frpos ;
Fcpos = Work->Fcpos ;
Work->fnzeros = 0 ;
ccdeg = Work->ccdeg ;
rrdeg = Work->rrdeg ;
fnrows = Work->fnrows ;
fncols = Work->fncols ;
/* if both pivrow and pivcol are in front, then we extend the old one */
/* in UMF_extend_front, rather than starting a new one here. */
ASSERT (! (Work->pivrow_in_front && Work->pivcol_in_front)) ;
/* ---------------------------------------------------------------------- */
/* place pivot column pattern in frontal matrix */
/* ---------------------------------------------------------------------- */
Fl = Work->Flblock ;
if (Work->pivcol_in_front)
{
/* Append the pivot column extension.
* Note that all we need to do is increment the size, since the
* candidate pivot column pattern is already in place in
* Frows [0 ... fnrows-1] (the old pattern), and
* Frows [fnrows ... fnrows + Work->ccdeg - 1] (the new
* pattern). Frpos is also properly defined. */
/* make a list of the new rows to scan */
Work->fscan_row = fnrows ; /* only scan the new rows */
Work->NewRows = Work->Wrp ;
Wy = Work->Wy ;
for (i = 0 ; i < fnrows ; i++)
{
Fl [i] = Wy [i] ;
}
fnrows_extended = fnrows + ccdeg ;
for (i = fnrows ; i < fnrows_extended ; i++)
{
Fl [i] = Wy [i] ;
/* flip the row, since Wrp must be < 0 */
row = Frows [i] ;
Work->NewRows [i] = FLIP (row) ;
}
fnrows = fnrows_extended ;
}
else
{
/* this is a completely new column */
Work->fscan_row = 0 ; /* scan all the rows */
Work->NewRows = Frows ;
Wm = Work->Wm ;
Wx = Work->Wx ;
for (i = 0 ; i < ccdeg ; i++)
{
Fl [i] = Wx [i] ;
row = Wm [i] ;
Frows [i] = row ;
Frpos [row] = i ;
}
fnrows = ccdeg ;
}
Work->fnrows = fnrows ;
#ifndef NDEBUG
DEBUG3 (("New Pivot col "ID" now in front, length "ID"\n",
Work->pivcol, fnrows)) ;
for (i = 0 ; i < fnrows ; i++)
{
DEBUG4 ((" "ID": row "ID"\n", i, Frows [i])) ;
ASSERT (Frpos [Frows [i]] == i) ;
}
#endif
/* ---------------------------------------------------------------------- */
/* place pivot row pattern in frontal matrix */
/* ---------------------------------------------------------------------- */
Wrow = Work->Wrow ;
if (Work->pivrow_in_front)
{
/* append the pivot row extension */
Work->fscan_col = fncols ; /* only scan the new columns */
Work->NewCols = Work->Wp ;
#ifndef NDEBUG
for (j = 0 ; j < fncols ; j++)
{
col = Fcols [j] ;
ASSERT (col >= 0 && col < Work->n_col) ;
ASSERT (Fcpos [col] == j * fnr_curr) ;
}
#endif
/* Wrow == Fcol for the IN_IN case, and for the OUT_IN case when
* the pivrow [IN][IN] happens to be the same as pivrow [OUT][IN].
* See UMF_local_search for more details. */
ASSERT (IMPLIES (Work->pivcol_in_front, Wrow == Fcols)) ;
if (Wrow == Fcols)
{
for (j = fncols ; j < rrdeg ; j++)
{
col = Wrow [j] ;
/* Fcols [j] = col ; not needed */
/* flip the col index, since Wp must be < 0 */
Work->NewCols [j] = FLIP (col) ;
Fcpos [col] = j * fnr_curr ;
}
}
else
{
for (j = fncols ; j < rrdeg ; j++)
{
col = Wrow [j] ;
Fcols [j] = col ;
/* flip the col index, since Wp must be < 0 */
Work->NewCols [j] = FLIP (col) ;
Fcpos [col] = j * fnr_curr ;
}
}
}
else
{
/* this is a completely new row */
Work->fscan_col = 0 ; /* scan all the columns */
Work->NewCols = Fcols ;
for (j = 0 ; j < rrdeg ; j++)
{
col = Wrow [j] ;
Fcols [j] = col ;
Fcpos [col] = j * fnr_curr ;
}
}
DEBUGm1 (("rrdeg "ID" fncols "ID"\n", rrdeg, fncols)) ;
fncols = rrdeg ;
Work->fncols = fncols ;
/* ---------------------------------------------------------------------- */
/* clear the frontal matrix */
/* ---------------------------------------------------------------------- */
ASSERT (fnrows == Work->fnrows_new + 1) ;
ASSERT (fncols == Work->fncols_new + 1) ;
Fcblock = Work->Fcblock ;
ASSERT (Fcblock != (Entry *) NULL) ;
zero_init_front (fncols, fnrows, Fcblock, fnr_curr) ;
#ifndef NDEBUG
DEBUG3 (("New Pivot row "ID" now in front, length "ID" fnr_curr "ID"\n",
Work->pivrow, fncols, fnr_curr)) ;
for (j = 0 ; j < fncols ; j++)
{
DEBUG4 (("col "ID" position "ID"\n", j, Fcols [j])) ;
ASSERT (Fcpos [Fcols [j]] == j * fnr_curr) ;
}
#endif
/* ---------------------------------------------------------------------- */
/* current workspace usage: */
/* ---------------------------------------------------------------------- */
/* Fcblock [0..fnr_curr-1, 0..fnc_curr-1]: space for the new frontal
* matrix. Fcblock (i,j) is located at Fcblock [i+j*fnr_curr] */
return (TRUE) ;
}
GLOBAL Int UMF_start_front /* returns TRUE if successful, FALSE otherwise */
(
Int chain,
NumericType *Numeric,
WorkType *Work,
SymbolicType *Symbolic
)
{
Int fnrows_max, fncols_max, fnr2, fnc2, fsize, fcurr_size, maxfrsize,
overflow, nb, f, cdeg ;
double maxbytes ;
nb = Symbolic->nb ;
fnrows_max = Symbolic->Chain_maxrows [chain] ;
fncols_max = Symbolic->Chain_maxcols [chain] ;
DEBUGm2 (("Start Front for chain "ID". fnrows_max "ID" fncols_max "ID"\n",
chain, fnrows_max, fncols_max)) ;
Work->fnrows_max = fnrows_max ;
Work->fncols_max = fncols_max ;
Work->any_skip = FALSE ;
maxbytes = sizeof (Entry) *
(double) (fnrows_max + nb) * (double) (fncols_max + nb) ;
fcurr_size = Work->fcurr_size ;
if (Symbolic->prefer_diagonal)
{
/* Get a rough upper bound on the degree of the first pivot column in
* this front. Note that Col_degree is not maintained if diagonal
* pivoting is preferred. For most matrices, the first pivot column
* of the first frontal matrix of a new chain has only one tuple in
* it anyway, so this bound is exact in that case. */
Int col, tpi, e, *E, *Col_tuples, *Col_tlen, *Cols ;
Tuple *tp, *tpend ;
Unit *Memory, *p ;
Element *ep ;
E = Work->E ;
Memory = Numeric->Memory ;
Col_tuples = Numeric->Lip ;
Col_tlen = Numeric->Lilen ;
col = Work->nextcand ;
tpi = Col_tuples [col] ;
tp = (Tuple *) Memory + tpi ;
tpend = tp + Col_tlen [col] ;
cdeg = 0 ;
DEBUGm3 (("\n=============== start front: col "ID" tlen "ID"\n",
col, Col_tlen [col])) ;
for ( ; tp < tpend ; tp++)
{
DEBUG1 (("Tuple ("ID","ID")\n", tp->e, tp->f)) ;
e = tp->e ;
if (!E [e]) continue ;
f = tp->f ;
p = Memory + E [e] ;
ep = (Element *) p ;
p += UNITS (Element, 1) ;
Cols = (Int *) p ;
if (Cols [f] == EMPTY) continue ;
DEBUG1 ((" nrowsleft "ID"\n", ep->nrowsleft)) ;
cdeg += ep->nrowsleft ;
}
#ifndef NDEBUG
DEBUGm3 (("start front cdeg: "ID" col "ID"\n", cdeg, col)) ;
UMF_dump_rowcol (1, Numeric, Work, col, FALSE) ;
#endif
/* cdeg is now the rough upper bound on the degree of the next pivot
* column. */
/* If AMD was called, we know the maximum number of nonzeros in any
* column of L. Use this as an upper bound for cdeg, but add 2 to
* account for a small amount of off-diagonal pivoting. */
if (Symbolic->amd_dmax > 0)
{
cdeg = MIN (cdeg, Symbolic->amd_dmax) ;
}
/* Increase it to account for larger columns later on.
* Also ensure that it's larger than zero. */
cdeg += 2 ;
/* cdeg cannot be larger than fnrows_max */
cdeg = MIN (cdeg, fnrows_max) ;
}
else
{
/* don't do the above cdeg computation */
cdeg = 0 ;
}
DEBUGm2 (("fnrows max "ID" fncols_max "ID"\n", fnrows_max, fncols_max)) ;
/* the current frontal matrix is empty */
ASSERT (Work->fnrows == 0 && Work->fncols == 0 && Work->fnpiv == 0) ;
/* maximum row dimension is always odd, to avoid bad cache effects */
ASSERT (fnrows_max >= 0) ;
ASSERT (fnrows_max % 2 == 1) ;
/* ----------------------------------------------------------------------
* allocate working array for current frontal matrix:
* minimum size: 1-by-1
* maximum size: fnrows_max-by-fncols_max
* desired size:
*
* if Numeric->front_alloc_init >= 0:
*
* for unsymmetric matrices:
* Numeric->front_alloc_init * (fnrows_max-by-fncols_max)
*
* for symmetric matrices (diagonal pivoting preference, actually):
* Numeric->front_alloc_init * (fnrows_max-by-fncols_max), or
* cdeg*cdeg, whichever is smaller.
*
* if Numeric->front_alloc_init < 0:
* allocate a front of size -Numeric->front_alloc_init.
*
* Allocate the whole thing if it's small (less than 2*nb^2). Make sure the
* leading dimension of the frontal matrix is odd.
*
* Also allocate the nb-by-nb LU block, the dr-by-nb L block, and the
* nb-by-dc U block.
* ---------------------------------------------------------------------- */
/* get the maximum front size, avoiding integer overflow */
overflow = INT_OVERFLOW (maxbytes) ;
if (overflow)
{
/* :: int overflow, max front size :: */
maxfrsize = Int_MAX / sizeof (Entry) ;
}
else
{
maxfrsize = (fnrows_max + nb) * (fncols_max + nb) ;
}
ASSERT (!INT_OVERFLOW ((double) maxfrsize * sizeof (Entry))) ;
if (Numeric->front_alloc_init < 0)
{
/* allocate a front of -Numeric->front_alloc_init entries */
fsize = -Numeric->front_alloc_init ;
fsize = MAX (1, fsize) ;
}
else
{
if (INT_OVERFLOW (Numeric->front_alloc_init * maxbytes))
{
/* :: int overflow, requested front size :: */
fsize = Int_MAX / sizeof (Entry) ;
}
else
{
fsize = Numeric->front_alloc_init * maxfrsize ;
}
if (cdeg > 0)
{
/* diagonal pivoting is in use. cdeg was computed above */
Int fsize2 ;
/* add the L and U blocks */
cdeg += nb ;
if (INT_OVERFLOW (((double) cdeg * (double) cdeg) * sizeof (Entry)))
{
/* :: int overflow, symmetric front size :: */
fsize2 = Int_MAX / sizeof (Entry) ;
}
else
{
fsize2 = MAX (cdeg * cdeg, fcurr_size) ;
}
fsize = MIN (fsize, fsize2) ;
}
}
fsize = MAX (fsize, 2*nb*nb) ;
/* fsize and maxfrsize are now safe from integer overflow. They both
* include the size of the pivot blocks. */
ASSERT (!INT_OVERFLOW ((double) fsize * sizeof (Entry))) ;
Work->fnrows_new = 0 ;
Work->fncols_new = 0 ;
/* desired size is fnr2-by-fnc2 (includes L and U blocks): */
DEBUGm2 ((" fsize "ID" fcurr_size "ID"\n", fsize, fcurr_size)) ;
DEBUGm2 ((" maxfrsize "ID" fnr_curr "ID" fnc_curr "ID"\n", maxfrsize,
Work->fnr_curr, Work->fnc_curr)) ;
if (fsize >= maxfrsize && !overflow)
{
/* max working array is small, allocate all of it */
fnr2 = fnrows_max + nb ;
fnc2 = fncols_max + nb ;
fsize = maxfrsize ;
DEBUGm1 ((" sufficient for ("ID"+"ID")-by-("ID"+"ID")\n",
fnrows_max, nb, fncols_max, nb)) ;
}
else
{
/* allocate a smaller working array */
if (fnrows_max <= fncols_max)
{
fnr2 = (Int) sqrt ((double) fsize) ;
/* make sure fnr2 is odd */
fnr2 = MAX (fnr2, 1) ;
if (fnr2 % 2 == 0) fnr2++ ;
fnr2 = MIN (fnr2, fnrows_max + nb) ;
fnc2 = fsize / fnr2 ;
}
else
{
fnc2 = (Int) sqrt ((double) fsize) ;
fnc2 = MIN (fnc2, fncols_max + nb) ;
fnr2 = fsize / fnc2 ;
/* make sure fnr2 is odd */
fnr2 = MAX (fnr2, 1) ;
if (fnr2 % 2 == 0)
{
fnr2++ ;
fnc2 = fsize / fnr2 ;
}
}
DEBUGm1 ((" smaller "ID"-by-"ID"\n", fnr2, fnc2)) ;
}
fnr2 = MIN (fnr2, fnrows_max + nb) ;
fnc2 = MIN (fnc2, fncols_max + nb) ;
ASSERT (fnr2 % 2 == 1) ;
ASSERT (fnr2 * fnc2 <= fsize) ;
fnr2 -= nb ;
fnc2 -= nb ;
ASSERT (fnr2 >= 0) ;
ASSERT (fnc2 >= 0) ;
if (fsize > fcurr_size)
{
DEBUGm1 ((" Grow front \n")) ;
Work->do_grow = TRUE ;
if (!UMF_grow_front (Numeric, fnr2, fnc2, Work, -1))
{
/* since the minimum front size is 1-by-1, it would be nearly
* impossible to run out of memory here. */
DEBUGm4 (("out of memory: start front\n")) ;
return (FALSE) ;
}
}
else
{
/* use the existing front */
DEBUGm1 ((" existing front ok\n")) ;
Work->fnr_curr = fnr2 ;
Work->fnc_curr = fnc2 ;
Work->Flblock = Work->Flublock + nb * nb ;
Work->Fublock = Work->Flblock + nb * fnr2 ;
Work->Fcblock = Work->Fublock + nb * fnc2 ;
}
ASSERT (Work->Flblock == Work->Flublock + Work->nb*Work->nb) ;
ASSERT (Work->Fublock == Work->Flblock + Work->fnr_curr*Work->nb) ;
ASSERT (Work->Fcblock == Work->Fublock + Work->nb*Work->fnc_curr) ;
return (TRUE) ;
}
GLOBAL Int UMF_kernel
(
const Int Ap [ ],
const Int Ai [ ],
const double Ax [ ],
#ifdef COMPLEX
const double Az [ ],
#endif
NumericType *Numeric,
WorkType *Work,
SymbolicType *Symbolic
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Int j, f1, f2, chain, nchains, *Chain_start, status, fixQ, evaporate,
*Front_npivcol, jmax, nb, drop ;
/* ---------------------------------------------------------------------- */
/* initialize memory space and load the matrix. Optionally scale. */
/* ---------------------------------------------------------------------- */
if (!UMF_kernel_init (Ap, Ai, Ax,
#ifdef COMPLEX
Az,
#endif
Numeric, Work, Symbolic))
{
/* UMF_kernel_init is guaranteed to succeed, since UMFPACK_numeric */
/* either allocates enough space or if not, UMF_kernel does not get */
/* called. So running out of memory here is a fatal error, and means */
/* that the user changed Ap and/or Ai since the call to */
/* UMFPACK_*symbolic. */
DEBUGm4 (("kernel init failed\n")) ;
return (UMFPACK_ERROR_different_pattern) ;
}
/* ---------------------------------------------------------------------- */
/* get the symbolic factorization */
/* ---------------------------------------------------------------------- */
nchains = Symbolic->nchains ;
Chain_start = Symbolic->Chain_start ;
Front_npivcol = Symbolic->Front_npivcol ;
nb = Symbolic->nb ;
fixQ = Symbolic->fixQ ;
drop = Numeric->droptol > 0.0 ;
#ifndef NDEBUG
for (chain = 0 ; chain < nchains ; chain++)
{
Int i ;
f1 = Chain_start [chain] ;
f2 = Chain_start [chain+1] - 1 ;
DEBUG1 (("\nCHain: "ID" start "ID" end "ID"\n", chain, f1, f2)) ;
for (i = f1 ; i <= f2 ; i++)
{
DEBUG1 (("Front "ID", npivcol "ID"\n", i, Front_npivcol [i])) ;
}
}
#endif
/* ---------------------------------------------------------------------- */
/* factorize each chain of frontal matrices */
/* ---------------------------------------------------------------------- */
for (chain = 0 ; chain < nchains ; chain++)
{
f1 = Chain_start [chain] ;
f2 = Chain_start [chain+1] - 1 ;
/* ------------------------------------------------------------------ */
/* get the initial frontal matrix size for this chain */
/* ------------------------------------------------------------------ */
DO (UMF_start_front (chain, Numeric, Work, Symbolic)) ;
/* ------------------------------------------------------------------ */
/* factorize each front in the chain */
/* ------------------------------------------------------------------ */
for (Work->frontid = f1 ; Work->frontid <= f2 ; Work->frontid++)
{
/* -------------------------------------------------------------- */
/* Initialize the pivot column candidate set */
/* -------------------------------------------------------------- */
Work->ncand = Front_npivcol [Work->frontid] ;
Work->lo = Work->nextcand ;
Work->hi = Work->nextcand + Work->ncand - 1 ;
jmax = MIN (MAX_CANDIDATES, Work->ncand) ;
DEBUGm1 ((">>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Starting front "
ID", npivcol: "ID"\n", Work->frontid, Work->ncand)) ;
if (fixQ)
{
/* do not modify the column order */
jmax = 1 ;
}
DEBUGm1 (("Initial candidates: ")) ;
for (j = 0 ; j < jmax ; j++)
{
DEBUGm1 ((" "ID, Work->nextcand)) ;
ASSERT (Work->nextcand <= Work->hi) ;
Work->Candidates [j] = Work->nextcand++ ;
}
Work->nCandidates = jmax ;
DEBUGm1 (("\n")) ;
/* -------------------------------------------------------------- */
/* Assemble and factorize the current frontal matrix */
/* -------------------------------------------------------------- */
while (Work->ncand > 0)
{
/* ---------------------------------------------------------- */
/* get the pivot row and column */
/* ---------------------------------------------------------- */
status = UMF_local_search (Numeric, Work, Symbolic) ;
if (status == UMFPACK_ERROR_different_pattern)
{
/* :: pattern change detected in umf_local_search :: */
/* input matrix has changed since umfpack_*symbolic */
DEBUGm4 (("local search failed\n")) ;
return (UMFPACK_ERROR_different_pattern) ;
}
if (status == UMFPACK_WARNING_singular_matrix)
{
/* no pivot found, discard and try again */
continue ;
}
/* ---------------------------------------------------------- */
/* update if front not extended or too many zeros in L,U */
/* ---------------------------------------------------------- */
if (Work->do_update)
{
UMF_blas3_update (Work) ;
if (drop)
{
DO (UMF_store_lu_drop (Numeric, Work)) ;
}
else
{
DO (UMF_store_lu (Numeric, Work)) ;
}
}
/* ---------------------------------------------------------- */
/* extend the frontal matrix, or start a new one */
/* ---------------------------------------------------------- */
if (Work->do_extend)
{
/* extend the current front */
DO (UMF_extend_front (Numeric, Work)) ;
}
else
{
/* finish the current front (if any) and start a new one */
DO (UMF_create_element (Numeric, Work, Symbolic)) ;
DO (UMF_init_front (Numeric, Work)) ;
}
/* ---------------------------------------------------------- */
/* Numerical & symbolic assembly into current frontal matrix */
/* ---------------------------------------------------------- */
if (fixQ)
{
UMF_assemble_fixq (Numeric, Work) ;
}
else
{
UMF_assemble (Numeric, Work) ;
}
/* ---------------------------------------------------------- */
/* scale the pivot column */
/* ---------------------------------------------------------- */
UMF_scale_column (Numeric, Work) ;
/* ---------------------------------------------------------- */
/* Numerical update if enough pivots accumulated */
/* ---------------------------------------------------------- */
evaporate = Work->fnrows == 0 || Work->fncols == 0 ;
if (Work->fnpiv >= nb || evaporate)
{
UMF_blas3_update (Work) ;
if (drop)
{
DO (UMF_store_lu_drop (Numeric, Work)) ;
}
else
{
DO (UMF_store_lu (Numeric, Work)) ;
}
}
Work->pivrow_in_front = FALSE ;
Work->pivcol_in_front = FALSE ;
/* ---------------------------------------------------------- */
/* If front is empty, evaporate it */
/* ---------------------------------------------------------- */
if (evaporate)
{
/* This does not create an element, just evaporates it.
* It ensures that a front is not 0-by-c or r-by-0. No
* memory is allocated, so it is guaranteed to succeed. */
(void) UMF_create_element (Numeric, Work, Symbolic) ;
Work->fnrows = 0 ;
Work->fncols = 0 ;
}
}
}
/* ------------------------------------------------------------------
* Wrapup the current frontal matrix. This is the last in a chain
* in the column elimination tree. The next frontal matrix
* cannot overlap with the current one, which will be its sibling
* in the column etree.
* ------------------------------------------------------------------ */
UMF_blas3_update (Work) ;
if (drop)
{
DO (UMF_store_lu_drop (Numeric, Work)) ;
}
else
{
DO (UMF_store_lu (Numeric, Work)) ;
}
Work->fnrows_new = Work->fnrows ;
Work->fncols_new = Work->fncols ;
DO (UMF_create_element (Numeric, Work, Symbolic)) ;
/* ------------------------------------------------------------------ */
/* current front is now empty */
/* ------------------------------------------------------------------ */
Work->fnrows = 0 ;
Work->fncols = 0 ;
}
/* ---------------------------------------------------------------------- */
/* end the last Lchain and Uchain and finalize the LU factors */
/* ---------------------------------------------------------------------- */
UMF_kernel_wrapup (Numeric, Symbolic, Work) ;
/* note that the matrix may be singular (this is OK) */
return (UMFPACK_OK) ;
}
