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 Int UMF_triplet_map_x
#else
GLOBAL Int UMF_triplet_map_nox
#endif
#else
#ifdef DO_VALUES
GLOBAL Int UMF_triplet_nomap_x
#else
GLOBAL Int UMF_triplet_nomap_nox
#endif
#endif
(
Int n_row,
Int n_col,
Int nz,
const Int Ti [ ], /* size nz */
const Int Tj [ ], /* size nz */
Int Ap [ ], /* size n_col + 1 */
Int Ai [ ], /* size nz */
Int Rp [ ], /* size n_row + 1 */
Int Rj [ ], /* size nz */
Int W [ ], /* size max (n_row, n_col) */
Int RowCount [ ] /* size n_row */
#ifdef DO_VALUES
, const double Tx [ ] /* size nz */
, double Ax [ ] /* size nz */
, double Rx [ ] /* size nz */
#ifdef COMPLEX
, const double Tz [ ] /* size nz */
, double Az [ ] /* size nz */
, double Rz [ ] /* size nz */
#endif
#endif
#ifdef DO_MAP
, Int Map [ ] /* size nz */
, Int Map2 [ ] /* size nz */
#endif
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Int i, j, k, p, cp, p1, p2, pdest, pj ;
#ifdef DO_MAP
Int duplicates ;
#endif
#ifdef DO_VALUES
#ifdef COMPLEX
Int split = SPLIT (Tz) && SPLIT (Az) && SPLIT (Rz) ;
#endif
#endif
/* ---------------------------------------------------------------------- */
/* count the entries in each row (also counting duplicates) */
/* ---------------------------------------------------------------------- */
/* use W as workspace for row counts (including duplicates) */
for (i = 0 ; i < n_row ; i++)
{
W [i] = 0 ;
}
for (k = 0 ; k < nz ; k++)
{
i = Ti [k] ;
j = Tj [k] ;
if (i < 0 || i >= n_row || j < 0 || j >= n_col)
{
return (UMFPACK_ERROR_invalid_matrix) ;
}
W [i]++ ;
#ifndef NDEBUG
DEBUG1 ((ID " triplet: "ID" "ID" ", k, i, j)) ;
#ifdef DO_VALUES
{
Entry tt ;
ASSIGN (tt, Tx, Tz, k, split) ;
EDEBUG2 (tt) ;
DEBUG1 (("\n")) ;
}
#endif
#endif
}
/* ---------------------------------------------------------------------- */
/* compute the row pointers */
/* ---------------------------------------------------------------------- */
Rp [0] = 0 ;
for (i = 0 ; i < n_row ; i++)
{
Rp [i+1] = Rp [i] + W [i] ;
W [i] = Rp [i] ;
}
/* W is now equal to the row pointers */
/* ---------------------------------------------------------------------- */
/* construct the row form */
/* ---------------------------------------------------------------------- */
for (k = 0 ; k < nz ; k++)
{
p = W [Ti [k]]++ ;
#ifdef DO_MAP
Map [k] = p ;
#endif
Rj [p] = Tj [k] ;
#ifdef DO_VALUES
#ifdef COMPLEX
if (split)
{
Rx [p] = Tx [k] ;
Rz [p] = Tz [k] ;
}
else
{
Rx [2*p ] = Tx [2*k ] ;
Rx [2*p+1] = Tx [2*k+1] ;
}
#else
Rx [p] = Tx [k] ;
#endif
#endif
}
/* Rp stays the same, but W [i] is advanced to the start of row i+1 */
#ifndef NDEBUG
for (i = 0 ; i < n_row ; i++)
{
ASSERT (W [i] == Rp [i+1]) ;
}
#ifdef DO_MAP
for (k = 0 ; k < nz ; k++)
{
/* make sure that kth triplet is mapped correctly */
p = Map [k] ;
DEBUG1 (("First row map: Map ["ID"] = "ID"\n", k, p)) ;
i = Ti [k] ;
j = Tj [k] ;
ASSERT (j == Rj [p]) ;
ASSERT (Rp [i] <= p && p < Rp [i+1]) ;
}
#endif
#endif
/* ---------------------------------------------------------------------- */
/* sum up duplicates */
/* ---------------------------------------------------------------------- */
/* use W [j] to hold position in Ri/Rx/Rz of a_ij, for row i [ */
for (j = 0 ; j < n_col ; j++)
{
W [j] = EMPTY ;
}
#ifdef DO_MAP
duplicates = FALSE ;
#endif
for (i = 0 ; i < n_row ; i++)
{
p1 = Rp [i] ;
p2 = Rp [i+1] ;
pdest = p1 ;
/* At this point, W [j] < p1 holds true for all columns j, */
/* because Ri/Rx/Rz is stored in row oriented order. */
#ifndef NDEBUG
if (UMF_debug >= -2)
{
for (j = 0 ; j < n_col ; j++)
{
ASSERT (W [j] < p1) ;
}
}
#endif
for (p = p1 ; p < p2 ; p++)
{
j = Rj [p] ;
ASSERT (j >= 0 && j < n_col) ;
pj = W [j] ;
if (pj >= p1)
{
/* this column index, j, is already in row i, at position pj */
ASSERT (pj < p) ;
ASSERT (Rj [pj] == j) ;
#ifdef DO_MAP
Map2 [p] = pj ;
duplicates = TRUE ;
#endif
#ifdef DO_VALUES
/* sum the entry */
#ifdef COMPLEX
if (split)
{
Rx [pj] += Rx [p] ;
Rz [pj] += Rz [p] ;
}
else
{
Rx[2*pj ] += Rx[2*p ] ;
Rx[2*pj+1] += Rx[2*p+1] ;
}
#else
Rx [pj] += Rx [p] ;
#endif
#endif
}
else
{
/* keep the entry */
/* also keep track in W[j] of position of a_ij for case above */
W [j] = pdest ;
#ifdef DO_MAP
Map2 [p] = pdest ;
#endif
/* no need to move the entry if pdest is equal to p */
if (pdest != p)
{
Rj [pdest] = j ;
#ifdef DO_VALUES
#ifdef COMPLEX
if (split)
{
Rx [pdest] = Rx [p] ;
Rz [pdest] = Rz [p] ;
}
else
{
Rx [2*pdest ] = Rx [2*p ] ;
Rx [2*pdest+1] = Rx [2*p+1] ;
}
#else
Rx [pdest] = Rx [p] ;
#endif
#endif
}
pdest++ ;
}
}
RowCount [i] = pdest - p1 ;
}
/* done using W for position of a_ij ] */
/* ---------------------------------------------------------------------- */
/* merge Map and Map2 into a single Map */
/* ---------------------------------------------------------------------- */
#ifdef DO_MAP
if (duplicates)
{
for (k = 0 ; k < nz ; k++)
{
Map [k] = Map2 [Map [k]] ;
}
}
#ifndef NDEBUG
else
{
/* no duplicates, so no need to recompute Map */
for (k = 0 ; k < nz ; k++)
{
ASSERT (Map2 [k] == k) ;
}
}
for (k = 0 ; k < nz ; k++)
{
/* make sure that kth triplet is mapped correctly */
p = Map [k] ;
DEBUG1 (("Second row map: Map ["ID"] = "ID"\n", k, p)) ;
i = Ti [k] ;
j = Tj [k] ;
ASSERT (j == Rj [p]) ;
ASSERT (Rp [i] <= p && p < Rp [i+1]) ;
}
#endif
#endif
/* now the kth triplet maps to p = Map [k], and thus to Rj/Rx [p] */
/* ---------------------------------------------------------------------- */
/* count the entries in each column */
/* ---------------------------------------------------------------------- */
/* [ use W as work space for column counts of A */
for (j = 0 ; j < n_col ; j++)
{
W [j] = 0 ;
}
for (i = 0 ; i < n_row ; i++)
{
for (p = Rp [i] ; p < Rp [i] + RowCount [i] ; p++)
{
j = Rj [p] ;
ASSERT (j >= 0 && j < n_col) ;
W [j]++ ;
}
}
/* ---------------------------------------------------------------------- */
/* create the column pointers */
/* ---------------------------------------------------------------------- */
Ap [0] = 0 ;
for (j = 0 ; j < n_col ; j++)
{
Ap [j+1] = Ap [j] + W [j] ;
}
/* done using W as workspace for column counts of A ] */
for (j = 0 ; j < n_col ; j++)
{
W [j] = Ap [j] ;
}
/* ---------------------------------------------------------------------- */
/* construct the column form */
/* ---------------------------------------------------------------------- */
for (i = 0 ; i < n_row ; i++)
{
for (p = Rp [i] ; p < Rp [i] + RowCount [i] ; p++)
{
cp = W [Rj [p]]++ ;
#ifdef DO_MAP
Map2 [p] = cp ;
#endif
Ai [cp] = i ;
#ifdef DO_VALUES
#ifdef COMPLEX
if (split)
{
Ax [cp] = Rx [p] ;
Az [cp] = Rz [p] ;
}
else
{
Ax [2*cp ] = Rx [2*p ] ;
Ax [2*cp+1] = Rx [2*p+1] ;
}
#else
Ax [cp] = Rx [p] ;
#endif
#endif
}
}
/* ---------------------------------------------------------------------- */
/* merge Map and Map2 into a single Map */
/* ---------------------------------------------------------------------- */
#ifdef DO_MAP
for (k = 0 ; k < nz ; k++)
{
Map [k] = Map2 [Map [k]] ;
}
#endif
/* now the kth triplet maps to p = Map [k], and thus to Ai/Ax [p] */
#ifndef NDEBUG
for (j = 0 ; j < n_col ; j++)
{
ASSERT (W [j] == Ap [j+1]) ;
}
UMF_dump_col_matrix (
#ifdef DO_VALUES
Ax,
#ifdef COMPLEX
Az,
#endif
#else
(double *) NULL,
#ifdef COMPLEX
(double *) NULL,
#endif
#endif
Ai, Ap, n_row, n_col, nz) ;
#ifdef DO_MAP
for (k = 0 ; k < nz ; k++)
{
/* make sure that kth triplet is mapped correctly */
p = Map [k] ;
DEBUG1 (("Col map: Map ["ID"] = "ID"\t", k, p)) ;
i = Ti [k] ;
j = Tj [k] ;
ASSERT (i == Ai [p]) ;
DEBUG1 ((" i "ID" j "ID" Ap[j] "ID" p "ID" Ap[j+1] "ID"\n",
i, j, Ap [j], p, Ap [j+1])) ;
ASSERT (Ap [j] <= p && p < Ap [j+1]) ;
}
#endif
#endif
return (UMFPACK_OK) ;
}
PRIVATE void get_U
(
Int Up [ ], /* of size n_col+1 */
Int Ui [ ], /* of size unz, where unz = Up [n_col] */
double Ux [ ], /* of size unz */
#ifdef COMPLEX
double Uz [ ], /* of size unz */
#endif
NumericType *Numeric,
Int Pattern [ ], /* workspace of size n_col */
Int Wi [ ] /* workspace of size n_col */
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Entry value ;
Entry *xp, *D, *Uval ;
Int deg, j, *ip, col, *Upos, *Uilen, *Uip, n_col, ulen, *Usi,
unz2, p, k, up, newUchain, pos, npiv, n1 ;
#ifdef COMPLEX
Int split = SPLIT (Uz) ;
#endif
#ifndef NDEBUG
Int nnzpiv = 0 ;
#endif
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
DEBUG4 (("get_U start:\n")) ;
n_col = Numeric->n_col ;
n1 = Numeric->n1 ;
npiv = Numeric->npiv ;
Upos = Numeric->Upos ;
Uilen = Numeric->Uilen ;
Uip = Numeric->Uip ;
D = Numeric->D ;
/* ---------------------------------------------------------------------- */
/* count the nonzeros in each column of U */
/* ---------------------------------------------------------------------- */
for (col = 0 ; col < npiv ; col++)
{
/* include the diagonal entry in the column counts */
DEBUG4 (("D ["ID"] = ", col)) ;
EDEBUG4 (D [col]) ;
Wi [col] = IS_NONZERO (D [col]) ;
DEBUG4 ((" is nonzero: "ID"\n", Wi [col])) ;
#ifndef NDEBUG
nnzpiv += IS_NONZERO (D [col]) ;
#endif
}
DEBUG4 (("nnzpiv "ID" "ID"\n", nnzpiv, Numeric->nnzpiv)) ;
ASSERT (nnzpiv == Numeric->nnzpiv) ;
for (col = npiv ; col < n_col ; col++)
{
/* diagonal entries are zero for structurally singular part */
Wi [col] = 0 ;
}
deg = Numeric->ulen ;
if (deg > 0)
{
/* make last pivot row of U (singular matrices only) */
DEBUG0 (("Last pivot row of U: ulen "ID"\n", deg)) ;
for (j = 0 ; j < deg ; j++)
{
Pattern [j] = Numeric->Upattern [j] ;
DEBUG0 ((" column "ID"\n", Pattern [j])) ;
}
}
/* non-singletons */
for (k = npiv-1 ; k >= n1 ; k--)
{
/* ------------------------------------------------------------------ */
/* use row k of U */
/* ------------------------------------------------------------------ */
up = Uip [k] ;
ulen = Uilen [k] ;
newUchain = (up < 0) ;
if (newUchain)
{
up = -up ;
xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
}
else
{
xp = (Entry *) (Numeric->Memory + up) ;
}
for (j = 0 ; j < deg ; j++)
{
DEBUG4 ((" k "ID" col "ID" value\n", k, Pattern [j])) ;
col = Pattern [j] ;
ASSERT (col >= 0 && col < n_col) ;
value = *xp++ ;
EDEBUG4 (value) ;
DEBUG4 (("\n")) ;
if (IS_NONZERO (value))
{
Wi [col]++ ;
}
}
/* ------------------------------------------------------------------ */
/* make row k-1 of U in Pattern [0..deg-1] */
/* ------------------------------------------------------------------ */
if (k == n1) break ;
if (newUchain)
{
/* next row is a new Uchain */
deg = ulen ;
DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ;
ip = (Int *) (Numeric->Memory + up) ;
for (j = 0 ; j < deg ; j++)
{
col = *ip++ ;
DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ;
ASSERT (k <= col) ;
Pattern [j] = col ;
}
}
else
{
deg -= ulen ;
DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k-1, deg));
ASSERT (deg >= 0) ;
pos = Upos [k] ;
if (pos != EMPTY)
{
/* add the pivot column */
DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ;
ASSERT (pos >= 0 && pos <= deg) ;
Pattern [deg++] = Pattern [pos] ;
Pattern [pos] = k ;
}
}
}
/* singletons */
for (k = n1 - 1 ; k >= 0 ; k--)
{
deg = Uilen [k] ;
DEBUG4 (("Singleton k "ID"\n", k)) ;
if (deg > 0)
{
up = Uip [k] ;
Usi = (Int *) (Numeric->Memory + up) ;
up += UNITS (Int, deg) ;
Uval = (Entry *) (Numeric->Memory + up) ;
for (j = 0 ; j < deg ; j++)
{
col = Usi [j] ;
value = Uval [j] ;
DEBUG4 ((" k "ID" col "ID" value", k, col)) ;
EDEBUG4 (value) ;
DEBUG4 (("\n")) ;
if (IS_NONZERO (value))
{
Wi [col]++ ;
}
}
}
}
/* ---------------------------------------------------------------------- */
/* construct the final column form of U */
/* ---------------------------------------------------------------------- */
/* create the column pointers */
unz2 = 0 ;
for (col = 0 ; col < n_col ; col++)
{
Up [col] = unz2 ;
unz2 += Wi [col] ;
}
Up [n_col] = unz2 ;
DEBUG1 (("Numeric->unz "ID" npiv "ID" nnzpiv "ID" unz2 "ID"\n",
Numeric->unz, npiv, Numeric->nnzpiv, unz2)) ;
ASSERT (Numeric->unz + Numeric->nnzpiv == unz2) ;
for (col = 0 ; col < n_col ; col++)
{
Wi [col] = Up [col+1] ;
}
/* add all of the diagonal entries */
for (col = 0 ; col < npiv ; col++)
{
if (IS_NONZERO (D [col]))
{
p = --(Wi [col]) ;
Ui [p] = col ;
#ifdef COMPLEX
if (split)
{
Ux [p] = REAL_COMPONENT (D [col]) ;
Uz [p] = IMAG_COMPONENT (D [col]) ;
}
else
{
Ux [2*p ] = REAL_COMPONENT (D [col]) ;
Ux [2*p+1] = IMAG_COMPONENT (D [col]) ;
}
#else
Ux [p] = D [col] ;
#endif
}
}
/* add all the entries from the rows of U */
deg = Numeric->ulen ;
if (deg > 0)
{
/* make last pivot row of U (singular matrices only) */
for (j = 0 ; j < deg ; j++)
{
Pattern [j] = Numeric->Upattern [j] ;
}
}
/* non-singletons */
for (k = npiv-1 ; k >= n1 ; k--)
{
/* ------------------------------------------------------------------ */
/* use row k of U */
/* ------------------------------------------------------------------ */
up = Uip [k] ;
ulen = Uilen [k] ;
newUchain = (up < 0) ;
if (newUchain)
{
up = -up ;
xp = (Entry *) (Numeric->Memory + up + UNITS (Int, ulen)) ;
}
else
{
xp = (Entry *) (Numeric->Memory + up) ;
}
xp += deg ;
for (j = deg-1 ; j >= 0 ; j--)
{
DEBUG4 ((" k "ID" col "ID" value", k, Pattern [j])) ;
col = Pattern [j] ;
ASSERT (col >= 0 && col < n_col) ;
value = *(--xp) ;
EDEBUG4 (value) ;
DEBUG4 (("\n")) ;
if (IS_NONZERO (value))
{
p = --(Wi [col]) ;
Ui [p] = k ;
#ifdef COMPLEX
if (split)
{
Ux [p] = REAL_COMPONENT (value) ;
Uz [p] = IMAG_COMPONENT (value) ;
}
else
{
Ux [2*p ] = REAL_COMPONENT (value) ;
Ux [2*p+1] = IMAG_COMPONENT (value) ;
}
#else
Ux [p] = value ;
#endif
}
}
/* ------------------------------------------------------------------ */
/* make row k-1 of U in Pattern [0..deg-1] */
/* ------------------------------------------------------------------ */
if (newUchain)
{
/* next row is a new Uchain */
deg = ulen ;
DEBUG4 (("end of chain for row of U "ID" deg "ID"\n", k-1, deg)) ;
ip = (Int *) (Numeric->Memory + up) ;
for (j = 0 ; j < deg ; j++)
{
col = *ip++ ;
DEBUG4 ((" k "ID" col "ID"\n", k-1, col)) ;
ASSERT (k <= col) ;
Pattern [j] = col ;
}
}
else
{
deg -= ulen ;
DEBUG4 (("middle of chain for row of U "ID" deg "ID"\n", k-1, deg));
ASSERT (deg >= 0) ;
pos = Upos [k] ;
if (pos != EMPTY)
{
/* add the pivot column */
DEBUG4 (("k "ID" add pivot entry at position "ID"\n", k, pos)) ;
ASSERT (pos >= 0 && pos <= deg) ;
Pattern [deg++] = Pattern [pos] ;
Pattern [pos] = k ;
}
}
}
/* singletons */
for (k = n1 - 1 ; k >= 0 ; k--)
{
deg = Uilen [k] ;
DEBUG4 (("Singleton k "ID"\n", k)) ;
if (deg > 0)
{
up = Uip [k] ;
Usi = (Int *) (Numeric->Memory + up) ;
up += UNITS (Int, deg) ;
Uval = (Entry *) (Numeric->Memory + up) ;
for (j = 0 ; j < deg ; j++)
{
col = Usi [j] ;
value = Uval [j] ;
DEBUG4 ((" k "ID" col "ID" value", k, col)) ;
EDEBUG4 (value) ;
DEBUG4 (("\n")) ;
if (IS_NONZERO (value))
{
p = --(Wi [col]) ;
Ui [p] = k ;
#ifdef COMPLEX
if (split)
{
Ux [p] = REAL_COMPONENT (value) ;
Uz [p] = IMAG_COMPONENT (value) ;
}
else
{
Ux [2*p ] = REAL_COMPONENT (value) ;
Ux [2*p+1] = IMAG_COMPONENT (value) ;
}
#else
Ux [p] = value ;
#endif
}
}
}
}
#ifndef NDEBUG
DEBUG6 (("U matrix:")) ;
UMF_dump_col_matrix (Ux,
#ifdef COMPLEX
Uz,
#endif
Ui, Up, Numeric->n_row, n_col, Numeric->unz + Numeric->nnzpiv) ;
#endif
}
GLOBAL Int UMF_transpose
(
Int n_row, /* A is n_row-by-n_col */
Int n_col,
const Int Ap [ ], /* size n_col+1 */
const Int Ai [ ], /* size nz = Ap [n_col] */
const double Ax [ ], /* size nz if present */
const Int P [ ], /* P [k] = i means original row i is kth row in A(P,Q)*/
/* P is identity if not present */
/* size n_row, if present */
const Int Q [ ], /* Q [k] = j means original col j is kth col in A(P,Q)*/
/* Q is identity if not present */
/* size nq, if present */
Int nq, /* size of Q, ignored if Q is (Int *) NULL */
/* output matrix: Rp, Ri, Rx, and Rz: */
Int Rp [ ], /* size n_row+1 */
Int Ri [ ], /* size nz */
double Rx [ ], /* size nz, if present */
Int W [ ], /* size max (n_row,n_col) workspace */
Int check /* if true, then check inputs */
#ifdef COMPLEX
, const double Az [ ] /* size nz */
, double Rz [ ] /* size nz */
, Int do_conjugate /* if true, then do conjugate transpose */
/* otherwise, do array transpose */
#endif
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Int i, j, k, p, bp, newj, do_values ;
#ifdef COMPLEX
Int split ;
#endif
/* ---------------------------------------------------------------------- */
/* check inputs */
/* ---------------------------------------------------------------------- */
#ifndef NDEBUG
Int nz ;
ASSERT (n_col >= 0) ;
nz = (Ap != (Int *) NULL) ? Ap [n_col] : 0 ;
DEBUG2 (("UMF_transpose: "ID"-by-"ID" nz "ID"\n", n_row, n_col, nz)) ;
#endif
if (check)
{
/* UMFPACK_symbolic skips this check */
/* UMFPACK_transpose always does this check */
if (!Ai || !Ap || !Ri || !Rp || !W)
{
return (UMFPACK_ERROR_argument_missing) ;
}
if (n_row <= 0 || n_col <= 0) /* n_row,n_col must be > 0 */
{
return (UMFPACK_ERROR_n_nonpositive) ;
}
if (!UMF_is_permutation (P, W, n_row, n_row) ||
!UMF_is_permutation (Q, W, nq, nq))
{
return (UMFPACK_ERROR_invalid_permutation) ;
}
if (!AMD_valid (n_row, n_col, Ap, Ai))
{
return (UMFPACK_ERROR_invalid_matrix) ;
}
}
#ifndef NDEBUG
DEBUG2 (("UMF_transpose, input matrix:\n")) ;
UMF_dump_col_matrix (Ax,
#ifdef COMPLEX
Az,
#endif
Ai, Ap, n_row, n_col, nz) ;
#endif
/* ---------------------------------------------------------------------- */
/* count the entries in each row of A */
/* ---------------------------------------------------------------------- */
/* use W as workspace for RowCount */
for (i = 0 ; i < n_row ; i++)
{
W [i] = 0 ;
Rp [i] = 0 ;
}
if (Q != (Int *) NULL)
{
for (newj = 0 ; newj < nq ; newj++)
{
j = Q [newj] ;
ASSERT (j >= 0 && j < n_col) ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
i = Ai [p] ;
ASSERT (i >= 0 && i < n_row) ;
W [i]++ ;
}
}
}
else
{
for (j = 0 ; j < n_col ; j++)
{
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
i = Ai [p] ;
ASSERT (i >= 0 && i < n_row) ;
W [i]++ ;
}
}
}
/* ---------------------------------------------------------------------- */
/* compute the row pointers for R = A (P,Q) */
/* ---------------------------------------------------------------------- */
if (P != (Int *) NULL)
{
Rp [0] = 0 ;
for (k = 0 ; k < n_row ; k++)
{
i = P [k] ;
ASSERT (i >= 0 && i < n_row) ;
Rp [k+1] = Rp [k] + W [i] ;
}
for (k = 0 ; k < n_row ; k++)
{
i = P [k] ;
ASSERT (i >= 0 && i < n_row) ;
W [i] = Rp [k] ;
}
}
else
{
Rp [0] = 0 ;
for (i = 0 ; i < n_row ; i++)
{
Rp [i+1] = Rp [i] + W [i] ;
}
for (i = 0 ; i < n_row ; i++)
{
W [i] = Rp [i] ;
}
}
ASSERT (Rp [n_row] <= Ap [n_col]) ;
/* at this point, W holds the permuted row pointers */
/* ---------------------------------------------------------------------- */
/* construct the row form of B */
/* ---------------------------------------------------------------------- */
do_values = Ax && Rx ;
#ifdef COMPLEX
split = SPLIT (Az) && SPLIT (Rz) ;
if (do_conjugate && do_values)
{
if (Q != (Int *) NULL)
{
if (split)
{
/* R = A (P,Q)' */
for (newj = 0 ; newj < nq ; newj++)
{
j = Q [newj] ;
ASSERT (j >= 0 && j < n_col) ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = newj ;
Rx [bp] = Ax [p] ;
Rz [bp] = -Az [p] ;
}
}
}
else
{
/* R = A (P,Q)' (merged complex values) */
for (newj = 0 ; newj < nq ; newj++)
{
j = Q [newj] ;
ASSERT (j >= 0 && j < n_col) ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = newj ;
Rx [2*bp] = Ax [2*p] ;
Rx [2*bp+1] = -Ax [2*p+1] ;
}
}
}
}
else
{
if (split)
{
/* R = A (P,:)' */
for (j = 0 ; j < n_col ; j++)
{
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = j ;
Rx [bp] = Ax [p] ;
Rz [bp] = -Az [p] ;
}
}
}
else
{
/* R = A (P,:)' (merged complex values) */
for (j = 0 ; j < n_col ; j++)
{
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = j ;
Rx [2*bp] = Ax [2*p] ;
Rx [2*bp+1] = -Ax [2*p+1] ;
}
}
}
}
}
else
#endif
{
if (Q != (Int *) NULL)
{
if (do_values)
{
#ifdef COMPLEX
if (split)
#endif
{
/* R = A (P,Q).' */
for (newj = 0 ; newj < nq ; newj++)
{
j = Q [newj] ;
ASSERT (j >= 0 && j < n_col) ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = newj ;
Rx [bp] = Ax [p] ;
#ifdef COMPLEX
Rz [bp] = Az [p] ;
#endif
}
}
}
#ifdef COMPLEX
else
{
/* R = A (P,Q).' (merged complex values) */
for (newj = 0 ; newj < nq ; newj++)
{
j = Q [newj] ;
ASSERT (j >= 0 && j < n_col) ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = newj ;
Rx [2*bp] = Ax [2*p] ;
Rx [2*bp+1] = Ax [2*p+1] ;
}
}
}
#endif
}
else
{
/* R = pattern of A (P,Q).' */
for (newj = 0 ; newj < nq ; newj++)
{
j = Q [newj] ;
ASSERT (j >= 0 && j < n_col) ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
Ri [W [Ai [p]]++] = newj ;
}
}
}
}
else
{
if (do_values)
{
#ifdef COMPLEX
if (split)
#endif
{
/* R = A (P,:).' */
for (j = 0 ; j < n_col ; j++)
{
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = j ;
Rx [bp] = Ax [p] ;
#ifdef COMPLEX
Rz [bp] = Az [p] ;
#endif
}
}
}
#ifdef COMPLEX
else
{
/* R = A (P,:).' (merged complex values) */
for (j = 0 ; j < n_col ; j++)
{
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = j ;
Rx [2*bp] = Ax [2*p] ;
Rx [2*bp+1] = Ax [2*p+1] ;
}
}
}
#endif
}
else
{
/* R = pattern of A (P,:).' */
for (j = 0 ; j < n_col ; j++)
{
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
Ri [W [Ai [p]]++] = j ;
}
}
}
}
}
#ifndef NDEBUG
for (k = 0 ; k < n_row ; k++)
{
if (P != (Int *) NULL)
{
i = P [k] ;
}
else
{
i = k ;
}
DEBUG3 ((ID": W[i] "ID" Rp[k+1] "ID"\n", i, W [i], Rp [k+1])) ;
ASSERT (W [i] == Rp [k+1]) ;
}
DEBUG2 (("UMF_transpose, output matrix:\n")) ;
UMF_dump_col_matrix (Rx,
#ifdef COMPLEX
Rz,
#endif
Ri, Rp, n_col, n_row, Rp [n_row]) ;
ASSERT (AMD_valid (n_col, n_row, Rp, Ri)) ;
#endif
return (UMFPACK_OK) ;
}
PRIVATE void get_L
(
Int Lp [ ], /* of size n_row+1 */
Int Lj [ ], /* of size lnz, where lnz = Lp [n_row] */
double Lx [ ], /* of size lnz */
#ifdef COMPLEX
double Lz [ ], /* of size lnz */
#endif
NumericType *Numeric,
Int Pattern [ ], /* workspace of size n_row */
Int Wi [ ] /* workspace of size n_row */
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Entry value ;
Entry *xp, *Lval ;
Int deg, *ip, j, row, n_row, n_col, n_inner, *Lpos, *Lilen, *Lip, p, llen,
lnz2, lp, newLchain, k, pos, npiv, *Li, n1 ;
#ifdef COMPLEX
Int split = SPLIT (Lz) ;
#endif
/* ---------------------------------------------------------------------- */
/* get parameters */
/* ---------------------------------------------------------------------- */
DEBUG4 (("get_L start:\n")) ;
n_row = Numeric->n_row ;
n_col = Numeric->n_col ;
n_inner = MIN (n_row, n_col) ;
npiv = Numeric->npiv ;
n1 = Numeric->n1 ;
Lpos = Numeric->Lpos ;
Lilen = Numeric->Lilen ;
Lip = Numeric->Lip ;
deg = 0 ;
/* ---------------------------------------------------------------------- */
/* count the nonzeros in each row of L */
/* ---------------------------------------------------------------------- */
#pragma ivdep
for (row = 0 ; row < n_inner ; row++)
{
/* include the diagonal entry in the row counts */
Wi [row] = 1 ;
}
#pragma ivdep
for (row = n_inner ; row < n_row ; row++)
{
Wi [row] = 0 ;
}
/* singletons */
for (k = 0 ; k < n1 ; k++)
{
DEBUG4 (("Singleton k "ID"\n", k)) ;
deg = Lilen [k] ;
if (deg > 0)
{
lp = Lip [k] ;
Li = (Int *) (Numeric->Memory + lp) ;
lp += UNITS (Int, deg) ;
Lval = (Entry *) (Numeric->Memory + lp) ;
for (j = 0 ; j < deg ; j++)
{
row = Li [j] ;
value = Lval [j] ;
DEBUG4 ((" row "ID" k "ID" value", row, k)) ;
EDEBUG4 (value) ;
DEBUG4 (("\n")) ;
if (IS_NONZERO (value))
{
Wi [row]++ ;
}
}
}
}
/* non-singletons */
for (k = n1 ; k < npiv ; k++)
{
/* ------------------------------------------------------------------ */
/* make column of L in Pattern [0..deg-1] */
/* ------------------------------------------------------------------ */
lp = Lip [k] ;
newLchain = (lp < 0) ;
if (newLchain)
{
lp = -lp ;
deg = 0 ;
DEBUG4 (("start of chain for column of L\n")) ;
}
/* remove pivot row */
pos = Lpos [k] ;
if (pos != EMPTY)
{
DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n",
k, Pattern [pos], pos)) ;
ASSERT (!newLchain) ;
ASSERT (deg > 0) ;
ASSERT (pos >= 0 && pos < deg) ;
ASSERT (Pattern [pos] == k) ;
Pattern [pos] = Pattern [--deg] ;
}
/* concatenate the pattern */
ip = (Int *) (Numeric->Memory + lp) ;
llen = Lilen [k] ;
for (j = 0 ; j < llen ; j++)
{
row = *ip++ ;
DEBUG4 ((" row "ID" k "ID"\n", row, k)) ;
ASSERT (row > k && row < n_row) ;
Pattern [deg++] = row ;
}
xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
for (j = 0 ; j < deg ; j++)
{
DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
row = Pattern [j] ;
value = *xp++ ;
EDEBUG4 (value) ;
DEBUG4 (("\n")) ;
if (IS_NONZERO (value))
{
Wi [row]++ ;
}
}
}
/* ---------------------------------------------------------------------- */
/* construct the final row form of L */
/* ---------------------------------------------------------------------- */
/* create the row pointers */
lnz2 = 0 ;
for (row = 0 ; row < n_row ; row++)
{
Lp [row] = lnz2 ;
lnz2 += Wi [row] ;
Wi [row] = Lp [row] ;
}
Lp [n_row] = lnz2 ;
ASSERT (Numeric->lnz + n_inner == lnz2) ;
/* add entries from the rows of L (singletons) */
for (k = 0 ; k < n1 ; k++)
{
DEBUG4 (("Singleton k "ID"\n", k)) ;
deg = Lilen [k] ;
if (deg > 0)
{
lp = Lip [k] ;
Li = (Int *) (Numeric->Memory + lp) ;
lp += UNITS (Int, deg) ;
Lval = (Entry *) (Numeric->Memory + lp) ;
for (j = 0 ; j < deg ; j++)
{
row = Li [j] ;
value = Lval [j] ;
DEBUG4 ((" row "ID" k "ID" value", row, k)) ;
EDEBUG4 (value) ;
DEBUG4 (("\n")) ;
if (IS_NONZERO (value))
{
p = Wi [row]++ ;
Lj [p] = k ;
#ifdef COMPLEX
if (split)
{
Lx [p] = REAL_COMPONENT (value) ;
Lz [p] = IMAG_COMPONENT (value) ;
}
else
{
Lx [2*p ] = REAL_COMPONENT (value) ;
Lx [2*p+1] = IMAG_COMPONENT (value) ;
}
#else
Lx [p] = value ;
#endif
}
}
}
}
/* add entries from the rows of L (non-singletons) */
for (k = n1 ; k < npiv ; k++)
{
/* ------------------------------------------------------------------ */
/* make column of L in Pattern [0..deg-1] */
/* ------------------------------------------------------------------ */
lp = Lip [k] ;
newLchain = (lp < 0) ;
if (newLchain)
{
lp = -lp ;
deg = 0 ;
DEBUG4 (("start of chain for column of L\n")) ;
}
/* remove pivot row */
pos = Lpos [k] ;
if (pos != EMPTY)
{
DEBUG4 ((" k "ID" removing row "ID" at position "ID"\n",
k, Pattern [pos], pos)) ;
ASSERT (!newLchain) ;
ASSERT (deg > 0) ;
ASSERT (pos >= 0 && pos < deg) ;
ASSERT (Pattern [pos] == k) ;
Pattern [pos] = Pattern [--deg] ;
}
/* concatenate the pattern */
ip = (Int *) (Numeric->Memory + lp) ;
llen = Lilen [k] ;
for (j = 0 ; j < llen ; j++)
{
row = *ip++ ;
DEBUG4 ((" row "ID" k "ID"\n", row, k)) ;
ASSERT (row > k) ;
Pattern [deg++] = row ;
}
xp = (Entry *) (Numeric->Memory + lp + UNITS (Int, llen)) ;
for (j = 0 ; j < deg ; j++)
{
DEBUG4 ((" row "ID" k "ID" value", Pattern [j], k)) ;
row = Pattern [j] ;
value = *xp++ ;
EDEBUG4 (value) ;
DEBUG4 (("\n")) ;
if (IS_NONZERO (value))
{
p = Wi [row]++ ;
Lj [p] = k ;
#ifdef COMPLEX
if (split)
{
Lx [p] = REAL_COMPONENT (value) ;
Lz [p] = IMAG_COMPONENT (value) ;
}
else
{
Lx [2*p ] = REAL_COMPONENT (value) ;
Lx [2*p+1] = IMAG_COMPONENT (value) ;
}
#else
Lx [p] = value ;
#endif
}
}
}
/* add all of the diagonal entries (L is unit diagonal) */
for (row = 0 ; row < n_inner ; row++)
{
p = Wi [row]++ ;
Lj [p] = row ;
#ifdef COMPLEX
if (split)
{
Lx [p] = 1. ;
Lz [p] = 0. ;
}
else
{
Lx [2*p ] = 1. ;
Lx [2*p+1] = 0. ;
}
#else
Lx [p] = 1. ;
#endif
ASSERT (Wi [row] == Lp [row+1]) ;
}
#ifndef NDEBUG
DEBUG6 (("L matrix (stored by rows):")) ;
UMF_dump_col_matrix (Lx,
#ifdef COMPLEX
Lz,
#endif
Lj, Lp, n_inner, n_row, Numeric->lnz+n_inner) ;
#endif
DEBUG4 (("get_L done:\n")) ;
}
