GLOBAL Int AMD_order
(
Int n,
const Int Ap [ ],
const Int Ai [ ],
Int P [ ],
double Control [ ],
double Info [ ]
)
{
Int slen, *Len, *S, nz, nzaat, i, *Pinv, info ;
#ifndef NDEBUG
AMD_debug_init ("amd") ;
#endif
/* clear the Info array, if it exists */
info = Info != (double *) NULL ;
if (info)
{
for (i = 0 ; i < AMD_INFO ; i++)
{
Info [i] = EMPTY ;
}
Info [AMD_N] = n ;
Info [AMD_STATUS] = AMD_OK ;
}
/* make sure inputs exist and n is >= 0 */
if (Ai == (Int *) NULL || Ap == (Int *) NULL || P == (Int *) NULL || n < 0)
{
if (info) Info [AMD_STATUS] = AMD_INVALID ;
return (AMD_INVALID) ; /* arguments are invalid */
}
if (n == 0)
{
return (AMD_OK) ; /* n is 0 so there's nothing to do */
}
nz = Ap [n] ;
if (info)
{
Info [AMD_NZ] = nz ;
}
if (nz < 0)
{
if (info) Info [AMD_STATUS] = AMD_INVALID ;
return (AMD_INVALID) ;
}
/* Avoid integer overflow in memory size calculations. The space required
* by AMD is at most 2.4nz + 8n for S, and n for Len.
* Note nz - n <= nzaat <= 2*nz, below. */
if ((2.4 * (double) nz + 8 * (double) n) > (double) Int_MAX / sizeof (Int))
{
/* :: int overflow :: */
if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
return (AMD_OUT_OF_MEMORY) ;
}
if (!AMD_valid (n, n, Ap, Ai))
{
if (info) Info [AMD_STATUS] = AMD_INVALID ;
return (AMD_INVALID) ; /* matrix is invalid */
}
/* --------------------------------------------------------------------- */
/* determine the symmetry and count off-diagonal nonzeros in A+A' */
/* --------------------------------------------------------------------- */
/* allocate size-n integer workspace */
Len = (Int *) amd_malloc (n * sizeof (Int)) ;
if (!Len)
{
/* :: out of memory :: */
if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
return (AMD_OUT_OF_MEMORY) ;
}
nzaat = AMD_aat (n, Ap, Ai, Len, P, Info) ;
AMD_DEBUG1 (("nzaat: "ID"\n", nzaat)) ;
ASSERT (nz-n <= nzaat && nzaat <= 2*nz) ;
/* --------------------------------------------------------------------- */
/* allocate workspace for matrix, elbow room, and 7 size-n vectors */
/* --------------------------------------------------------------------- */
slen = (nzaat + nzaat/5 + n) + 7*n ;
if (info)
{
/* memory usage (Len and S), in bytes. */
Info [AMD_MEMORY] = ((double) slen + n) * sizeof (Int) ;
}
S = (Int *) amd_malloc (slen * sizeof (Int)) ;
AMD_DEBUG1 ((" S "ID" Len "ID" n "ID" nzaat "ID" slen "ID"\n",
(Int) S, (Int) Len, n, nzaat, slen)) ;
if (S == (Int *) NULL)
{
/* :: out of memory :: */
amd_free (Len) ;
if (Info != (double *) NULL) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
return (AMD_OUT_OF_MEMORY) ;
}
/* allocate space from S for Pinv */
Pinv = S + slen - n ;
slen -= n ;
/* --------------------------------------------------------------------- */
/* order the matrix */
/* --------------------------------------------------------------------- */
AMD_1 (n, Ap, Ai, P, Pinv, Len, slen, S, Control, Info) ;
/* --------------------------------------------------------------------- */
/* free the workspace */
/* --------------------------------------------------------------------- */
amd_free (Len) ;
amd_free (S) ;
return (AMD_OK) ; /* successful ordering */
}
GLOBAL void AMD_preprocess
(
Int n, /* input matrix: A is n-by-n */
const Int Ap [ ], /* size n+1 */
const Int Ai [ ], /* size nz = Ap [n] */
/* output matrix R: */
Int Rp [ ], /* size n+1 */
Int Ri [ ], /* size nz (or less, if duplicates present) */
Int W [ ], /* workspace of size n */
Int Flag [ ] /* workspace of size n */
)
{
/* --------------------------------------------------------------------- */
/* local variables */
/* --------------------------------------------------------------------- */
Int i, j, p, p2 ;
ASSERT (AMD_valid (n, n, Ap, Ai) != AMD_INVALID) ;
/* --------------------------------------------------------------------- */
/* count the entries in each row of A (excluding duplicates) */
/* --------------------------------------------------------------------- */
for (i = 0 ; i < n ; i++)
{
W [i] = 0 ; /* # of nonzeros in row i (excl duplicates) */
Flag [i] = EMPTY ; /* Flag [i] = j if i appears in column j */
}
for (j = 0 ; j < n ; j++)
{
p2 = Ap [j+1] ;
for (p = Ap [j] ; p < p2 ; p++)
{
i = Ai [p] ;
if (Flag [i] != j)
{
/* row index i has not yet appeared in column j */
W [i]++ ; /* one more entry in row i */
Flag [i] = j ; /* flag row index i as appearing in col j*/
}
}
}
/* --------------------------------------------------------------------- */
/* compute the row pointers for R */
/* --------------------------------------------------------------------- */
Rp [0] = 0 ;
for (i = 0 ; i < n ; i++)
{
Rp [i+1] = Rp [i] + W [i] ;
}
for (i = 0 ; i < n ; i++)
{
W [i] = Rp [i] ;
Flag [i] = EMPTY ;
}
/* --------------------------------------------------------------------- */
/* construct the row form matrix R */
/* --------------------------------------------------------------------- */
/* R = row form of pattern of A */
for (j = 0 ; j < n ; j++)
{
p2 = Ap [j+1] ;
for (p = Ap [j] ; p < p2 ; p++)
{
i = Ai [p] ;
if (Flag [i] != j)
{
/* row index i has not yet appeared in column j */
Ri [W [i]++] = j ; /* put col j in row i */
Flag [i] = j ; /* flag row index i as appearing in col j*/
}
}
}
#ifndef NDEBUG
ASSERT (AMD_valid (n, n, Rp, Ri) == AMD_OK) ;
for (j = 0 ; j < n ; j++)
{
ASSERT (W [j] == Rp [j+1]) ;
}
#endif
}
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) ;
}
void amdtest (cholmod_sparse *A)
{
double Control [AMD_CONTROL], Info [AMD_INFO], alpha ;
Int *P, *Cp, *Ci, *Sp, *Si, *Bp, *Bi, *Ep, *Ei, *Fp, *Fi,
*Len, *Nv, *Next, *Head, *Elen, *Deg, *Wi, *W, *Flag ;
cholmod_sparse *C, *B, *S, *E, *F ;
Int i, j, n, nrow, ncol, ok, cnz, bnz, p, trial, sorted ;
/* ---------------------------------------------------------------------- */
/* get inputs */
/* ---------------------------------------------------------------------- */
printf ("\nAMD test\n") ;
if (A == NULL)
{
return ;
}
if (A->stype)
{
B = CHOLMOD(copy) (A, 0, 0, cm) ;
}
else
{
B = CHOLMOD(aat) (A, NULL, 0, 0, cm) ;
}
if (A->nrow != A->ncol)
{
F = CHOLMOD(copy_sparse) (B, cm) ;
OK (F->nrow == F->ncol) ;
CHOLMOD(sort) (F, cm) ;
}
else
{
/* A is square and unsymmetric, and may have entries in A+A' that
* are not in A */
F = CHOLMOD(copy_sparse) (A, cm) ;
CHOLMOD(sort) (F, cm) ;
}
C = CHOLMOD(copy_sparse) (B, cm) ;
nrow = C->nrow ;
ncol = C->ncol ;
n = nrow ;
OK (nrow == ncol) ;
Cp = C->p ;
Ci = C->i ;
Bp = B->p ;
Bi = B->i ;
/* ---------------------------------------------------------------------- */
/* S = sorted form of B, using AMD_preprocess */
/* ---------------------------------------------------------------------- */
cnz = CHOLMOD(nnz) (C, cm) ;
S = CHOLMOD(allocate_sparse) (n, n, cnz, TRUE, TRUE, 0, CHOLMOD_PATTERN,
cm);
Sp = S->p ;
Si = S->i ;
W = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Flag = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
/* ---------------------------------------------------------------------- */
/* allocate workspace for amd */
/* ---------------------------------------------------------------------- */
P = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ;
Len = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Nv = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Next = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Head = CHOLMOD(malloc) (n+1, sizeof (Int), cm) ;
Elen = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Deg = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
Wi = CHOLMOD(malloc) (n, sizeof (Int), cm) ;
/* ---------------------------------------------------------------------- */
for (sorted = 0 ; sorted <= 1 ; sorted++)
{
if (sorted) CHOLMOD(sort) (C, cm) ;
Cp = C->p ;
Ci = C->i ;
/* ------------------------------------------------------------------ */
/* order C with AMD_order */
/* ------------------------------------------------------------------ */
AMD_defaults (Control) ;
AMD_defaults (NULL) ;
AMD_control (Control) ;
AMD_control (NULL) ;
AMD_info (NULL) ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation", cm)) ;
/* no dense rows/cols */
alpha = Control [AMD_DENSE] ;
Control [AMD_DENSE] = -1 ;
AMD_control (Control) ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (alpha=-1)", cm)) ;
/* many dense rows/cols */
Control [AMD_DENSE] = 0 ;
AMD_control (Control) ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (alpha=0)", cm)) ;
Control [AMD_DENSE] = alpha ;
/* no aggressive absorption */
Control [AMD_AGGRESSIVE] = FALSE ;
AMD_control (Control) ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation (no agg) ", cm)) ;
Control [AMD_AGGRESSIVE] = TRUE ;
/* ------------------------------------------------------------------ */
/* order F with AMD_order */
/* ------------------------------------------------------------------ */
Fp = F->p ;
Fi = F->i ;
ok = AMD_order (n, Fp, Fi, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "F: AMD permutation", cm)) ;
/* ------------------------------------------------------------------ */
/* order S with AMD_order */
/* ------------------------------------------------------------------ */
ok = AMD_order (n, Sp, Si, P, Control, Info) ;
printf ("amd return value: "ID"\n", ok) ;
AMD_info (Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD permutation", cm)) ;
/* ------------------------------------------------------------------ */
/* order E with AMD_2, which destroys its contents */
/* ------------------------------------------------------------------ */
E = CHOLMOD(copy) (B, 0, -1, cm) ; /* remove diagonal entries */
bnz = CHOLMOD(nnz) (E, cm) ;
/* add the bare minimum extra space to E */
ok = CHOLMOD(reallocate_sparse) (bnz + n, E, cm) ;
OK (ok) ;
Ep = E->p ;
Ei = E->i ;
for (j = 0 ; j < n ; j++)
{
Len [j] = Ep [j+1] - Ep [j] ;
}
printf ("calling AMD_2:\n") ;
if (n > 0)
{
AMD_2 (n, Ep, Ei, Len, E->nzmax, Ep [n], Nv, Next, P, Head, Elen,
Deg, Wi, Control, Info) ;
AMD_info (Info) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD2 permutation", cm)) ;
}
/* ------------------------------------------------------------------ */
/* error tests */
/* ------------------------------------------------------------------ */
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
ok = AMD_order (-1, Cp, Ci, P, Control, Info) ;
OK (ok == AMD_INVALID);
ok = AMD_order (0, Cp, Ci, P, Control, Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
ok = AMD_order (n, NULL, Ci, P, Control, Info) ;
OK (ok == AMD_INVALID);
ok = AMD_order (n, Cp, NULL, P, Control, Info) ;
OK (ok == AMD_INVALID);
ok = AMD_order (n, Cp, Ci, NULL, Control, Info) ;
OK (ok == AMD_INVALID);
if (n > 0)
{
printf ("AMD error tests:\n") ;
p = Cp [n] ;
Cp [n] = -1 ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
OK (ok == AMD_INVALID) ;
if (Size_max/2 == Int_max)
{
Cp [n] = Int_max ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
printf ("AMD status is "ID"\n", ok) ;
OK (ok == AMD_OUT_OF_MEMORY) ;
}
Cp [n] = p ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
if (Cp [n] > 0)
{
printf ("Mangle column zero:\n") ;
i = Ci [0] ;
Ci [0] = -1 ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
AMD_info (Info) ;
OK (ok == AMD_INVALID) ;
Ci [0] = i ;
}
}
ok = AMD_valid (n, n, Sp, Si) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
ok = AMD_valid (-1, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
ok = AMD_valid (n, -1, Sp, Si) ; OK (ok == AMD_INVALID) ;
ok = AMD_valid (n, n, NULL, Si) ; OK (ok == AMD_INVALID) ;
ok = AMD_valid (n, n, Sp, NULL) ; OK (ok == AMD_INVALID) ;
if (n > 0 && Sp [n] > 0)
{
p = Sp [n] ;
Sp [n] = -1 ;
ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
Sp [n] = p ;
p = Sp [0] ;
Sp [0] = -1 ;
ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
Sp [0] = p ;
p = Sp [1] ;
Sp [1] = -1 ;
ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
Sp [1] = p ;
i = Si [0] ;
Si [0] = -1 ;
ok = AMD_valid (n, n, Sp, Si) ; OK (ok == AMD_INVALID) ;
Si [0] = i ;
}
ok = AMD_valid (n, n, Sp, Si) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
ok = AMD_valid (n, n, Sp, Si) ;
OK (ok == AMD_OK) ;
if (n > 0 && Bp [n] > 0)
{
p = Bp [n] ;
Bp [n] = -1 ;
ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ;
Bp [n] = p ;
p = Bp [1] ;
Bp [1] = -1 ;
ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ;
Bp [1] = p ;
i = Bi [0] ;
Bi [0] = -1 ;
ok = AMD_valid (n, n, Bp, Bi) ; OK (ok == AMD_INVALID) ;
Bi [0] = i ;
}
AMD_preprocess (n, Bp, Bi, Sp, Si, W, Flag) ;
Info [AMD_STATUS] = 777 ;
AMD_info (Info) ;
/* ------------------------------------------------------------------ */
/* memory tests */
/* ------------------------------------------------------------------ */
if (n > 0)
{
amd_malloc = cm->malloc_memory ;
amd_free = cm->free_memory ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
OK (sorted ? (ok == AMD_OK) : (ok >= AMD_OK)) ;
test_memory_handler ( ) ;
amd_malloc = cm->malloc_memory ;
amd_free = cm->free_memory ;
for (trial = 0 ; trial < 6 ; trial++)
{
my_tries = trial ;
printf ("AMD memory trial "ID"\n", trial) ;
ok = AMD_order (n, Cp, Ci, P, Control, Info) ;
AMD_info (Info) ;
OK (ok == AMD_OUT_OF_MEMORY
|| (sorted ? (ok == AMD_OK) : (ok >= AMD_OK))) ;
}
normal_memory_handler ( ) ;
OK (CHOLMOD(print_perm) (P, n, n, "AMD2 permutation", cm)) ;
amd_malloc = cm->malloc_memory ;
amd_free = cm->free_memory ;
}
CHOLMOD(free_sparse) (&E, cm) ;
}
/* ---------------------------------------------------------------------- */
/* free everything */
/* ---------------------------------------------------------------------- */
CHOLMOD(free) (n, sizeof (Int), Len, cm) ;
CHOLMOD(free) (n, sizeof (Int), Nv, cm) ;
CHOLMOD(free) (n, sizeof (Int), Next, cm) ;
CHOLMOD(free) (n+1, sizeof (Int), Head, cm) ;
CHOLMOD(free) (n, sizeof (Int), Elen, cm) ;
CHOLMOD(free) (n, sizeof (Int), Deg, cm) ;
CHOLMOD(free) (n, sizeof (Int), Wi, cm) ;
CHOLMOD(free) (n+1, sizeof (Int), P, cm) ;
CHOLMOD(free) (n, sizeof (Int), W, cm) ;
CHOLMOD(free) (n, sizeof (Int), Flag, cm) ;
CHOLMOD(free_sparse) (&S, cm) ;
CHOLMOD(free_sparse) (&B, cm) ;
CHOLMOD(free_sparse) (&C, cm) ;
CHOLMOD(free_sparse) (&F, cm) ;
}
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 void AMD_1
(
Int n, /* n > 0 */
const Int Ap [ ], /* input of size n+1, not modified */
const Int Ai [ ], /* input of size nz = Ap [n], not modified */
Int P [ ], /* size n output permutation */
Int Pinv [ ], /* size n output inverse permutation */
Int Len [ ], /* size n input, undefined on output */
Int slen, /* slen >= sum (Len [0..n-1]) + 7n,
* ideally slen = 1.2 * sum (Len) + 8n */
Int S [ ], /* size slen workspace */
double Control [ ], /* input array of size AMD_CONTROL */
double Info [ ] /* output array of size AMD_INFO */
)
{
Int i, j, k, p, pfree, iwlen, pj, p1, p2, pj2, *Iw, *Pe, *Nv, *Head,
*Elen, *Degree, *s, *W, *Sp, *Tp ;
/* --------------------------------------------------------------------- */
/* construct the matrix for AMD_2 */
/* --------------------------------------------------------------------- */
ASSERT (n > 0) ;
iwlen = slen - 6*n ;
s = S ;
Pe = s ; s += n ;
Nv = s ; s += n ;
Head = s ; s += n ;
Elen = s ; s += n ;
Degree = s ; s += n ;
W = s ; s += n ;
Iw = s ; s += iwlen ;
ASSERT (AMD_valid (n, n, Ap, Ai)) ;
/* construct the pointers for A+A' */
Sp = Nv ; /* use Nv and W as workspace for Sp and Tp [ */
Tp = W ;
pfree = 0 ;
for (j = 0 ; j < n ; j++)
{
Pe [j] = pfree ;
Sp [j] = pfree ;
pfree += Len [j] ;
}
/* Note that this restriction on iwlen is slightly more restrictive than
* what is strictly required in AMD_2. AMD_2 can operate with no elbow
* room at all, but it will be very slow. For better performance, at
* least size-n elbow room is enforced. */
ASSERT (iwlen >= pfree + n) ;
#ifndef NDEBUG
for (p = 0 ; p < iwlen ; p++) Iw [p] = EMPTY ;
#endif
for (k = 0 ; k < n ; k++)
{
AMD_DEBUG1 (("Construct row/column k= "ID" of A+A'\n", k)) ;
p1 = Ap [k] ;
p2 = Ap [k+1] ;
/* construct A+A' */
for (p = p1 ; p < p2 ; )
{
/* scan the upper triangular part of A */
j = Ai [p] ;
ASSERT (j >= 0 && j < n) ;
if (j < k)
{
/* entry A (j,k) in the strictly upper triangular part */
ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
ASSERT (Sp [k] < (k == n-1 ? pfree : Pe [k+1])) ;
Iw [Sp [j]++] = k ;
Iw [Sp [k]++] = j ;
p++ ;
}
else if (j == k)
{
/* skip the diagonal */
p++ ;
break ;
}
else /* j > k */
{
/* first entry below the diagonal */
break ;
}
/* scan lower triangular part of A, in column j until reaching
* row k. Start where last scan left off. */
ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ;
pj2 = Ap [j+1] ;
for (pj = Tp [j] ; pj < pj2 ; )
{
i = Ai [pj] ;
ASSERT (i >= 0 && i < n) ;
if (i < k)
{
/* A (i,j) is only in the lower part, not in upper */
ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ;
ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
Iw [Sp [i]++] = j ;
Iw [Sp [j]++] = i ;
pj++ ;
}
else if (i == k)
{
/* entry A (k,j) in lower part and A (j,k) in upper */
pj++ ;
break ;
}
else /* i > k */
{
/* consider this entry later, when k advances to i */
break ;
}
}
Tp [j] = pj ;
}
Tp [k] = p ;
}
/* clean up, for remaining mismatched entries */
for (j = 0 ; j < n ; j++)
{
for (pj = Tp [j] ; pj < Ap [j+1] ; pj++)
{
i = Ai [pj] ;
ASSERT (i >= 0 && i < n) ;
/* A (i,j) is only in the lower part, not in upper */
ASSERT (Sp [i] < (i == n-1 ? pfree : Pe [i+1])) ;
ASSERT (Sp [j] < (j == n-1 ? pfree : Pe [j+1])) ;
Iw [Sp [i]++] = j ;
Iw [Sp [j]++] = i ;
}
}
#ifndef NDEBUG
for (j = 0 ; j < n-1 ; j++) ASSERT (Sp [j] == Pe [j+1]) ;
ASSERT (Sp [n-1] == pfree) ;
#endif
/* Tp and Sp no longer needed ] */
/* --------------------------------------------------------------------- */
/* order the matrix */
/* --------------------------------------------------------------------- */
AMD_2 (n, Pe, Iw, Len, iwlen, pfree,
Nv, Pinv, P, Head, Elen, Degree, W, Control, Info) ;
}
GLOBAL Int AMD_order
(
Int n,
const Int Ap [ ],
const Int Ai [ ],
Int P [ ],
double Control [ ],
double Info [ ]
)
{
Int *Len, *S, nz, i, *Pinv, info, status, *Rp, *Ri, *Cp, *Ci, ok ;
size_t nzaat, slen ;
double mem = 0 ;
#ifndef NDEBUG
AMD_debug_init ("amd") ;
#endif
/* clear the Info array, if it exists */
info = Info != (double *) NULL ;
if (info)
{
for (i = 0 ; i < AMD_INFO ; i++)
{
Info [i] = EMPTY ;
}
Info [AMD_N] = n ;
Info [AMD_STATUS] = AMD_OK ;
}
/* make sure inputs exist and n is >= 0 */
if (Ai == (Int *) NULL || Ap == (Int *) NULL || P == (Int *) NULL || n < 0)
{
if (info) Info [AMD_STATUS] = AMD_INVALID ;
return (AMD_INVALID) ; /* arguments are invalid */
}
if (n == 0)
{
return (AMD_OK) ; /* n is 0 so there's nothing to do */
}
nz = Ap [n] ;
if (info)
{
Info [AMD_NZ] = nz ;
}
if (nz < 0)
{
if (info) Info [AMD_STATUS] = AMD_INVALID ;
return (AMD_INVALID) ;
}
/* check if n or nz will cause size_t overflow */
if (((size_t) n) >= SIZE_T_MAX / sizeof (Int)
|| ((size_t) nz) >= SIZE_T_MAX / sizeof (Int))
{
if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
return (AMD_OUT_OF_MEMORY) ; /* problem too large */
}
/* check the input matrix: AMD_OK, AMD_INVALID, or AMD_OK_BUT_JUMBLED */
status = AMD_valid (n, n, Ap, Ai) ;
if (status == AMD_INVALID)
{
if (info) Info [AMD_STATUS] = AMD_INVALID ;
return (AMD_INVALID) ; /* matrix is invalid */
}
/* allocate two size-n integer workspaces */
Len = (Int*)amd_malloc (n * sizeof (Int)) ;
Pinv = (Int*)amd_malloc (n * sizeof (Int)) ;
mem += n ;
mem += n ;
if (!Len || !Pinv)
{
/* :: out of memory :: */
amd_free (Len) ;
amd_free (Pinv) ;
if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
return (AMD_OUT_OF_MEMORY) ;
}
if (status == AMD_OK_BUT_JUMBLED)
{
/* sort the input matrix and remove duplicate entries */
AMD_DEBUG1 (("Matrix is jumbled\n")) ;
Rp = (Int*)amd_malloc ((n+1) * sizeof (Int)) ;
Ri = (Int*)amd_malloc (MAX (nz,1) * sizeof (Int)) ;
mem += (n+1) ;
mem += MAX (nz,1) ;
if (!Rp || !Ri)
{
/* :: out of memory :: */
amd_free (Rp) ;
amd_free (Ri) ;
amd_free (Len) ;
amd_free (Pinv) ;
if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
return (AMD_OUT_OF_MEMORY) ;
}
/* use Len and Pinv as workspace to create R = A' */
AMD_preprocess (n, Ap, Ai, Rp, Ri, Len, Pinv) ;
Cp = Rp ;
Ci = Ri ;
}
else
{
/* order the input matrix as-is. No need to compute R = A' first */
Rp = NULL ;
Ri = NULL ;
Cp = (Int *) Ap ;
Ci = (Int *) Ai ;
}
/* --------------------------------------------------------------------- */
/* determine the symmetry and count off-diagonal nonzeros in A+A' */
/* --------------------------------------------------------------------- */
nzaat = AMD_aat (n, Cp, Ci, Len, P, Info) ;
AMD_DEBUG1 (("nzaat: %g\n", (double) nzaat)) ;
ASSERT ((MAX (nz-n, 0) <= nzaat) && (nzaat <= 2 * (size_t) nz)) ;
/* --------------------------------------------------------------------- */
/* allocate workspace for matrix, elbow room, and 6 size-n vectors */
/* --------------------------------------------------------------------- */
S = NULL ;
slen = nzaat ; /* space for matrix */
ok = ((slen + nzaat/5) >= slen) ; /* check for size_t overflow */
slen += nzaat/5 ; /* add elbow room */
for (i = 0 ; ok && i < 7 ; i++)
{
ok = ((slen + n) > slen) ; /* check for size_t overflow */
slen += n ; /* size-n elbow room, 6 size-n work */
}
mem += slen ;
ok = ok && (slen < SIZE_T_MAX / sizeof (Int)) ; /* check for overflow */
ok = ok && (slen < Int_MAX) ; /* S[i] for Int i must be OK */
if (ok)
{
S = (Int*)amd_malloc (slen * sizeof (Int)) ;
}
AMD_DEBUG1 (("slen %g\n", (double) slen)) ;
if (!S)
{
/* :: out of memory :: (or problem too large) */
amd_free (Rp) ;
amd_free (Ri) ;
amd_free (Len) ;
amd_free (Pinv) ;
if (info) Info [AMD_STATUS] = AMD_OUT_OF_MEMORY ;
return (AMD_OUT_OF_MEMORY) ;
}
if (info)
{
/* memory usage, in bytes. */
Info [AMD_MEMORY] = mem * sizeof (Int) ;
}
/* --------------------------------------------------------------------- */
/* order the matrix */
/* --------------------------------------------------------------------- */
AMD_1 (n, Cp, Ci, P, Pinv, Len, slen, S, Control, Info) ;
/* --------------------------------------------------------------------- */
/* free the workspace */
/* --------------------------------------------------------------------- */
amd_free (Rp) ;
amd_free (Ri) ;
amd_free (Len) ;
amd_free (Pinv) ;
amd_free (S) ;
if (info) Info [AMD_STATUS] = status ;
return (status) ; /* successful ordering */
}
GLOBAL size_t AMD_aat /* returns nz in A+A' */
(
Int n,
const Int Ap [ ],
const Int Ai [ ],
Int Len [ ], /* Len [j]: length of column j of A+A', excl diagonal*/
Int Tp [ ], /* workspace of size n */
double Info [ ]
)
{
Int p1, p2, p, i, j, pj, pj2, k, nzdiag, nzboth, nz ;
double sym ;
size_t nzaat ;
#ifndef NDEBUG
AMD_debug_init ("AMD AAT") ;
for (k = 0 ; k < n ; k++) Tp [k] = EMPTY ;
ASSERT (AMD_valid (n, n, Ap, Ai) == AMD_OK) ;
#endif
if (Info != (double *) NULL)
{
/* clear the Info array, if it exists */
for (i = 0 ; i < AMD_INFO ; i++)
{
Info [i] = EMPTY ;
}
Info [AMD_STATUS] = AMD_OK ;
}
for (k = 0 ; k < n ; k++)
{
Len [k] = 0 ;
}
nzdiag = 0 ;
nzboth = 0 ;
nz = Ap [n] ;
for (k = 0 ; k < n ; k++)
{
p1 = Ap [k] ;
p2 = Ap [k+1] ;
AMD_DEBUG2 (("\nAAT Column: "ID" p1: "ID" p2: "ID"\n", k, p1, p2)) ;
/* construct A+A' */
for (p = p1 ; p < p2 ; )
{
/* scan the upper triangular part of A */
j = Ai [p] ;
if (j < k)
{
/* entry A (j,k) is in the strictly upper triangular part,
* add both A (j,k) and A (k,j) to the matrix A+A' */
Len [j]++ ;
Len [k]++ ;
AMD_DEBUG3 ((" upper ("ID","ID") ("ID","ID")\n", j,k, k,j));
p++ ;
}
else if (j == k)
{
/* skip the diagonal */
p++ ;
nzdiag++ ;
break ;
}
else /* j > k */
{
/* first entry below the diagonal */
break ;
}
/* scan lower triangular part of A, in column j until reaching
* row k. Start where last scan left off. */
ASSERT (Tp [j] != EMPTY) ;
ASSERT (Ap [j] <= Tp [j] && Tp [j] <= Ap [j+1]) ;
pj2 = Ap [j+1] ;
for (pj = Tp [j] ; pj < pj2 ; )
{
i = Ai [pj] ;
if (i < k)
{
/* A (i,j) is only in the lower part, not in upper.
* add both A (i,j) and A (j,i) to the matrix A+A' */
Len [i]++ ;
Len [j]++ ;
AMD_DEBUG3 ((" lower ("ID","ID") ("ID","ID")\n",
i,j, j,i)) ;
pj++ ;
}
else if (i == k)
{
/* entry A (k,j) in lower part and A (j,k) in upper */
pj++ ;
nzboth++ ;
break ;
}
else /* i > k */
{
/* consider this entry later, when k advances to i */
break ;
}
}
Tp [j] = pj ;
}
/* Tp [k] points to the entry just below the diagonal in column k */
Tp [k] = p ;
}
/* clean up, for remaining mismatched entries */
for (j = 0 ; j < n ; j++)
{
for (pj = Tp [j] ; pj < Ap [j+1] ; pj++)
{
i = Ai [pj] ;
/* A (i,j) is only in the lower part, not in upper.
* add both A (i,j) and A (j,i) to the matrix A+A' */
Len [i]++ ;
Len [j]++ ;
AMD_DEBUG3 ((" lower cleanup ("ID","ID") ("ID","ID")\n",
i,j, j,i)) ;
}
}
/* --------------------------------------------------------------------- */
/* compute the symmetry of the nonzero pattern of A */
/* --------------------------------------------------------------------- */
/* Given a matrix A, the symmetry of A is:
* B = tril (spones (A), -1) + triu (spones (A), 1) ;
* sym = nnz (B & B') / nnz (B) ;
* or 1 if nnz (B) is zero.
*/
if (nz == nzdiag)
{
sym = 1 ;
}
else
{
sym = (2 * (double) nzboth) / ((double) (nz - nzdiag)) ;
}
nzaat = 0 ;
for (k = 0 ; k < n ; k++)
{
nzaat += Len [k] ;
}
AMD_DEBUG1 (("AMD nz in A+A', excluding diagonal (nzaat) = %g\n",
(double) nzaat)) ;
AMD_DEBUG1 ((" nzboth: "ID" nz: "ID" nzdiag: "ID" symmetry: %g\n",
nzboth, nz, nzdiag, sym)) ;
if (Info != (double *) NULL)
{
Info [AMD_STATUS] = AMD_OK ;
Info [AMD_N] = n ;
Info [AMD_NZ] = nz ;
Info [AMD_SYMMETRY] = sym ; /* symmetry of pattern of A */
Info [AMD_NZDIAG] = nzdiag ; /* nonzeros on diagonal of A */
Info [AMD_NZ_A_PLUS_AT] = nzaat ; /* nonzeros in A+A' */
}
return (nzaat) ;
}
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) ;
}