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 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) ;
}