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 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 */
}
