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//------------------------------------------------------------------------------
// CAMD/Source/camd_1: construct input matrix and then order with camd_2
//------------------------------------------------------------------------------
// CAMD, Copyright (c) 2007-2022, Timothy A. Davis, Yanqing Chen, Patrick R.
// Amestoy, and Iain S. Duff. All Rights Reserved.
// SPDX-License-Identifier: BSD-3-clause
//------------------------------------------------------------------------------
/* CAMD_1: Construct A+A' for a sparse matrix A and perform the CAMD ordering.
*
* The n-by-n sparse matrix A can be unsymmetric. It is stored in MATLAB-style
* compressed-column form, with sorted row indices in each column, and no
* duplicate entries. Diagonal entries may be present, but they are ignored.
* Row indices of column j of A are stored in Ai [Ap [j] ... Ap [j+1]-1].
* Ap [0] must be zero, and nz = Ap [n] is the number of entries in A. The
* size of the matrix, n, must be greater than or equal to zero.
*
* This routine must be preceded by a call to CAMD_aat, which computes the
* number of entries in each row/column in A+A', excluding the diagonal.
* Len [j], on input, is the number of entries in row/column j of A+A'. This
* routine constructs the matrix A+A' and then calls CAMD_2. No error checking
* is performed (this was done in CAMD_valid).
*/
#include "camd_internal.h"
void CAMD_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+2,
* ideally slen = 1.2 * sum (Len) + 8n+2 */
Int S [ ], /* size slen workspace */
double Control [ ], /* input array of size CAMD_CONTROL */
double Info [ ], /* output array of size CAMD_INFO */
const Int C [ ] /* Constraint set of size n */
)
{
Int i, j, k, p, pfree, iwlen, pj, p1, p2, pj2, *Iw, *Pe, *Nv, *Head,
*Elen, *Degree, *s, *W, *Sp, *Tp, *BucketSet ;
/* --------------------------------------------------------------------- */
/* construct the matrix for CAMD_2 */
/* --------------------------------------------------------------------- */
ASSERT (n > 0) ;
iwlen = slen - (7*n+2) ; /* allocate 7*n+2 workspace from S */
s = S ;
Pe = s ; s += n ;
Nv = s ; s += n ;
Head = s ; s += n+1 ; /* NOTE: was size n in AMD; size n+1 in CAMD */
Elen = s ; s += n ;
Degree = s ; s += n ;
W = s ; s += n+1 ; /* NOTE: was size n in AMD; size n+1 in CAMD */
BucketSet = s ; s += n ;
Iw = s ; s += iwlen ;
ASSERT (CAMD_valid (n, n, Ap, Ai) == CAMD_OK) ;
ASSERT (CAMD_cvalid (n, C)) ;
/* 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 CAMD_2. CAMD_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++)
{
CAMD_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 */
/* --------------------------------------------------------------------- */
CAMD_2 (n, Pe, Iw, Len, iwlen, pfree,
Nv, Pinv, P, Head, Elen, Degree, W, Control, Info, C, BucketSet) ;
}
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