//------------------------------------------------------------------------------
// CHOLMOD/Cholesky/cholmod_amd: AMD interface for CHOLMOD
//------------------------------------------------------------------------------

// CHOLMOD/Cholesky Module.  Copyright (C) 2005-2022, Timothy A. Davis
// All Rights Reserved.
// SPDX-License-Identifier: LGPL-2.1+

//------------------------------------------------------------------------------

/* CHOLMOD interface to the AMD ordering routine.  Orders A if the matrix is
 * symmetric.  On output, Perm [k] = i if row/column i of A is the kth
 * row/column of P*A*P'.  This corresponds to A(p,p) in MATLAB notation.
 *
 * If A is unsymmetric, cholmod_amd orders A*A'.  On output, Perm [k] = i if
 * row/column i of A*A' is the kth row/column of P*A*A'*P'.  This corresponds to
 * A(p,:)*A(p,:)' in MATLAB notation.  If f is present, A(p,f)*A(p,f)' is
 * ordered.
 *
 * Computes the flop count for a subsequent LL' factorization, the number
 * of nonzeros in L, and the number of nonzeros in the matrix ordered (A,
 * A*A' or A(:,f)*A(:,f)').
 *
 * workspace: Iwork (6*nrow). Head (nrow).
 *
 * Allocates a temporary copy of A+A' or A*A' (with
 * both upper and lower triangular parts) as input to AMD.
 *
 * Supports any xtype (pattern, real, complex, or zomplex)
 */

#include "cholmod_internal.h"

#ifndef NCHOLESKY

#include "amd.h"
#if (!defined (AMD_VERSION) || (AMD_VERSION < AMD_VERSION_CODE (2,0)))
#error "AMD v2.0 or later is required"
#endif

/* ========================================================================== */
/* === cholmod_amd ========================================================== */
/* ========================================================================== */

int CHOLMOD(amd)
(
    /* ---- input ---- */
    cholmod_sparse *A,	/* matrix to order */
    Int *fset,		/* subset of 0:(A->ncol)-1 */
    size_t fsize,	/* size of fset */
    /* ---- output --- */
    Int *Perm,		/* size A->nrow, output permutation */
    /* --------------- */
    cholmod_common *Common
)
{
    double Info [AMD_INFO], Control2 [AMD_CONTROL], *Control ;
    Int *Cp, *Len, *Nv, *Head, *Elen, *Degree, *Wi, *Iwork, *Next ;
    cholmod_sparse *C ;
    Int j, n, cnz ;
    size_t s ;
    int ok = TRUE ;

    /* ---------------------------------------------------------------------- */
    /* get inputs */
    /* ---------------------------------------------------------------------- */

    RETURN_IF_NULL_COMMON (FALSE) ;
    RETURN_IF_NULL (A, FALSE) ;
    n = A->nrow ;

    RETURN_IF_NULL (Perm, FALSE) ;
    RETURN_IF_XTYPE_INVALID (A, CHOLMOD_PATTERN, CHOLMOD_ZOMPLEX, FALSE) ;
    Common->status = CHOLMOD_OK ;
    if (n == 0)
    {
	/* nothing to do */
	Common->fl = 0 ;
	Common->lnz = 0 ;
	Common->anz = 0 ;
	return (TRUE) ;
    }

    /* ---------------------------------------------------------------------- */
    /* get workspace */
    /* ---------------------------------------------------------------------- */

    /* Note: this is less than the space used in cholmod_analyze, so if
     * cholmod_amd is being called by that routine, no space will be
     * allocated.
     */

    /* s = MAX (6*n, A->ncol) */
    s = CHOLMOD(mult_size_t) (n, 6, &ok) ;
    if (!ok)
    {
	ERROR (CHOLMOD_TOO_LARGE, "problem too large") ;
	return (FALSE) ;
    }
    s = MAX (s, A->ncol) ;

    CHOLMOD(allocate_work) (n, s, 0, Common) ;
    if (Common->status < CHOLMOD_OK)
    {
	return (FALSE) ;
    }

    Iwork  = Common->Iwork ;
    Degree = Iwork ;			/* size n */
    Wi     = Iwork + n ;		/* size n */
    Len    = Iwork + 2*((size_t) n) ;	/* size n */
    Nv     = Iwork + 3*((size_t) n) ;   /* size n */
    Next   = Iwork + 4*((size_t) n) ;   /* size n */
    Elen   = Iwork + 5*((size_t) n) ;   /* size n */

    Head = Common->Head ;   /* size n+1, but only n is used */

    /* ---------------------------------------------------------------------- */
    /* construct the input matrix for AMD */
    /* ---------------------------------------------------------------------- */

    if (A->stype == 0)
    {
	/* C = A*A' or A(:,f)*A(:,f)', add extra space of nnz(C)/2+n to C */
	C = CHOLMOD(aat) (A, fset, fsize, -2, Common) ;
    }
    else
    {
	/* C = A+A', but use only the upper triangular part of A if A->stype = 1
	 * and only the lower part of A if A->stype = -1.  Add extra space of
	 * nnz(C)/2+n to C. */
	C = CHOLMOD(copy) (A, 0, -2, Common) ;
    }

    if (Common->status < CHOLMOD_OK)
    {
	/* out of memory, fset invalid, or other error */
	return (FALSE) ;
    }

    Cp = C->p ;
    for (j = 0 ; j < n ; j++)
    {
	Len [j] = Cp [j+1] - Cp [j] ;
    }

    /* C does not include the diagonal, and both upper and lower parts.
     * Common->anz includes the diagonal, and just the lower part of C */
    cnz = Cp [n] ;
    Common->anz = cnz / 2 + n ;

    /* ---------------------------------------------------------------------- */
    /* order C using AMD */
    /* ---------------------------------------------------------------------- */

    /* get parameters */
    if (Common->current < 0 || Common->current >= CHOLMOD_MAXMETHODS)
    {
	/* use AMD defaults */
	Control = NULL ;
    }
    else
    {
	Control = Control2 ;
	Control [AMD_DENSE] = Common->method [Common->current].prune_dense ;
	Control [AMD_AGGRESSIVE] = Common->method [Common->current].aggressive ;
    }

#if ( ITYPE == CHOLMOD_LONG )
    amd_l2 (n, C->p,  C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen,
	    Degree, Wi, Control, Info) ;
#else
    amd_2 (n, C->p,  C->i, Len, C->nzmax, cnz, Nv, Next, Perm, Head, Elen,
	    Degree, Wi, Control, Info) ;
#endif

    /* LL' flop count.  Need to subtract n for LL' flop count.  Note that this
     * is a slight upper bound which is often exact (see AMD/Source/amd_2.c for
     * details).  cholmod_analyze computes an exact flop count and fill-in. */
    Common->fl = Info [AMD_NDIV] + 2 * Info [AMD_NMULTSUBS_LDL] + n ;

    /* Info [AMD_LNZ] excludes the diagonal */
    Common->lnz = n + Info [AMD_LNZ] ;

    /* ---------------------------------------------------------------------- */
    /* free the AMD workspace and clear the persistent workspace in Common */
    /* ---------------------------------------------------------------------- */

    ASSERT (IMPLIES (Common->status == CHOLMOD_OK,
		CHOLMOD(dump_perm) (Perm, n, n, "AMD2 perm", Common))) ;
    CHOLMOD(free_sparse) (&C, Common) ;
    for (j = 0 ; j <= n ; j++)
    {
	Head [j] = EMPTY ;
    }
    return (TRUE) ;
}
#endif
