/* ========================================================================= */

 /* === AMD_1 =============================================================== */

 /* ========================================================================= */

 /* ------------------------------------------------------------------------- */

 /* AMD, Copyright (c) Timothy A. Davis,                                      */

 /* Patrick R. Amestoy, and Iain S. Duff.  See ../README.txt for License.     */

 /* email: davis at cise.ufl.edu    CISE Department, Univ. of Florida.        */

 /* web: http://www.cise.ufl.edu/research/sparse/amd                          */

 /* ------------------------------------------------------------------------- */

 /* AMD_1: Construct A+A' for a sparse matrix A and perform the AMD 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 AMD_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 AMD_2.  No error checking

  * is performed (this was done in AMD_valid).

  */

 #include "amd_internal.h"

 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) == AMD_OK) ;

     /* 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) ;

 }