text: /* ========================================================================= */
  /* === AMD:  approximate minimum degree ordering =========================== */
  /* ========================================================================= */
  
  /* ------------------------------------------------------------------------- */
  /* AMD Version 2.4, Copyright (c) 1996-2013 by Timothy A. Davis,             */
  /* Patrick R. Amestoy, and Iain S. Duff.  See ../README.txt for License.     */
  /* email: DrTimothyAldenDavis@gmail.com                                      */
  /* ------------------------------------------------------------------------- */
  
  /* AMD finds a symmetric ordering P of a matrix A so that the Cholesky
   * factorization of P*A*P' has fewer nonzeros and takes less work than the
   * Cholesky factorization of A.  If A is not symmetric, then it performs its
   * ordering on the matrix A+A'.  Two sets of user-callable routines are
   * provided, one for int integers and the other for SuiteSparse_long integers.
   *
   * The method is based on the approximate minimum degree algorithm, discussed
   * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm",
   * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp.
   * 886-905, 1996.  This package can perform both the AMD ordering (with
   * aggressive absorption), and the AMDBAR ordering (without aggressive
   * absorption) discussed in the above paper.  This package differs from the
   * Fortran codes discussed in the paper:
   *
   *       (1) it can ignore "dense" rows and columns, leading to faster run times
   *       (2) it computes the ordering of A+A' if A is not symmetric
   *       (3) it is followed by a depth-first post-ordering of the assembly tree
   *           (or supernodal elimination tree)
   *
   * For historical reasons, the Fortran versions, amd.f and amdbar.f, have
   * been left (nearly) unchanged.  They compute the identical ordering as
   * described in the above paper.
   */
  
  #ifndef EL_AMD_H
  #define EL_AMD_H
  
  /* make it easy for C++ programs to include AMD */
  #ifdef __cplusplus
  extern "C" {
  #endif
  
  /* get the definition of size_t: */
  #include <stddef.h>
  
  #include "ElSuiteSparse/config.h"
  
  int El_amd_order               /* returns AMD_OK, AMD_OK_BUT_JUMBLED,
                                  * AMD_INVALID, or AMD_OUT_OF_MEMORY */
  (
      int n,                     /* A is n-by-n.  n must be >= 0. */
      const int Ap [ ],          /* column pointers for A, of size n+1 */
      const int Ai [ ],          /* row indices of A, of size nz = Ap [n] */
      int P [ ],                 /* output permutation, of size n */
      double Control [ ],        /* input Control settings, of size AMD_CONTROL */
      double Info [ ]            /* output Info statistics, of size AMD_INFO */
  ) ;
  
  ElSuiteSparse_long El_amd_l_order /* see above for description of arguments */
  (
      ElSuiteSparse_long n,
      const ElSuiteSparse_long Ap [ ],
      const ElSuiteSparse_long Ai [ ],
      ElSuiteSparse_long P [ ],
      double Control [ ],
      double Info [ ]
  ) ;
  
  /* Input arguments (not modified):
   *
   *       n: the matrix A is n-by-n.
   *       Ap: an int/SuiteSparse_long array of size n+1, containing column
   *              pointers of A.
   *       Ai: an int/SuiteSparse_long array of size nz, containing the row
   *              indices of A, where nz = Ap [n].
   *       Control:  a double array of size AMD_CONTROL, containing control
   *           parameters.  Defaults are used if Control is NULL.
   *
   * Output arguments (not defined on input):
   *
   *       P: an int/SuiteSparse_long array of size n, containing the output
   *           permutation. If row i is the kth pivot row, then P [k] = i.  In
   *           MATLAB notation, the reordered matrix is A (P,P).
   *       Info: a double array of size AMD_INFO, containing statistical
   *           information.  Ignored if Info is NULL.
   *
   * On input, the matrix A is stored in column-oriented form.  The row indices
   * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1].
   *
   * If the row indices appear in ascending order in each column, and there
   * are no duplicate entries, then amd_order is slightly more efficient in
   * terms of time and memory usage.  If this condition does not hold, a copy
   * of the matrix is created (where these conditions do hold), and the copy is
   * ordered.  This feature is new to v2.0 (v1.2 and earlier required this
   * condition to hold for the input matrix).
   * 
   * Row indices must be in the range 0 to
   * n-1.  Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros
   * in A.  The array Ap is of size n+1, and the array Ai is of size nz = Ap [n].
   * The matrix does not need to be symmetric, and the diagonal does not need to
   * be present (if diagonal entries are present, they are ignored except for
   * the output statistic Info [AMD_NZDIAG]).  The arrays Ai and Ap are not
   * modified.  This form of the Ap and Ai arrays to represent the nonzero
   * pattern of the matrix A is the same as that used internally by MATLAB.
   * If you wish to use a more flexible input structure, please see the
   * umfpack_*_triplet_to_col routines in the UMFPACK package, at
   * http://www.suitesparse.com.
   *
   * Restrictions:  n >= 0.  Ap [0] = 0.  Ap [j] <= Ap [j+1] for all j in the
   *       range 0 to n-1.  nz = Ap [n] >= 0.  Ai [0..nz-1] must be in the range 0
   *       to n-1.  Finally, Ai, Ap, and P must not be NULL.  If any of these
   *       restrictions are not met, AMD returns AMD_INVALID.
   *
   * AMD returns:
   *
   *       AMD_OK if the matrix is valid and sufficient memory can be allocated to
   *           perform the ordering.
   *
   *       AMD_OUT_OF_MEMORY if not enough memory can be allocated.
   *
   *       AMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is
   *           NULL.
   *
   *       AMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate
   *           entries, but was otherwise valid.
   *
   * The AMD routine first forms the pattern of the matrix A+A', and then
   * computes a fill-reducing ordering, P.  If P [k] = i, then row/column i of
   * the original is the kth pivotal row.  In MATLAB notation, the permuted
   * matrix is A (P,P), except that 0-based indexing is used instead of the
   * 1-based indexing in MATLAB.
   *
   * The Control array is used to set various parameters for AMD.  If a NULL
   * pointer is passed, default values are used.  The Control array is not
   * modified.
   *
   *       Control [AMD_DENSE]:  controls the threshold for "dense" rows/columns.
   *           A dense row/column in A+A' can cause AMD to spend a lot of time in
   *           ordering the matrix.  If Control [AMD_DENSE] >= 0, rows/columns
   *           with more than Control [AMD_DENSE] * sqrt (n) entries are ignored
   *           during the ordering, and placed last in the output order.  The
   *           default value of Control [AMD_DENSE] is 10.  If negative, no
   *           rows/columns are treated as "dense".  Rows/columns with 16 or
   *           fewer off-diagonal entries are never considered "dense".
   *
   *       Control [AMD_AGGRESSIVE]: controls whether or not to use aggressive
   *           absorption, in which a prior element is absorbed into the current
   *           element if is a subset of the current element, even if it is not
   *           adjacent to the current pivot element (refer to Amestoy, Davis,
   *           & Duff, 1996, for more details).  The default value is nonzero,
   *           which means to perform aggressive absorption.  This nearly always
   *           leads to a better ordering (because the approximate degrees are
   *           more accurate) and a lower execution time.  There are cases where
   *           it can lead to a slightly worse ordering, however.  To turn it off,
   *           set Control [AMD_AGGRESSIVE] to 0.
   *
   *       Control [2..4] are not used in the current version, but may be used in
   *           future versions.
   *
   * The Info array provides statistics about the ordering on output.  If it is
   * not present, the statistics are not returned.  This is not an error
   * condition.
   * 
   *       Info [AMD_STATUS]:  the return value of AMD, either AMD_OK,
   *           AMD_OK_BUT_JUMBLED, AMD_OUT_OF_MEMORY, or AMD_INVALID.
   *
   *       Info [AMD_N]: n, the size of the input matrix
   *
   *       Info [AMD_NZ]: the number of nonzeros in A, nz = Ap [n]
   *
   *       Info [AMD_SYMMETRY]:  the symmetry of the matrix A.  It is the number
   *           of "matched" off-diagonal entries divided by the total number of
   *           off-diagonal entries.  An entry A(i,j) is matched if A(j,i) is also
   *           an entry, for any pair (i,j) for which i != j.  In MATLAB notation,
   *                S = spones (A) ;
   *                B = tril (S, -1) + triu (S, 1) ;
   *                symmetry = nnz (B & B') / nnz (B) ;
   *
   *       Info [AMD_NZDIAG]: the number of entries on the diagonal of A.
   *
   *       Info [AMD_NZ_A_PLUS_AT]:  the number of nonzeros in A+A', excluding the
   *           diagonal.  If A is perfectly symmetric (Info [AMD_SYMMETRY] = 1)
   *           with a fully nonzero diagonal, then Info [AMD_NZ_A_PLUS_AT] = nz-n
   *           (the smallest possible value).  If A is perfectly unsymmetric
   *           (Info [AMD_SYMMETRY] = 0, for an upper triangular matrix, for
   *           example) with no diagonal, then Info [AMD_NZ_A_PLUS_AT] = 2*nz
   *           (the largest possible value).
   *
   *       Info [AMD_NDENSE]: the number of "dense" rows/columns of A+A' that were
   *           removed from A prior to ordering.  These are placed last in the
   *           output order P.
   *
   *       Info [AMD_MEMORY]: the amount of memory used by AMD, in bytes.  In the
   *           current version, this is 1.2 * Info  [AMD_NZ_A_PLUS_AT] + 9*n
   *           times the size of an integer.  This is at most 2.4nz + 9n.  This
   *           excludes the size of the input arguments Ai, Ap, and P, which have
   *           a total size of nz + 2*n + 1 integers.
   *
   *       Info [AMD_NCMPA]: the number of garbage collections performed.
   *
   *       Info [AMD_LNZ]: the number of nonzeros in L (excluding the diagonal).
   *           This is a slight upper bound because mass elimination is combined
   *           with the approximate degree update.  It is a rough upper bound if
   *           there are many "dense" rows/columns.  The rest of the statistics,
   *           below, are also slight or rough upper bounds, for the same reasons.
   *           The post-ordering of the assembly tree might also not exactly
   *           correspond to a true elimination tree postordering.
   *
   *       Info [AMD_NDIV]: the number of divide operations for a subsequent LDL'
   *           or LU factorization of the permuted matrix A (P,P).
   *
   *       Info [AMD_NMULTSUBS_LDL]:  the number of multiply-subtract pairs for a
   *           subsequent LDL' factorization of A (P,P).
   *
   *       Info [AMD_NMULTSUBS_LU]:  the number of multiply-subtract pairs for a
   *           subsequent LU factorization of A (P,P), assuming that no numerical
   *           pivoting is required.
   *
   *       Info [AMD_DMAX]:  the maximum number of nonzeros in any column of L,
   *           including the diagonal.
   *
   *       Info [14..19] are not used in the current version, but may be used in
   *           future versions.
   */    
  
  /* ------------------------------------------------------------------------- */
  /* direct interface to AMD */
  /* ------------------------------------------------------------------------- */
  
  /* amd_2 is the primary AMD ordering routine.  It is not meant to be
   * user-callable because of its restrictive inputs and because it destroys
   * the user's input matrix.  It does not check its inputs for errors, either.
   * However, if you can work with these restrictions it can be faster than
   * amd_order and use less memory (assuming that you can create your own copy
   * of the matrix for AMD to destroy).  Refer to AMD/Source/amd_2.c for a
   * description of each parameter. */
  
  void El_amd_2
  (
      int n,
      int Pe [ ],
      int Iw [ ],
      int Len [ ],
      int iwlen,
      int pfree,
      int Nv [ ],
      int Next [ ], 
      int Last [ ],
      int Head [ ],
      int Elen [ ],
      int Degree [ ],
      int W [ ],
      double Control [ ],
      double Info [ ]
  ) ;
  
  void El_amd_l2
  (
      ElSuiteSparse_long n,
      ElSuiteSparse_long Pe [ ],
      ElSuiteSparse_long Iw [ ],
      ElSuiteSparse_long Len [ ],
      ElSuiteSparse_long iwlen,
      ElSuiteSparse_long pfree,
      ElSuiteSparse_long Nv [ ],
      ElSuiteSparse_long Next [ ], 
      ElSuiteSparse_long Last [ ],
      ElSuiteSparse_long Head [ ],
      ElSuiteSparse_long Elen [ ],
      ElSuiteSparse_long Degree [ ],
      ElSuiteSparse_long W [ ],
      double Control [ ],
      double Info [ ]
  ) ;
  
  /* ------------------------------------------------------------------------- */
  /* amd_valid */
  /* ------------------------------------------------------------------------- */
  
  /* Returns AMD_OK or AMD_OK_BUT_JUMBLED if the matrix is valid as input to
   * amd_order; the latter is returned if the matrix has unsorted and/or
   * duplicate row indices in one or more columns.  Returns AMD_INVALID if the
   * matrix cannot be passed to amd_order.  For amd_order, the matrix must also
   * be square.  The first two arguments are the number of rows and the number
   * of columns of the matrix.  For its use in AMD, these must both equal n.
   *
   * NOTE: this routine returned TRUE/FALSE in v1.2 and earlier.
   */
  
  int El_amd_valid
  (
      int n_row,                 /* # of rows */
      int n_col,                 /* # of columns */
      const int Ap [ ],          /* column pointers, of size n_col+1 */
      const int Ai [ ]           /* row indices, of size Ap [n_col] */
  ) ;
  
  ElSuiteSparse_long El_amd_l_valid
  (
      ElSuiteSparse_long n_row,
      ElSuiteSparse_long n_col,
      const ElSuiteSparse_long Ap [ ],
      const ElSuiteSparse_long Ai [ ]
  ) ;
  
  /* ------------------------------------------------------------------------- */
  /* AMD memory manager and printf routines */
  /* ------------------------------------------------------------------------- */
  
      /* moved to SuiteSparse_config.c */
  
  /* ------------------------------------------------------------------------- */
  /* AMD Control and Info arrays */
  /* ------------------------------------------------------------------------- */
  
  /* amd_defaults:  sets the default control settings */
  void El_amd_defaults   (double Control [ ]) ;
  void El_amd_l_defaults (double Control [ ]) ;
  
  /* amd_control: prints the control settings */
  void El_amd_control    (double Control [ ]) ;
  void El_amd_l_control  (double Control [ ]) ;
  
  /* amd_info: prints the statistics */
  void El_amd_info       (double Info [ ]) ;
  void El_amd_l_info     (double Info [ ]) ;
  
  #define EL_AMD_CONTROL 5          /* size of Control array */
  #define EL_AMD_INFO 20            /* size of Info array */
  
  /* contents of Control */
  #define EL_AMD_DENSE 0       /* "dense" if degree > Control [0] * sqrt (n) */
  #define EL_AMD_AGGRESSIVE 1  /* do aggressive absorption if Control [1] != 0 */
  
  /* default Control settings */
  #define EL_AMD_DEFAULT_DENSE 10.0   /* default "dense" degree 10*sqrt(n) */
  #define EL_AMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */
  
  /* contents of Info */
  #define EL_AMD_STATUS 0    /* return value of amd_order and amd_l_order */
  #define EL_AMD_N 1         /* A is n-by-n */
  #define EL_AMD_NZ 2        /* number of nonzeros in A */ 
  #define EL_AMD_SYMMETRY 3  /* symmetry of pattern (1 is sym., 0 is unsym.) */
  #define EL_AMD_NZDIAG 4    /* # of entries on diagonal */
  #define EL_AMD_NZ_A_PLUS_AT 5 /* nz in A+A' */
  #define EL_AMD_NDENSE 6       /* number of "dense" rows/columns in A */
  #define EL_AMD_MEMORY 7       /* amount of memory used by AMD */
  #define EL_AMD_NCMPA 8        /* number of garbage collections in AMD */
  #define EL_AMD_LNZ 9          /* approx. nz in L, excluding the diagonal */
  #define EL_AMD_NDIV 10        /* number of fl. point divides for LU and LDL' */
  #define EL_AMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */
  #define EL_AMD_NMULTSUBS_LU 12  /* number of fl. point (*,-) pairs for LU */
  #define EL_AMD_DMAX 13          /* max nz. in any column of L, incl. diagonal */
  
  /* ------------------------------------------------------------------------- */
  /* return values of AMD */
  /* ------------------------------------------------------------------------- */
  
  #define EL_AMD_OK 0             /* success */
  #define EL_AMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */
  #define EL_AMD_INVALID -2       /* input arguments are not valid */
  #define EL_AMD_OK_BUT_JUMBLED 1 /* input matrix is OK for amd_order, but
      * columns were not sorted, and/or duplicate entries were present.  AMD had
      * to do extra work before ordering the matrix.  This is a warning, not an
      * error.  */
  
  /* ========================================================================== */
  /* === AMD version ========================================================== */
  /* ========================================================================== */
  
  /* AMD Version 1.2 and later include the following definitions.
   * As an example, to test if the version you are using is 1.2 or later:
   *
   * #ifdef AMD_VERSION
   *       if (AMD_VERSION >= AMD_VERSION_CODE (1,2)) ...
   * #endif
   *
   * This also works during compile-time:
   *
   *       #if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE (1,2))
   *           printf ("This is version 1.2 or later\n") ;
   *       #else
   *           printf ("This is an early version\n") ;
   *       #endif
   *
   * Versions 1.1 and earlier of AMD do not include a #define'd version number.
   */
  
  #define EL_AMD_DATE "Oct 10, 2014"
  #define EL_AMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
  #define EL_AMD_MAIN_VERSION 2
  #define EL_AMD_SUB_VERSION 4
  #define EL_AMD_SUBSUB_VERSION 1
  #define EL_AMD_VERSION \
   EL_AMD_VERSION_CODE(EL_AMD_MAIN_VERSION,EL_AMD_SUB_VERSION)
  
  #ifdef __cplusplus
  }
  #endif
  
  #endif
  