File: colamd.cc

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/*

Copyright (C) 2004-2015 David Bateman
Copyright (C) 1998-2004 Andy Adler

This file is part of Octave.

Octave is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

Octave is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

You should have received a copy of the GNU General Public License
along with Octave; see the file COPYING.  If not, see
<http://www.gnu.org/licenses/>.

*/

// This is the octave interface to colamd, which bore the copyright given
// in the help of the functions.

#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include <stdlib.h>

#include <string>
#include <vector>

#include "ov.h"
#include "defun-dld.h"
#include "pager.h"
#include "ov-re-mat.h"

#include "ov-re-sparse.h"
#include "ov-cx-sparse.h"

#include "oct-sparse.h"
#include "oct-locbuf.h"

#ifdef USE_64_BIT_IDX_T
#define COLAMD_NAME(name) colamd_l ## name
#define SYMAMD_NAME(name) symamd_l ## name
#else
#define COLAMD_NAME(name) colamd ## name
#define SYMAMD_NAME(name) symamd ## name
#endif

// The symmetric column elimination tree code take from the Davis LDL code.
// Copyright given elsewhere in this file.
static void
symetree (const octave_idx_type *ridx, const octave_idx_type *cidx,
          octave_idx_type *Parent, octave_idx_type *P, octave_idx_type n)
{
  OCTAVE_LOCAL_BUFFER (octave_idx_type, Flag, n);
  OCTAVE_LOCAL_BUFFER (octave_idx_type, Pinv, (P ? n : 0));
  if (P)
    // If P is present then compute Pinv, the inverse of P
    for (octave_idx_type k = 0 ; k < n ; k++)
      Pinv[P[k]] = k ;

  for (octave_idx_type k = 0 ; k < n ; k++)
    {
      // L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k)
      Parent[k] = n ;                // parent of k is not yet known
      Flag[k] = k ;                  // mark node k as visited
      octave_idx_type kk = (P) ? P[k]  // kth original, or permuted, column
                               : (k) ;
      octave_idx_type p2 = cidx[kk+1] ;
      for (octave_idx_type p = cidx[kk] ; p < p2 ; p++)
        {
          // A (i,k) is nonzero (original or permuted A)
          octave_idx_type i = (Pinv) ? (Pinv[ridx[p]]) : (ridx[p]) ;
          if (i < k)
            {
              // follow path from i to root of etree, stop at flagged node
              for ( ; Flag[i] != k ; i = Parent[i])
                {
                  // find parent of i if not yet determined
                  if (Parent[i] == n)
                    Parent[i] = k ;
                  Flag[i] = k ;        // mark i as visited
                }
            }
        }
    }
}

// The elimination tree post-ordering code below is taken from SuperLU
static inline octave_idx_type
make_set (octave_idx_type i, octave_idx_type *pp)
{
  pp[i] = i;
  return i;
}

static inline octave_idx_type
link (octave_idx_type s, octave_idx_type t, octave_idx_type *pp)
{
  pp[s] = t;
  return t;
}

static inline octave_idx_type
find (octave_idx_type i, octave_idx_type *pp)
{
  register octave_idx_type p, gp;

  p = pp[i];
  gp = pp[p];

  while (gp != p)
    {
      pp[i] = gp;
      i = gp;
      p = pp[i];
      gp = pp[p];
    }

  return p;
}

static octave_idx_type
etdfs (octave_idx_type v, octave_idx_type *first_kid,
       octave_idx_type *next_kid, octave_idx_type *post,
       octave_idx_type postnum)
{
  for (octave_idx_type w = first_kid[v]; w != -1; w = next_kid[w])
    postnum = etdfs (w, first_kid, next_kid, post, postnum);

  post[postnum++] = v;

  return postnum;
}

static void
tree_postorder (octave_idx_type n, octave_idx_type *parent,
                octave_idx_type *post)
{
  // Allocate storage for working arrays and results
  OCTAVE_LOCAL_BUFFER (octave_idx_type, first_kid, n+1);
  OCTAVE_LOCAL_BUFFER (octave_idx_type, next_kid, n+1);

  // Set up structure describing children
  for (octave_idx_type v = 0; v <= n; first_kid[v++] = -1)
    /* do nothing */;

  for (octave_idx_type v = n-1; v >= 0; v--)
    {
      octave_idx_type dad = parent[v];
      next_kid[v] = first_kid[dad];
      first_kid[dad] = v;
    }

  // Depth-first search from dummy root vertex #n
  etdfs (n, first_kid, next_kid, post, 0);
}

static void
coletree (const octave_idx_type *ridx, const octave_idx_type *colbeg,
          octave_idx_type *colend, octave_idx_type *parent,
          octave_idx_type nr, octave_idx_type nc)
{
  OCTAVE_LOCAL_BUFFER (octave_idx_type, root, nc);
  OCTAVE_LOCAL_BUFFER (octave_idx_type, pp, nc);
  OCTAVE_LOCAL_BUFFER (octave_idx_type, firstcol, nr);

  // Compute firstcol[row] = first nonzero column in row
  for (octave_idx_type row = 0; row < nr; firstcol[row++] = nc)
    /* do nothing */;

  for (octave_idx_type col = 0; col < nc; col++)
    for (octave_idx_type p = colbeg[col]; p < colend[col]; p++)
      {
        octave_idx_type row = ridx[p];
        if (firstcol[row] > col)
          firstcol[row] = col;
      }

  // Compute etree by Liu's algorithm for symmetric matrices,
  // except use (firstcol[r],c) in place of an edge (r,c) of A.
  // Thus each row clique in A'*A is replaced by a star
  // centered at its first vertex, which has the same fill.
  for (octave_idx_type col = 0; col < nc; col++)
    {
      octave_idx_type cset = make_set (col, pp);
      root[cset] = col;
      parent[col] = nc;
      for (octave_idx_type p = colbeg[col]; p < colend[col]; p++)
        {
          octave_idx_type row = firstcol[ridx[p]];
          if (row >= col)
            continue;
          octave_idx_type rset = find (row, pp);
          octave_idx_type rroot = root[rset];
          if (rroot != col)
            {
              parent[rroot] = col;
              cset = link (cset, rset, pp);
              root[cset] = col;
            }
        }
    }
}

DEFUN_DLD (colamd, args, nargout,
           "-*- texinfo -*-\n\
@deftypefn  {Loadable Function} {@var{p} =} colamd (@var{S})\n\
@deftypefnx {Loadable Function} {@var{p} =} colamd (@var{S}, @var{knobs})\n\
@deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} colamd (@var{S})\n\
@deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} colamd (@var{S}, @var{knobs})\n\
\n\
Compute the column approximate minimum degree permutation.\n\
\n\
@code{@var{p} = colamd (@var{S})} returns the column approximate minimum\n\
degree permutation vector for the sparse matrix @var{S}.  For a\n\
non-symmetric matrix @var{S}, @code{@var{S}(:,@var{p})} tends to have\n\
sparser LU@tie{}factors than @var{S}.  The Cholesky@tie{}factorization of\n\
@code{@var{S}(:,@var{p})' * @var{S}(:,@var{p})} also tends to be sparser\n\
than that of @code{@var{S}' * @var{S}}.\n\
\n\
@var{knobs} is an optional one- to three-element input vector.  If @var{S} is\n\
m-by-n, then rows with more than @code{max(16,@var{knobs}(1)*sqrt(n))}\n\
entries are ignored.  Columns with more than\n\
@code{max (16,@var{knobs}(2)*sqrt(min(m,n)))} entries are removed prior to\n\
ordering, and ordered last in the output permutation @var{p}.  Only\n\
completely dense rows or columns are removed if @code{@var{knobs}(1)} and\n\
@code{@var{knobs}(2)} are < 0, respectively.  If @code{@var{knobs}(3)} is\n\
nonzero, @var{stats} and @var{knobs} are printed.  The default is\n\
@code{@var{knobs} = [10 10 0]}.  Note that @var{knobs} differs from earlier\n\
versions of colamd.\n\
\n\
@var{stats} is an optional 20-element output vector that provides data\n\
about the ordering and the validity of the input matrix @var{S}.  Ordering\n\
statistics are in @code{@var{stats}(1:3)}.  @code{@var{stats}(1)} and\n\
@code{@var{stats}(2)} are the number of dense or empty rows and columns\n\
ignored by @sc{colamd} and @code{@var{stats}(3)} is the number of garbage\n\
collections performed on the internal data structure used by @sc{colamd}\n\
(roughly of size @code{2.2 * nnz(@var{S}) + 4 * @var{m} + 7 * @var{n}}\n\
integers).\n\
\n\
Octave built-in functions are intended to generate valid sparse matrices,\n\
with no duplicate entries, with ascending row indices of the nonzeros\n\
in each column, with a non-negative number of entries in each column (!)\n\
and so on.  If a matrix is invalid, then @sc{colamd} may or may not be able\n\
to continue.  If there are duplicate entries (a row index appears two or\n\
more times in the same column) or if the row indices in a column are out\n\
of order, then @sc{colamd} can correct these errors by ignoring the duplicate\n\
entries and sorting each column of its internal copy of the matrix\n\
@var{S} (the input matrix @var{S} is not repaired, however).  If a matrix\n\
is invalid in other ways then @sc{colamd} cannot continue, an error message\n\
is printed, and no output arguments (@var{p} or @var{stats}) are returned.\n\
@sc{colamd} is thus a simple way to check a sparse matrix to see if it's\n\
valid.\n\
\n\
@code{@var{stats}(4:7)} provide information if @sc{colamd} was able to\n\
continue.  The matrix is OK if @code{@var{stats}(4)} is zero, or 1 if\n\
invalid.  @code{@var{stats}(5)} is the rightmost column index that is\n\
unsorted or contains duplicate entries, or zero if no such column exists.\n\
@code{@var{stats}(6)} is the last seen duplicate or out-of-order row\n\
index in the column index given by @code{@var{stats}(5)}, or zero if no\n\
such row index exists.  @code{@var{stats}(7)} is the number of duplicate\n\
or out-of-order row indices.  @code{@var{stats}(8:20)} is always zero in\n\
the current version of @sc{colamd} (reserved for future use).\n\
\n\
The ordering is followed by a column elimination tree post-ordering.\n\
\n\
The authors of the code itself are @nospell{Stefan I. Larimore} and\n\
@nospell{Timothy A. Davis @email{davis@@cise.ufl.edu}}, University of Florida.  The algorithm was developed in collaboration with @nospell{John Gilbert},\n\
Xerox PARC, and @nospell{Esmond Ng}, Oak Ridge National Laboratory.  (see\n\
@url{http://www.cise.ufl.edu/research/sparse/colamd})\n\
@seealso{colperm, symamd, ccolamd}\n\
@end deftypefn")
{
  octave_value_list retval;

#ifdef HAVE_COLAMD

  int nargin = args.length ();
  int spumoni = 0;

  if (nargout > 2 || nargin < 1 || nargin > 2)
    print_usage ();
  else
    {
      // Get knobs
      OCTAVE_LOCAL_BUFFER (double, knobs, COLAMD_KNOBS);
      COLAMD_NAME (_set_defaults) (knobs);

      // Check for user-passed knobs
      if (nargin == 2)
        {
          NDArray User_knobs = args(1).array_value ();
          int nel_User_knobs = User_knobs.length ();

          if (nel_User_knobs > 0)
            knobs[COLAMD_DENSE_ROW] = User_knobs(0);
          if (nel_User_knobs > 1)
            knobs[COLAMD_DENSE_COL] = User_knobs(1) ;
          if (nel_User_knobs > 2)
            spumoni = static_cast<int> (User_knobs(2));

          // print knob settings if spumoni is set
          if (spumoni)
            {

              octave_stdout << "\ncolamd version " << COLAMD_MAIN_VERSION
                            << "." <<  COLAMD_SUB_VERSION
                            << ", " << COLAMD_DATE << ":\n";

              if (knobs[COLAMD_DENSE_ROW] >= 0)
                octave_stdout << "knobs(1): " << User_knobs (0)
                              << ", rows with > max (16,"
                              << knobs[COLAMD_DENSE_ROW] << "*sqrt (size(A,2)))"
                              << " entries removed\n";
              else
                octave_stdout << "knobs(1): " << User_knobs (0)
                              << ", only completely dense rows removed\n";

              if (knobs[COLAMD_DENSE_COL] >= 0)
                octave_stdout << "knobs(2): " << User_knobs (1)
                              << ", cols with > max (16,"
                              << knobs[COLAMD_DENSE_COL] << "*sqrt (size(A)))"
                              << " entries removed\n";
              else
                octave_stdout << "knobs(2): " << User_knobs (1)
                              << ", only completely dense columns removed\n";

              octave_stdout << "knobs(3): " << User_knobs (2)
                            << ", statistics and knobs printed\n";

            }
        }

      octave_idx_type n_row, n_col, nnz;
      octave_idx_type *ridx, *cidx;
      SparseComplexMatrix scm;
      SparseMatrix sm;

      if (args(0).is_sparse_type ())
        {
          if (args(0).is_complex_type ())
            {
              scm = args(0). sparse_complex_matrix_value ();
              n_row = scm.rows ();
              n_col = scm.cols ();
              nnz = scm.nnz ();
              ridx = scm.xridx ();
              cidx = scm.xcidx ();
            }
          else
            {
              sm = args(0).sparse_matrix_value ();

              n_row = sm.rows ();
              n_col = sm.cols ();
              nnz = sm.nnz ();
              ridx = sm.xridx ();
              cidx = sm.xcidx ();
            }
        }
      else
        {
          if (args(0).is_complex_type ())
            sm = SparseMatrix (real (args(0).complex_matrix_value ()));
          else
            sm = SparseMatrix (args(0).matrix_value ());

          n_row = sm.rows ();
          n_col = sm.cols ();
          nnz = sm.nnz ();
          ridx = sm.xridx ();
          cidx = sm.xcidx ();
        }

      // Allocate workspace for colamd
      OCTAVE_LOCAL_BUFFER (octave_idx_type, p, n_col+1);
      for (octave_idx_type i = 0; i < n_col+1; i++)
        p[i] = cidx[i];

      octave_idx_type Alen = COLAMD_NAME (_recommended) (nnz, n_row, n_col);
      OCTAVE_LOCAL_BUFFER (octave_idx_type, A, Alen);
      for (octave_idx_type i = 0; i < nnz; i++)
        A[i] = ridx[i];

      // Order the columns (destroys A)
      OCTAVE_LOCAL_BUFFER (octave_idx_type, stats, COLAMD_STATS);
      if (! COLAMD_NAME () (n_row, n_col, Alen, A, p, knobs, stats))
        {
          COLAMD_NAME (_report) (stats) ;
          error ("colamd: internal error!");
          return retval;
        }

      // column elimination tree post-ordering (reuse variables)
      OCTAVE_LOCAL_BUFFER (octave_idx_type, colbeg, n_col + 1);
      OCTAVE_LOCAL_BUFFER (octave_idx_type, colend, n_col + 1);
      OCTAVE_LOCAL_BUFFER (octave_idx_type, etree, n_col + 1);

      for (octave_idx_type i = 0; i < n_col; i++)
        {
          colbeg[i] = cidx[p[i]];
          colend[i] = cidx[p[i]+1];
        }

      coletree (ridx, colbeg, colend, etree, n_row, n_col);

      // Calculate the tree post-ordering
      tree_postorder (n_col, etree, colbeg);

      // return the permutation vector
      NDArray out_perm (dim_vector (1, n_col));
      for (octave_idx_type i = 0; i < n_col; i++)
        out_perm(i) = p[colbeg[i]] + 1;

      retval(0) = out_perm;

      // print stats if spumoni > 0
      if (spumoni > 0)
        COLAMD_NAME (_report) (stats) ;

      // Return the stats vector
      if (nargout == 2)
        {
          NDArray out_stats (dim_vector (1, COLAMD_STATS));
          for (octave_idx_type i = 0 ; i < COLAMD_STATS ; i++)
            out_stats(i) = stats[i] ;
          retval(1) = out_stats;

          // fix stats (5) and (6), for 1-based information on
          // jumbled matrix.  note that this correction doesn't
          // occur if symamd returns FALSE
          out_stats (COLAMD_INFO1) ++ ;
          out_stats (COLAMD_INFO2) ++ ;
        }
    }

#else

  error ("colamd: not available in this version of Octave");

#endif

  return retval;
}

DEFUN_DLD (symamd, args, nargout,
           "-*- texinfo -*-\n\
@deftypefn  {Loadable Function} {@var{p} =} symamd (@var{S})\n\
@deftypefnx {Loadable Function} {@var{p} =} symamd (@var{S}, @var{knobs})\n\
@deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} symamd (@var{S})\n\
@deftypefnx {Loadable Function} {[@var{p}, @var{stats}] =} symamd (@var{S}, @var{knobs})\n\
\n\
For a symmetric positive definite matrix @var{S}, returns the permutation\n\
vector p such that @code{@var{S}(@var{p}, @var{p})} tends to have a\n\
sparser Cholesky@tie{}factor than @var{S}.\n\
\n\
Sometimes @code{symamd} works well for symmetric indefinite matrices too. \n\
The matrix @var{S} is assumed to be symmetric; only the strictly lower\n\
triangular part is referenced.  @var{S} must be square.\n\
\n\
@var{knobs} is an optional one- to two-element input vector.  If @var{S} is\n\
n-by-n, then rows and columns with more than\n\
@code{max (16,@var{knobs}(1)*sqrt(n))} entries are removed prior to ordering,\n\
and ordered last in the output permutation @var{p}.  No rows/columns are\n\
removed if @code{@var{knobs}(1) < 0}.  If @code{@var{knobs} (2)} is nonzero,\n\
@code{stats} and @var{knobs} are printed.  The default is\n\
@code{@var{knobs} = [10 0]}.  Note that @var{knobs} differs from earlier\n\
versions of @code{symamd}.\n\
\n\
@var{stats} is an optional 20-element output vector that provides data\n\
about the ordering and the validity of the input matrix @var{S}.  Ordering\n\
statistics are in @code{@var{stats}(1:3)}.\n\
@code{@var{stats}(1) = @var{stats}(2)} is the number of dense or empty rows\n\
and columns ignored by SYMAMD and @code{@var{stats}(3)} is the number of\n\
garbage collections performed on the internal data structure used by SYMAMD\n\
(roughly of size @code{8.4 * nnz (tril (@var{S}, -1)) + 9 * @var{n}}\n\
integers).\n\
\n\
Octave built-in functions are intended to generate valid sparse matrices,\n\
with no duplicate entries, with ascending row indices of the nonzeros\n\
in each column, with a non-negative number of entries in each column (!)\n\
and so on.  If a matrix is invalid, then SYMAMD may or may not be able\n\
to continue.  If there are duplicate entries (a row index appears two or\n\
more times in the same column) or if the row indices in a column are out\n\
of order, then SYMAMD can correct these errors by ignoring the duplicate\n\
entries and sorting each column of its internal copy of the matrix S (the\n\
input matrix S is not repaired, however).  If a matrix is invalid in\n\
other ways then SYMAMD cannot continue, an error message is printed, and\n\
no output arguments (@var{p} or @var{stats}) are returned.  SYMAMD is\n\
thus a simple way to check a sparse matrix to see if it's valid.\n\
\n\
@code{@var{stats}(4:7)} provide information if SYMAMD was able to\n\
continue.  The matrix is OK if @code{@var{stats} (4)} is zero, or 1\n\
if invalid.  @code{@var{stats}(5)} is the rightmost column index that\n\
is unsorted or contains duplicate entries, or zero if no such column\n\
exists.  @code{@var{stats}(6)} is the last seen duplicate or out-of-order\n\
row index in the column index given by @code{@var{stats}(5)}, or zero\n\
if no such row index exists.  @code{@var{stats}(7)} is the number of\n\
duplicate or out-of-order row indices.  @code{@var{stats}(8:20)} is\n\
always zero in the current version of SYMAMD (reserved for future use).\n\
\n\
The ordering is followed by a column elimination tree post-ordering.\n\
\n\
The authors of the code itself are @nospell{Stefan I. Larimore} and\n\
@nospell{Timothy A. Davis @email{davis@@cise.ufl.edu}}, University of Florida.  The algorithm was developed in collaboration with @nospell{John Gilbert},\n\
Xerox PARC, and @nospell{Esmond Ng}, Oak Ridge National Laboratory.  (see\n\
@url{http://www.cise.ufl.edu/research/sparse/colamd})\n\
@seealso{colperm, colamd}\n\
@end deftypefn")
{
  octave_value_list retval;

#ifdef HAVE_COLAMD

  int nargin = args.length ();
  int spumoni = 0;

  if (nargout > 2 || nargin < 1 || nargin > 2)
    print_usage ();
  else
    {
      // Get knobs
      OCTAVE_LOCAL_BUFFER (double, knobs, COLAMD_KNOBS);
      COLAMD_NAME (_set_defaults) (knobs);

      // Check for user-passed knobs
      if (nargin == 2)
        {
          NDArray User_knobs = args(1).array_value ();
          int nel_User_knobs = User_knobs.length ();

          if (nel_User_knobs > 0)
            knobs[COLAMD_DENSE_ROW] = User_knobs(COLAMD_DENSE_ROW);
          if (nel_User_knobs > 1)
            spumoni = static_cast<int> (User_knobs (1));
        }

      // print knob settings if spumoni is set
      if (spumoni > 0)
        octave_stdout << "symamd: dense row/col fraction: "
                      << knobs[COLAMD_DENSE_ROW] << std::endl;

      octave_idx_type n_row, n_col;
      octave_idx_type *ridx, *cidx;
      SparseMatrix sm;
      SparseComplexMatrix scm;

      if (args(0).is_sparse_type ())
        {
          if (args(0).is_complex_type ())
            {
              scm = args(0).sparse_complex_matrix_value ();
              n_row = scm.rows ();
              n_col = scm.cols ();
              ridx = scm.xridx ();
              cidx = scm.xcidx ();
            }
          else
            {
              sm = args(0).sparse_matrix_value ();
              n_row = sm.rows ();
              n_col = sm.cols ();
              ridx = sm.xridx ();
              cidx = sm.xcidx ();
            }
        }
      else
        {
          if (args(0).is_complex_type ())
            sm = SparseMatrix (real (args(0).complex_matrix_value ()));
          else
            sm = SparseMatrix (args(0).matrix_value ());

          n_row = sm.rows ();
          n_col = sm.cols ();
          ridx = sm.xridx ();
          cidx = sm.xcidx ();
        }

      if (n_row != n_col)
        {
          error ("symamd: matrix S must be square");
          return retval;
        }

      // Allocate workspace for symamd
      OCTAVE_LOCAL_BUFFER (octave_idx_type, perm, n_col+1);
      OCTAVE_LOCAL_BUFFER (octave_idx_type, stats, COLAMD_STATS);
      if (!SYMAMD_NAME () (n_col, ridx, cidx, perm,
                           knobs, stats, &calloc, &free))
        {
          SYMAMD_NAME (_report) (stats) ;
          error ("symamd: internal error!") ;
          return retval;
        }

      // column elimination tree post-ordering
      OCTAVE_LOCAL_BUFFER (octave_idx_type, etree, n_col + 1);
      symetree (ridx, cidx, etree, perm, n_col);

      // Calculate the tree post-ordering
      OCTAVE_LOCAL_BUFFER (octave_idx_type, post, n_col + 1);
      tree_postorder (n_col, etree, post);

      // return the permutation vector
      NDArray out_perm (dim_vector (1, n_col));
      for (octave_idx_type i = 0; i < n_col; i++)
        out_perm(i) = perm[post[i]] + 1;

      retval(0) = out_perm;

      // print stats if spumoni > 0
      if (spumoni > 0)
        SYMAMD_NAME (_report) (stats) ;

      // Return the stats vector
      if (nargout == 2)
        {
          NDArray out_stats (dim_vector (1, COLAMD_STATS));
          for (octave_idx_type i = 0 ; i < COLAMD_STATS ; i++)
            out_stats(i) = stats[i] ;
          retval(1) = out_stats;

          // fix stats (5) and (6), for 1-based information on
          // jumbled matrix.  note that this correction doesn't
          // occur if symamd returns FALSE
          out_stats (COLAMD_INFO1) ++ ;
          out_stats (COLAMD_INFO2) ++ ;
        }
    }

#else

  error ("symamd: not available in this version of Octave");

#endif

  return retval;
}

DEFUN_DLD (etree, args, nargout,
           "-*- texinfo -*-\n\
@deftypefn  {Loadable Function} {@var{p} =} etree (@var{S})\n\
@deftypefnx {Loadable Function} {@var{p} =} etree (@var{S}, @var{typ})\n\
@deftypefnx {Loadable Function} {[@var{p}, @var{q}] =} etree (@var{S}, @var{typ})\n\
\n\
Return the elimination tree for the matrix @var{S}.\n\
\n\
By default @var{S} is assumed to be symmetric and the symmetric elimination\n\
tree is returned.  The argument @var{typ} controls whether a symmetric or\n\
column elimination tree is returned.  Valid values of @var{typ} are\n\
@qcode{\"sym\"} or @qcode{\"col\"}, for symmetric or column elimination tree\n\
respectively.\n\
\n\
Called with a second argument, @code{etree} also returns the postorder\n\
permutations on the tree.\n\
@end deftypefn")
{
  octave_value_list retval;

  int nargin = args.length ();

  if (nargout > 2 || nargin < 1 || nargin > 2)
    print_usage ();
  else
    {
      octave_idx_type n_row, n_col;
      octave_idx_type *ridx, *cidx;
      bool is_sym = true;
      SparseMatrix sm;
      SparseComplexMatrix scm;

      if (args(0).is_sparse_type ())
        {
          if (args(0).is_complex_type ())
            {
              scm = args(0).sparse_complex_matrix_value ();
              n_row = scm.rows ();
              n_col = scm.cols ();
              ridx = scm.xridx ();
              cidx = scm.xcidx ();
            }
          else
            {
              sm = args(0).sparse_matrix_value ();
              n_row = sm.rows ();
              n_col = sm.cols ();
              ridx = sm.xridx ();
              cidx = sm.xcidx ();
            }

        }
      else
        {
          error ("etree: S must be a sparse matrix");
          return retval;
        }

      if (nargin == 2)
        {
          if (args(1).is_string ())
            {
              std::string str = args(1).string_value ();
              if (str.find ("C") == 0 || str.find ("c") == 0)
                is_sym = false;
            }
          else
            {
              error ("etree: TYP must be a string");
              return retval;
            }
        }

      // column elimination tree post-ordering (reuse variables)
      OCTAVE_LOCAL_BUFFER (octave_idx_type, etree, n_col + 1);

      if (is_sym)
        {
          if (n_row != n_col)
            {
              error ("etree: S is marked as symmetric, but is not square");
              return retval;
            }

          symetree (ridx, cidx, etree, 0, n_col);
        }
      else
        {
          OCTAVE_LOCAL_BUFFER (octave_idx_type, colbeg, n_col);
          OCTAVE_LOCAL_BUFFER (octave_idx_type, colend, n_col);

          for (octave_idx_type i = 0; i < n_col; i++)
            {
              colbeg[i] = cidx[i];
              colend[i] = cidx[i+1];
            }

          coletree (ridx, colbeg, colend, etree, n_row, n_col);
        }

      NDArray tree (dim_vector (1, n_col));
      for (octave_idx_type i = 0; i < n_col; i++)
        // We flag a root with n_col while Matlab does it with zero
        // Convert for matlab compatiable output
        if (etree[i] == n_col)
          tree(i) = 0;
        else
          tree(i) = etree[i] + 1;

      retval(0) = tree;

      if (nargout == 2)
        {
          // Calculate the tree post-ordering
          OCTAVE_LOCAL_BUFFER (octave_idx_type, post, n_col + 1);
          tree_postorder (n_col, etree, post);

          NDArray postorder (dim_vector (1, n_col));
          for (octave_idx_type i = 0; i < n_col; i++)
            postorder(i) = post[i] + 1;

          retval(1) = postorder;
        }
    }

  return retval;
}