/*

Copyright (C) 2005-2018 David Bateman

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
<https://www.gnu.org/licenses/>.

*/

#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif

#include <algorithm>

#include "ov.h"
#include "defun.h"
#include "error.h"
#include "ov-re-mat.h"
#include "ov-cx-mat.h"
#include "ov-re-sparse.h"
#include "ov-cx-sparse.h"
#include "MatrixType.h"
#include "oct-locbuf.h"

DEFUN (matrix_type, args, ,
       doc: /* -*- texinfo -*-
@deftypefn  {} {@var{type} =} matrix_type (@var{A})
@deftypefnx {} {@var{type} =} matrix_type (@var{A}, "nocompute")
@deftypefnx {} {@var{A} =} matrix_type (@var{A}, @var{type})
@deftypefnx {} {@var{A} =} matrix_type (@var{A}, "upper", @var{perm})
@deftypefnx {} {@var{A} =} matrix_type (@var{A}, "lower", @var{perm})
@deftypefnx {} {@var{A} =} matrix_type (@var{A}, "banded", @var{nl}, @var{nu})
Identify the matrix type or mark a matrix as a particular type.

This allows more rapid solutions of linear equations involving @var{A} to be
performed.

Called with a single argument, @code{matrix_type} returns the type of the
matrix and caches it for future use.

Called with more than one argument, @code{matrix_type} allows the type of
the matrix to be defined.

If the option @qcode{"nocompute"} is given, the function will not attempt
to guess the type if it is still unknown.  This is useful for debugging
purposes.

The possible matrix types depend on whether the matrix is full or sparse,
and can be one of the following

@table @asis
@item @qcode{"unknown"}
Remove any previously cached matrix type, and mark type as unknown.

@item @qcode{"full"}
Mark the matrix as full.

@item @qcode{"positive definite"}
Probable full positive definite matrix.

@item @qcode{"diagonal"}
Diagonal matrix.  (Sparse matrices only)

@item @qcode{"permuted diagonal"}
Permuted Diagonal matrix.  The permutation does not need to be specifically
indicated, as the structure of the matrix explicitly gives this.  (Sparse
matrices only)

@item @qcode{"upper"}
Upper triangular.  If the optional third argument @var{perm} is given, the
matrix is assumed to be a permuted upper triangular with the permutations
defined by the vector @var{perm}.

@item @qcode{"lower"}
Lower triangular.  If the optional third argument @var{perm} is given, the
matrix is assumed to be a permuted lower triangular with the permutations
defined by the vector @var{perm}.

@item  @qcode{"banded"}
@itemx @qcode{"banded positive definite"}
Banded matrix with the band size of @var{nl} below the diagonal and @var{nu}
above it.  If @var{nl} and @var{nu} are 1, then the matrix is tridiagonal
and treated with specialized code.  In addition the matrix can be marked as
probably a positive definite.  (Sparse matrices only)

@item @qcode{"singular"}
The matrix is assumed to be singular and will be treated with a minimum norm
solution.

@end table

Note that the matrix type will be discovered automatically on the first
attempt to solve a linear equation involving @var{A}.  Therefore
@code{matrix_type} is only useful to give Octave hints of the matrix type.
Incorrectly defining the matrix type will result in incorrect results from
solutions of linear equations; it is entirely @strong{the responsibility of
the user} to correctly identify the matrix type.

Also, the test for positive definiteness is a low-cost test for a Hermitian
matrix with a real positive diagonal.  This does not guarantee that the
matrix is positive definite, but only that it is a probable candidate.  When
such a matrix is factorized, a Cholesky@tie{}factorization is first
attempted, and if that fails the matrix is then treated with an
LU@tie{}factorization.  Once the matrix has been factorized,
@code{matrix_type} will return the correct classification of the matrix.
@end deftypefn */)
{
  int nargin = args.length ();

  if (nargin == 0 || nargin > 4)
    print_usage ();

  bool autocomp = true;
  if (nargin == 2 && args(1).is_string ()
      && args(1).string_value () == "nocompute")
    {
      nargin = 1;
      autocomp = false;
    }

  octave_value retval;

  if (args(0).is_scalar_type ())
    {
      if (nargin == 1)
        retval = octave_value ("Diagonal");
      else
        retval = args(0);
    }
  else if (args(0).issparse ())
    {
      if (nargin == 1)
        {
          MatrixType mattyp;

          if (args(0).iscomplex ())
            {
              mattyp = args(0).matrix_type ();

              if (mattyp.is_unknown () && autocomp)
                {
                  SparseComplexMatrix m =
                    args(0).sparse_complex_matrix_value ();

                  mattyp = MatrixType (m);
                  args(0).matrix_type (mattyp);
                }
            }
          else
            {
              mattyp = args(0).matrix_type ();

              if (mattyp.is_unknown () && autocomp)
                {
                  SparseMatrix m = args(0).sparse_matrix_value ();

                  mattyp = MatrixType (m);
                  args(0).matrix_type (mattyp);
                }
            }

          int typ = mattyp.type ();

          if (typ == MatrixType::Diagonal)
            retval = octave_value ("Diagonal");
          else if (typ == MatrixType::Permuted_Diagonal)
            retval = octave_value ("Permuted Diagonal");
          else if (typ == MatrixType::Upper)
            retval = octave_value ("Upper");
          else if (typ == MatrixType::Permuted_Upper)
            retval = octave_value ("Permuted Upper");
          else if (typ == MatrixType::Lower)
            retval = octave_value ("Lower");
          else if (typ == MatrixType::Permuted_Lower)
            retval = octave_value ("Permuted Lower");
          else if (typ == MatrixType::Banded)
            retval = octave_value ("Banded");
          else if (typ == MatrixType::Banded_Hermitian)
            retval = octave_value ("Banded Positive Definite");
          else if (typ == MatrixType::Tridiagonal)
            retval = octave_value ("Tridiagonal");
          else if (typ == MatrixType::Tridiagonal_Hermitian)
            retval = octave_value ("Tridiagonal Positive Definite");
          else if (typ == MatrixType::Hermitian)
            retval = octave_value ("Positive Definite");
          else if (typ == MatrixType::Rectangular)
            {
              if (args(0).rows () == args(0).columns ())
                retval = octave_value ("Singular");
              else
                retval = octave_value ("Rectangular");
            }
          else if (typ == MatrixType::Full)
            retval = octave_value ("Full");
          else
            retval = octave_value ("Unknown");
        }
      else
        {
          // Ok, we're changing the matrix type
          std::string str_typ = args(1).xstring_value ("matrix_type: TYPE must be a string");

          // FIXME: why do I have to explicitly call the constructor?
          MatrixType mattyp = MatrixType ();

          octave_idx_type nl = 0;
          octave_idx_type nu = 0;

          // Use STL function to convert to lower case
          std::transform (str_typ.begin (), str_typ.end (),
                          str_typ.begin (), tolower);

          if (str_typ == "diagonal")
            mattyp.mark_as_diagonal ();
          if (str_typ == "permuted diagonal")
            mattyp.mark_as_permuted_diagonal ();
          else if (str_typ == "upper")
            mattyp.mark_as_upper_triangular ();
          else if (str_typ == "lower")
            mattyp.mark_as_lower_triangular ();
          else if (str_typ == "banded"
                   || str_typ == "banded positive definite")
            {
              if (nargin != 4)
                error ("matrix_type: banded matrix type requires 4 arguments");

              nl = args(2).xnint_value ("matrix_type: band size NL, NU must be integers");
              nu = args(3).xnint_value ("matrix_type: band size NL, NU must be integers");

              if (nl == 1 && nu == 1)
                mattyp.mark_as_tridiagonal ();
              else
                mattyp.mark_as_banded (nu, nl);

              if (str_typ == "banded positive definite")
                mattyp.mark_as_symmetric ();
            }
          else if (str_typ == "positive definite")
            {
              mattyp.mark_as_full ();
              mattyp.mark_as_symmetric ();
            }
          else if (str_typ == "singular")
            mattyp.mark_as_rectangular ();
          else if (str_typ == "full")
            mattyp.mark_as_full ();
          else if (str_typ == "unknown")
            mattyp.invalidate_type ();
          else
            error ("matrix_type: Unknown matrix type %s", str_typ.c_str ());

          if (nargin == 3
              && (str_typ == "upper" || str_typ == "lower"))
            {
              const ColumnVector perm = args(2).vector_value ("matrix_type: Invalid permutation vector PERM");

              octave_idx_type len = perm.numel ();
              dim_vector dv = args(0).dims ();

              if (len != dv(0))
                error ("matrix_type: Invalid permutation vector PERM");

              OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len);

              for (octave_idx_type i = 0; i < len; i++)
                p[i] = static_cast<octave_idx_type> (perm (i)) - 1;

              mattyp.mark_as_permuted (len, p);
            }
          else if (nargin != 2
                   && str_typ != "banded positive definite"
                   && str_typ != "banded")
            error ("matrix_type: Invalid number of arguments");

          // Set the matrix type
          if (args(0).iscomplex ())
            retval = octave_value (args(0).sparse_complex_matrix_value (),
                                   mattyp);
          else
            retval = octave_value (args(0).sparse_matrix_value (),
                                   mattyp);
        }
    }
  else
    {
      if (nargin == 1)
        {
          MatrixType mattyp;

          if (args(0).iscomplex ())
            {
              mattyp = args(0).matrix_type ();

              if (mattyp.is_unknown () && autocomp)
                {
                  if (args(0).is_single_type ())
                    {
                      FloatComplexMatrix m;
                      m = args(0).float_complex_matrix_value ();

                      mattyp = MatrixType (m);
                      args(0).matrix_type (mattyp);
                    }
                  else
                    {
                      ComplexMatrix m = args(0).complex_matrix_value ();

                      mattyp = MatrixType (m);
                      args(0).matrix_type (mattyp);
                    }
                }
            }
          else
            {
              mattyp = args(0).matrix_type ();

              if (mattyp.is_unknown () && autocomp)
                {
                  if (args(0).is_single_type ())
                    {
                      FloatMatrix m = args(0).float_matrix_value ();

                      mattyp = MatrixType (m);
                      args(0).matrix_type (mattyp);
                    }
                  else
                    {
                      Matrix m = args(0).matrix_value ();

                      mattyp = MatrixType (m);
                      args(0).matrix_type (mattyp);
                    }
                }
            }

          int typ = mattyp.type ();

          if (typ == MatrixType::Upper)
            retval = octave_value ("Upper");
          else if (typ == MatrixType::Permuted_Upper)
            retval = octave_value ("Permuted Upper");
          else if (typ == MatrixType::Lower)
            retval = octave_value ("Lower");
          else if (typ == MatrixType::Permuted_Lower)
            retval = octave_value ("Permuted Lower");
          else if (typ == MatrixType::Hermitian)
            retval = octave_value ("Positive Definite");
          else if (typ == MatrixType::Rectangular)
            {
              if (args(0).rows () == args(0).columns ())
                retval = octave_value ("Singular");
              else
                retval = octave_value ("Rectangular");
            }
          else if (typ == MatrixType::Full)
            retval = octave_value ("Full");
          else
            retval = octave_value ("Unknown");
        }
      else
        {
          // Ok, we're changing the matrix type
          std::string str_typ = args(1).xstring_value ("matrix_type: TYPE must be a string");

          // FIXME: why do I have to explicitly call the constructor?
          MatrixType mattyp = MatrixType (MatrixType::Unknown, true);

          // Use STL function to convert to lower case
          std::transform (str_typ.begin (), str_typ.end (),
                          str_typ.begin (), tolower);

          if (str_typ == "upper")
            mattyp.mark_as_upper_triangular ();
          else if (str_typ == "lower")
            mattyp.mark_as_lower_triangular ();
          else if (str_typ == "positive definite")
            {
              mattyp.mark_as_full ();
              mattyp.mark_as_symmetric ();
            }
          else if (str_typ == "singular")
            mattyp.mark_as_rectangular ();
          else if (str_typ == "full")
            mattyp.mark_as_full ();
          else if (str_typ == "unknown")
            mattyp.invalidate_type ();
          else
            error ("matrix_type: Unknown matrix type %s", str_typ.c_str ());

          if (nargin == 3 && (str_typ == "upper" || str_typ == "lower"))
            {
              const ColumnVector perm = args(2).vector_value ("matrix_type: Invalid permutation vector PERM");

              octave_idx_type len = perm.numel ();
              dim_vector dv = args(0).dims ();

              if (len != dv(0))
                error ("matrix_type: Invalid permutation vector PERM");

              OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len);

              for (octave_idx_type i = 0; i < len; i++)
                p[i] = static_cast<octave_idx_type> (perm (i)) - 1;

              mattyp.mark_as_permuted (len, p);
            }
          else if (nargin != 2)
            error ("matrix_type: Invalid number of arguments");

          // Set the matrix type
          if (args(0).is_single_type ())
            {
              if (args(0).iscomplex ())
                retval = octave_value (args(0).float_complex_matrix_value (),
                                       mattyp);
              else
                retval = octave_value (args(0).float_matrix_value (),
                                       mattyp);
            }
          else
            {
              if (args(0).iscomplex ())
                retval = octave_value (args(0).complex_matrix_value (),
                                       mattyp);
              else
                retval = octave_value (args(0).matrix_value (), mattyp);
            }
        }
    }

  return retval;
}

/*
## FIXME:
## Disable tests for lower under-determined and upper over-determined
## matrices as this detection is disabled in MatrixType due to issues
## of non minimum norm solution being found.

%!assert (matrix_type (speye (10,10)), "Diagonal")
%!assert (matrix_type (speye (10,10)([2:10,1],:)), "Permuted Diagonal")
%!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]]), "Upper")
%!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]](:,[2,1,3:11])), "Permuted Upper")
%!assert (matrix_type ([speye(10,10),sparse(10,1);1,sparse(1,9),1]), "Lower")
%!assert (matrix_type ([speye(10,10),sparse(10,1);1,sparse(1,9),1]([2,1,3:11],:)), "Permuted Lower")

%!test
%! bnd = spparms ("bandden");
%! spparms ("bandden", 0.5);
%! a = spdiags (rand (10,3)-0.5,[-1,0,1],10,10);
%! assert (matrix_type (a), "Tridiagonal");
%! assert (matrix_type (a'+a+2*speye (10)), "Tridiagonal Positive Definite");
%! spparms ("bandden", bnd);
%!test
%! bnd=spparms ("bandden");
%! spparms ("bandden", 0.5);
%! a = spdiags (randn (10,4),[-2:1],10,10);
%! assert (matrix_type (a), "Banded");
%! assert (matrix_type (a'*a), "Banded Positive Definite");
%! spparms ("bandden", bnd);
%!test
%! a = [speye(10,10),[sparse(9,1);1];-1,sparse(1,9),1];
%! assert (matrix_type (a), "Full");
%! assert (matrix_type (a'*a), "Positive Definite");

%!assert (matrix_type (speye (10,11)), "Diagonal")
%!assert (matrix_type (speye (10,11)([2:10,1],:)), "Permuted Diagonal")
%!assert (matrix_type (speye (11,10)), "Diagonal")
%!assert (matrix_type (speye (11,10)([2:11,1],:)), "Permuted Diagonal")
%#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]]), "Upper")
%#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]](:,[2,1,3:12])), "Permuted Upper")
%!assert (matrix_type ([speye(11,9),[1;sparse(8,1);1;0]]), "Upper")
%!assert (matrix_type ([speye(11,9),[1;sparse(8,1);1;0]](:,[2,1,3:10])), "Permuted Upper")
%#!assert (matrix_type ([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]), "Lower")
%#!assert (matrix_type ([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]([2,1,3:12],:)), "Permuted Lower")
%!assert (matrix_type ([speye(9,11);[1,sparse(1,8),1,0]]), "Lower")
%!assert (matrix_type ([speye(9,11);[1,sparse(1,8),1,0]]([2,1,3:10],:)), "Permuted Lower")
%!assert (matrix_type (spdiags (randn (10,4),[-2:1],10,9)), "Rectangular")

%!assert (matrix_type (1i*speye (10,10)), "Diagonal")
%!assert (matrix_type (1i*speye (10,10)([2:10,1],:)), "Permuted Diagonal")
%!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]]), "Upper")
%!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]](:,[2,1,3:11])), "Permuted Upper")
%!assert (matrix_type ([speye(10,10),sparse(10,1);1i,sparse(1,9),1]), "Lower")
%!assert (matrix_type ([speye(10,10),sparse(10,1);1i,sparse(1,9),1]([2,1,3:11],:)), "Permuted Lower")

%!test
%! bnd = spparms ("bandden");
%! spparms ("bandden", 0.5);
%! assert (matrix_type (spdiags (1i*randn (10,3),[-1,0,1],10,10)), "Tridiagonal");
%! a = 1i*(rand (9,1)-0.5);
%! a = [[a;0],ones(10,1),[0;-a]];
%! assert (matrix_type (spdiags (a,[-1,0,1],10,10)), "Tridiagonal Positive Definite");
%! spparms ("bandden", bnd);
%!test
%! bnd = spparms ("bandden");
%! spparms ("bandden", 0.5);
%! assert (matrix_type (spdiags (1i*randn (10,4),[-2:1],10,10)), "Banded");
%! a = 1i*(rand (9,2)-0.5);
%! a = [[a;[0,0]],ones(10,1),[[0;-a(:,2)],[0;0;-a(1:8,1)]]];
%! assert (matrix_type (spdiags (a,[-2:2],10,10)), "Banded Positive Definite");
%! spparms ("bandden", bnd);
%!test
%! a = [speye(10,10),[sparse(9,1);1i];-1,sparse(1,9),1];
%! assert (matrix_type (a), "Full");
%! assert (matrix_type (a'*a), "Positive Definite");

%!assert (matrix_type (1i*speye (10,11)), "Diagonal")
%!assert (matrix_type (1i*speye (10,11)([2:10,1],:)), "Permuted Diagonal")
%!assert (matrix_type (1i*speye (11,10)), "Diagonal")
%!assert (matrix_type (1i*speye (11,10)([2:11,1],:)), "Permuted Diagonal")
%#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]]), "Upper")
%#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]](:,[2,1,3:12])), "Permuted Upper")
%!assert (matrix_type ([speye(11,9),[1i;sparse(8,1);1i;0]]), "Upper")
%!assert (matrix_type ([speye(11,9),[1i;sparse(8,1);1i;0]](:,[2,1,3:10])), "Permuted Upper")
%#!assert (matrix_type ([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]), "Lower")
%#!assert (matrix_type ([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]([2,1,3:12],:)), "Permuted Lower")
%!assert (matrix_type ([speye(9,11);[1i,sparse(1,8),1i,0]]), "Lower")
%!assert (matrix_type ([speye(9,11);[1i,sparse(1,8),1i,0]]([2,1,3:10],:)), "Permuted Lower")
%!assert (matrix_type (1i*spdiags(randn(10,4),[-2:1],10,9)), "Rectangular")

%!test
%! a = matrix_type (spdiags (randn (10,3),[-1,0,1],10,10), "Singular");
%! assert (matrix_type (a), "Singular");

%!assert (matrix_type (triu (ones(10,10))), "Upper")
%!assert (matrix_type (triu (ones(10,10),-1)), "Full")
%!assert (matrix_type (tril (ones(10,10))), "Lower")
%!assert (matrix_type (tril (ones(10,10),1)), "Full")
%!assert (matrix_type (10*eye (10,10) + ones (10,10)), "Positive Definite")
%!assert (matrix_type (ones (11,10)), "Rectangular")
%!test
%! a = matrix_type (ones (10,10), "Singular");
%! assert (matrix_type (a), "Singular");

%!assert (matrix_type (triu (1i*ones (10,10))), "Upper")
%!assert (matrix_type (triu (1i*ones (10,10),-1)), "Full")
%!assert (matrix_type (tril (1i*ones (10,10))), "Lower")
%!assert (matrix_type (tril (1i*ones (10,10),1)), "Full")
%!assert (matrix_type (10*eye (10,10) + 1i*triu (ones (10,10),1) -1i*tril (ones (10,10),-1)), "Positive Definite")
%!assert (matrix_type (ones (11,10)), "Rectangular")
%!test
%! a = matrix_type (ones (10,10), "Singular");
%! assert (matrix_type (a), "Singular");
*/
