/*

Copyright (C) 1996-2018 John W. Eaton

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 <string>

#include "CollocWt.h"
#include "lo-mappers.h"

#include "defun.h"
#include "error.h"
#include "ovl.h"
#include "utils.h"

DEFUN (colloc, args, ,
       doc: /* -*- texinfo -*-
@deftypefn {} {[@var{r}, @var{amat}, @var{bmat}, @var{q}] =} colloc (@var{n}, "left", "right")
Compute derivative and integral weight matrices for orthogonal collocation.

Reference: @nospell{J. Villadsen}, @nospell{M. L. Michelsen},
@cite{Solution of Differential Equation Models by Polynomial Approximation}.
@end deftypefn */)
{
  int nargin = args.length ();

  if (nargin < 1 || nargin > 3)
    print_usage ();

  if (! args(0).is_scalar_type ())
    error ("colloc: N must be a scalar");

  double tmp = args(0).double_value ();
  if (octave::math::isnan (tmp))
    error ("colloc: N cannot be NaN");

  octave_idx_type ncol = octave::math::nint_big (tmp);
  if (ncol < 0)
    error ("colloc: N must be positive");

  octave_idx_type ntot = ncol;
  octave_idx_type left = 0;
  octave_idx_type right = 0;

  for (int i = 1; i < nargin; i++)
    {
      std::string s = args(i).xstring_value ("colloc: optional arguments must be strings");

      if ((s.length () == 1 && (s[0] == 'R' || s[0] == 'r')) || s == "right")
        right = 1;
      else if ((s.length () == 1 && (s[0] == 'L' || s[0] == 'l'))
               || s == "left")
        left = 1;
      else
        error (R"(colloc: string argument must be "left" or "right")");
    }

  ntot += left + right;
  if (ntot < 1)
    error ("colloc: the total number of roots must be positive");

  CollocWt wts (ncol, left, right);

  ColumnVector r = wts.roots ();
  Matrix A = wts.first ();
  Matrix B = wts.second ();
  ColumnVector q = wts.quad_weights ();

  return ovl (r, A, B, q);
}

/*

%!assert (colloc (1), 0.5)
%!assert (colloc (1, "left"), [0; 0.5])
%!assert (colloc (1, "right"), [0.5; 1])
%!assert (colloc (1, "left", "right"), [0; 0.5; 1])

*/