/*

Copyright (C) 1997-2016 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
<http://www.gnu.org/licenses/>.

*/

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

#include "lo-specfun.h"

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


DEFUN (betainc, args, ,
       doc: /* -*- texinfo -*-
@deftypefn {} {} betainc (@var{x}, @var{a}, @var{b})
Compute the regularized incomplete Beta function.

The regularized incomplete Beta function is defined by
@tex
$$
 I (x, a, b) = {1 \over {B (a, b)}} \int_0^x t^{(a-z)} (1-t)^{(b-1)} dt.
$$
@end tex
@ifnottex
@c Set example in small font to prevent overfull line

@smallexample
@group
                                   x
                          1       /
betainc (x, a, b) = -----------   | t^(a-1) (1-t)^(b-1) dt.
                    beta (a, b)   /
                               t=0
@end group
@end smallexample

@end ifnottex

If @var{x} has more than one component, both @var{a} and @var{b} must be
scalars.  If @var{x} is a scalar, @var{a} and @var{b} must be of
compatible dimensions.
@seealso{betaincinv, beta, betaln}
@end deftypefn */)
{
  if (args.length () != 3)
    print_usage ();

  octave_value retval;

  octave_value x_arg = args(0);
  octave_value a_arg = args(1);
  octave_value b_arg = args(2);

  // FIXME: Can we make a template version of the duplicated code below
  if (x_arg.is_single_type () || a_arg.is_single_type ()
      || b_arg.is_single_type ())
    {
      if (x_arg.is_scalar_type ())
        {
          float x = x_arg.float_value ();

          if (a_arg.is_scalar_type ())
            {
              float a = a_arg.float_value ();

              if (b_arg.is_scalar_type ())
                {
                  float b = b_arg.float_value ();

                  retval = octave::math::betainc (x, a, b);
                }
              else
                {
                  Array<float> b = b_arg.float_array_value ();

                  retval = octave::math::betainc (x, a, b);
                }
            }
          else
            {
              Array<float> a = a_arg.float_array_value ();

              if (b_arg.is_scalar_type ())
                {
                  float b = b_arg.float_value ();

                  retval = octave::math::betainc (x, a, b);
                }
              else
                {
                  Array<float> b = b_arg.float_array_value ();

                  retval = octave::math::betainc (x, a, b);
                }
            }
        }
      else
        {
          Array<float> x = x_arg.float_array_value ();

          if (a_arg.is_scalar_type ())
            {
              float a = a_arg.float_value ();

              if (b_arg.is_scalar_type ())
                {
                  float b = b_arg.float_value ();

                  retval = octave::math::betainc (x, a, b);
                }
              else
                {
                  Array<float> b = b_arg.float_array_value ();

                  retval = octave::math::betainc (x, a, b);
                }
            }
          else
            {
              Array<float> a = a_arg.float_array_value ();

              if (b_arg.is_scalar_type ())
                {
                  float b = b_arg.float_value ();

                  retval = octave::math::betainc (x, a, b);
                }
              else
                {
                  Array<float> b = b_arg.float_array_value ();

                  retval = octave::math::betainc (x, a, b);
                }
            }
        }
    }
  else
    {
      if (x_arg.is_scalar_type ())
        {
          double x = x_arg.double_value ();

          if (a_arg.is_scalar_type ())
            {
              double a = a_arg.double_value ();

              if (b_arg.is_scalar_type ())
                {
                  double b = b_arg.double_value ();

                  retval = octave::math::betainc (x, a, b);
                }
              else
                {
                  Array<double> b = b_arg.array_value ();

                  retval = octave::math::betainc (x, a, b);
                }
            }
          else
            {
              Array<double> a = a_arg.array_value ();

              if (b_arg.is_scalar_type ())
                {
                  double b = b_arg.double_value ();

                  retval = octave::math::betainc (x, a, b);
                }
              else
                {
                  Array<double> b = b_arg.array_value ();

                  retval = octave::math::betainc (x, a, b);
                }
            }
        }
      else
        {
          Array<double> x = x_arg.array_value ();

          if (a_arg.is_scalar_type ())
            {
              double a = a_arg.double_value ();

              if (b_arg.is_scalar_type ())
                {
                  double b = b_arg.double_value ();

                  retval = octave::math::betainc (x, a, b);
                }
              else
                {
                  Array<double> b = b_arg.array_value ();

                  retval = octave::math::betainc (x, a, b);
                }
            }
          else
            {
              Array<double> a = a_arg.array_value ();

              if (b_arg.is_scalar_type ())
                {
                  double b = b_arg.double_value ();

                  retval = octave::math::betainc (x, a, b);
                }
              else
                {
                  Array<double> b = b_arg.array_value ();

                  retval = octave::math::betainc (x, a, b);
                }
            }
        }
    }

  return retval;
}

/*
## Double precision
%!test
%! a = [1, 1.5, 2, 3];
%! b = [4, 3, 2, 1];
%! v1 = betainc (1,a,b);
%! v2 = [1,1,1,1];
%! x = [.2, .4, .6, .8];
%! v3 = betainc (x, a, b);
%! v4 = 1 - betainc (1.-x, b, a);
%! assert (v1, v2, sqrt (eps));
%! assert (v3, v4, sqrt (eps));

## Single precision
%!test
%! a = single ([1, 1.5, 2, 3]);
%! b = single ([4, 3, 2, 1]);
%! v1 = betainc (1,a,b);
%! v2 = single ([1,1,1,1]);
%! x = single ([.2, .4, .6, .8]);
%! v3 = betainc (x, a, b);
%! v4 = 1 - betainc (1.-x, b, a);
%! assert (v1, v2, sqrt (eps ("single")));
%! assert (v3, v4, sqrt (eps ("single")));

## Mixed double/single precision
%!test
%! a = single ([1, 1.5, 2, 3]);
%! b = [4, 3, 2, 1];
%! v1 = betainc (1,a,b);
%! v2 = single ([1,1,1,1]);
%! x = [.2, .4, .6, .8];
%! v3 = betainc (x, a, b);
%! v4 = 1-betainc (1.-x, b, a);
%! assert (v1, v2, sqrt (eps ("single")));
%! assert (v3, v4, sqrt (eps ("single")));

%!error betainc ()
%!error betainc (1)
%!error betainc (1,2)
%!error betainc (1,2,3,4)
*/

DEFUN (betaincinv, args, ,
       doc: /* -*- texinfo -*-
@deftypefn {} {} betaincinv (@var{y}, @var{a}, @var{b})
Compute the inverse of the incomplete Beta function.

The inverse is the value @var{x} such that

@example
@var{y} == betainc (@var{x}, @var{a}, @var{b})
@end example
@seealso{betainc, beta, betaln}
@end deftypefn */)
{
  if (args.length () != 3)
    print_usage ();

  octave_value retval;

  octave_value x_arg = args(0);
  octave_value a_arg = args(1);
  octave_value b_arg = args(2);

  if (x_arg.is_scalar_type ())
    {
      double x = x_arg.double_value ();

      if (a_arg.is_scalar_type ())
        {
          double a = a_arg.double_value ();

          if (b_arg.is_scalar_type ())
            {
              double b = b_arg.double_value ();

              retval = octave::math::betaincinv (x, a, b);
            }
          else
            {
              Array<double> b = b_arg.array_value ();

              retval = octave::math::betaincinv (x, a, b);
            }
        }
      else
        {
          Array<double> a = a_arg.array_value ();

          if (b_arg.is_scalar_type ())
            {
              double b = b_arg.double_value ();

              retval = octave::math::betaincinv (x, a, b);
            }
          else
            {
              Array<double> b = b_arg.array_value ();

              retval = octave::math::betaincinv (x, a, b);
            }
        }
    }
  else
    {
      Array<double> x = x_arg.array_value ();

      if (a_arg.is_scalar_type ())
        {
          double a = a_arg.double_value ();

          if (b_arg.is_scalar_type ())
            {
              double b = b_arg.double_value ();

              retval = octave::math::betaincinv (x, a, b);
            }
          else
            {
              Array<double> b = b_arg.array_value ();

              retval = octave::math::betaincinv (x, a, b);
            }
        }
      else
        {
          Array<double> a = a_arg.array_value ();

          if (b_arg.is_scalar_type ())
            {
              double b = b_arg.double_value ();

              retval = octave::math::betaincinv (x, a, b);
            }
          else
            {
              Array<double> b = b_arg.array_value ();

              retval = octave::math::betaincinv (x, a, b);
            }
        }
    }

  // FIXME: It would be better to have an algorithm for betaincinv which
  // accepted float inputs and returned float outputs.  As it is, we do
  // extra work to calculate betaincinv to double precision and then throw
  // that precision away.
  if (x_arg.is_single_type () || a_arg.is_single_type ()
      || b_arg.is_single_type ())
    {
      retval = Array<float> (retval.array_value ());
    }

  return retval;
}

/*
%!assert (betaincinv ([0.875 0.6875], [1 2], 3), [0.5 0.5], sqrt (eps))
%!assert (betaincinv (0.5, 3, 3), 0.5, sqrt (eps))
%!assert (betaincinv (0.34375, 4, 3), 0.5, sqrt (eps))
%!assert (betaincinv (0.2265625, 5, 3), 0.5, sqrt (eps))
%!assert (betaincinv (0.14453125, 6, 3), 0.5, sqrt (eps))
%!assert (betaincinv (0.08984375, 7, 3), 0.5, sqrt (eps))
%!assert (betaincinv (0.0546875, 8, 3), 0.5, sqrt (eps))
%!assert (betaincinv (0.03271484375, 9, 3), 0.5, sqrt (eps))
%!assert (betaincinv (0.019287109375, 10, 3), 0.5, sqrt (eps))

## Test class single as well
%!assert (betaincinv ([0.875 0.6875], [1 2], single (3)), [0.5 0.5], sqrt (eps ("single")))
%!assert (betaincinv (0.5, 3, single (3)), 0.5, sqrt (eps ("single")))
%!assert (betaincinv (0.34375, 4, single (3)), 0.5, sqrt (eps ("single")))

## Extreme values
%!assert (betaincinv (0, 42, 42), 0, sqrt (eps))
%!assert (betaincinv (1, 42, 42), 1, sqrt (eps))

%!error betaincinv ()
%!error betaincinv (1, 2)
*/

