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update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2021. In all .txi and .texi files except gpl.txi and gpl.texi in the doc/liboctave and doc/interpreter directories, change the copyright to "Octave Project Developers", the same as used for other source files. Update copyright notices for 2022 (not done since 2019). For gpl.txi and gpl.texi, change the copyright notice to be "Free Software Foundation, Inc." and leave the date at 2007 only because this file only contains the text of the GPL, not anything created by the Octave Project Developers. Add Paul Thomas to contributors.in.
author John W. Eaton <jwe@octave.org>
date Tue, 28 Dec 2021 18:22:40 -0500
parents 7d6709900da7
children e88a07dec498
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////////////////////////////////////////////////////////////////////////
//
// Copyright (C) 2013-2022 The Octave Project Developers
//
// See the file COPYRIGHT.md in the top-level directory of this
// distribution or <https://octave.org/copyright/>.
//
// 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 "defun.h"
#include "error.h"
#include "lo-specfun.h"

OCTAVE_NAMESPACE_BEGIN

DEFUN (ellipj, args, ,
       doc: /* -*- texinfo -*-
@deftypefn  {} {[@var{sn}, @var{cn}, @var{dn}, @var{err}] =} ellipj (@var{u}, @var{m})
@deftypefnx {} {[@var{sn}, @var{cn}, @var{dn}, @var{err}] =} ellipj (@var{u}, @var{m}, @var{tol})
Compute the Jacobi elliptic functions @var{sn}, @var{cn}, and @var{dn}
of complex argument @var{u} and real parameter @var{m}.

If @var{m} is a scalar, the results are the same size as @var{u}.
If @var{u} is a scalar, the results are the same size as @var{m}.
If @var{u} is a column vector and @var{m} is a row vector, the
results are matrices with @code{length (@var{u})} rows and
@code{length (@var{m})} columns.  Otherwise, @var{u} and
@var{m} must conform in size and the results will be the same size as the
inputs.

The value of @var{u} may be complex.
The value of @var{m} must be 0 @leq{} @var{m} @leq{} 1.

The optional input @var{tol} is currently ignored (@sc{matlab} uses this to
allow faster, less accurate approximation).

If requested, @var{err} contains the following status information
and is the same size as the result.

@enumerate 0
@item
Normal return.

@item
Error---no computation, algorithm termination condition not met,
return @code{NaN}.
@end enumerate

Reference: Milton @nospell{Abramowitz} and Irene A @nospell{Stegun},
@cite{Handbook of Mathematical Functions}, Chapter 16 (Sections 16.4, 16.13,
and 16.15), Dover, 1965.

@seealso{ellipke}
@end deftypefn */)
{
  int nargin = args.length ();

  if (nargin < 2 || nargin > 3)
    print_usage ();

  octave_value u_arg = args(0);
  octave_value m_arg = args(1);

  if (m_arg.is_scalar_type ())
    {
      double m = args(1).xdouble_value ("ellipj: M must be a scalar or matrix");

      if (u_arg.is_scalar_type ())
        {
          if (u_arg.isreal ())
            {
              // u real, m scalar
              double u = args(0).xdouble_value ("ellipj: U must be a scalar or matrix");

              double sn, cn, dn;
              double err = 0;

              math::ellipj (u, m, sn, cn, dn, err);

              return ovl (sn, cn, dn, err);
            }
          else
            {
              // u complex, m scalar
              Complex u = u_arg.xcomplex_value ("ellipj: U must be a scalar or matrix");

              Complex sn, cn, dn;
              double err = 0;

              math::ellipj (u, m, sn, cn, dn, err);

              return ovl (sn, cn, dn, err);
            }
        }
      else
        {
          // u is matrix, m is scalar
          ComplexNDArray u = u_arg.xcomplex_array_value ("ellipj: U must be a scalar or matrix");

          dim_vector sz_u = u.dims ();

          ComplexNDArray sn (sz_u), cn (sz_u), dn (sz_u);
          NDArray err (sz_u);

          const Complex *pu = u.data ();
          Complex *psn = sn.fortran_vec ();
          Complex *pcn = cn.fortran_vec ();
          Complex *pdn = dn.fortran_vec ();
          double *perr = err.fortran_vec ();
          octave_idx_type nel = u.numel ();

          for (octave_idx_type i = 0; i < nel; i++)
            math::ellipj (pu[i], m, psn[i], pcn[i], pdn[i], perr[i]);

          return ovl (sn, cn, dn, err);
        }
    }
  else
    {
      NDArray m = args(1).xarray_value ("ellipj: M must be a scalar or matrix");

      dim_vector sz_m = m.dims ();

      if (u_arg.is_scalar_type ())
        {
          // u is scalar, m is array
          if (u_arg.isreal ())
            {
              // u is real scalar, m is array
              double u = u_arg.xdouble_value ("ellipj: U must be a scalar or matrix");

              NDArray sn (sz_m), cn (sz_m), dn (sz_m);
              NDArray err (sz_m);

              const double *pm = m.data ();
              double *psn = sn.fortran_vec ();
              double *pcn = cn.fortran_vec ();
              double *pdn = dn.fortran_vec ();
              double *perr = err.fortran_vec ();
              octave_idx_type nel = m.numel ();

              for (octave_idx_type i = 0; i < nel; i++)
                math::ellipj (u, pm[i], psn[i], pcn[i], pdn[i], perr[i]);

              return ovl (sn, cn, dn, err);
            }
          else
            {
              // u is complex scalar, m is array
              Complex u = u_arg.xcomplex_value ("ellipj: U must be a scalar or matrix");

              ComplexNDArray sn (sz_m), cn (sz_m), dn (sz_m);
              NDArray err (sz_m);

              const double *pm = m.data ();
              Complex *psn = sn.fortran_vec ();
              Complex *pcn = cn.fortran_vec ();
              Complex *pdn = dn.fortran_vec ();
              double *perr = err.fortran_vec ();
              octave_idx_type nel = m.numel ();

              for (octave_idx_type i = 0; i < nel; i++)
                math::ellipj (u, pm[i], psn[i], pcn[i], pdn[i], perr[i]);

              return ovl (sn, cn, dn, err);
            }
        }
      else
        {
          // u is array, m is array
          if (u_arg.isreal ())
            {
              // u is real array, m is array
              NDArray u = u_arg.xarray_value ("ellipj: U must be a scalar or matrix");

              dim_vector sz_u = u.dims ();

              if (sz_u.ndims () == 2 && sz_m.ndims () == 2
                  && sz_u(1) == 1 && sz_m(0) == 1)
                {
                  // u is real column vector, m is row vector
                  octave_idx_type ur = sz_u(0);
                  octave_idx_type mc = sz_m(1);
                  dim_vector sz_out (ur, mc);

                  NDArray sn (sz_out), cn (sz_out), dn (sz_out);
                  NDArray err (sz_out);

                  const double *pu = u.data ();
                  const double *pm = m.data ();

                  for (octave_idx_type j = 0; j < mc; j++)
                    for (octave_idx_type i = 0; i < ur; i++)
                      math::ellipj (pu[i], pm[j], sn(i,j), cn(i,j), dn(i,j), err(i,j));

                  return ovl (sn, cn, dn, err);
                }
              else if (sz_m == sz_u)
                {
                  NDArray sn (sz_m), cn (sz_m), dn (sz_m);
                  NDArray err (sz_m);

                  const double *pu = u.data ();
                  const double *pm = m.data ();
                  double *psn = sn.fortran_vec ();
                  double *pcn = cn.fortran_vec ();
                  double *pdn = dn.fortran_vec ();
                  double *perr = err.fortran_vec ();
                  octave_idx_type nel = m.numel ();

                  for (octave_idx_type i = 0; i < nel; i++)
                    math::ellipj (pu[i], pm[i], psn[i], pcn[i], pdn[i], perr[i]);

                  return ovl (sn, cn, dn, err);
                }
              else
                error ("ellipj: Invalid size combination for U and M");
            }
          else
            {
              // u is complex array, m is array
              ComplexNDArray u = u_arg.xcomplex_array_value ("ellipj: U must be a scalar or matrix");

              dim_vector sz_u = u.dims ();

              if (sz_u.ndims () == 2 && sz_m.ndims () == 2
                  && sz_u(1) == 1 && sz_m(0) == 1)
                {
                  // u is complex column vector, m is row vector
                  octave_idx_type ur = sz_u(0);
                  octave_idx_type mc = sz_m(1);
                  dim_vector sz_out (ur, mc);

                  ComplexNDArray sn (sz_out), cn (sz_out), dn (sz_out);
                  NDArray err (sz_out);

                  const Complex *pu = u.data ();
                  const double  *pm = m.data ();

                  for (octave_idx_type j = 0; j < mc; j++)
                    for (octave_idx_type i = 0; i < ur; i++)
                      math::ellipj (pu[i], pm[j], sn(i,j), cn(i,j), dn(i,j), err(i,j));

                  return ovl (sn, cn, dn, err);
                }
              else if (sz_m == sz_u)
                {
                  ComplexNDArray sn (sz_m), cn (sz_m), dn (sz_m);
                  NDArray err (sz_m);

                  const Complex *pu = u.data ();
                  const double  *pm = m.data ();
                  Complex *psn = sn.fortran_vec ();
                  Complex *pcn = cn.fortran_vec ();
                  Complex *pdn = dn.fortran_vec ();
                  double *perr = err.fortran_vec ();
                  octave_idx_type nel = m.numel ();

                  for (octave_idx_type i = 0; i < nel; i++)
                    math::ellipj (pu[i], pm[i], psn[i], pcn[i], pdn[i], perr[i]);

                  return ovl (sn, cn, dn, err);
                }
              else
                error ("ellipj: Invalid size combination for U and M");
            }
        }
    }  // m matrix

  return ovl ();
}

/*
## demos taken from inst/ellipj.m

%!demo
%! N = 150;
%! # m = [1-logspace(0,log(eps),N-1), 1]; # m near 1
%! # m = [0, logspace(log(eps),0,N-1)];   # m near 0
%!   m = linspace (0,1,N);                # m equally spaced
%! u = linspace (-20, 20, N);
%! M = ones (length (u), 1) * m;
%! U = u' * ones (1, length (m));
%! [sn, cn, dn] = ellipj (U,M);
%!
%! ## Plotting
%! data = {sn,cn,dn};
%! dname = {"sn","cn","dn"};
%! for i=1:3
%!   subplot (1,3,i);
%!   data{i}(data{i} > 1) = 1;
%!   data{i}(data{i} < -1) = -1;
%!   image (m,u,32*data{i}+32);
%!   title (dname{i});
%! endfor
%! colormap (hot (64));

%!demo
%! N = 200;
%! # m = [1-logspace(0,log(eps),N-1), 1]; # m near 1
%! # m = [0, logspace(log(eps),0,N-1)];   # m near 0
%!   m = linspace (0,1,N);                # m equally spaced
%! u = linspace (0,20,5);
%! M = ones (length (u), 1) * m;
%! U = u' * ones (1, length (m));
%! [sn, cn, dn] = ellipj (U,M);
%!
%! ## Plotting
%! data = {sn,cn,dn};
%! dname = {"sn","cn","dn"};
%! for i=1:3
%!   subplot (1,3,i);
%!   plot (m, data{i});
%!   title (dname{i});
%!   grid on;
%! endfor
*/

/*
## tests taken from inst/test_sncndn.m

%!test
%! k = (tan (pi/8))^2;  m = k*k;
%! SN = [
%! -1. + I * 0. ,  -0.8392965923 + 0. * I
%! -1. + I * 0.2 ,  -0.8559363407 + 0.108250955 * I
%! -1. + I * 0.4 ,  -0.906529758 + 0.2204040232 * I
%! -1. + I * 0.6 ,  -0.9931306727 + 0.3403783409 * I
%! -1. + I * 0.8 ,  -1.119268095 + 0.4720784944 * I
%! -1. + I * 1. ,  -1.29010951 + 0.6192468708 * I
%! -1. + I * 1.2 ,  -1.512691987 + 0.7850890595 * I
%! -1. + I * 1.4 ,  -1.796200374 + 0.9714821804 * I
%! -1. + I * 1.6 ,  -2.152201882 + 1.177446413 * I
%! -1. + I * 1.8 ,  -2.594547417 + 1.396378892 * I
%! -1. + I * 2. ,  -3.138145339 + 1.611394819 * I
%! -0.8 + I * 0. ,  -0.7158157937 + 0. * I
%! -0.8 + I * 0.2 ,  -0.7301746722 + 0.1394690862 * I
%! -0.8 + I * 0.4 ,  -0.7738940898 + 0.2841710966 * I
%! -0.8 + I * 0.6 ,  -0.8489542135 + 0.4394411376 * I
%! -0.8 + I * 0.8 ,  -0.9588386397 + 0.6107824358 * I
%! -0.8 + I * 1. ,  -1.108848724 + 0.8038415767 * I
%! -0.8 + I * 1.2 ,  -1.306629972 + 1.024193359 * I
%! -0.8 + I * 1.4 ,  -1.563010199 + 1.276740951 * I
%! -0.8 + I * 1.6 ,  -1.893274688 + 1.564345558 * I
%! -0.8 + I * 1.8 ,  -2.318944084 + 1.88491973 * I
%! -0.8 + I * 2. ,  -2.869716809 + 2.225506523 * I
%! -0.6 + I * 0. ,  -0.5638287208 + 0. * I
%! -0.6 + I * 0.2 ,  -0.5752723012 + 0.1654722474 * I
%! -0.6 + I * 0.4 ,  -0.610164314 + 0.3374004736 * I
%! -0.6 + I * 0.6 ,  -0.6702507087 + 0.5224614298 * I
%! -0.6 + I * 0.8 ,  -0.7586657365 + 0.7277663879 * I
%! -0.6 + I * 1. ,  -0.8803349115 + 0.9610513652 * I
%! -0.6 + I * 1.2 ,  -1.042696526 + 1.230800819 * I
%! -0.6 + I * 1.4 ,  -1.256964505 + 1.546195843 * I
%! -0.6 + I * 1.6 ,  -1.540333527 + 1.916612621 * I
%! -0.6 + I * 1.8 ,  -1.919816065 + 2.349972151 * I
%! -0.6 + I * 2. ,  -2.438761841 + 2.848129496 * I
%! -0.4 + I * 0. ,  -0.3891382858 + 0. * I
%! -0.4 + I * 0.2 ,  -0.3971152026 + 0.1850563793 * I
%! -0.4 + I * 0.4 ,  -0.4214662882 + 0.3775700801 * I
%! -0.4 + I * 0.6 ,  -0.4635087491 + 0.5853434119 * I
%! -0.4 + I * 0.8 ,  -0.5256432877 + 0.8168992398 * I
%! -0.4 + I * 1. ,  -0.611733177 + 1.081923504 * I
%! -0.4 + I * 1.2 ,  -0.7278102331 + 1.391822501 * I
%! -0.4 + I * 1.4 ,  -0.8833807998 + 1.760456461 * I
%! -0.4 + I * 1.6 ,  -1.093891878 + 2.205107766 * I
%! -0.4 + I * 1.8 ,  -1.385545188 + 2.747638761 * I
%! -0.4 + I * 2. ,  -1.805081271 + 3.41525351 * I
%! -0.2 + I * 0. ,  -0.1986311721 + 0. * I
%! -0.2 + I * 0.2 ,  -0.2027299916 + 0.1972398665 * I
%! -0.2 + I * 0.4 ,  -0.2152524522 + 0.402598347 * I
%! -0.2 + I * 0.6 ,  -0.2369100139 + 0.6246336356 * I
%! -0.2 + I * 0.8 ,  -0.2690115146 + 0.8728455227 * I
%! -0.2 + I * 1. ,  -0.3136938773 + 1.158323088 * I
%! -0.2 + I * 1.2 ,  -0.3743615191 + 1.494672508 * I
%! -0.2 + I * 1.4 ,  -0.4565255082 + 1.899466033 * I
%! -0.2 + I * 1.6 ,  -0.5694611346 + 2.39667232 * I
%! -0.2 + I * 1.8 ,  -0.7296612675 + 3.020990664 * I
%! -0.2 + I * 2. ,  -0.9685726188 + 3.826022536 * I
%! 0. + I * 0. ,  0. + 0. * I
%! 0. + I * 0.2 ,  0. + 0.201376364 * I
%! 0. + I * 0.4 ,  0. + 0.4111029248 * I
%! 0. + I * 0.6 ,  0. + 0.6380048435 * I
%! 0. + I * 0.8 ,  0. + 0.8919321473 * I
%! 0. + I * 1. ,  0. + 1.184486615 * I
%! 0. + I * 1.2 ,  0. + 1.530096023 * I
%! 0. + I * 1.4 ,  0. + 1.947754612 * I
%! 0. + I * 1.6 ,  0. + 2.464074356 * I
%! 0. + I * 1.8 ,  0. + 3.119049475 * I
%! 0. + I * 2. ,  0. + 3.97786237 * I
%! 0.2 + I * 0. ,  0.1986311721 + 0. * I
%! 0.2 + I * 0.2 ,  0.2027299916 + 0.1972398665 * I
%! 0.2 + I * 0.4 ,  0.2152524522 + 0.402598347 * I
%! 0.2 + I * 0.6 ,  0.2369100139 + 0.6246336356 * I
%! 0.2 + I * 0.8 ,  0.2690115146 + 0.8728455227 * I
%! 0.2 + I * 1. ,  0.3136938773 + 1.158323088 * I
%! 0.2 + I * 1.2 ,  0.3743615191 + 1.494672508 * I
%! 0.2 + I * 1.4 ,  0.4565255082 + 1.899466033 * I
%! 0.2 + I * 1.6 ,  0.5694611346 + 2.39667232 * I
%! 0.2 + I * 1.8 ,  0.7296612675 + 3.020990664 * I
%! 0.2 + I * 2. ,  0.9685726188 + 3.826022536 * I
%! 0.4 + I * 0. ,  0.3891382858 + 0. * I
%! 0.4 + I * 0.2 ,  0.3971152026 + 0.1850563793 * I
%! 0.4 + I * 0.4 ,  0.4214662882 + 0.3775700801 * I
%! 0.4 + I * 0.6 ,  0.4635087491 + 0.5853434119 * I
%! 0.4 + I * 0.8 ,  0.5256432877 + 0.8168992398 * I
%! 0.4 + I * 1. ,  0.611733177 + 1.081923504 * I
%! 0.4 + I * 1.2 ,  0.7278102331 + 1.391822501 * I
%! 0.4 + I * 1.4 ,  0.8833807998 + 1.760456461 * I
%! 0.4 + I * 1.6 ,  1.093891878 + 2.205107766 * I
%! 0.4 + I * 1.8 ,  1.385545188 + 2.747638761 * I
%! 0.4 + I * 2. ,  1.805081271 + 3.41525351 * I
%! 0.6 + I * 0. ,  0.5638287208 + 0. * I
%! 0.6 + I * 0.2 ,  0.5752723012 + 0.1654722474 * I
%! 0.6 + I * 0.4 ,  0.610164314 + 0.3374004736 * I
%! 0.6 + I * 0.6 ,  0.6702507087 + 0.5224614298 * I
%! 0.6 + I * 0.8 ,  0.7586657365 + 0.7277663879 * I
%! 0.6 + I * 1. ,  0.8803349115 + 0.9610513652 * I
%! 0.6 + I * 1.2 ,  1.042696526 + 1.230800819 * I
%! 0.6 + I * 1.4 ,  1.256964505 + 1.546195843 * I
%! 0.6 + I * 1.6 ,  1.540333527 + 1.916612621 * I
%! 0.6 + I * 1.8 ,  1.919816065 + 2.349972151 * I
%! 0.6 + I * 2. ,  2.438761841 + 2.848129496 * I
%! 0.8 + I * 0. ,  0.7158157937 + 0. * I
%! 0.8 + I * 0.2 ,  0.7301746722 + 0.1394690862 * I
%! 0.8 + I * 0.4 ,  0.7738940898 + 0.2841710966 * I
%! 0.8 + I * 0.6 ,  0.8489542135 + 0.4394411376 * I
%! 0.8 + I * 0.8 ,  0.9588386397 + 0.6107824358 * I
%! 0.8 + I * 1. ,  1.108848724 + 0.8038415767 * I
%! 0.8 + I * 1.2 ,  1.306629972 + 1.024193359 * I
%! 0.8 + I * 1.4 ,  1.563010199 + 1.276740951 * I
%! 0.8 + I * 1.6 ,  1.893274688 + 1.564345558 * I
%! 0.8 + I * 1.8 ,  2.318944084 + 1.88491973 * I
%! 0.8 + I * 2. ,  2.869716809 + 2.225506523 * I
%! 1. + I * 0. ,  0.8392965923 + 0. * I
%! 1. + I * 0.2 ,  0.8559363407 + 0.108250955 * I
%! 1. + I * 0.4 ,  0.906529758 + 0.2204040232 * I
%! 1. + I * 0.6 ,  0.9931306727 + 0.3403783409 * I
%! 1. + I * 0.8 ,  1.119268095 + 0.4720784944 * I
%! 1. + I * 1. ,  1.29010951 + 0.6192468708 * I
%! 1. + I * 1.2 ,  1.512691987 + 0.7850890595 * I
%! 1. + I * 1.4 ,  1.796200374 + 0.9714821804 * I
%! 1. + I * 1.6 ,  2.152201882 + 1.177446413 * I
%! 1. + I * 1.8 ,  2.594547417 + 1.396378892 * I
%! 1. + I * 2. ,  3.138145339 + 1.611394819 * I
%! ];
%! CN = [
%! -1. + I * 0. , 0.5436738271 + 0. * I
%! -1. + I * 0.2 , 0.5541219664 + 0.1672121517 * I
%! -1. + I * 0.4 , 0.5857703552 + 0.3410940893 * I
%! -1. + I * 0.6 , 0.6395034233 + 0.5285979063 * I
%! -1. + I * 0.8 , 0.716688504 + 0.7372552987 * I
%! -1. + I * 1. , 0.8189576795 + 0.9755037374 * I
%! -1. + I * 1.2 , 0.9477661951 + 1.253049471 * I
%! -1. + I * 1.4 , 1.103540657 + 1.581252712 * I
%! -1. + I * 1.6 , 1.284098214 + 1.973449038 * I
%! -1. + I * 1.8 , 1.481835651 + 2.4449211 * I
%! -1. + I * 2. , 1.679032464 + 3.011729224 * I
%! -0.8 + I * 0. , 0.6982891589 + 0. * I
%! -0.8 + I * 0.2 , 0.71187169 + 0.1430549855 * I
%! -0.8 + I * 0.4 , 0.7530744458 + 0.2920273465 * I
%! -0.8 + I * 0.6 , 0.8232501212 + 0.4531616768 * I
%! -0.8 + I * 0.8 , 0.9245978896 + 0.6334016187 * I
%! -0.8 + I * 1. , 1.060030206 + 0.8408616109 * I
%! -0.8 + I * 1.2 , 1.232861756 + 1.085475913 * I
%! -0.8 + I * 1.4 , 1.446126965 + 1.379933558 * I
%! -0.8 + I * 1.6 , 1.701139468 + 1.741030588 * I
%! -0.8 + I * 1.8 , 1.994526268 + 2.191509596 * I
%! -0.8 + I * 2. , 2.312257188 + 2.762051518 * I
%! -0.6 + I * 0. , 0.8258917445 + 0. * I
%! -0.6 + I * 0.2 , 0.842151698 + 0.1130337928 * I
%! -0.6 + I * 0.4 , 0.8915487431 + 0.2309124769 * I
%! -0.6 + I * 0.6 , 0.975948103 + 0.3588102098 * I
%! -0.6 + I * 0.8 , 1.098499209 + 0.5026234141 * I
%! -0.6 + I * 1. , 1.263676101 + 0.6695125973 * I
%! -0.6 + I * 1.2 , 1.477275851 + 0.8687285705 * I
%! -0.6 + I * 1.4 , 1.746262523 + 1.112955966 * I
%! -0.6 + I * 1.6 , 2.078179075 + 1.420581466 * I
%! -0.6 + I * 1.8 , 2.479425208 + 1.819580713 * I
%! -0.6 + I * 2. , 2.950586798 + 2.354077344 * I
%! -0.4 + I * 0. , 0.9211793498 + 0. * I
%! -0.4 + I * 0.2 , 0.9395019377 + 0.07822091534 * I
%! -0.4 + I * 0.4 , 0.9952345231 + 0.1598950363 * I
%! -0.4 + I * 0.6 , 1.090715991 + 0.2487465067 * I
%! -0.4 + I * 0.8 , 1.229998843 + 0.34910407 * I
%! -0.4 + I * 1. , 1.419103868 + 0.4663848201 * I
%! -0.4 + I * 1.2 , 1.666426377 + 0.607877235 * I
%! -0.4 + I * 1.4 , 1.983347336 + 0.7841054404 * I
%! -0.4 + I * 1.6 , 2.385101684 + 1.01134031 * I
%! -0.4 + I * 1.8 , 2.89185416 + 1.316448705 * I
%! -0.4 + I * 2. , 3.529393374 + 1.74670531 * I
%! -0.2 + I * 0. , 0.9800743122 + 0. * I
%! -0.2 + I * 0.2 , 0.9997019476 + 0.03999835809 * I
%! -0.2 + I * 0.4 , 1.059453907 + 0.08179712295 * I
%! -0.2 + I * 0.6 , 1.16200643 + 0.1273503824 * I
%! -0.2 + I * 0.8 , 1.312066413 + 0.1789585449 * I
%! -0.2 + I * 1. , 1.516804331 + 0.2395555269 * I
%! -0.2 + I * 1.2 , 1.786613221 + 0.313189147 * I
%! -0.2 + I * 1.4 , 2.136422971 + 0.405890925 * I
%! -0.2 + I * 1.6 , 2.588021972 + 0.527357091 * I
%! -0.2 + I * 1.8 , 3.174302819 + 0.6944201617 * I
%! -0.2 + I * 2. , 3.947361147 + 0.9387994989 * I
%! 0. + I * 0. , 1. + 0. * I
%! 0. + I * 0.2 , 1.020074723 + 0. * I
%! 0. + I * 0.4 , 1.08120563 + 0. * I
%! 0. + I * 0.6 , 1.18619146 + 0. * I
%! 0. + I * 0.8 , 1.339978715 + 0. * I
%! 0. + I * 1. , 1.550164037 + 0. * I
%! 0. + I * 1.2 , 1.827893279 + 0. * I
%! 0. + I * 1.4 , 2.189462954 + 0. * I
%! 0. + I * 1.6 , 2.659259752 + 0. * I
%! 0. + I * 1.8 , 3.275434266 + 0. * I
%! 0. + I * 2. , 4.101632484 + 0. * I
%! 0.2 + I * 0. , 0.9800743122 + 0. * I
%! 0.2 + I * 0.2 , 0.9997019476 - 0.03999835809 * I
%! 0.2 + I * 0.4 , 1.059453907 - 0.08179712295 * I
%! 0.2 + I * 0.6 , 1.16200643 - 0.1273503824 * I
%! 0.2 + I * 0.8 , 1.312066413 - 0.1789585449 * I
%! 0.2 + I * 1. , 1.516804331 - 0.2395555269 * I
%! 0.2 + I * 1.2 , 1.786613221 - 0.313189147 * I
%! 0.2 + I * 1.4 , 2.136422971 - 0.405890925 * I
%! 0.2 + I * 1.6 , 2.588021972 - 0.527357091 * I
%! 0.2 + I * 1.8 , 3.174302819 - 0.6944201617 * I
%! 0.2 + I * 2. , 3.947361147 - 0.9387994989 * I
%! 0.4 + I * 0. , 0.9211793498 + 0. * I
%! 0.4 + I * 0.2 , 0.9395019377 - 0.07822091534 * I
%! 0.4 + I * 0.4 , 0.9952345231 - 0.1598950363 * I
%! 0.4 + I * 0.6 , 1.090715991 - 0.2487465067 * I
%! 0.4 + I * 0.8 , 1.229998843 - 0.34910407 * I
%! 0.4 + I * 1. , 1.419103868 - 0.4663848201 * I
%! 0.4 + I * 1.2 , 1.666426377 - 0.607877235 * I
%! 0.4 + I * 1.4 , 1.983347336 - 0.7841054404 * I
%! 0.4 + I * 1.6 , 2.385101684 - 1.01134031 * I
%! 0.4 + I * 1.8 , 2.89185416 - 1.316448705 * I
%! 0.4 + I * 2. , 3.529393374 - 1.74670531 * I
%! 0.6 + I * 0. , 0.8258917445 + 0. * I
%! 0.6 + I * 0.2 , 0.842151698 - 0.1130337928 * I
%! 0.6 + I * 0.4 , 0.8915487431 - 0.2309124769 * I
%! 0.6 + I * 0.6 , 0.975948103 - 0.3588102098 * I
%! 0.6 + I * 0.8 , 1.098499209 - 0.5026234141 * I
%! 0.6 + I * 1. , 1.263676101 - 0.6695125973 * I
%! 0.6 + I * 1.2 , 1.477275851 - 0.8687285705 * I
%! 0.6 + I * 1.4 , 1.746262523 - 1.112955966 * I
%! 0.6 + I * 1.6 , 2.078179075 - 1.420581466 * I
%! 0.6 + I * 1.8 , 2.479425208 - 1.819580713 * I
%! 0.6 + I * 2. , 2.950586798 - 2.354077344 * I
%! 0.8 + I * 0. , 0.6982891589 + 0. * I
%! 0.8 + I * 0.2 , 0.71187169 - 0.1430549855 * I
%! 0.8 + I * 0.4 , 0.7530744458 - 0.2920273465 * I
%! 0.8 + I * 0.6 , 0.8232501212 - 0.4531616768 * I
%! 0.8 + I * 0.8 , 0.9245978896 - 0.6334016187 * I
%! 0.8 + I * 1. , 1.060030206 - 0.8408616109 * I
%! 0.8 + I * 1.2 , 1.232861756 - 1.085475913 * I
%! 0.8 + I * 1.4 , 1.446126965 - 1.379933558 * I
%! 0.8 + I * 1.6 , 1.701139468 - 1.741030588 * I
%! 0.8 + I * 1.8 , 1.994526268 - 2.191509596 * I
%! 0.8 + I * 2. , 2.312257188 - 2.762051518 * I
%! 1. + I * 0. , 0.5436738271 + 0. * I
%! 1. + I * 0.2 , 0.5541219664 - 0.1672121517 * I
%! 1. + I * 0.4 , 0.5857703552 - 0.3410940893 * I
%! 1. + I * 0.6 , 0.6395034233 - 0.5285979063 * I
%! 1. + I * 0.8 , 0.716688504 - 0.7372552987 * I
%! 1. + I * 1. , 0.8189576795 - 0.9755037374 * I
%! 1. + I * 1.2 , 0.9477661951 - 1.253049471 * I
%! 1. + I * 1.4 , 1.103540657 - 1.581252712 * I
%! 1. + I * 1.6 , 1.284098214 - 1.973449038 * I
%! 1. + I * 1.8 , 1.481835651 - 2.4449211 * I
%! 1. + I * 2. , 1.679032464 - 3.011729224 * I
%! ];
%! DN = [
%! -1. + I * 0. , 0.9895776106 + 0. * I
%! -1. + I * 0.2 , 0.9893361555 + 0.002756935338 * I
%! -1. + I * 0.4 , 0.9885716856 + 0.005949639805 * I
%! -1. + I * 0.6 , 0.9871564855 + 0.01008044183 * I
%! -1. + I * 0.8 , 0.9848512162 + 0.01579337596 * I
%! -1. + I * 1. , 0.9812582484 + 0.02396648455 * I
%! -1. + I * 1.2 , 0.9757399152 + 0.0358288294 * I
%! -1. + I * 1.4 , 0.9672786056 + 0.0531049859 * I
%! -1. + I * 1.6 , 0.954237868 + 0.0781744383 * I
%! -1. + I * 1.8 , 0.933957524 + 0.1141918269 * I
%! -1. + I * 2. , 0.9020917489 + 0.1650142936 * I
%! -0.8 + I * 0. , 0.992429635 + 0. * I
%! -0.8 + I * 0.2 , 0.9924147861 + 0.003020708044 * I
%! -0.8 + I * 0.4 , 0.99236555 + 0.00652359532 * I
%! -0.8 + I * 0.6 , 0.9922655715 + 0.0110676219 * I
%! -0.8 + I * 0.8 , 0.9920785856 + 0.01737733806 * I
%! -0.8 + I * 1. , 0.9917291795 + 0.02645738598 * I
%! -0.8 + I * 1.2 , 0.9910606387 + 0.03974949378 * I
%! -0.8 + I * 1.4 , 0.9897435004 + 0.05935252515 * I
%! -0.8 + I * 1.6 , 0.987077644 + 0.08832675281 * I
%! -0.8 + I * 1.8 , 0.9815667458 + 0.1310872821 * I
%! -0.8 + I * 2. , 0.970020127 + 0.1938136793 * I
%! -0.6 + I * 0. , 0.9953099088 + 0. * I
%! -0.6 + I * 0.2 , 0.995526009 + 0.002814772354 * I
%! -0.6 + I * 0.4 , 0.9962071136 + 0.006083312292 * I
%! -0.6 + I * 0.6 , 0.9974557125 + 0.01033463525 * I
%! -0.6 + I * 0.8 , 0.9994560563 + 0.01626207722 * I
%! -0.6 + I * 1. , 1.00249312 + 0.02484336286 * I
%! -0.6 + I * 1.2 , 1.006973922 + 0.0375167093 * I
%! -0.6 + I * 1.4 , 1.013436509 + 0.05645315628 * I
%! -0.6 + I * 1.6 , 1.022504295 + 0.08499262247 * I
%! -0.6 + I * 1.8 , 1.034670023 + 0.1283564595 * I
%! -0.6 + I * 2. , 1.049599899 + 0.194806122 * I
%! -0.4 + I * 0. , 0.9977686897 + 0. * I
%! -0.4 + I * 0.2 , 0.9981836165 + 0.002167241934 * I
%! -0.4 + I * 0.4 , 0.9994946045 + 0.004686808612 * I
%! -0.4 + I * 0.6 , 1.001910789 + 0.00797144174 * I
%! -0.4 + I * 0.8 , 1.005817375 + 0.01256717724 * I
%! -0.4 + I * 1. , 1.011836374 + 0.01925509038 * I
%! -0.4 + I * 1.2 , 1.020923572 + 0.02920828367 * I
%! -0.4 + I * 1.4 , 1.034513743 + 0.04425213602 * I
%! -0.4 + I * 1.6 , 1.054725746 + 0.06732276244 * I
%! -0.4 + I * 1.8 , 1.08462027 + 0.1033236812 * I
%! -0.4 + I * 2. , 1.128407402 + 0.1608240664 * I
%! -0.2 + I * 0. , 0.9994191176 + 0. * I
%! -0.2 + I * 0.2 , 0.9999683719 + 0.001177128019 * I
%! -0.2 + I * 0.4 , 1.001705496 + 0.00254669712 * I
%! -0.2 + I * 0.6 , 1.004913944 + 0.004334880912 * I
%! -0.2 + I * 0.8 , 1.010120575 + 0.006842775622 * I
%! -0.2 + I * 1. , 1.018189543 + 0.01050520136 * I
%! -0.2 + I * 1.2 , 1.030482479 + 0.01598431001 * I
%! -0.2 + I * 1.4 , 1.049126108 + 0.02433134655 * I
%! -0.2 + I * 1.6 , 1.077466003 + 0.0372877718 * I
%! -0.2 + I * 1.8 , 1.120863308 + 0.05789156398 * I
%! -0.2 + I * 2. , 1.188162088 + 0.09181238708 * I
%! 0. + I * 0. , 1. + 0. * I
%! 0. + I * 0.2 , 1.000596698 + 0. * I
%! 0. + I * 0.4 , 1.002484444 + 0. * I
%! 0. + I * 0.6 , 1.005973379 + 0. * I
%! 0. + I * 0.8 , 1.011641536 + 0. * I
%! 0. + I * 1. , 1.020441432 + 0. * I
%! 0. + I * 1.2 , 1.033885057 + 0. * I
%! 0. + I * 1.4 , 1.054361188 + 0. * I
%! 0. + I * 1.6 , 1.085694733 + 0. * I
%! 0. + I * 1.8 , 1.134186672 + 0. * I
%! 0. + I * 2. , 1.210701071 + 0. * I
%! 0.2 + I * 0. , 0.9994191176 + 0. * I
%! 0.2 + I * 0.2 , 0.9999683719 - 0.001177128019 * I
%! 0.2 + I * 0.4 , 1.001705496 - 0.00254669712 * I
%! 0.2 + I * 0.6 , 1.004913944 - 0.004334880912 * I
%! 0.2 + I * 0.8 , 1.010120575 - 0.006842775622 * I
%! 0.2 + I * 1. , 1.018189543 - 0.01050520136 * I
%! 0.2 + I * 1.2 , 1.030482479 - 0.01598431001 * I
%! 0.2 + I * 1.4 , 1.049126108 - 0.02433134655 * I
%! 0.2 + I * 1.6 , 1.077466003 - 0.0372877718 * I
%! 0.2 + I * 1.8 , 1.120863308 - 0.05789156398 * I
%! 0.2 + I * 2. , 1.188162088 - 0.09181238708 * I
%! 0.4 + I * 0. , 0.9977686897 + 0. * I
%! 0.4 + I * 0.2 , 0.9981836165 - 0.002167241934 * I
%! 0.4 + I * 0.4 , 0.9994946045 - 0.004686808612 * I
%! 0.4 + I * 0.6 , 1.001910789 - 0.00797144174 * I
%! 0.4 + I * 0.8 , 1.005817375 - 0.01256717724 * I
%! 0.4 + I * 1. , 1.011836374 - 0.01925509038 * I
%! 0.4 + I * 1.2 , 1.020923572 - 0.02920828367 * I
%! 0.4 + I * 1.4 , 1.034513743 - 0.04425213602 * I
%! 0.4 + I * 1.6 , 1.054725746 - 0.06732276244 * I
%! 0.4 + I * 1.8 , 1.08462027 - 0.1033236812 * I
%! 0.4 + I * 2. , 1.128407402 - 0.1608240664 * I
%! 0.6 + I * 0. , 0.9953099088 + 0. * I
%! 0.6 + I * 0.2 , 0.995526009 - 0.002814772354 * I
%! 0.6 + I * 0.4 , 0.9962071136 - 0.006083312292 * I
%! 0.6 + I * 0.6 , 0.9974557125 - 0.01033463525 * I
%! 0.6 + I * 0.8 , 0.9994560563 - 0.01626207722 * I
%! 0.6 + I * 1. , 1.00249312 - 0.02484336286 * I
%! 0.6 + I * 1.2 , 1.006973922 - 0.0375167093 * I
%! 0.6 + I * 1.4 , 1.013436509 - 0.05645315628 * I
%! 0.6 + I * 1.6 , 1.022504295 - 0.08499262247 * I
%! 0.6 + I * 1.8 , 1.034670023 - 0.1283564595 * I
%! 0.6 + I * 2. , 1.049599899 - 0.194806122 * I
%! 0.8 + I * 0. , 0.992429635 + 0. * I
%! 0.8 + I * 0.2 , 0.9924147861 - 0.003020708044 * I
%! 0.8 + I * 0.4 , 0.99236555 - 0.00652359532 * I
%! 0.8 + I * 0.6 , 0.9922655715 - 0.0110676219 * I
%! 0.8 + I * 0.8 , 0.9920785856 - 0.01737733806 * I
%! 0.8 + I * 1. , 0.9917291795 - 0.02645738598 * I
%! 0.8 + I * 1.2 , 0.9910606387 - 0.03974949378 * I
%! 0.8 + I * 1.4 , 0.9897435004 - 0.05935252515 * I
%! 0.8 + I * 1.6 , 0.987077644 - 0.08832675281 * I
%! 0.8 + I * 1.8 , 0.9815667458 - 0.1310872821 * I
%! 0.8 + I * 2. , 0.970020127 - 0.1938136793 * I
%! 1. + I * 0. , 0.9895776106 + 0. * I
%! 1. + I * 0.2 , 0.9893361555 - 0.002756935338 * I
%! 1. + I * 0.4 , 0.9885716856 - 0.005949639805 * I
%! 1. + I * 0.6 , 0.9871564855 - 0.01008044183 * I
%! 1. + I * 0.8 , 0.9848512162 - 0.01579337596 * I
%! 1. + I * 1. , 0.9812582484 - 0.02396648455 * I
%! 1. + I * 1.2 , 0.9757399152 - 0.0358288294 * I
%! 1. + I * 1.4 , 0.9672786056 - 0.0531049859 * I
%! 1. + I * 1.6 , 0.954237868 - 0.0781744383 * I
%! 1. + I * 1.8 , 0.933957524 - 0.1141918269 * I
%! 1. + I * 2. , 0.9020917489 - 0.1650142936 * I
%! ];
%! tol = 1e-9;
%! for x = 0:10
%!   for y = 0:10
%!     ur = -1 + x * 0.2;
%!     ui =  y * 0.2;
%!     ii = 1 + y + x*11;
%!     [sn, cn, dn] = ellipj (ur + I * ui, m);
%!     assert (sn, SN(ii, 2), tol);
%!     assert (cn, CN(ii, 2), tol);
%!     assert (dn, DN(ii, 2), tol);
%!   endfor
%! endfor

## tests taken from test_ellipj.m
%!test
%! u1 = pi/3; m1 = 0;
%! res1 = [sin(pi/3), cos(pi/3), 1];
%! [sn,cn,dn] = ellipj (u1,m1);
%! assert ([sn,cn,dn], res1, 10*eps);

%!test
%! u2 = log (2); m2 = 1;
%! res2 = [ 3/5, 4/5, 4/5 ];
%! [sn,cn,dn] = ellipj (u2,m2);
%! assert ([sn,cn,dn], res2, 10*eps);

%!test
%! u3 = log (2)*1i; m3 = 0;
%! res3 = [3i/4,5/4,1];
%! [sn,cn,dn] = ellipj (u3,m3);
%! assert ([sn,cn,dn], res3, 10*eps);

%!test
%! u4 = -1; m4 = tan (pi/8)^4;
%! res4 = [-0.8392965923,0.5436738271,0.9895776106];
%! [sn,cn,dn] = ellipj (u4, m4);
%! assert ([sn,cn,dn], res4, 1e-10);

%!test
%! u5 = -0.2 + 0.4i; m5 = tan (pi/8)^4;
%! res5 = [ -0.2152524522 + 0.402598347i, ...
%!           1.059453907  + 0.08179712295i, ...
%!           1.001705496  + 0.00254669712i ];
%! [sn,cn,dn] = ellipj (u5,m5);
%! assert ([sn,cn,dn], res5, 1e-9);

%!test
%! u6 = 0.2 + 0.6i; m6 = tan (pi/8)^4;
%! res6 = [ 0.2369100139 + 0.624633635i, ...
%!          1.16200643   - 0.1273503824i, ...
%!          1.004913944  - 0.004334880912i ];
%! [sn,cn,dn] = ellipj (u6,m6);
%! assert ([sn,cn,dn], res6, 1e-8);

%!test
%! u7 = 0.8 + 0.8i; m7 = tan (pi/8)^4;
%! res7 = [0.9588386397 + 0.6107824358i, ...
%!         0.9245978896 - 0.6334016187i, ...
%!         0.9920785856 - 0.01737733806i ];
%! [sn,cn,dn] = ellipj (u7,m7);
%! assert ([sn,cn,dn], res7, 1e-10);

%!test
%! u = [0,pi/6,pi/4,pi/2]; m=0;
%! res = [0,1/2,1/sqrt(2),1;1,cos(pi/6),1/sqrt(2),0;1,1,1,1];
%! [sn,cn,dn] = ellipj (u,m);
%! assert ([sn;cn;dn], res, 100*eps);
%! [sn,cn,dn] = ellipj (u',0);
%! assert ([sn,cn,dn], res', 100*eps);

## FIXME: need to check [real,complex]x[scalar,rowvec,colvec,matrix]x[u,m]

## One test for u column vector x m row vector
%!test
%! u = [0,pi/6,pi/4,pi/2]';  m = [0 0 0 0];
%! res = [0,1/2,1/sqrt(2),1;1,cos(pi/6),1/sqrt(2),0;1,1,1,1]';
%! [sn,cn,dn] = ellipj (u,m);
%! assert (sn, repmat (res(:,1), [1,4]), 100*eps);
%! assert (cn, repmat (res(:,2), [1,4]), 100*eps);
%! assert (dn, repmat (res(:,3), [1,4]), 100*eps);

%!test
%! ## Test Jacobi elliptic functions
%! ## against "exact" solution from Mathematica 3.0
%! ## David Billinghurst <David.Billinghurst@riotinto.com>
%! ## 1 February 2001
%! u = [ 0.25; 0.25; 0.20; 0.20; 0.672; 0.5];
%! m = [ 0.0;  1.0;  0.19; 0.81; 0.36;  0.9999999999];
%! S = [ sin(0.25);
%!       tanh(0.25);
%!       0.19842311013970879516;
%!       0.19762082367187648571;
%!       0.6095196917919021945;
%!       0.4621171572617320908 ];
%! C = [ cos(0.25);
%!       sech(0.25);
%!       0.9801164570409401062;
%!       0.9802785369736752032;
%!       0.7927709286533560550;
%!       0.8868188839691764094 ];
%! D = [ 1.0;
%!       sech(0.25);
%!       0.9962526643271134302;
%!       0.9840560289645665155;
%!       0.9307281387786906491;
%!       0.8868188839812167635 ];
%! [sn,cn,dn] = ellipj (u,m);
%! assert (sn, S, 8*eps);
%! assert (cn, C, 8*eps);
%! assert (dn, D, 8*eps);

%!test <*43344>
%! ## Test continuity of dn when cn is near zero
%! m = 0.5;
%! u = ellipke (0.5);
%! x = [-1e-3, -1e-12, 0, 1e-12, 1e-3];
%! [~, ~, dn] = ellipj (u + x, m);
%! D = 1/sqrt (2) * ones (size (x));
%! assert (dn, D, 1e-6);

%!error ellipj ()
%!error ellipj (1)
%!error ellipj (1,2,3,4)
%!warning <required value 0 <= M <= 1> ellipj (1,2);
## FIXME: errors commented out until lasterr() truly returns the last error.
%!#error <M must be a scalar or matrix> ellipj (1, "1")
%!#error <U must be a scalar or matrix> ellipj ("1", 1)
%!#error <U must be a scalar or matrix> ellipj ({1}, 1)
%!#error <U must be a scalar or matrix> ellipj ({1, 2}, 1)
%!#error <M must be a scalar or matrix> ellipj (1, {1, 2})
%!#error <U must be a scalar or matrix> ellipj ("1", [1, 2])
%!#error <U must be a scalar or matrix> ellipj ({1}, [1, 2])
%!#error <U must be a scalar or matrix> ellipj ({1}, [1, 2])
%!#error <U must be a scalar or matrix> ellipj ("1,2", [1, 2])
%!#error <U must be a scalar or matrix> ellipj ({1, 2}, [1, 2])
%!error <Invalid size combination for U and M> ellipj ([1:4], [1:3])
%!error <Invalid size combination for U and M> ellipj (complex (1:4,1:4), [1:3])

*/

OCTAVE_NAMESPACE_END