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view libinterp/corefcn/ellipj.cc @ 20500:44eb1102f8a8

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don't recycle scanf format string if all conversions are done (bug #45808) * oct-stream.cc, oct-stream.h (scanf_format_elt::special_conversion): New enum value, no_conversion. (scanf_format_list::next): If not cycling through the list, return dummy scanf_format_elt after list has been exhausted. (octave_base_stream::do_scanf): Only cycle through the format list more than once if there are conversions to make and the limit on the number of values to convert has not been reached.
author John W. Eaton <jwe@octave.org>
date Wed, 26 Aug 2015 16:05:49 -0400
parents 4197fc428c7d
children
line wrap: on
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/*

Copyright (C) 2013-2015 Leopoldo Cerbaro <redbliss@libero.it>

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/>.

*/

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

#include "defun.h"
#include "error.h"
#include "lo-specfun.h"

static void
gripe_ellipj_arg (const char *arg)
{
  error ("ellipj: expecting scalar or matrix as %s argument", arg);
}

DEFUN (ellipj, args, nargout,
       "-*- texinfo -*-\n\
@deftypefn  {Built-in Function} {[@var{sn}, @var{cn}, @var{dn}, @var{err}] =} ellipj (@var{u}, @var{m})\n\
@deftypefnx {Built-in Function} {[@var{sn}, @var{cn}, @var{dn}, @var{err}] =} ellipj (@var{u}, @var{m}, @var{tol})\n\
Compute the Jacobi elliptic functions @var{sn}, @var{cn}, and @var{dn}\n\
of complex argument @var{u} and real parameter @var{m}.\n\
\n\
If @var{m} is a scalar, the results are the same size as @var{u}.\n\
If @var{u} is a scalar, the results are the same size as @var{m}.\n\
If @var{u} is a column vector and @var{m} is a row vector, the\n\
results are matrices with @code{length (@var{u})} rows and\n\
@code{length (@var{m})} columns.  Otherwise, @var{u} and\n\
@var{m} must conform in size and the results will be the same size as the\n\
inputs.\n\
\n\
The value of @var{u} may be complex.\n\
The value of @var{m} must be 0 @leq{} @var{m} @leq{} 1.\n\
\n\
The optional input @var{tol} is currently ignored (@sc{matlab} uses this to\n\
allow faster, less accurate approximation).\n\
\n\
If requested, @var{err} contains the following status information\n\
and is the same size as the result.\n\
\n\
@enumerate 0\n\
@item\n\
Normal return.\n\
\n\
@item\n\
Error---no computation, algorithm termination condition not met,\n\
return @code{NaN}.\n\
@end enumerate\n\
\n\
Reference: Milton @nospell{Abramowitz} and Irene A @nospell{Stegun},\n\
@cite{Handbook of Mathematical Functions}, Chapter 16 (Sections 16.4, 16.13,\n\
and 16.15), Dover, 1965.\n\
\n\
@seealso{ellipke}\n\
@end deftypefn")
{
  octave_value_list retval;

  int nargin = args.length ();

  if (nargin < 2 || nargin > 3)
    {
      print_usage ();
      return retval;
    }

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

  if (m_arg.is_scalar_type ())
    {
      double m = args(1).double_value ();

      if (error_state)
        {
          gripe_ellipj_arg ("second");
          return retval;
        }

      if (u_arg.is_scalar_type ())
        {
          if (u_arg.is_real_type ())
            {
              // u real, m scalar
              double u = args(0).double_value ();

              if (error_state)
                {
                  gripe_ellipj_arg ("first");
                  return retval;
                }

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

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

              if (nargout > 3)
                retval(3) = err;
              retval(2) = dn;
              retval(1) = cn;
              retval(0) = sn;
            }
          else
            {
              // u complex, m scalar
              Complex u = u_arg.complex_value ();

              if (error_state)
                {
                  gripe_ellipj_arg ("first");
                  return retval;
                }

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

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

              if (nargout > 3)
                retval(3) = err;
              retval(2) = dn;
              retval(1) = cn;
              retval(0) = sn;
            }
        }
      else
        {
          // u is matrix, m is scalar
          ComplexNDArray u = u_arg.complex_array_value ();

          if (error_state)
            {
              gripe_ellipj_arg ("first");
              return retval;
            }

          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++)
            ellipj (pu[i], m, psn[i], pcn[i], pdn[i], perr[i]);

          if (nargout > 3)
            retval(3) = err;
          retval(2) = dn;
          retval(1) = cn;
          retval(0) = sn;
        }
    }
  else
    {
      NDArray m = args(1).array_value ();

      if (error_state)
        {
          gripe_ellipj_arg ("second");
          return retval;
        }

      dim_vector sz_m = m.dims ();

      if (u_arg.is_scalar_type ())
        {
          // u is scalar, m is array
          if (u_arg.is_real_type ())
            {
              // u is real scalar, m is array
              double u = u_arg.double_value ();

              if (error_state)
                {
                  gripe_ellipj_arg ("first");
                  return retval;
                }

              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++)
                ellipj (u, pm[i], psn[i], pcn[i], pdn[i], perr[i]);

              if (nargout > 3)
                retval(3) = err;
              retval(2) = dn;
              retval(1) = cn;
              retval(0) = sn;
            }
          else
            {
              // u is complex scalar, m is array
              Complex u = u_arg.complex_value ();

              if (error_state)
                {
                  gripe_ellipj_arg ("first");
                  return retval;
                }

              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++)
                ellipj (u, pm[i], psn[i], pcn[i], pdn[i], perr[i]);

              if (nargout > 3)
                retval(3) = err;
              retval(2) = dn;
              retval(1) = cn;
              retval(0) = sn;
            }
        }
      else
        {
          // u is array, m is array
          if (u_arg.is_real_type ())
            {
              // u is real array, m is array
              NDArray u = u_arg.array_value ();

              if (error_state)
                {
                  gripe_ellipj_arg ("first");
                  return retval;
                }

              dim_vector sz_u = u.dims ();

              if (sz_u.length () == 2 && sz_m.length () == 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++)
                      ellipj (pu[i], pm[j], sn(i,j), cn(i,j), dn(i,j),
                              err(i,j));

                  if (nargout > 3)
                    retval(3) = err;
                  retval(2) = dn;
                  retval(1) = cn;
                  retval(0) = sn;
                }
              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++)
                    ellipj (pu[i], pm[i], psn[i], pcn[i], pdn[i], perr[i]);

                  if (nargout > 3)
                    retval(3) = err;
                  retval(2) = dn;
                  retval(1) = cn;
                  retval(0) = sn;
                }
              else
                error ("ellipj: Invalid size combination for U and M");
            }
          else
            {
              // u is complex array, m is array
              ComplexNDArray u = u_arg.complex_array_value ();

              if (error_state)
                {
                  gripe_ellipj_arg ("second");
                  return retval;
                }

              dim_vector sz_u = u.dims ();

              if (sz_u.length () == 2 && sz_m.length () == 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++)
                      ellipj (pu[i], pm[j], sn(i,j), cn(i,j), dn(i,j),
                              err(i,j));

                  if (nargout > 3)
                    retval(3) = err;
                  retval(2) = dn;
                  retval(1) = cn;
                  retval(0) = sn;
                }
              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++)
                    ellipj (pu[i], pm[i], psn[i], pcn[i], pdn[i], perr[i]);

                  if (nargout > 3)
                    retval(3) = err;
                  retval(2) = dn;
                  retval(1) = cn;
                  retval(0) = sn;
                }
              else
                error ("ellipj: Invalid size combination for U and M");
            }
        }
    }  // m matrix

  return retval;
}

/*
## 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
%! ## Test continuity of dn when cn is near zero (bug #43344)
%! 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 <expecting 0 <= M <= 1> ellipj (1,2);
## FIXME: errors commented out untill lasterr() truly returns the last error.
%!#error <expecting scalar or matrix as second argument> ellipj (1, "1")
%!#error <expecting scalar or matrix as first argument> ellipj ("1", 1)
%!#error <expecting scalar or matrix as first argument> ellipj ({1}, 1)
%!#error <expecting scalar or matrix as first argument> ellipj ({1, 2}, 1)
%!#error <expecting scalar or matrix as second argument> ellipj (1, {1, 2})
%!#error <expecting scalar or matrix as first argument> ellipj ("1", [1, 2])
%!#error <expecting scalar or matrix as first argument> ellipj ({1}, [1, 2])
%!#error <expecting scalar or matrix as first argument> ellipj ({1}, [1, 2])
%!#error <expecting scalar or matrix as first argument> ellipj ("1,2", [1, 2])
%!#error <expecting scalar or matrix as first argument> 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])

*/