fft2.cc

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////////////////////////////////////////////////////////////////////////
//
// Copyright (C) 1996-2021 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/>.
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////////////////////////////////////////////////////////////////////////
 
#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif
 
#include "lo-mappers.h"
 
#include "defun.h"
#include "error.h"
#include "errwarn.h"
#include "ovl.h"
#include "utils.h"
 
// This function should be merged with Fifft.
 
static octave_value
do_fft2 (const octave_value_list& args, const char *fcn, int type)
{
  int nargin = args.length ();
 
  if (nargin < 1 || nargin > 3)
    print_usage ();
 
  octave_value retval;
  octave_value arg = args(0);
  dim_vector dims = arg.dims ();
  octave_idx_type n_rows = -1;
 
  if (nargin > 1)
    {
      double dval = args(1).double_value ();
      if (octave::math::isnan (dval))
        error ("%s: number of rows (N) cannot be NaN", fcn);
 
      n_rows = octave::math::nint_big (dval);
      if (n_rows < 0)
        error ("%s: number of rows (N) must be greater than zero", fcn);
    }
 
  octave_idx_type n_cols = -1;
  if (nargin > 2)
    {
      double dval = args(2).double_value ();
      if (octave::math::isnan (dval))
        error ("%s: number of columns (M) cannot be NaN", fcn);
 
      n_cols = octave::math::nint_big (dval);
      if (n_cols < 0)
        error ("%s: number of columns (M) must be greater than zero", fcn);
    }
 
  for (int i = 0; i < dims.ndims (); i++)
    if (dims(i) < 0)
      return retval;
 
  if (n_rows < 0)
    n_rows = dims(0);
  else
    dims(0) = n_rows;
 
  if (n_cols < 0)
    n_cols = dims(1);
  else
    dims(1) = n_cols;
 
  if (dims.all_zero () || n_rows == 0 || n_cols == 0)
    {
      if (arg.is_single_type ())
        return octave_value (FloatMatrix ());
      else
        return octave_value (Matrix ());
    }
 
  if (arg.is_single_type ())
    {
      if (arg.isreal ())
        {
          FloatNDArray nda = arg.float_array_value ();
 
          nda.resize (dims, 0.0);
          retval = (type != 0 ? nda.ifourier2d () : nda.fourier2d ());
        }
      else
        {
          FloatComplexNDArray cnda = arg.float_complex_array_value ();
 
          cnda.resize (dims, 0.0);
          retval = (type != 0 ? cnda.ifourier2d () : cnda.fourier2d ());
        }
    }
  else
    {
      if (arg.isreal ())
        {
          NDArray nda = arg.array_value ();
 
          nda.resize (dims, 0.0);
          retval = (type != 0 ? nda.ifourier2d () : nda.fourier2d ());
        }
      else if (arg.iscomplex ())
        {
          ComplexNDArray cnda = arg.complex_array_value ();
 
          cnda.resize (dims, 0.0);
          retval = (type != 0 ? cnda.ifourier2d () : cnda.fourier2d ());
        }
      else
        err_wrong_type_arg (fcn, arg);
    }
 
  return retval;
}
 
DEFUN (fft2, args, ,
       doc: /* -*- texinfo -*-
@deftypefn  {} {} fft2 (@var{A})
@deftypefnx {} {} fft2 (@var{A}, @var{m}, @var{n})
Compute the two-dimensional discrete Fourier transform of @var{A} using
a Fast Fourier Transform (FFT) algorithm.
 
The optional arguments @var{m} and @var{n} may be used specify the number of
rows and columns of @var{A} to use.  If either of these is larger than the
size of @var{A}, @var{A} is resized and padded with zeros.
 
If @var{A} is a multi-dimensional matrix, each two-dimensional sub-matrix
of @var{A} is treated separately.
@seealso{ifft2, fft, fftn, fftw}
@end deftypefn */)
{
  return do_fft2 (args, "fft2", 0);
}
 
 
DEFUN (ifft2, args, ,
       doc: /* -*- texinfo -*-
@deftypefn  {} {} ifft2 (@var{A})
@deftypefnx {} {} ifft2 (@var{A}, @var{m}, @var{n})
Compute the inverse two-dimensional discrete Fourier transform of @var{A}
using a Fast Fourier Transform (FFT) algorithm.
 
The optional arguments @var{m} and @var{n} may be used specify the number of
rows and columns of @var{A} to use.  If either of these is larger than the
size of @var{A}, @var{A} is resized and padded with zeros.
 
If @var{A} is a multi-dimensional matrix, each two-dimensional sub-matrix
of @var{A} is treated separately.
@seealso{fft2, ifft, ifftn, fftw}
@end deftypefn */)
{
  return do_fft2 (args, "ifft2", 1);
}
 
/*
## Author: David Billinghurst (David.Billinghurst@riotinto.com.au)
##         Comalco Research and Technology
##         02 May 2000
%!testif HAVE_FFTW
%! M = 16;
%! N = 8;
%!
%! m = 5;
%! n = 3;
%!
%! x = 2*pi*(0:1:M-1)/M;
%! y = 2*pi*(0:1:N-1)/N;
%! sx = cos (m*x);
%! sy = sin (n*y);
%! s = kron (sx',sy);
%! S = fft2 (s);
%! answer = kron (fft (sx)', fft (sy));
%! assert (S, answer, 4*M*N*eps);
 
## Author: David Billinghurst (David.Billinghurst@riotinto.com.au)
##         Comalco Research and Technology
##         02 May 2000
%!testif HAVE_FFTW
%! M = 12;
%! N = 7;
%!
%! m = 3;
%! n = 2;
%!
%! x = 2*pi*(0:1:M-1)/M;
%! y = 2*pi*(0:1:N-1)/N;
%!
%! sx = cos (m*x);
%! sy = cos (n*y);
%!
%! S = kron (fft (sx)', fft (sy));
%! answer = kron (sx', sy);
%! s = ifft2 (S);
%!
%! assert (s, answer, 30*eps);
 
## Author: David Billinghurst (David.Billinghurst@riotinto.com.au)
##         Comalco Research and Technology
##         02 May 2000
%!testif HAVE_FFTW
%! M = 16;
%! N = 8;
%!
%! m = 5;
%! n = 3;
%!
%! x = 2*pi*(0:1:M-1)/M;
%! y = 2*pi*(0:1:N-1)/N;
%! sx = single (cos (m*x));
%! sy = single (sin (n*y));
%! s = kron (sx', sy);
%! S = fft2 (s);
%! answer = kron (fft (sx)', fft (sy));
%! assert (S, answer, 4*M*N*eps ("single"));
 
## Author: David Billinghurst (David.Billinghurst@riotinto.com.au)
##         Comalco Research and Technology
##         02 May 2000
%!testif HAVE_FFTW
%! M = 12;
%! N = 7;
%!
%! m = 3;
%! n = 2;
%!
%! x = single (2*pi*(0:1:M-1)/M);
%! y = single (2*pi*(0:1:N-1)/N);
%!
%! sx = cos (m*x);
%! sy = cos (n*y);
%!
%! S = kron (fft (sx)', fft (sy));
%! answer = kron (sx', sy);
%! s = ifft2 (S);
%!
%! assert (s, answer, 30*eps ("single"));
*/