update packages

[CreaPhase.git] / octave_packages / m / general / interpft.m

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+## Copyright (C) 2001-2012 Paul Kienzle
+##
+## 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/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {} interpft (@var{x}, @var{n})
+## @deftypefnx {Function File} {} interpft (@var{x}, @var{n}, @var{dim})
+##
+## Fourier interpolation.  If @var{x} is a vector, then @var{x} is
+## resampled with @var{n} points.  The data in @var{x} is assumed to be
+## equispaced.  If @var{x} is an array, then operate along each column of
+## the array separately.  If @var{dim} is specified, then interpolate
+## along the dimension @var{dim}.
+##
+## @code{interpft} assumes that the interpolated function is periodic,
+## and so assumptions are made about the endpoints of the interpolation.
+##
+## @seealso{interp1}
+## @end deftypefn
+
+## Author: Paul Kienzle
+## 2001-02-11
+##    * initial version
+## 2002-03-17 aadler
+##    * added code to work on matrices as well
+## 2006-05-25 dbateman
+##    * Make it matlab compatiable, cutting out the 2-D interpolation
+
+function z = interpft (x, n, dim)
+
+  if (nargin < 2 || nargin > 3)
+    print_usage ();
+  endif
+
+  if (! (isscalar (n) && n == fix (n)))
+    error ("interpft: N must be a scalar integer");
+  endif
+
+  if (nargin == 2)
+    if (isrow (x))
+      dim = 2;
+    else
+      dim = 1;
+    endif
+  endif
+
+  nd = ndims (x);
+
+  if (dim < 1 || dim > nd)
+    error ("interpft: invalid dimension DIM");
+  endif
+
+  perm = [dim:nd, 1:(dim-1)];
+  x = permute (x, perm);
+  m = rows (x);
+
+  inc = max (1, fix (m/n));
+  y = fft (x) / m;
+  k = floor (m / 2);
+  sz = size (x);
+  sz(1) = n * inc - m;
+
+  idx = repmat ({':'}, nd, 1);
+  idx{1} = 1:k;
+  z = cat (1, y(idx{:}), zeros (sz));
+  idx{1} = k+1:m;
+  z = cat (1, z, y(idx{:}));
+  z = n * ifft (z);
+
+  if (inc != 1)
+    sz(1) = n;
+    z = inc * reshape (z(1:inc:end), sz);
+  endif
+
+  z = ipermute (z, perm);
+
+endfunction
+
+
+%!demo
+%! t = 0 : 0.3 : pi; dt = t(2)-t(1);
+%! n = length (t); k = 100;
+%! ti = t(1) + [0 : k-1]*dt*n/k;
+%! y = sin (4*t + 0.3) .* cos (3*t - 0.1);
+%! yp = sin (4*ti + 0.3) .* cos (3*ti - 0.1);
+%! plot (ti, yp, 'g', ti, interp1(t, y, ti, 'spline'), 'b', ...
+%!       ti, interpft (y, k), 'c', t, y, 'r+');
+%! legend ('sin(4t+0.3)cos(3t-0.1','spline','interpft','data');
+
+%!shared n,y
+%! x = [0:10]'; y = sin(x); n = length (x);
+%!assert (interpft(y, n), y, 20*eps);
+%!assert (interpft(y', n), y', 20*eps);
+%!assert (interpft([y,y],n), [y,y], 20*eps);
+
+%% Test input validation
+%!error interpft ()
+%!error interpft (1)
+%!error interpft (1,2,3)
+%!error (interpft(1,[n,n]))
+%!error (interpft(1,2,0))
+%!error (interpft(1,2,3))