/*
Copyright (C) 1996-2013 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
.
*/
// Based on Tony Richardson's filter.m.
//
// Originally translated to C++ by KH (Kurt.Hornik@wu-wien.ac.at)
// with help from Fritz Leisch and Andreas Weingessel on Oct 20, 1994.
//
// Rewritten to use templates to handle both real and complex cases by
// jwe, Wed Nov 1 19:15:29 1995.
#ifdef HAVE_CONFIG_H
#include
#endif
#include "quit.h"
#include "defun.h"
#include "error.h"
#include "oct-obj.h"
#if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
extern MArray
filter (MArray&, MArray&, MArray&, int dim);
extern MArray
filter (MArray&, MArray&, MArray&, int dim);
extern MArray
filter (MArray&, MArray&, MArray&, int dim);
extern MArray
filter (MArray&, MArray&, MArray&,
int dim);
#endif
template
MArray
filter (MArray& b, MArray& a, MArray& x, MArray& si,
int dim = 0)
{
MArray y;
octave_idx_type a_len = a.length ();
octave_idx_type b_len = b.length ();
octave_idx_type ab_len = a_len > b_len ? a_len : b_len;
// FIXME: The two lines below should be unecessary because
// this template is called with a and b as column vectors
// already. However the a.resize line is currently (2011/04/26)
// necessary to stop bug #33164.
b.resize (dim_vector (ab_len, 1), 0.0);
if (a_len > 1)
a.resize (dim_vector (ab_len, 1), 0.0);
T norm = a (0);
if (norm == static_cast(0.0))
{
error ("filter: the first element of A must be non-zero");
return y;
}
dim_vector x_dims = x.dims ();
if (dim < 0 || dim > x_dims.length ())
{
error ("filter: DIM must be a valid dimension");
return y;
}
octave_idx_type x_len = x_dims(dim);
dim_vector si_dims = si.dims ();
octave_idx_type si_len = si_dims(0);
if (si_len != ab_len - 1)
{
error ("filter: first dimension of SI must be of length max (length (a), length (b)) - 1");
return y;
}
if (si_dims.length () != x_dims.length ())
{
error ("filter: dimensionality of SI and X must agree");
return y;
}
for (octave_idx_type i = 1; i < dim; i++)
{
if (si_dims(i) != x_dims(i-1))
{
error ("filter: dimensionality of SI and X must agree");
return y;
}
}
for (octave_idx_type i = dim+1; i < x_dims.length (); i++)
{
if (si_dims(i) != x_dims(i))
{
error ("filter: dimensionality of SI and X must agree");
return y;
}
}
if (x_len == 0)
return x;
if (norm != static_cast(1.0))
{
a = a / norm;
b = b / norm;
}
if (a_len <= 1 && si_len <= 0)
return b(0) * x;
y.resize (x_dims, 0.0);
int x_stride = 1;
for (int i = 0; i < dim; i++)
x_stride *= x_dims(i);
octave_idx_type x_num = x_dims.numel () / x_len;
for (octave_idx_type num = 0; num < x_num; num++)
{
octave_idx_type x_offset;
if (x_stride == 1)
x_offset = num * x_len;
else
{
octave_idx_type x_offset2 = 0;
x_offset = num;
while (x_offset >= x_stride)
{
x_offset -= x_stride;
x_offset2++;
}
x_offset += x_offset2 * x_stride * x_len;
}
octave_idx_type si_offset = num * si_len;
if (a_len > 1)
{
T *py = y.fortran_vec ();
T *psi = si.fortran_vec ();
const T *pa = a.data ();
const T *pb = b.data ();
const T *px = x.data ();
psi += si_offset;
for (octave_idx_type i = 0, idx = x_offset;
i < x_len;
i++, idx += x_stride)
{
py[idx] = psi[0] + pb[0] * px[idx];
if (si_len > 0)
{
for (octave_idx_type j = 0; j < si_len - 1; j++)
{
OCTAVE_QUIT;
psi[j] = psi[j+1] - pa[j+1] * py[idx] + pb[j+1] * px[idx];
}
psi[si_len-1] = pb[si_len] * px[idx] - pa[si_len] * py[idx];
}
else
{
OCTAVE_QUIT;
psi[0] = pb[si_len] * px[idx] - pa[si_len] * py[idx];
}
}
}
else if (si_len > 0)
{
T *py = y.fortran_vec ();
T *psi = si.fortran_vec ();
const T *pb = b.data ();
const T *px = x.data ();
psi += si_offset;
for (octave_idx_type i = 0, idx = x_offset;
i < x_len;
i++, idx += x_stride)
{
py[idx] = psi[0] + pb[0] * px[idx];
if (si_len > 1)
{
for (octave_idx_type j = 0; j < si_len - 1; j++)
{
OCTAVE_QUIT;
psi[j] = psi[j+1] + pb[j+1] * px[idx];
}
psi[si_len-1] = pb[si_len] * px[idx];
}
else
{
OCTAVE_QUIT;
psi[0] = pb[1] * px[idx];
}
}
}
}
return y;
}
#if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
extern MArray
filter (MArray&, MArray&, MArray&,
MArray&, int dim);
extern MArray
filter (MArray&, MArray&, MArray&,
MArray&, int dim);
extern MArray
filter (MArray&, MArray&, MArray&,
MArray&, int dim);
extern MArray
filter (MArray&, MArray&, MArray&,
MArray&, int dim);
#endif
template
MArray
filter (MArray& b, MArray& a, MArray& x, int dim = -1)
{
dim_vector x_dims = x.dims ();
if (dim < 0)
{
// Find first non-singleton dimension
while (dim < x_dims.length () && x_dims(dim) <= 1)
dim++;
// All dimensions singleton, pick first dimension
if (dim == x_dims.length ())
dim = 0;
}
else if (dim < 0 || dim > x_dims.length ())
{
error ("filter: DIM must be a valid dimension");
return MArray ();
}
octave_idx_type a_len = a.length ();
octave_idx_type b_len = b.length ();
octave_idx_type si_len = (a_len > b_len ? a_len : b_len) - 1;
dim_vector si_dims = x.dims ();
for (int i = dim; i > 0; i--)
si_dims(i) = si_dims(i-1);
si_dims(0) = si_len;
MArray si (si_dims, T (0.0));
return filter (b, a, x, si, dim);
}
DEFUN (filter, args, nargout,
"-*- texinfo -*-\n\
@deftypefn {Built-in Function} {y =} filter (@var{b}, @var{a}, @var{x})\n\
@deftypefnx {Built-in Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si})\n\
@deftypefnx {Built-in Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, [], @var{dim})\n\
@deftypefnx {Built-in Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si}, @var{dim})\n\
Return the solution to the following linear, time-invariant difference\n\
equation:\n\
@tex\n\
$$\n\
\\sum_{k=0}^N a_{k+1} y_{n-k} = \\sum_{k=0}^M b_{k+1} x_{n-k}, \\qquad\n\
1 \\le n \\le P\n\
$$\n\
@end tex\n\
@ifnottex\n\
@c Set example in small font to prevent overfull line\n\
\n\
@smallexample\n\
@group\n\
N M\n\
SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k) for 1<=n<=length(x)\n\
k=0 k=0\n\
@end group\n\
@end smallexample\n\
\n\
@end ifnottex\n\
\n\
@noindent\n\
where\n\
@ifnottex\n\
N=length(a)-1 and M=length(b)-1.\n\
@end ifnottex\n\
@tex\n\
$a \\in \\Re^{N-1}$, $b \\in \\Re^{M-1}$, and $x \\in \\Re^P$.\n\
@end tex\n\
The result is calculated over the first non-singleton dimension of @var{x}\n\
or over @var{dim} if supplied.\n\
\n\
An equivalent form of the equation is:\n\
@tex\n\
$$\n\
y_n = -\\sum_{k=1}^N c_{k+1} y_{n-k} + \\sum_{k=0}^M d_{k+1} x_{n-k}, \\qquad\n\
1 \\le n \\le P\n\
$$\n\
@end tex\n\
@ifnottex\n\
@c Set example in small font to prevent overfull line\n\
\n\
@smallexample\n\
@group\n\
N M\n\
y(n) = - SUM c(k+1) y(n-k) + SUM d(k+1) x(n-k) for 1<=n<=length(x)\n\
k=1 k=0\n\
@end group\n\
@end smallexample\n\
\n\
@end ifnottex\n\
\n\
@noindent\n\
where\n\
@ifnottex\n\
c = a/a(1) and d = b/a(1).\n\
@end ifnottex\n\
@tex\n\
$c = a/a_1$ and $d = b/a_1$.\n\
@end tex\n\
\n\
If the fourth argument @var{si} is provided, it is taken as the\n\
initial state of the system and the final state is returned as\n\
@var{sf}. The state vector is a column vector whose length is\n\
equal to the length of the longest coefficient vector minus one.\n\
If @var{si} is not supplied, the initial state vector is set to all\n\
zeros.\n\
\n\
In terms of the Z Transform, y is the result of passing the discrete-\n\
time signal x through a system characterized by the following rational\n\
system function:\n\
@tex\n\
$$\n\
H(z) = {\\displaystyle\\sum_{k=0}^M d_{k+1} z^{-k}\n\
\\over 1 + \\displaystyle\\sum_{k+1}^N c_{k+1} z^{-k}}\n\
$$\n\
@end tex\n\
@ifnottex\n\
\n\
@example\n\
@group\n\
M\n\
SUM d(k+1) z^(-k)\n\
k=0\n\
H(z) = ---------------------\n\
N\n\
1 + SUM c(k+1) z^(-k)\n\
k=1\n\
@end group\n\
@end example\n\
\n\
@end ifnottex\n\
@seealso{filter2, fftfilt, freqz}\n\
@end deftypefn")
{
octave_value_list retval;
int nargin = args.length ();
if (nargin < 3 || nargin > 5)
{
print_usage ();
return retval;
}
const char *errmsg = "filter: arguments a and b must be vectors";
int dim;
dim_vector x_dims = args(2).dims ();
if (nargin == 5)
{
dim = args(4).nint_value () - 1;
if (dim < 0 || dim >= x_dims.length ())
{
error ("filter: DIM must be a valid dimension");
return retval;
}
}
else
{
// Find first non-singleton dimension
dim = 0;
while (dim < x_dims.length () && x_dims(dim) <= 1)
dim++;
// All dimensions singleton, pick first dimension
if (dim == x_dims.length ())
dim = 0;
}
bool isfloat = (args(0).is_single_type ()
|| args(1).is_single_type ()
|| args(2).is_single_type ()
|| (nargin >= 4 && args(3).is_single_type ()));
if (args(0).is_complex_type ()
|| args(1).is_complex_type ()
|| args(2).is_complex_type ()
|| (nargin >= 4 && args(3).is_complex_type ()))
{
if (isfloat)
{
FloatComplexColumnVector b (args(0).float_complex_vector_value ());
FloatComplexColumnVector a (args(1).float_complex_vector_value ());
FloatComplexNDArray x (args(2).float_complex_array_value ());
if (! error_state)
{
FloatComplexNDArray si;
if (nargin == 3 || args(3).is_empty ())
{
octave_idx_type a_len = a.length ();
octave_idx_type b_len = b.length ();
octave_idx_type si_len = (a_len > b_len ? a_len : b_len) - 1;
dim_vector si_dims = x.dims ();
for (int i = dim; i > 0; i--)
si_dims(i) = si_dims(i-1);
si_dims(0) = si_len;
si.resize (si_dims, 0.0);
}
else
{
si = args(3).float_complex_array_value ();
if (si.is_vector () && x.is_vector ())
si = si.reshape (dim_vector (si.numel (), 1));
}
if (! error_state)
{
FloatComplexNDArray y (filter (b, a, x, si, dim));
if (nargout == 2)
retval(1) = si;
retval(0) = y;
}
else
error (errmsg);
}
else
error (errmsg);
}
else
{
ComplexColumnVector b (args(0).complex_vector_value ());
ComplexColumnVector a (args(1).complex_vector_value ());
ComplexNDArray x (args(2).complex_array_value ());
if (! error_state)
{
ComplexNDArray si;
if (nargin == 3 || args(3).is_empty ())
{
octave_idx_type a_len = a.length ();
octave_idx_type b_len = b.length ();
octave_idx_type si_len = (a_len > b_len ? a_len : b_len) - 1;
dim_vector si_dims = x.dims ();
for (int i = dim; i > 0; i--)
si_dims(i) = si_dims(i-1);
si_dims(0) = si_len;
si.resize (si_dims, 0.0);
}
else
{
si = args(3).complex_array_value ();
if (si.is_vector () && x.is_vector ())
si = si.reshape (dim_vector (si.numel (), 1));
}
if (! error_state)
{
ComplexNDArray y (filter (b, a, x, si, dim));
if (nargout == 2)
retval(1) = si;
retval(0) = y;
}
else
error (errmsg);
}
else
error (errmsg);
}
}
else
{
if (isfloat)
{
FloatColumnVector b (args(0).float_vector_value ());
FloatColumnVector a (args(1).float_vector_value ());
FloatNDArray x (args(2).float_array_value ());
if (! error_state)
{
FloatNDArray si;
if (nargin == 3 || args(3).is_empty ())
{
octave_idx_type a_len = a.length ();
octave_idx_type b_len = b.length ();
octave_idx_type si_len = (a_len > b_len ? a_len : b_len) - 1;
dim_vector si_dims = x.dims ();
for (int i = dim; i > 0; i--)
si_dims(i) = si_dims(i-1);
si_dims(0) = si_len;
si.resize (si_dims, 0.0);
}
else
{
si = args(3).float_array_value ();
if (si.is_vector () && x.is_vector ())
si = si.reshape (dim_vector (si.numel (), 1));
}
if (! error_state)
{
FloatNDArray y (filter (b, a, x, si, dim));
if (nargout == 2)
retval(1) = si;
retval(0) = y;
}
else
error (errmsg);
}
else
error (errmsg);
}
else
{
ColumnVector b (args(0).vector_value ());
ColumnVector a (args(1).vector_value ());
NDArray x (args(2).array_value ());
if (! error_state)
{
NDArray si;
if (nargin == 3 || args(3).is_empty ())
{
octave_idx_type a_len = a.length ();
octave_idx_type b_len = b.length ();
octave_idx_type si_len = (a_len > b_len ? a_len : b_len) - 1;
dim_vector si_dims = x.dims ();
for (int i = dim; i > 0; i--)
si_dims(i) = si_dims(i-1);
si_dims(0) = si_len;
si.resize (si_dims, 0.0);
}
else
{
si = args(3).array_value ();
if (si.is_vector () && x.is_vector ())
si = si.reshape (dim_vector (si.numel (), 1));
}
if (! error_state)
{
NDArray y (filter (b, a, x, si, dim));
if (nargout == 2)
retval(1) = si;
retval(0) = y;
}
else
error (errmsg);
}
else
error (errmsg);
}
}
return retval;
}
template MArray
filter (MArray&, MArray&, MArray&,
MArray&, int dim);
template MArray
filter (MArray&, MArray&, MArray&, int dim);
template MArray
filter (MArray&, MArray&, MArray&,
MArray&, int dim);
template MArray
filter (MArray&, MArray&, MArray&, int dim);
template MArray
filter (MArray&, MArray&, MArray&,
MArray&, int dim);
template MArray
filter (MArray&, MArray&, MArray&, int dim);
template MArray
filter (MArray&, MArray&, MArray&,
MArray&, int dim);
template MArray
filter (MArray&, MArray&, MArray&,
int dim);
/*
%!shared a, b, x, r
%!test
%! a = [1 1];
%! b = [1 1];
%! x = zeros (1,10); x(1) = 1;
%! assert (filter (b, [1], x ), [1 1 0 0 0 0 0 0 0 0]);
%! assert (filter (b, [1], x.'), [1 1 0 0 0 0 0 0 0 0].');
%! assert (filter (b.', [1], x ), [1 1 0 0 0 0 0 0 0 0] );
%! assert (filter (b.', [1], x.'), [1 1 0 0 0 0 0 0 0 0].');
%! assert (filter ([1], a, x ), [+1 -1 +1 -1 +1 -1 +1 -1 +1 -1] );
%! assert (filter ([1], a, x.'), [+1 -1 +1 -1 +1 -1 +1 -1 +1 -1].');
%! assert (filter ([1], a.', x ), [+1 -1 +1 -1 +1 -1 +1 -1 +1 -1] );
%! assert (filter ([1], a.', x.'), [+1 -1 +1 -1 +1 -1 +1 -1 +1 -1].');
%! assert (filter (b, a, x ), [1 0 0 0 0 0 0 0 0 0] );
%! assert (filter (b.', a, x ), [1 0 0 0 0 0 0 0 0 0] );
%! assert (filter (b, a.', x ), [1 0 0 0 0 0 0 0 0 0] );
%! assert (filter (b.', a, x ), [1 0 0 0 0 0 0 0 0 0] );
%! assert (filter (b, a, x.'), [1 0 0 0 0 0 0 0 0 0].');
%! assert (filter (b.', a, x.'), [1 0 0 0 0 0 0 0 0 0].');
%! assert (filter (b, a.', x.'), [1 0 0 0 0 0 0 0 0 0].');
%! assert (filter (b.', a, x.'), [1 0 0 0 0 0 0 0 0 0].');
%!test
%! r = sqrt (1/2) * (1+i);
%! a = a*r;
%! b = b*r;
%! assert (filter (b, [1], x ), r*[1 1 0 0 0 0 0 0 0 0] );
%! assert (filter (b, [1], r*x ), r*r*[1 1 0 0 0 0 0 0 0 0] );
%! assert (filter (b, [1], x.' ), r*[1 1 0 0 0 0 0 0 0 0].' );
%! assert (filter (b, a, x ), [1 0 0 0 0 0 0 0 0 0] );
%! assert (filter (b, a, r*x ), r*[1 0 0 0 0 0 0 0 0 0] );
%!shared a, b, x, y, so
%!test
%! a = [1,1];
%! b = [1,1];
%! x = zeros (1,10); x(1) = 1;
%! [y, so] = filter (b, [1], x, [-1]);
%! assert (y, [0 1 0 0 0 0 0 0 0 0]);
%! assert (so, 0);
%!test
%! x = zeros (10,3); x(1,1) = -1; x(1,2) = 1;
%! y0 = zeros (10,3); y0(1:2,1) = -1; y0(1:2,2) = 1;
%! y = filter (b, [1], x);
%! assert (y, y0);
%!test
%! a = [1,1];
%! b=[1,1];
%! x = zeros (4,4,2); x(1,1:4,1) = +1; x(1,1:4,2) = -1;
%! y0 = zeros (4,4,2); y0(1:2,1:4,1) = +1; y0(1:2,1:4,2) = -1;
%! y = filter (b, [1], x);
%! assert (y, y0);
%!assert (filter (1, ones (10,1) / 10, []), [])
%!assert (filter (1, ones (10,1) / 10, zeros (0,10)), zeros (0,10))
%!assert (filter (1, ones (10,1) / 10, single (1:5)), repmat (single (10), 1, 5))
%% Test using initial conditions
%!assert (filter ([1, 1, 1], [1, 1], [1 2], [1, 1]), [2 2])
%!assert (filter ([1, 1, 1], [1, 1], [1 2], [1, 1]'), [2 2])
%!assert (filter ([1, 3], [1], [1 2; 3 4; 5 6], [4, 5]), [5 7; 6 10; 14 18])
%!error (filter ([1, 3], [1], [1 2; 3 4; 5 6], [4, 5]'))
%!assert (filter ([1, 3, 2], [1], [1 2; 3 4; 5 6], [1 0 0; 1 0 0], 2), [2 6; 3 13; 5 21])
## Test of DIM parameter
%!test
%! x = ones (2, 1, 3, 4);
%! x(1,1,:,:) = [1 2 3 4; 5 6 7 8; 9 10 11 12];
%! y0 = [1 1 6 2 15 3 2 1 8 2 18 3 3 1 10 2 21 3 4 1 12 2 24 3];
%! y0 = reshape (y0, size (x));
%! y = filter ([1 1 1], 1, x, [], 3);
%! assert (y, y0);
*/