Mercurial > octave
view libinterp/corefcn/filter.cc @ 30249:bc22395f60fa
maint: merge stable to default.
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 22 Oct 2021 12:05:59 -0400 |
parents | e3e0193963ea |
children | 91c6288781ba 796f54d4ddbf |
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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/>. // //////////////////////////////////////////////////////////////////////// // 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. #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include "quit.h" #include "defun.h" #include "error.h" #include "ovl.h" OCTAVE_NAMESPACE_BEGIN template <typename T> MArray<T> filter (MArray<T>& b, MArray<T>& a, MArray<T>& x, MArray<T>& si, int dim = 0) { MArray<T> y; octave_idx_type a_len = a.numel (); octave_idx_type b_len = b.numel (); octave_idx_type ab_len = (a_len > b_len ? a_len : b_len); // FIXME: The two lines below should be unnecessary 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<T> (0.0)) error ("filter: the first element of A must be nonzero"); dim_vector x_dims = x.dims (); if (dim < 0 || dim > x_dims.ndims ()) error ("filter: DIM must be a valid dimension"); 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"); if (si_dims.ndims () != x_dims.ndims ()) error ("filter: dimensionality of SI and X must agree"); 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"); } for (octave_idx_type i = dim+1; i < x_dims.ndims (); i++) { if (si_dims(i) != x_dims(i)) error ("filter: dimensionality of SI and X must agree"); } if (x_len == 0) return x; if (norm != static_cast<T> (1.0)) { a /= norm; b /= norm; } if (a_len <= 1 && si_len <= 0) return b(0) * x; y.resize (x_dims, 0.0); octave_idx_type 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 { x_offset = num; octave_idx_type n_strides = num / x_stride; x_offset += n_strides * x_stride * (x_len - 1); } 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; } template <typename T> MArray<T> filter (MArray<T>& b, MArray<T>& a, MArray<T>& x, int dim = -1) { dim_vector x_dims = x.dims (); if (dim < 0) dim = x_dims.first_non_singleton (); else if (dim > x_dims.ndims ()) error ("filter: DIM must be a valid dimension"); octave_idx_type a_len = a.numel (); octave_idx_type b_len = b.numel (); 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<T> si (si_dims, T (0.0)); return filter (b, a, x, si, dim); } DEFUN (filter, args, , doc: /* -*- texinfo -*- @deftypefn {} {@var{y} =} filter (@var{b}, @var{a}, @var{x}) @deftypefnx {} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si}) @deftypefnx {} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, [], @var{dim}) @deftypefnx {} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si}, @var{dim}) Apply a 1-D digital filter to the data @var{x}. @code{filter} returns the solution to the following linear, time-invariant difference equation: @tex $$ \sum_{k=0}^N a_{k+1} y_{n-k} = \sum_{k=0}^M b_{k+1} x_{n-k}, \qquad 1 \le n \le P $$ @end tex @ifnottex @c Set example in small font to prevent overfull line @smallexample @group N M SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k) for 1<=n<=length(x) k=0 k=0 @end group @end smallexample @end ifnottex @noindent where @ifnottex N=length(a)-1 and M=length(b)-1. @end ifnottex @tex $a \in \Re^{N-1}$, $b \in \Re^{M-1}$, and $x \in \Re^P$. @end tex The result is calculated over the first non-singleton dimension of @var{x} or over @var{dim} if supplied. An equivalent form of the equation is: @tex $$ y_n = -\sum_{k=1}^N c_{k+1} y_{n-k} + \sum_{k=0}^M d_{k+1} x_{n-k}, \qquad 1 \le n \le P $$ @end tex @ifnottex @c Set example in small font to prevent overfull line @smallexample @group N M y(n) = - SUM c(k+1) y(n-k) + SUM d(k+1) x(n-k) for 1<=n<=length(x) k=1 k=0 @end group @end smallexample @end ifnottex @noindent where @ifnottex c = a/a(1) and d = b/a(1). @end ifnottex @tex $c = a/a_1$ and $d = b/a_1$. @end tex If the fourth argument @var{si} is provided, it is taken as the initial state of the system and the final state is returned as @var{sf}. The state vector is a column vector whose length is equal to the length of the longest coefficient vector minus one. If @var{si} is not supplied, the initial state vector is set to all zeros. In terms of the Z Transform, @var{y} is the result of passing the discrete-time signal @var{x} through a system characterized by the following rational system function: @tex $$ H(z) = {\displaystyle\sum_{k=0}^M d_{k+1} z^{-k} \over 1 + \displaystyle\sum_{k+1}^N c_{k+1} z^{-k}} $$ @end tex @ifnottex @example @group M SUM d(k+1) z^(-k) k=0 H(z) = --------------------- N 1 + SUM c(k+1) z^(-k) k=1 @end group @end example @end ifnottex @seealso{filter2, fftfilt, freqz} @end deftypefn */) { int nargin = args.length (); if (nargin < 3 || nargin > 5) print_usage (); int dim; dim_vector x_dims = args(2).dims (); if (nargin == 5) { dim = args(4).nint_value () - 1; if (dim < 0 || dim >= x_dims.ndims ()) error ("filter: DIM must be a valid dimension"); } else dim = x_dims.first_non_singleton (); octave_value_list retval; const char *a_b_errmsg = "filter: A and B must be vectors"; const char *x_si_errmsg = "filter: X and SI must be arrays"; 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).iscomplex () || args(1).iscomplex () || args(2).iscomplex () || (nargin >= 4 && args(3).iscomplex ())) { if (isfloat) { FloatComplexColumnVector b = args(0).xfloat_complex_vector_value (a_b_errmsg); FloatComplexColumnVector a = args(1).xfloat_complex_vector_value (a_b_errmsg); FloatComplexNDArray x = args(2).xfloat_complex_array_value (x_si_errmsg); FloatComplexNDArray si; if (nargin == 3 || args(3).isempty ()) { octave_idx_type a_len = a.numel (); octave_idx_type b_len = b.numel (); 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).xfloat_complex_array_value (x_si_errmsg); if (si.isvector () && x.isvector ()) si = si.reshape (dim_vector (si.numel (), 1)); } FloatComplexNDArray y (filter (b, a, x, si, dim)); retval = ovl (y, si); } else { ComplexColumnVector b = args(0).xcomplex_vector_value (a_b_errmsg); ComplexColumnVector a = args(1).xcomplex_vector_value (a_b_errmsg); ComplexNDArray x = args(2).xcomplex_array_value (x_si_errmsg); ComplexNDArray si; if (nargin == 3 || args(3).isempty ()) { octave_idx_type a_len = a.numel (); octave_idx_type b_len = b.numel (); 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).xcomplex_array_value (x_si_errmsg); if (si.isvector () && x.isvector ()) si = si.reshape (dim_vector (si.numel (), 1)); } ComplexNDArray y (filter (b, a, x, si, dim)); retval = ovl (y, si); } } else { if (isfloat) { FloatColumnVector b = args(0).xfloat_vector_value (a_b_errmsg); FloatColumnVector a = args(1).xfloat_vector_value (a_b_errmsg); FloatNDArray x = args(2).xfloat_array_value (x_si_errmsg); FloatNDArray si; if (nargin == 3 || args(3).isempty ()) { octave_idx_type a_len = a.numel (); octave_idx_type b_len = b.numel (); 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).xfloat_array_value (x_si_errmsg); if (si.isvector () && x.isvector ()) si = si.reshape (dim_vector (si.numel (), 1)); } FloatNDArray y (filter (b, a, x, si, dim)); retval = ovl (y, si); } else { ColumnVector b = args(0).xvector_value (a_b_errmsg); ColumnVector a = args(1).xvector_value (a_b_errmsg); NDArray x = args(2).xarray_value (x_si_errmsg); NDArray si; if (nargin == 3 || args(3).isempty ()) { octave_idx_type a_len = a.numel (); octave_idx_type b_len = b.numel (); 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).xarray_value (x_si_errmsg); if (si.isvector () && x.isvector ()) si = si.reshape (dim_vector (si.numel (), 1)); } NDArray y (filter (b, a, x, si, dim)); retval = ovl (y, si); } } return retval; } template MArray<double> filter (MArray<double>&, MArray<double>&, MArray<double>&, MArray<double>&, int dim); template MArray<double> filter (MArray<double>&, MArray<double>&, MArray<double>&, int dim); template MArray<Complex> filter (MArray<Complex>&, MArray<Complex>&, MArray<Complex>&, MArray<Complex>&, int dim); template MArray<Complex> filter (MArray<Complex>&, MArray<Complex>&, MArray<Complex>&, int dim); template MArray<float> filter (MArray<float>&, MArray<float>&, MArray<float>&, MArray<float>&, int dim); template MArray<float> filter (MArray<float>&, MArray<float>&, MArray<float>&, int dim); template MArray<FloatComplex> filter (MArray<FloatComplex>&, MArray<FloatComplex>&, MArray<FloatComplex>&, MArray<FloatComplex>&, int dim); template MArray<FloatComplex> filter (MArray<FloatComplex>&, MArray<FloatComplex>&, MArray<FloatComplex>&, 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); */ OCTAVE_NAMESPACE_END