This file is indexed.

/usr/share/octave/packages/signal-1.3.2/residued.m is in octave-signal 1.3.2-5.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
## Copyright (C) 2005 Julius O. Smith III <jos@ccrma.stanford.edu>
##
## This program 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.
##
## This program 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
## this program; if not, see <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{r}, @var{p}, @var{f}, @var{m}] =} residued (@var{b}, @var{a})
## Compute the partial fraction expansion (PFE) of filter
## @math{H(z) = B(z)/A(z)}.  In the usual PFE function @code{residuez}, the
## IIR part (poles @var{p} and residues @var{r}) is driven @emph{in parallel}
## with the FIR part (@var{f}).  In this variant, the IIR part is driven by
## the @emph{output} of the FIR part.  This structure can be more accurate in
## signal modeling applications.
##
## INPUTS:
## @var{b} and @var{a} are vectors specifying the digital filter
## @math{H(z) = B(z)/A(z)}.  See @code{help filter} for documentation of the
## @var{b} and @var{a} filter coefficients.
##
## RETURNED:
## @itemize
## @item @var{r} = column vector containing the filter-pole residues
## @item @var{p} = column vector containing the filter poles
## @item @var{f} = row vector containing the FIR part, if any
## @item @var{m} = column vector of pole multiplicities
## @end itemize
##
## EXAMPLES:
## @example
## See @code{test residued verbose} to see a number of examples.
## @end example
##
## For the theory of operation, see
## @indicateurl{http://ccrma.stanford.edu/~jos/filters/residued.html}
##
## @seealso{residue, residued}
## @end deftypefn

function [r, p, f, m] = residued(b, a, toler)

  ## RESIDUED - return residues, poles, and FIR part of B(z)/A(z)
  ##
  ## Let nb = length(b), na = length(a), and N=na-1 = no. of poles.
  ## If nb<na, then f will be empty, and the returned filter is
  ##
  ##             r(1)                      r(N)
  ## H(z) = ----------------  + ... + ----------------- = R(z)
  ##        [ 1-p(1)/z ]^e(1)         [ 1-p(N)/z ]^e(N)
  ##
  ## This is the same result as returned by RESIDUEZ.
  ## Otherwise, the FIR part f will be nonempty,
  ## and the returned filter is
  ##
  ## H(z) = f(1) + f(2)/z + f(3)/z^2 + ... + f(nf)/z^M + R(z)/z^M
  ##
  ## where R(z) is the parallel one-pole filter bank defined above,
  ## and M is the order of F(z) = length(f)-1 = nb-na.
  ##
  ## Note, in particular, that the impulse-response of the parallel
  ## (complex) one-pole filter bank starts AFTER that of the the FIR part.
  ## In the result returned by RESIDUEZ, R(z) is not divided by z^M,
  ## so its impulse response starts at time 0 in parallel with f(n).
  ##
  ## J.O. Smith, 9/19/05

  if nargin==3,
    warning("tolerance ignored");
  endif
  NUM = b(:)';
  DEN = a(:)';
  nb = length(NUM);
  na = length(DEN);
  f = [];
  if na<=nb
    f = filter(NUM,DEN,[1,zeros(nb-na)]);
    NUM = NUM - conv(DEN,f);
    NUM = NUM(nb-na+2:end);
  endif
  [r,p,f2,m] = residuez(NUM,DEN);
  if f2, error('f2 not empty as expected'); endif

endfunction

%!test
%! B=1; A=[1 -1];
%! [r,p,f,m] = residued(B,A);
%! assert({r,p,f,m},{1,1,[],1},100*eps);
%! [r2,p2,f2,m2] = residuez(B,A);
%! assert({r,p,f,m},{r2,p2,f2,m2},100*eps);
% residuez and residued should be identical when length(B)<length(A)

%!test
%! B=[1 -2 1]; A=[1 -1];
%! [r,p,f,m] = residued(B,A);
%! assert({r,p,f,m},{0,1,[1 -1],1},100*eps);

%!test
%! B=[1 -2 1]; A=[1 -0.5];
%! [r,p,f,m] = residued(B,A);
%! assert({r,p,f,m},{0.25,0.5,[1 -1.5],1},100*eps);

%!test
%! B=1; A=[1 -0.75 0.125];
%! [r,p,f,m] = residued(B,A);
%! [r2,p2,f2,m2] = residuez(B,A);
%! assert({r,p,f,m},{r2,p2,f2,m2},100*eps);
% residuez and residued should be identical when length(B)<length(A)

%!test
%! B=1; A=[1 -2 1];
%! [r,p,f,m] = residued(B,A);
%! [r2,p2,f2,m2] = residuez(B,A);
%! assert({r,p,f,m},{r2,p2,f2,m2},100*eps);
% residuez and residued should be identical when length(B)<length(A)

%!test
%! B=[6,2]; A=[1 -2 1];
%! [r,p,f,m] = residued(B,A);
%! [r2,p2,f2,m2] = residuez(B,A);
%! assert({r,p,f,m},{r2,p2,f2,m2},100*eps);
% residuez and residued should be identical when length(B)<length(A)

%!test
%! B=[1 1 1]; A=[1 -2 1];
%! [r,p,f,m] = residued(B,A);
%! assert(r,[0;3],1e-7);
%! assert(p,[1;1],1e-8);
%! assert(f,1,100*eps);
%! assert(m,[1;2],100*eps);

%!test
%! B=[2 6 6 2]; A=[1 -2 1];
%! [r,p,f,m] = residued(B,A);
%! assert(r,[8;16],3e-7);
%! assert(p,[1;1],1e-8);
%! assert(f,[2,10],100*eps);
%! assert(m,[1;2],100*eps);

%!test
%! B=[1,6,2]; A=[1 -2 1];
%! [r,p,f,m] = residued(B,A);
%! assert(r,[-1;9],3e-7);
%! assert(p,[1;1],1e-8);
%! assert(f,1,100*eps);
%! assert(m,[1;2],100*eps);

%!test
%! B=[1 0 0 0 1]; A=[1 0 0 0 -1];
%! [r,p,f,m] = residued(B,A);
%! [~,is] = sort(angle(p));
%! assert(r(is),[-1/2;-j/2;1/2;j/2],100*eps);
%! assert(p(is),[-1;-j;1;j],100*eps);
%! assert(f,1,100*eps);
%! assert(m,[1;1;1;1],100*eps);
%  Verified in maxima: ratsimp(%I/2/(1-%I * d) - %I/2/(1+%I * d)); etc.