roots.m

JAVA 数学程序库 提供常规的数值计算程序包

## Copyright (C) 1996, 1997 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 2, 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, write to the Free
## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
## 02110-1301, USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} roots (@var{v})
##
## For a vector @var{v} with @math{N} components, return
## the roots of the polynomial
## @iftex
## @tex
## $$
## v_1 z^{N-1} + \cdots + v_{N-1} z + v_N.
## $$
## @end tex
## @end iftex
## @ifinfo
##
## @example
## v(1) * z^(N-1) + ... + v(N-1) * z + v(N)
## @end example
## @end ifinfo
## @end deftypefn

## Author: KH <[e-mail]>
## Created: 24 December 1993
## Adapted-By: jwe

function r = roots (v)

  if (min (size (v)) > 1 || nargin != 1)
    print_usage ();
  endif

  n = length (v);
  v = reshape (v, 1, n);

  ## If v = [ 0 ... 0 v(k+1) ... v(k+l) 0 ... 0 ], we can remove the
  ## leading k zeros and n - k - l roots of the polynomial are zero.

  f = find (v);
  m = max (size (f));

  if (m > 0 && n > 1)
    v = v(f(1):f(m));
    l = max (size (v));
    if (l > 1)
      A = diag (ones (1, l-2), -1);
      A(1,:) = -v(2:l) ./ v(1);
      r = eig (A);
      if (f(m) < n)
        tmp = zeros (n - f(m), 1);
        r = [r; tmp];
      endif
    else
      r = zeros (n - f(m), 1);
    endif
  else
    r = [];
  endif

endfunction

/*
@GROUP
polynomial
@SYNTAX
y = roots (x)
@DOC
.
@NOTES
@EXAMPLES
@SEE
poly, polyreduce, polyval, polyinteg, unmkpp
*/