view scripts/polynomial/roots.m @ 787:c5d35bb139b6

[project @ 1994-10-11 00:34:13 by jwe] Initial revision
author jwe
date Tue, 11 Oct 1994 00:34:39 +0000
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children 3470f1e25a79
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function r = roots (v)
  #
  # For a vector v with n components, return the roots of the
  # polynomial v(1) * z^(n-1) + ... + v(n-1) * z + v(n).
  
  # Written by KH (Kurt.Hornik@neuro.tuwien.ac.at) on Dec 24, 1993
  # Copyright Dept of Probability Theory and Statistics TU Wien
  
  [nr, nc] = size(v);
  if !((nr == 1 && nc > 1) || (nc == 1 && nr > 1))
    error ("usage:  roots (v), where v is a nonzero vector");
  endif

  n = nr + nc - 1;
  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)
    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)
	r = [r; zeros (n - f(m), 1)];
      endif
    else
      r = zeros (n - f(m), 1);
    endif
  else
    error ("usage:  roots(v), where v is a nonzero vector");
  endif
  
endfunction