Mercurial > octave-nkf
view scripts/polynomial/poly.m @ 18840:4a4edf0f2077 nkf-ready
fix LLVM 3.4 build (bug #41061)
* configure.ac: Call new functions OCTAVE_LLVM_RAW_FD_OSTREAM_API and
OCTAVE_LLVM_LEGACY_PASSMANAGER_API, check for Verifier.h header file
* m4/acinclude.m4 (OCTAVE_LLVM_RAW_FD_OSTREAM_API): New function to
detect correct raw_fd_ostream API
* m4/acinclude.m4 (OCTAVE_LLVM_LEGACY_PASSMANAGER_API): New function
to detect legacy passmanager API
* libinterp/corefcn/jit-util.h: Use legacy passmanager namespace if
necessary
* libinterp/corefcn/pt-jit.h (class tree_jit): Use legacy passmanager
class if necessary
* libinterp/corefcn/pt-jit.cc: Include appropriate header files
* libinterp/corefcn/pt-jit.cc (tree_jit::initialize): Use legacy
passmanager if necessary
* libinterp/corefcn/pt-jit.cc (tree_jit::optimize): Use correct API
* libinterp/corefcn/jit-typeinfo.cc: Include appropriate header file
author | Stefan Mahr <dac922@gmx.de> |
---|---|
date | Sun, 11 May 2014 02:28:33 +0200 |
parents | d63878346099 |
children | 446c46af4b42 |
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## Copyright (C) 1994-2013 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 ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} poly (@var{A}) ## @deftypefnx {Function File} {} poly (@var{x}) ## If @var{A} is a square @math{N}-by-@math{N} matrix, @code{poly (@var{A})} ## is the row vector of the coefficients of @code{det (z * eye (N) - A)}, ## the characteristic polynomial of @var{A}. For example, ## the following code finds the eigenvalues of @var{A} which are the roots of ## @code{poly (@var{A})}. ## ## @example ## @group ## roots (poly (eye (3))) ## @result{} 1.00001 + 0.00001i ## 1.00001 - 0.00001i ## 0.99999 + 0.00000i ## @end group ## @end example ## ## In fact, all three eigenvalues are exactly 1 which emphasizes that for ## numerical performance the @code{eig} function should be used to compute ## eigenvalues. ## ## If @var{x} is a vector, @code{poly (@var{x})} is a vector of the ## coefficients of the polynomial whose roots are the elements of @var{x}. ## That is, if @var{c} is a polynomial, then the elements of @code{@var{d} = ## roots (poly (@var{c}))} are contained in @var{c}. The vectors @var{c} and ## @var{d} are not identical, however, due to sorting and numerical errors. ## @seealso{roots, eig} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Created: 24 December 1993 ## Adapted-By: jwe function y = poly (x) if (nargin != 1) print_usage (); endif m = min (size (x)); n = max (size (x)); if (m == 0) y = 1; return; elseif (m == 1) v = x; elseif (m == n) v = eig (x); else print_usage (); endif y = zeros (1, n+1); y(1) = 1; for j = 1:n; y(2:(j+1)) = y(2:(j+1)) - v(j) .* y(1:j); endfor if (all (all (imag (x) == 0))) y = real (y); endif endfunction %!assert (poly ([]), 1) %!assert (poly ([1, 2, 3]), [1, -6, 11, -6]) %!assert (poly ([1, 2; 3, 4]), [1, -5, -2], sqrt (eps)) %!error poly ([1, 2, 3; 4, 5, 6])