Mercurial > hg > octave-nkf
changeset 18657:f57148641869 gui-release
polyeig.m: Overhaul function for Matlab compatibility (bug #41865).
* NEWS: Announce change in return format of polyeig.
* polyeig.m: Return a row vector of eigenvalues rather than a matrix with
eigenvalues on the diagonal. Improve docstring. Improve input validation.
Add %!error tests for input validation.
author | Rik <rik@octave.org> |
---|---|
date | Sat, 15 Mar 2014 16:29:46 -0700 |
parents | 6b4f9cab88d6 |
children | ebd063b7b1c6 |
files | NEWS scripts/polynomial/polyeig.m |
diffstat | 2 files changed, 39 insertions(+), 26 deletions(-) [+] |
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--- a/NEWS +++ b/NEWS @@ -21,6 +21,10 @@ is now set to "on" by default instead of "error" by default and "on" for --traditional. + ** polyeig now returns a row vector of eigenvalues rather than a matrix + with the eigenvalues on the diagonal. This change was made for Matlab + compatibility. + ** Other new functions added in 4.0.0: validateattributes
--- a/scripts/polynomial/polyeig.m +++ b/scripts/polynomial/polyeig.m @@ -26,68 +26,77 @@ ## @code{@var{C}(s) = @var{C0} + @var{C1} s + @dots{} + @var{Cl} s^l} ## polyeig solves the eigenvalue problem ## @code{(@var{C0} + @var{C1} + @dots{} + @var{Cl})v = 0}. +## ## Note that the eigenvalues @var{z} are the zeros of the matrix polynomial. -## @var{z} is an @var{lxn} vector and @var{v} is an (@var{n} x @var{n})l matrix -## with columns that correspond to the eigenvectors. +## @var{z} is a row vector with @var{n*l} elements. @var{v} is a matrix +## (@var{n} x @var{n}*@var{l}) with columns that correspond to the +## eigenvectors. ## ## @seealso{eig, eigs, compan} ## @end deftypefn ## Author: Fotios Kasolis -function [ z, varargout ] = polyeig (varargin) +function [z, v] = polyeig (varargin) - if ( nargout > 2 ) + if (nargin < 1 || nargout > 2) print_usage (); endif nin = numel (varargin); - - n = zeros (1, nin); + n = rows (varargin{1}); - for cnt = 1 : nin - if (! issquare (varargin{cnt})) - error ("polyeig: coefficients must be square matrices"); + for i = 1 : nin + if (! issquare (varargin{i})) + error ("polyeig: coefficients must be square matrices"); endif - n(cnt) = size (varargin{cnt}, 1); + if (rows (varargin{i}) != n) + error ("polyeig: coefficients must have the same dimensions"); + endif endfor - if (numel (unique (n)) > 1) - error ("polyeig: coefficients must have the same dimensions"); - endif - n = unique (n); - ## matrix polynomial degree l = nin - 1; ## form needed matrices C = [ zeros(n * (l - 1), n), eye(n * (l - 1)); - -cell2mat(varargin(1 : end - 1)) ]; + -cell2mat(varargin(1:end-1)) ]; D = [ eye(n * (l - 1)), zeros(n * (l - 1), n); zeros(n, n * (l - 1)), varargin{end} ]; ## solve generalized eigenvalue problem - if ( isequal (nargout, 1) ) - z = eig (C, D); - else - [ z, v ] = eig (C, D); - varargout{1} = v; - ## return n-element eigenvectors normalized so - ## that the infinity-norm = 1 + if (nargout == 2) + [z, v] = eig (C, D); + v = diag (v); + ## return n-element eigenvectors normalized so that the infinity-norm = 1 z = z(1:n,:); ## max() takes the abs if complex: t = max (z); z /= diag (t); + else + z = eig (C, D); endif endfunction +%!shared C0, C1 +%! C0 = [8, 0; 0, 4]; C1 = [1, 0; 0, 1]; + %!test -%! C0 = [8, 0; 0, 4]; C1 = [1, 0; 0, 1]; +%! z = polyeig (C0, C1); +%! assert (z, [-8; -4]); + +%!test %! [v,z] = polyeig (C0, C1); -%! assert (isequal (z(1), -8), true); +%! assert (z, [-8; -4]); +%! z = diag (z); %! d = C0*v + C1*v*z; -%! assert (isequal (norm(d), 0.0), true); +%! assert (norm (d), 0.0); +%% Input validation tests +%!error polyeig () +%!error [a,b,c] = polyeig (1) +%!error <coefficients must be square matrices> polyeig (ones (3,2)) +%!error <coefficients must have the same dimensions> polyeig (ones (3,3), ones (2,2))