Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / linear-algebra-2.2.0 / circulant_eig.m

diff --git a/octave_packages/linear-algebra-2.2.0/circulant_eig.m b/octave_packages/linear-algebra-2.2.0/circulant_eig.m
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+## Copyright (C) 2012 Nir Krakauer <nkrakauer@ccny.cuny.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{lambda} =} circulant_eig (@var{v})
+## @deftypefnx{Function File} {[@var{vs}, @var{lambda}] =} circulant_eig (@var{v})
+##
+## Fast, compact calculation of eigenvalues and eigenvectors of a circulant matrix@*
+## Given an @var{n}*1 vector @var{v}, return the eigenvalues @var{lambda} and optionally eigenvectors @var{vs} of the @var{n}*@var{n} circulant matrix @var{C} that has @var{v} as its first column
+##
+## Theoretically same as @code{eig(make_circulant_matrix(v))}, but many fewer computations; does not form @var{C} explicitly
+##
+## Reference: Robert M. Gray, Toeplitz and Circulant Matrices: A Review, Now Publishers, http://ee.stanford.edu/~gray/toeplitz.pdf, Chapter 3
+##
+## @seealso{circulant_make_matrix, circulant_matrix_vector_product, circulant_inv}
+## @end deftypefn
+
+function [a, b] = circulant_eig (v)
+
+  ## FIXME when warning for broadcastin is turned off by default, this
+  ## unwind_protect block could be removed
+
+  ## we are using broadcasting on the code below so we turn off the
+  ## warnings but will restore to previous state at the end
+  bc_warn = warning ("query", "Octave:broadcast");
+  unwind_protect
+    warning ("off", "Octave:broadcast");
+
+    #find the eigenvalues
+    n = numel(v);
+    lambda = ones(n, 1);
+    s = (0:(n-1));
+    lambda = sum(v .* exp(-2*pi*i*s'*s/n))';
+
+    if nargout < 2
+      a = lambda;
+      return
+    endif
+
+    #find the eigenvectors (which in fact do not depend on v)
+    a = exp(-2*i*pi*s'*s/n) / sqrt(n);
+    b = diag(lambda);
+  unwind_protect_cleanup
+    ## restore broadcats warning status
+    warning (bc_warn.state, "Octave:broadcast");
+  end_unwind_protect
+
+endfunction
+
+%!shared v,C,vs,lambda
+%! v = [1 2 3]';
+%! C = circulant_make_matrix(v);
+%! [vs lambda] = circulant_eig(v);
+%!assert (vs*lambda, C*vs, 100*eps);