Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/linear-algebra-2.2.0/circulant_make_matrix.m b/octave_packages/linear-algebra-2.2.0/circulant_make_matrix.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{C} =} circulant_make_matrix (@var{v})
+##
+## Produce a full circulant matrix given the first column@*
+## Given an @var{n}*1 vector @var{v}, returns the @var{n}*@var{n} circulant matrix @var{C} where @var{v} is the left column and all other columns are downshifted versions of @var{v}
+##
+## Note: If the first row @var{r} of a circulant matrix is given, the first column @var{v} can be obtained as @code{v = r([1 end:-1:2])}
+##
+## Reference: Gene H. Golub and Charles F. Van Loan, Matrix Computations, 3rd Ed., Section 4.7.7
+##
+## @seealso{circulant_matrix_vector_product, circulant_eig, circulant_inv}
+## @end deftypefn
+
+function C = circulant_make_matrix(v)
+
+  n = numel(v);
+  C = ones(n, n);
+  for i = 1:n
+    C(:, i) = v([(end-i+2):end 1:(end-i+1)]); #or circshift(v, i-1)
+  endfor
+
+endfunction
+
+%!shared v,C
+%! v = [1 2 3]'; C = [1 3 2; 2 1 3; 3 2 1];
+%!assert (circulant_make_matrix(v), C);