Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/linear-algebra-2.2.0/circulant_matrix_vector_product.m b/octave_packages/linear-algebra-2.2.0/circulant_matrix_vector_product.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{y} =} circulant_matrix_vector_product (@var{v}, @var{x})
+##
+## Fast, compact calculation of the product of a circulant matrix with a vector@*
+## Given @var{n}*1 vectors @var{v} and @var{x}, return the matrix-vector product @var{y} = @var{C}@var{x}, where @var{C} is the @var{n}*@var{n} circulant matrix that has @var{v} as its first column
+##
+## Theoretically the same as @code{make_circulant_matrix(x) * v}, but does not form @var{C} explicitly; uses the discrete Fourier transform
+##
+## Because of roundoff, the returned @var{y} may have a small imaginary component even if @var{v} and @var{x} are real (use @code{real(y)} to remedy this)
+##
+## Reference: Gene H. Golub and Charles F. Van Loan, Matrix Computations, 3rd Ed., Section 4.7.7
+##
+## @seealso{circulant_make_matrix, circulant_eig, circulant_inv}
+## @end deftypefn
+
+function y = circulant_matrix_vector_product (v, x)
+
+  xf = fft(x);
+  vf = fft(v);
+  z = vf .* xf;
+  y = ifft(z);
+
+endfunction
+
+%!shared v,x
+%! v = [1 2 3]'; x = [2 5 6]';
+%!assert (circulant_matrix_vector_product(v, x), circulant_make_matrix(v)*x, eps);