Mercurial > octave
view scripts/linear-algebra/planerot.m @ 31246:43a6be589387
doc: New documentation for memoization techniques (bug #60860)
vectorize.texi: New section on memoization
octave.texi: List new section
author | Arun Giridhar <arungiridhar@gmail.com> |
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date | Thu, 29 Sep 2022 20:31:52 -0400 |
parents | 796f54d4ddbf |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2008-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {[@var{G}, @var{y}] =} planerot (@var{x}) ## Compute the Givens rotation matrix for the two-element column vector ## @var{x}. ## ## @tex ## The Givens matrix is a $2\times 2$ orthogonal matrix ## $$ ## G = \left[\matrix{c & s\cr -s'& c\cr}\right] ## $$ ## such that ## $$ ## G \left[\matrix{x(1)\cr x(2)}\right] = \left[\matrix{\ast\cr 0}\right] ## $$ ## @end tex ## @ifnottex ## The Givens matrix is a 2-by-2 orthogonal matrix ## ## @example ## @group ## @var{G} = [ @var{c} , @var{s} ## -@var{s}', @var{c}] ## @end group ## @end example ## ## @noindent ## such that ## ## @example ## @var{y} = @var{G} * [@var{x}(1); @var{x}(2)] @equiv{} [*; 0] ## @end example ## ## @end ifnottex ## ## Note: The Givens matrix represents a counterclockwise rotation of a 2-D ## plane and can be used to introduce zeros into a matrix prior to complete ## factorization. ## @seealso{givens, qr} ## @end deftypefn function [G, y] = planerot (x) if (nargin < 1) print_usage (); elseif (! (isvector (x) && numel (x) == 2)) error ("planerot: X must be a 2-element vector"); endif G = givens (x(1), x(2)); y = G * x(:); endfunction %!test %! x = [3 4]; %! [g y] = planerot (x); %! assert (g, [x(1) x(2); -x(2) x(1)] / sqrt (x(1)^2 + x(2)^2), 2e-8); %! assert (y(2), 0, 2e-8); ## Test input validation %!error <Invalid call> planerot () %!error <X must be a 2-element vector> planerot (ones (2,2)) %!error <X must be a 2-element vector> planerot ([0 0 0])