Mercurial > octave-nkf
view scripts/linear-algebra/normest.m @ 20266:83792dd9bcc1
Use in-place operators in m-files where possible.
* scripts/audio/@audioplayer/set.m, scripts/audio/@audiorecorder/set.m,
scripts/audio/mu2lin.m, scripts/elfun/cosd.m, scripts/general/del2.m,
scripts/general/profexplore.m, scripts/general/quadl.m, scripts/general/rat.m,
scripts/general/rotdim.m, scripts/help/get_first_help_sentence.m,
scripts/help/private/__strip_html_tags__.m, scripts/image/cubehelix.m,
scripts/io/textread.m, scripts/linear-algebra/duplication_matrix.m,
scripts/linear-algebra/housh.m, scripts/linear-algebra/krylov.m,
scripts/linear-algebra/logm.m, scripts/linear-algebra/normest.m,
scripts/linear-algebra/onenormest.m, scripts/optimization/fminsearch.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/qp.m,
scripts/plot/appearance/annotation.m, scripts/plot/appearance/axis.m,
scripts/plot/appearance/legend.m, scripts/plot/appearance/specular.m,
scripts/plot/draw/colorbar.m, scripts/plot/draw/hist.m,
scripts/plot/draw/plotmatrix.m, scripts/plot/draw/private/__stem__.m,
scripts/plot/util/__actual_axis_position__.m,
scripts/plot/util/__gnuplot_drawnow__.m, scripts/plot/util/findobj.m,
scripts/plot/util/print.m, scripts/plot/util/private/__go_draw_axes__.m,
scripts/plot/util/private/__print_parse_opts__.m, scripts/plot/util/rotate.m,
scripts/polynomial/pchip.m, scripts/polynomial/polyaffine.m,
scripts/polynomial/polyder.m, scripts/polynomial/private/__splinefit__.m,
scripts/polynomial/residue.m, scripts/signal/arch_fit.m,
scripts/signal/arch_rnd.m, scripts/signal/bartlett.m,
scripts/signal/blackman.m, scripts/signal/freqz.m, scripts/signal/hamming.m,
scripts/signal/hanning.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/signal/stft.m,
scripts/sparse/bicgstab.m, scripts/sparse/cgs.m,
scripts/sparse/private/__sprand_impl__.m, scripts/sparse/qmr.m,
scripts/sparse/sprandsym.m, scripts/sparse/svds.m, scripts/specfun/legendre.m,
scripts/special-matrix/gallery.m, scripts/statistics/base/gls.m,
scripts/statistics/models/logistic_regression.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/wilcoxon_test.m,
scripts/time/datevec.m:
Use in-place operators in m-files where possible.
author | Rik <rik@octave.org> |
---|---|
date | Tue, 26 May 2015 21:07:42 -0700 |
parents | cc5ffacb15ab |
children |
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## Copyright (C) 2006-2015 David Bateman and Marco Caliari ## Copyright (C) 2009 VZLU Prague ## ## 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 ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{n} =} normest (@var{A}) ## @deftypefnx {Function File} {@var{n} =} normest (@var{A}, @var{tol}) ## @deftypefnx {Function File} {[@var{n}, @var{c}] =} normest (@dots{}) ## Estimate the 2-norm of the matrix @var{A} using a power series analysis. ## ## This is typically used for large matrices, where the cost of calculating ## @code{norm (@var{A})} is prohibitive and an approximation to the 2-norm is ## acceptable. ## ## @var{tol} is the tolerance to which the 2-norm is calculated. By default ## @var{tol} is 1e-6. ## ## The optional output @var{c} returns the number of iterations needed for ## @code{normest} to converge. ## @end deftypefn function [n, c] = normest (A, tol = 1e-6) if (nargin != 1 && nargin != 2) print_usage (); endif if (! (isnumeric (A) && ndims (A) == 2)) error ("normest: A must be a numeric 2-D matrix"); endif if (! (isscalar (tol) && isreal (tol))) error ("normest: TOL must be a real scalar"); endif if (! isfloat (A)) A = double (A); endif tol = max (tol, eps (class (A))); ## Set random number generator to depend on target matrix v = rand ("state"); rand ("state", full (trace (A))); ncols = columns (A); ## Randomize y to avoid bad guesses for important matrices. y = rand (ncols, 1); c = 0; n = 0; do n0 = n; x = A * y; normx = norm (x); if (normx == 0) x = rand (ncols, 1); else x /= normx; endif y = A' * x; n = norm (y); c += 1; until (abs (n - n0) <= tol * n) rand ("state", v); # restore state of random number generator endfunction %!test %! A = toeplitz ([-2,1,0,0]); %! assert (normest (A), norm (A), 1e-6); %!test %! A = rand (10); %! assert (normest (A), norm (A), 1e-6); ## Test input validation %!error normest () %!error normest (1, 2, 3) %!error normest ([true true]) %!error normest (ones (3,3,3)) %!error normest (1, [1, 2]) %!error normest (1, 1+1i)