octave-lyh: scripts/linear-algebra/normest.m annotate

annotate scripts/linear-algebra/normest.m @ 17198:df4c4b7708a4

Add titles and clean-up plotting %!demos. * scripts/plot/area.m, scripts/plot/axis.m, scripts/plot/bar.m, scripts/plot/barh.m, scripts/plot/clabel.m, scripts/plot/colorbar.m, scripts/plot/comet.m, scripts/plot/comet3.m, scripts/plot/contour.m, scripts/plot/contour3.m, scripts/plot/contourf.m, scripts/plot/cylinder.m, scripts/plot/ellipsoid.m, scripts/plot/errorbar.m, scripts/plot/ezplot.m, scripts/plot/ezplot3.m, scripts/plot/ezpolar.m, scripts/plot/feather.m, scripts/plot/fplot.m, scripts/plot/hold.m, scripts/plot/isosurface.m, scripts/plot/legend.m, scripts/plot/loglog.m, scripts/plot/loglogerr.m, scripts/plot/mesh.m, scripts/plot/meshc.m, scripts/plot/meshz.m, scripts/plot/patch.m, scripts/plot/pcolor.m, scripts/plot/pie.m, scripts/plot/pie3.m, scripts/plot/plot.m, scripts/plot/plot3.m, scripts/plot/polar.m, scripts/plot/rectangle.m, scripts/plot/ribbon.m, scripts/plot/rose.m, scripts/plot/scatter.m, scripts/plot/scatter3.m, scripts/plot/semilogx.m, scripts/plot/semilogxerr.m, scripts/plot/semilogy.m, scripts/plot/semilogyerr.m, scripts/plot/sombrero.m, scripts/plot/stem3.m, scripts/plot/surf.m, scripts/plot/surfc.m, scripts/plot/surfl.m, scripts/plot/title.m, scripts/plot/waterfall.m: Add titles and clean-up plotting %!demos.

author	Rik <rik@octave.org>
date	Tue, 06 Aug 2013 14:34:20 -0700
parents	f3d52523cde1
children

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 11587 diff changeset	1 ## Copyright (C) 2006-2012 David Bateman and Marco Caliari
9871 87595d714005 move normest to linear-algebra, improve it Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	2 ## Copyright (C) 2009 VZLU Prague
6212 cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	3 ##
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	4 ## This file is part of Octave.
6212 cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	5 ##
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	7 ## under the terms of the GNU General Public License as published by
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	8 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	9 ## your option) any later version.
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	10 ##
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	11 ## Octave is distributed in the hope that it will be useful, but
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	14 ## General Public License for more details.
6212 cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	15 ##
cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	16 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	17 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6498 diff changeset	18 ## <http://www.gnu.org/licenses/>.
6212 cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	19
cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	20 ## -- texinfo --
11470 eb9e0b597d61 Use common names for variables in documentation and code for a few more m-script files. Rik <octave@nomad.inbox5.com> parents: 11113 diff changeset	21 ## @deftypefn {Function File} {@var{n} =} normest (@var{A})
eb9e0b597d61 Use common names for variables in documentation and code for a few more m-script files. Rik <octave@nomad.inbox5.com> parents: 11113 diff changeset	22 ## @deftypefnx {Function File} {@var{n} =} normest (@var{A}, @var{tol})
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	23 ## @deftypefnx {Function File} {[@var{n}, @var{c}] =} normest (@dots{})
11470 eb9e0b597d61 Use common names for variables in documentation and code for a few more m-script files. Rik <octave@nomad.inbox5.com> parents: 11113 diff changeset	24 ## Estimate the 2-norm of the matrix @var{A} using a power series
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	25 ## analysis. This is typically used for large matrices, where the cost
11470 eb9e0b597d61 Use common names for variables in documentation and code for a few more m-script files. Rik <octave@nomad.inbox5.com> parents: 11113 diff changeset	26 ## of calculating @code{norm (@var{A})} is prohibitive and an approximation
6212 cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	27 ## to the 2-norm is acceptable.
cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	28 ##
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	29 ## @var{tol} is the tolerance to which the 2-norm is calculated. By default
1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	30 ## @var{tol} is 1e-6. @var{c} returns the number of iterations needed for
6212 cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	31 ## @code{normest} to converge.
cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	32 ## @end deftypefn
cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	33
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	34 function [n, c] = normest (A, tol = 1e-6)
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	35
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	36 if (nargin != 1 && nargin != 2)
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	37 print_usage ();
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	38 endif
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	39
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	40 if (! (isnumeric (A) && ndims (A) == 2))
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	41 error ("normest: A must be a numeric 2-D matrix");
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	42 endif
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	43
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	44 if (! (isscalar (tol) && isreal (tol)))
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	45 error ("normest: TOL must be a real scalar");
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	46 endif
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	47
9871 87595d714005 move normest to linear-algebra, improve it Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	48 if (! isfloat (A))
87595d714005 move normest to linear-algebra, improve it Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	49 A = double (A);
87595d714005 move normest to linear-algebra, improve it Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	50 endif
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	51
9871 87595d714005 move normest to linear-algebra, improve it Jaroslav Hajek <highegg@gmail.com> parents: 9051 diff changeset	52 tol = max (tol, eps (class (A)));
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	53 ## Set random number generator to depend on target matrix
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	54 v = rand ("state");
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	55 rand ("state", trace (A));
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	56 ncols = columns (A);
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	57 ## Randomize y to avoid bad guesses for important matrices.
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	58 y = rand (ncols, 1);
6212 cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	59 c = 0;
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	60 n = 0;
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	61 do
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	62 n0 = n;
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	63 x = A * y;
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	64 normx = norm (x);
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	65 if (normx == 0)
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	66 x = rand (ncols, 1);
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	67 else
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	68 x = x / normx;
11113 a8ac114ec9ab Stylefixes, replace end by endif. Thorsten Meyer <thorsten.meyier@gmx.de> parents: 10788 diff changeset	69 endif
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	70 y = A' * x;
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	71 n = norm (y);
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	72 c += 1;
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	73 until (abs (n - n0) <= tol * n)
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	74
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	75 rand ("state", v); # restore state of random number generator
6212 cc34c0be7b00 [project @ 2006-12-08 11:17:12 by dbateman] dbateman parents: diff changeset	76 endfunction
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	77
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	78
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	79 %!test
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	80 %! A = toeplitz ([-2,1,0,0]);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	81 %! assert (normest (A), norm (A), 1e-6);
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	82
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	83 %!test
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	84 %! A = rand (10);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	85 %! assert (normest (A), norm (A), 1e-6);
10788 c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	86
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	87 %% Test input validation
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	88 %!error normest ()
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	89 %!error normest (1, 2, 3)
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	90 %!error normest ([true true])
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	91 %!error normest (ones (3,3,3))
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	92 %!error normest (1, [1, 2])
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	93 %!error normest (1, 1+1i)
c69252eb2f2b normest.m: Set the "state" of the random number generator to depend on trace(A). Rik <octave@nomad.inbox5.com> parents: 9875 diff changeset	94

Mercurial > hg > octave-lyh

annotate scripts/linear-algebra/normest.m @ 17198:df4c4b7708a4