octave: scripts/linear-algebra/subspace.m annotate

annotate scripts/linear-algebra/subspace.m @ 27978:a4268efb7334

maint: Eliminate single "Author:" lines from code base. * color-picker.cc, color-picker.h, octave-qscintilla.cc, octave-qscintilla.h, octave-txt-lexer.cc, octave-txt-lexer.h, balance.cc, kron.cc, lookup.cc, ls-hdf5.cc, ls-mat5.cc, ls-oct-text.cc, sylvester.cc, tsearch.cc, jit-ir.cc, jit-ir.h, jit-typeinfo.cc, jit-typeinfo.h, jit-util.cc, jit-util.h, pt-jit.cc, pt-jit.h, Array-jit.cc, bsxfun.h, url-transfer.cc, url-transfer.h, acosd.m, acotd.m, acscd.m, asecd.m, asind.m, atand.m, cosd.m, cotd.m, cscd.m, secd.m, sind.m, tand.m, cart2pol.m, cart2sph.m, curl.m, del2.m, divergence.m, flip.m, pol2cart.m, randi.m, sortrows.m, sph2cart.m, griddata3.m, griddatan.m, rectint.m, voronoi.m, dialog.m, guidata.m, guihandles.m, __file_filter__.m, __fltk_file_filter__.m, __get_funcname__.m, __is_function__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m, __uiobject_split_args__.m, __uiputfile_fltk__.m, uibuttongroup.m, uicontextmenu.m, uicontrol.m, uigetdir.m, uigetfile.m, uimenu.m, uipanel.m, uipushtool.m, uiputfile.m, uiresume.m, uitoggletool.m, uitoolbar.m, uiwait.m, doc.m, autumn.m, bone.m, cmpermute.m, cmunique.m, cool.m, copper.m, cubehelix.m, flag.m, frame2im.m, hot.m, hsv.m, hsv2rgb.m, im2frame.m, imfinfo.m, imformats.m, iscolormap.m, jet.m, pink.m, prism.m, __imfinfo__.m, rainbow.m, rgb2hsv.m, spinmap.m, spring.m, viridis.m, white.m, winter.m, importdata.m, strmatch.m, bandwidth.m, isbanded.m, isdiag.m, istril.m, istriu.m, krylov.m, linsolve.m, logm.m, lscov.m, subspace.m, bunzip2.m, compare_versions.m, edit.m, fullfile.m, getfield.m, gunzip.m, inputParser.m, license.m, nargchk.m, narginchk.m, nthargout.m, python.m, setfield.m, tar.m, unpack.m, ver.m, zip.m, odeplot.m, fminbnd.m, fminunc.m, fsolve.m, fzero.m, glpk.m, humps.m, pathdef.m, savepath.m, diffuse.m, lighting.m, material.m, shading.m, specular.m, contour.m, ellipsoid.m, isocaps.m, isocolors.m, isonormals.m, isosurface.m, light.m, pcolor.m, __interp_cube__.m, __marching_cube__.m, __patch__.m, __stem__.m, reducepatch.m, reducevolume.m, ribbon.m, shrinkfaces.m, slice.m, stem.m, surf.m, surfl.m, tetramesh.m, waterfall.m, __actual_axis_position__.m, __next_line_color__.m, allchild.m, figure.m, findall.m, findobj.m, gcf.m, hggroup.m, isprop.m, ndgrid.m, __add_default_menu__.m, saveas.m, __splinefit__.m, prefdir.m, preferences.m, profexplore.m, profexport.m, profile.m, profshow.m, setdiff.m, freqz.m, freqz_plot.m, sinc.m, unwrap.m, pcr.m, qmr.m, sprandn.m, betaincinv.m, cosint.m, ellipke.m, factor.m, gammaincinv.m, legendre.m, nchoosek.m, primes.m, invhilb.m, toeplitz.m, erase.m, mat2str.m, strtrim.m, validatestring.m, fail.m, compare_plot_demos.m, dump_demos.m, html_compare_plot_demos.m, addtodate.m, datenum.m, jit.tst: Eliminate single "Author:" lines from code base.

author	Rik <rik@octave.org>
date	Tue, 21 Jan 2020 12:53:13 -0800
parents	bd51beb6205e
children	b09432b20a84

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ########################################################################
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 ##
27919 1891570abac8 update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 27918 diff changeset	3 ## Copyright (C) 2008-2020 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	4 ##
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 ## distribution or <https://octave.org/copyright/>.
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	7 ##
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	8 ## This file is part of Octave.
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	9 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	11 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	13 ## (at your option) any later version.
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	14 ##
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	15 ## Octave is distributed in the hope that it will be useful, but
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	18 ## GNU General Public License for more details.
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	19 ##
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	20 ## You should have received a copy of the GNU General Public License
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	21 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	22 ## <https://www.gnu.org/licenses/>.
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 ##
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ########################################################################
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	25
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	26 ## -- texinfo --
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20711 diff changeset	27 ## @deftypefn {} {@var{angle} =} subspace (@var{A}, @var{B})
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	28 ## Determine the largest principal angle between two subspaces
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 8920 diff changeset	29 ## spanned by the columns of matrices @var{A} and @var{B}.
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	30 ## @end deftypefn
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	31
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	32 ## reference:
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	33 ## [1] Andrew V. Knyazev, Merico E. Argentati:
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 19697 diff changeset	34 ## Principal Angles between Subspaces in an A-Based Scalar Product:
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 19697 diff changeset	35 ## Algorithms and Perturbation Estimates.
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 19697 diff changeset	36 ## SIAM Journal on Scientific Computing, Vol. 23 no. 6, pp. 2008-2040
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	37 ##
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	38 ## other texts are also around...
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	39
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 8920 diff changeset	40 function ang = subspace (A, B)
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	41
7612 c1702f963a5e error check for subspace.m Jaroslav Hajek <highegg@gmail.com> parents: 7611 diff changeset	42 if (nargin != 2)
c1702f963a5e error check for subspace.m Jaroslav Hajek <highegg@gmail.com> parents: 7611 diff changeset	43 print_usage ();
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 8920 diff changeset	44 elseif (ndims (A) != 2 \|\| ndims (B) != 2)
20711 7b608fadc663 Make error messages more specific about the variable and problem encountered. Rik <rik@octave.org> parents: 20194 diff changeset	45 error ("subspace: A and B must be 2-dimensional arrays");
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 8920 diff changeset	46 elseif (rows (A) != rows (B))
c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 8920 diff changeset	47 error ("subspace: column dimensions of A and B must match");
7612 c1702f963a5e error check for subspace.m Jaroslav Hajek <highegg@gmail.com> parents: 7611 diff changeset	48 endif
c1702f963a5e error check for subspace.m Jaroslav Hajek <highegg@gmail.com> parents: 7611 diff changeset	49
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 8920 diff changeset	50 A = orth (A);
c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 8920 diff changeset	51 B = orth (B);
c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 8920 diff changeset	52 c = A'*B;
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	53 scos = min (svd (c));
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	54 if (scos^2 > 1/2)
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 8920 diff changeset	55 if (columns (A) >= columns (B))
c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 8920 diff changeset	56 c = B - A*c;
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	57 else
11469 c776f063fefe Overhaul m-script files to use common variable name between code and documentation. Rik <octave@nomad.inbox5.com> parents: 8920 diff changeset	58 c = A - B*c';
7611 4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	59 endif
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	60 ssin = max (svd (c));
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	61 ang = asin (min (ssin, 1));
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	62 else
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	63 ang = acos (scos);
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	64 endif
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	65
4f903c303c3c implement subspace function Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	66 endfunction
17338 1c89599167a6 maint: End m-files with 1 blank line. Rik <rik@octave.org> parents: 14138 diff changeset	67
19306 314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	68
24839 55021b03884d subspace.m: Change BIST tests to more accurately test function (bug #53242). Daniel J Sebald <daniel.sebald@ieee.org> parents: 24534 diff changeset	69 %!assert (subspace (1, 1), 0)
55021b03884d subspace.m: Change BIST tests to more accurately test function (bug #53242). Daniel J Sebald <daniel.sebald@ieee.org> parents: 24534 diff changeset	70 %!assert (subspace ([1, 0]', [1, 1; 0, 1]'), 0, 3*eps)
55021b03884d subspace.m: Change BIST tests to more accurately test function (bug #53242). Daniel J Sebald <daniel.sebald@ieee.org> parents: 24534 diff changeset	71 %!assert (subspace ([1, 0, 1]', [1, 1, 0; 1, -1, 0]'), pi/4, 3*eps)
55021b03884d subspace.m: Change BIST tests to more accurately test function (bug #53242). Daniel J Sebald <daniel.sebald@ieee.org> parents: 24534 diff changeset	72 %!assert (subspace ([1 5 0 0; -3 2 0 0]', [0 0 4 2; 0 0 4 3]'), pi/2)
55021b03884d subspace.m: Change BIST tests to more accurately test function (bug #53242). Daniel J Sebald <daniel.sebald@ieee.org> parents: 24534 diff changeset	73 %!assert (subspace ([1 1 1 1; 1 2 3 4]', [1 -1 -1 1]'), pi/2)
19306 314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	74
314b4de4bb6d Add BIST tests for subspace, t_test, z_test. Pooja Rao <poojarao12@gmail.com> parents: 17744 diff changeset	75 %!test
24839 55021b03884d subspace.m: Change BIST tests to more accurately test function (bug #53242). Daniel J Sebald <daniel.sebald@ieee.org> parents: 24534 diff changeset	76 %! ## For small angle between subspaces
55021b03884d subspace.m: Change BIST tests to more accurately test function (bug #53242). Daniel J Sebald <daniel.sebald@ieee.org> parents: 24534 diff changeset	77 %! theta = pi/200;
55021b03884d subspace.m: Change BIST tests to more accurately test function (bug #53242). Daniel J Sebald <daniel.sebald@ieee.org> parents: 24534 diff changeset	78 %! Ry = [cos(theta), 0, sin(theta);0, 1, 0;-sin(theta), 0, cos(theta)];
55021b03884d subspace.m: Change BIST tests to more accurately test function (bug #53242). Daniel J Sebald <daniel.sebald@ieee.org> parents: 24534 diff changeset	79 %! a = Ry[3e, 0, 0]';
55021b03884d subspace.m: Change BIST tests to more accurately test function (bug #53242). Daniel J Sebald <daniel.sebald@ieee.org> parents: 24534 diff changeset	80 %! b = [1, 1, 0; 1, -1, 0]';
55021b03884d subspace.m: Change BIST tests to more accurately test function (bug #53242). Daniel J Sebald <daniel.sebald@ieee.org> parents: 24534 diff changeset	81 %! assert (theta, subspace (a, b), eps);

Mercurial > octave

annotate scripts/linear-algebra/subspace.m @ 27978:a4268efb7334