Mercurial > hg > octave-lyh
annotate scripts/linear-algebra/housh.m @ 14868:5d3a684236b0
maint: Use Octave coding conventions for cuddling parentheses in scripts directory
* lin2mu.m, loadaudio.m, wavread.m, accumarray.m, bicubic.m, celldisp.m,
colon.m, cplxpair.m, dblquad.m, divergence.m, genvarname.m, gradient.m,
int2str.m, interp1.m, interp1q.m, interp2.m, interpn.m, loadobj.m, nthargout.m,
__isequal__.m, __splinen__.m, quadgk.m, quadl.m, quadv.m, rat.m, rot90.m,
rotdim.m, saveobj.m, subsindex.m, triplequad.m, delaunay3.m, griddata.m,
inpolygon.m, tsearchn.m, voronoi.m, get_first_help_sentence.m, which.m,
gray2ind.m, pink.m, dlmwrite.m, strread.m, textread.m, textscan.m, housh.m,
ishermitian.m, issymmetric.m, krylov.m, logm.m, null.m, rref.m,
compare_versions.m, copyfile.m, dump_prefs.m, edit.m, fileparts.m,
getappdata.m, isappdata.m, movefile.m, orderfields.m, parseparams.m,
__xzip__.m, rmappdata.m, setappdata.m, swapbytes.m, unpack.m, ver.m, fminbnd.m,
fminunc.m, fsolve.m, glpk.m, lsqnonneg.m, qp.m, sqp.m, configure_make.m,
copy_files.m, describe.m, get_description.m, get_forge_pkg.m, install.m,
installed_packages.m, is_architecture_dependent.m, load_package_dirs.m,
print_package_description.m, rebuild.m, repackage.m, save_order.m, shell.m,
allchild.m, ancestor.m, area.m, axes.m, axis.m, clabel.m, close.m, colorbar.m,
comet.m, comet3.m, contour.m, cylinder.m, ezmesh.m, ezsurf.m, findobj.m,
fplot.m, hist.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m,
mesh.m, meshz.m, pareto.m, pcolor.m, peaks.m, plot3.m, plotmatrix.m, plotyy.m,
polar.m, print.m, __add_datasource__.m, __add_default_menu__.m,
__axes_limits__.m, __bar__.m, __clabel__.m, __contour__.m, __errcomm__.m,
__errplot__.m, __ezplot__.m, __file_filter__.m, __fltk_print__.m,
__ghostscript__.m, __gnuplot_print__.m, __go_draw_axes__.m,
__go_draw_figure__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m,
__pie__.m, __plt__.m, __print_parse_opts__.m, __quiver__.m, __scatter__.m,
__stem__.m, __tight_eps_bbox__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m,
__uiputfile_fltk__.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m,
ribbon.m, scatter.m, semilogy.m, shading.m, slice.m, subplot.m, surface.m,
surfl.m, surfnorm.m, text.m, uigetfile.m, uiputfile.m, whitebg.m, deconv.m,
mkpp.m, pchip.m, polyaffine.m, polyder.m, polygcd.m, polyout.m, polyval.m,
ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, splinefit.m,
addpref.m, getpref.m, setpref.m, ismember.m, setxor.m, arch_fit.m, arch_rnd.m,
arch_test.m, autoreg_matrix.m, diffpara.m, fftconv.m, filter2.m, hanning.m,
hurst.m, periodogram.m, triangle_sw.m, sinc.m, spectral_xdf.m, spencer.m,
stft.m, synthesis.m, unwrap.m, yulewalker.m, bicgstab.m, gmres.m, pcg.m, pcr.m,
__sprand_impl__.m, speye.m, spfun.m, sprandn.m, spstats.m, svds.m,
treelayout.m, treeplot.m, bessel.m, factor.m, legendre.m, perms.m, primes.m,
magic.m, toeplitz.m, corr.m, cov.m, mean.m, median.m, mode.m, qqplot.m,
quantile.m, ranks.m, zscore.m, logistic_regression_likelihood.m,
bartlett_test.m, chisquare_test_homogeneity.m, chisquare_test_independence.m,
kolmogorov_smirnov_test.m, run_test.m, u_test.m, wilcoxon_test.m, z_test.m,
z_test_2.m, bin2dec.m, dec2base.m, mat2str.m, strcat.m, strchr.m, strjust.m,
strtok.m, substr.m, untabify.m, assert.m, demo.m, example.m, fail.m, speed.m,
test.m, now.m: Use Octave coding conventions for cuddling parentheses in
scripts directory.
author | Rik <octave@nomad.inbox5.com> |
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date | Tue, 17 Jul 2012 07:08:39 -0700 |
parents | f3d52523cde1 |
children | a4969508008e |
rev | line source |
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1 ## Copyright (C) 1995-2012 A. Scottedward Hodel |
3427 | 2 ## |
3 ## This file is part of Octave. | |
4 ## | |
5 ## Octave is free software; you can redistribute it and/or modify it | |
7016 | 6 ## under the terms of the GNU General Public License as published by |
7 ## the Free Software Foundation; either version 3 of the License, or (at | |
8 ## your option) any later version. | |
3427 | 9 ## |
7016 | 10 ## Octave is distributed in the hope that it will be useful, but |
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
13 ## General Public License for more details. | |
3427 | 14 ## |
15 ## You should have received a copy of the GNU General Public License | |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | |
3211 | 18 |
3439 | 19 ## -*- texinfo -*- |
20 ## @deftypefn {Function File} {[@var{housv}, @var{beta}, @var{zer}] =} housh (@var{x}, @var{j}, @var{z}) | |
7201 | 21 ## Compute Householder reflection vector @var{housv} to reflect @var{x} |
8494 | 22 ## to be the j-th column of identity, i.e., |
7201 | 23 ## |
24 ## @example | |
25 ## @group | |
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26 ## (I - beta*housv*housv')x = norm (x)*e(j) if x(j) < 0, |
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27 ## (I - beta*housv*housv')x = -norm (x)*e(j) if x(j) >= 0 |
7201 | 28 ## @end group |
29 ## @end example | |
30 ## | |
31 ## @noindent | |
32 ## Inputs | |
33 ## | |
34 ## @table @var | |
35 ## @item x | |
36 ## vector | |
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37 ## |
7201 | 38 ## @item j |
39 ## index into vector | |
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40 ## |
7201 | 41 ## @item z |
42 ## threshold for zero (usually should be the number 0) | |
43 ## @end table | |
44 ## | |
45 ## @noindent | |
46 ## Outputs (see Golub and Van Loan): | |
47 ## | |
48 ## @table @var | |
49 ## @item beta | |
50 ## If beta = 0, then no reflection need be applied (zer set to 0) | |
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51 ## |
7201 | 52 ## @item housv |
53 ## householder vector | |
54 ## @end table | |
3439 | 55 ## @end deftypefn |
3211 | 56 |
3427 | 57 ## Author: A. S. Hodel |
3439 | 58 ## Created: August 1995 |
3427 | 59 |
60 function [housv, beta, zer] = housh (x, j, z) | |
3211 | 61 |
7125 | 62 if (nargin != 3) |
63 print_usage (); | |
64 endif | |
65 | |
66 ## Check for valid inputs. | |
67 if (! isvector (x) && ! isscalar (x)) | |
8664 | 68 error ("housh: first input must be a vector"); |
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69 elseif (! isscalar (j)) |
8664 | 70 error ("housh: second argment must be an integer scalar"); |
3211 | 71 else |
72 housv = x; | |
3427 | 73 m = max (abs (housv)); |
74 if (m != 0.0) | |
75 housv = housv / m; | |
76 alpha = norm (housv); | |
3426 | 77 if (alpha > z) |
3427 | 78 beta = 1.0 / (alpha * (alpha + abs (housv(j)))); |
79 sg = sign (housv(j)); | |
80 if (sg == 0) | |
3211 | 81 sg = 1; |
82 endif | |
83 housv(j) = housv(j) + alpha*sg; | |
84 else | |
85 beta = 0.0; | |
86 endif | |
87 else | |
88 beta = 0.0; | |
89 endif | |
90 zer = (beta == 0); | |
91 endif | |
3427 | 92 |
3211 | 93 endfunction |
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94 |
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95 |
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96 %!test |
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97 %! x = [1 2 3]'; |
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98 %! j = 3; |
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99 %! [hv, b, z] = housh (x, j, 0); |
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100 %! r = (eye (3) - b*hv*hv') * x; |
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101 %! d = - norm (x) * [0 0 1]'; |
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102 %! assert (r, d, 2e-8); |
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103 %! assert (z, 0, 2e-8); |
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104 |
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105 %!test |
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106 %! x = [7 -3 1]'; |
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107 %! j = 2; |
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108 %! [hv, b, z] = housh (x, j, 0); |
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109 %! r = (eye (3) - b*hv*hv') * x; |
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110 %! d = norm (x) * [0 1 0]'; |
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111 %! assert (r, d, 2e-8); |
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112 %! assert (z, 0, 2e-8); |
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113 |
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114 %!test |
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115 %! x = [1 0 0]'; |
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116 %! j = 1; |
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117 %! [hv, b, z] = housh (x, j, 10); |
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118 %! r = (eye (3) - b*hv*hv') * x; |
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119 %! d = norm (x) * [1 0 0]'; |
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120 %! assert (r, d, 2e-8); |
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121 %! assert (z, 1, 2e-8); |
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122 |
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123 %!test |
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124 %! x = [5 0 4 1]'; |
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125 %! j = 2; |
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126 %! [hv, b, z] = housh (x, j, 0); |
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127 %! r = (eye (4) - b*hv*hv') * x; |
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128 %! d = - norm (x) * [0 1 0 0]'; |
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129 %! assert (r, d, 2e-8); |
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130 %! assert (z, 0, 2e-8); |
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131 |
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132 %!error housh ([0]) |
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133 %!error housh () |
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134 |