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doc: Update more docstrings to have one sentence summary as first line. Reviewed io, java, linear-algebra, prefs, and set script directories. * scripts/io/beep.m, scripts/io/dlmwrite.m, scripts/io/importdata.m, scripts/io/strread.m, scripts/io/textread.m, scripts/java/javaArray.m, scripts/java/java_get.m, scripts/java/java_set.m, scripts/java/javaaddpath.m, scripts/java/javachk.m, scripts/java/javaclasspath.m, scripts/java/javamem.m, scripts/java/javarmpath.m, scripts/linear-algebra/bandwidth.m, scripts/linear-algebra/commutation_matrix.m, scripts/linear-algebra/cond.m, scripts/linear-algebra/condest.m, scripts/linear-algebra/cross.m, scripts/linear-algebra/duplication_matrix.m, scripts/linear-algebra/expm.m, scripts/linear-algebra/housh.m, scripts/linear-algebra/isdefinite.m, scripts/linear-algebra/ishermitian.m, scripts/linear-algebra/issymmetric.m, scripts/linear-algebra/istril.m, scripts/linear-algebra/istriu.m, scripts/linear-algebra/krylov.m, scripts/linear-algebra/logm.m, scripts/linear-algebra/normest.m, scripts/linear-algebra/null.m, scripts/linear-algebra/onenormest.m, scripts/linear-algebra/orth.m, scripts/linear-algebra/qzhess.m, scripts/linear-algebra/rank.m, scripts/linear-algebra/rref.m, scripts/linear-algebra/vech.m, scripts/path/matlabroot.m, scripts/prefs/addpref.m, scripts/prefs/getpref.m, scripts/prefs/ispref.m, scripts/prefs/rmpref.m, scripts/prefs/setpref.m, scripts/set/powerset.m, scripts/set/setdiff.m: Update more docstrings to have one sentence summary as first line.
author Rik <rik@octave.org>
date Sun, 03 May 2015 15:36:23 -0700
parents 9fc020886ae9
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 ## Copyright (C) 1993-2015 John W. Eaton
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {[@var{aa}, @var{bb}, @var{q}, @var{z}] =} qzhess (@var{A}, @var{B})
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21 ## Compute the Hessenberg-triangular decomposition of the matrix pencil
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22 ## @code{(@var{A}, @var{B})}, returning
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23 ## @code{@var{aa} = @var{q} * @var{A} * @var{z}},
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24 ## @code{@var{bb} = @var{q} * @var{B} * @var{z}}, with @var{q} and @var{z}
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25 ## orthogonal.
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26 ##
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27 ## For example:
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28 ##
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29 ## @example
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30 ## @group
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31 ## [aa, bb, q, z] = qzhess ([1, 2; 3, 4], [5, 6; 7, 8])
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32 ## @result{} aa = [ -3.02244, -4.41741; 0.92998, 0.69749 ]
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33 ## @result{} bb = [ -8.60233, -9.99730; 0.00000, -0.23250 ]
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34 ## @result{} q = [ -0.58124, -0.81373; -0.81373, 0.58124 ]
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35 ## @result{} z = [ 1, 0; 0, 1 ]
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36 ## @end group
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37 ## @end example
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38 ##
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39 ## The Hessenberg-triangular decomposition is the first step in
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40 ## @nospell{Moler and Stewart's} QZ@tie{}decomposition algorithm.
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41 ##
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42 ## Algorithm taken from @nospell{Golub and Van Loan},
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43 ## @cite{Matrix Computations, 2nd edition}.
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44 ##
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45 ## @seealso{lu, chol, hess, qr, qz, schur, svd}
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46 ## @end deftypefn
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48 ## Author: A. S. Hodel <scotte@eng.auburn.edu>
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49 ## Created: August 1993
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50 ## Adapted-By: jwe
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52 function [aa, bb, q, z] = qzhess (A, B)
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54 if (nargin != 2)
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55 print_usage ();
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56 endif
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57
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58 [na, ma] = size (A);
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59 [nb, mb] = size (B);
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60 if (na != ma || na != nb || nb != mb)
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61 error ("qzhess: incompatible dimensions");
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62 endif
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63
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64 ## Reduce to hessenberg-triangular form.
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66 [q, bb] = qr (B);
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67 aa = q' * A;
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68 q = q';
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69 z = eye (na);
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70 for j = 1:(na-2)
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71 for i = na:-1:(j+2)
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72
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73 ## disp (["zero out aa(", num2str(i), ",", num2str(j), ")"])
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75 rot = givens (aa (i-1, j), aa (i, j));
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76 aa((i-1):i, :) = rot *aa((i-1):i, :);
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77 bb((i-1):i, :) = rot *bb((i-1):i, :);
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78 q((i-1):i, :) = rot * q((i-1):i, :);
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79
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80 ## disp (["now zero out bb(", num2str(i), ",", num2str(i-1), ")"])
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81
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82 rot = givens (bb (i, i), bb (i, i-1))';
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83 bb(:, (i-1):i) = bb(:, (i-1):i) * rot';
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84 aa(:, (i-1):i) = aa(:, (i-1):i) * rot';
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85 z(:, (i-1):i) = z(:, (i-1):i) * rot';
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86
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87 endfor
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88 endfor
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89
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90 bb(2, 1) = 0.0;
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91 for i = 3:na
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92 bb (i, 1:(i-1)) = zeros (1, i-1);
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93 aa (i, 1:(i-2)) = zeros (1, i-2);
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94 endfor
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95
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96 endfunction
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99 %!test
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100 %! a = [1 2 1 3;
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101 %! 2 5 3 2;
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102 %! 5 5 1 0;
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103 %! 4 0 3 2];
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104 %! b = [0 4 2 1;
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105 %! 2 3 1 1;
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106 %! 1 0 2 1;
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107 %! 2 5 3 2];
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108 %! mask = [0 0 0 0;
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109 %! 0 0 0 0;
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110 %! 1 0 0 0;
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111 %! 1 1 0 0];
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112 %! [aa, bb, q, z] = qzhess (a, b);
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113 %! assert (inv (q) - q', zeros (4), 2e-8);
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114 %! assert (inv (z) - z', zeros (4), 2e-8);
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115 %! assert (q * a * z, aa, 2e-8);
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116 %! assert (aa .* mask, zeros (4), 2e-8);
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117 %! assert (q * b * z, bb, 2e-8);
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118 %! assert (bb .* mask, zeros (4), 2e-8);
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119
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120 %!test
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121 %! a = [1 2 3 4 5;
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122 %! 3 2 3 1 0;
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123 %! 4 3 2 1 1;
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diff changeset
124 %! 0 1 0 1 0;
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
125 %! 3 2 1 0 5];
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
126 %! b = [5 0 4 0 1;
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
127 %! 1 1 1 2 5;
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
128 %! 0 3 2 1 0;
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
129 %! 4 3 0 3 5;
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
130 %! 2 1 2 1 3];
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
131 %! mask = [0 0 0 0 0;
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
132 %! 0 0 0 0 0;
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
133 %! 1 0 0 0 0;
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
134 %! 1 1 0 0 0;
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
135 %! 1 1 1 0 0];
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
136 %! [aa, bb, q, z] = qzhess (a, b);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
137 %! assert (inv (q) - q', zeros (5), 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
138 %! assert (inv (z) - z', zeros (5), 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
139 %! assert (q * a * z, aa, 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
140 %! assert (aa .* mask, zeros (5), 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
141 %! assert (q * b * z, bb, 2e-8);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
142 %! assert (bb .* mask, zeros (5), 2e-8);
13048
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
143
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
144 %!error qzhess ([0])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
145 %!error qzhess ()
13048
c5c94b63931f codesprint: linear algebra tests: cross, housh, planerot, qzhess, rref
Roman Belov <romblv@gmail.com>
parents: 11593
diff changeset
146