annotate scripts/linear-algebra/rank.m @ 20160:03b9d17a2d95 stable

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 4197fc428c7d
children
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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} {} rank (@var{A})
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21 ## @deftypefnx {Function File} {} rank (@var{A}, @var{tol})
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22 ## Compute the rank of matrix @var{A}, using the singular value decomposition.
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23 ##
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24 ## The rank is taken to be the number of singular values of @var{A} that are
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25 ## greater than the specified tolerance @var{tol}. If the second argument is
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26 ## omitted, it is taken to be
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27 ##
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28 ## @example
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29 ## tol = max (size (@var{A})) * sigma(1) * eps;
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30 ## @end example
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31 ##
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32 ## @noindent
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33 ## where @code{eps} is machine precision and @code{sigma(1)} is the largest
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34 ## singular value of @var{A}.
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35 ##
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36 ## The rank of a matrix is the number of linearly independent rows or columns
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37 ## and determines how many particular solutions exist to a system of equations.
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38 ## Use @code{null} for finding the remaining homogenous solutions.
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39 ##
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40 ## Example:
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41 ##
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42 ## @example
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43 ## @group
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44 ## x = [1 2 3
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45 ## 4 5 6
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46 ## 7 8 9];
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47 ## rank (x)
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48 ## @result{} 2
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49 ## @end group
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50 ## @end example
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51 ##
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52 ## @noindent
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53 ## The number of linearly independent rows is only 2 because the final row is a
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54 ## linear combination of -1*row1 + 2*row2.
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55 ##
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56 ## @seealso{null, sprank, svd}
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57 ## @end deftypefn
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58
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59 ## Author: jwe
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60
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61 function retval = rank (A, tol)
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62
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63 if (nargin == 1)
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64 sigma = svd (A);
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65 if (isempty (sigma))
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66 tolerance = 0;
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67 else
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68 if (isa (A, "single"))
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69 tolerance = max (size (A)) * sigma (1) * eps ("single");
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70 else
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71 tolerance = max (size (A)) * sigma (1) * eps;
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72 endif
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73 endif
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74 elseif (nargin == 2)
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75 sigma = svd (A);
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76 tolerance = tol;
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77 else
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78 print_usage ();
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79 endif
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80
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81 retval = sum (sigma > tolerance);
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82
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83 endfunction
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84
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85
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86 %!test
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87 %! A = [1 2 3 4 5 6 7;
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88 %! 4 5 6 7 8 9 12;
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89 %! 1 2 3.1 4 5 6 7;
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90 %! 2 3 4 5 6 7 8;
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91 %! 3 4 5 6 7 8 9;
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92 %! 4 5 6 7 8 9 10;
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93 %! 5 6 7 8 9 10 11];
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94 %! assert (rank (A), 4);
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95
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96 %!test
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97 %! A = [1 2 3 4 5 6 7;
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98 %! 4 5 6 7 8 9 12;
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99 %! 1 2 3.0000001 4 5 6 7;
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100 %! 4 5 6 7 8 9 12.00001;
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101 %! 3 4 5 6 7 8 9;
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102 %! 4 5 6 7 8 9 10;
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103 %! 5 6 7 8 9 10 11];
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104 %! assert (rank (A), 4);
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105
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106 %!test
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107 %! A = [1 2 3 4 5 6 7;
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108 %! 4 5 6 7 8 9 12;
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109 %! 1 2 3 4 5 6 7;
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110 %! 4 5 6 7 8 9 12.00001;
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111 %! 3 4 5 6 7 8 9;
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112 %! 4 5 6 7 8 9 10;
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113 %! 5 6 7 8 9 10 11];
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114 %! assert (rank (A), 3);
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115
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116 %!test
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117 %! A = [1 2 3 4 5 6 7;
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118 %! 4 5 6 7 8 9 12;
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119 %! 1 2 3 4 5 6 7;
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120 %! 4 5 6 7 8 9 12;
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121 %! 3 4 5 6 7 8 9;
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122 %! 4 5 6 7 8 9 10;
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123 %! 5 6 7 8 9 10 11];
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124 %! assert (rank (A), 3);
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125
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126 %!test
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127 %! A = eye (100);
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128 %! assert (rank (A), 100);
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129
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130 %!assert (rank ([]), 0)
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131 %!assert (rank ([1:9]), 1)
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132 %!assert (rank ([1:9]'), 1)
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133
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8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m
David Wells <drwells@vt.edu>
parents: 12584
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134 %!test
8c4605b4d0c8 codesprint: Wrote 6 tests for rank.m
David Wells <drwells@vt.edu>
parents: 12584
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135 %! A = [1, 2, 3; 1, 2.001, 3; 1, 2, 3.0000001];
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
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136 %! assert (rank (A), 3);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
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137 %! assert (rank (A,0.0009), 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
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138 %! assert (rank (A,0.0006), 2);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
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139 %! assert (rank (A,0.00000002), 3);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
140