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update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2021. In all .txi and .texi files except gpl.txi and gpl.texi in the doc/liboctave and doc/interpreter directories, change the copyright to "Octave Project Developers", the same as used for other source files. Update copyright notices for 2022 (not done since 2019). For gpl.txi and gpl.texi, change the copyright notice to be "Free Software Foundation, Inc." and leave the date at 2007 only because this file only contains the text of the GPL, not anything created by the Octave Project Developers. Add Paul Thomas to contributors.in.
author John W. Eaton <jwe@octave.org>
date Tue, 28 Dec 2021 18:22:40 -0500
parents 7fa1d6f670f5
children 397d29f7135c
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30564
796f54d4ddbf update Octave Project Developers copyright for the new year
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1 @c Copyright (C) 1996-2022 The Octave Project Developers
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2 @c
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3 @c This file is part of Octave.
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4 @c
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5 @c Octave is free software: you can redistribute it and/or modify it
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6 @c under the terms of the GNU General Public License as published by
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7 @c the Free Software Foundation, either version 3 of the License, or
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8 @c (at your option) any later version.
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9 @c
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10 @c Octave is distributed in the hope that it will be useful, but
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11 @c WITHOUT ANY WARRANTY; without even the implied warranty of
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12 @c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 @c GNU General Public License for more details.
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14 @c
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15 @c You should have received a copy of the GNU General Public License
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16 @c along with Octave; see the file COPYING. If not, see
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17 @c <https://www.gnu.org/licenses/>.
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18
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19 @node Matrix Manipulation
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20 @chapter Matrix Manipulation
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21
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22 There are a number of functions available for checking to see if the
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23 elements of a matrix meet some condition, and for rearranging the
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24 elements of a matrix. For example, Octave can easily tell you if all
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25 the elements of a matrix are finite, or are less than some specified
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26 value. Octave can also rotate the elements, extract the upper- or
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27 lower-triangular parts, or sort the columns of a matrix.
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28
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29 @menu
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30 * Finding Elements and Checking Conditions::
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31 * Rearranging Matrices::
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32 * Special Utility Matrices::
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33 * Famous Matrices::
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34 @end menu
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35
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36 @node Finding Elements and Checking Conditions
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37 @section Finding Elements and Checking Conditions
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38
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39 The functions @code{any} and @code{all} are useful for determining
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40 whether any or all of the elements of a matrix satisfy some condition.
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41 The @code{find} function is also useful in determining which elements of
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42 a matrix meet a specified condition.
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43
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44 @DOCSTRING(any)
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45
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46 @DOCSTRING(all)
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47
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48 Since the comparison operators (@pxref{Comparison Ops}) return matrices
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49 of ones and zeros, it is easy to test a matrix for many things, not just
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50 whether the elements are nonzero. For example,
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51
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52 @example
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53 @group
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54 all (all (rand (5) < 0.9))
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55 @result{} 0
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56 @end group
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57 @end example
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58
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59 @noindent
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60 tests a random 5 by 5 matrix to see if all of its elements are less
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61 than 0.9.
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62
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63 Note that in conditional contexts (like the test clause of @code{if} and
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64 @code{while} statements) Octave treats the test as if you had typed
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65 @code{all (all (condition))}.
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66
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67 @DOCSTRING(xor)
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68
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69 @DOCSTRING(diff)
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70
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71 @DOCSTRING(isinf)
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72
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73 @DOCSTRING(isnan)
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74
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75 @DOCSTRING(isfinite)
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76
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77 @DOCSTRING(common_size)
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78
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79 @DOCSTRING(find)
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80
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81 @DOCSTRING(lookup)
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82
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83 If you wish to check if a variable exists at all, instead of properties
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84 its elements may have, consult @ref{Status of Variables}.
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85
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86 @node Rearranging Matrices
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87 @section Rearranging Matrices
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88
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89 @DOCSTRING(fliplr)
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90
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91 @DOCSTRING(flipud)
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92
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93 @DOCSTRING(flip)
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94
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95 @DOCSTRING(rot90)
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96
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97 @DOCSTRING(rotdim)
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98
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99 @DOCSTRING(cat)
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100
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101 @DOCSTRING(horzcat)
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102
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103 @DOCSTRING(vertcat)
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104
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105 @DOCSTRING(permute)
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106
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107 @DOCSTRING(ipermute)
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108
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109 @DOCSTRING(reshape)
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110
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111 @DOCSTRING(resize)
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112
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113 @DOCSTRING(circshift)
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114
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115 @DOCSTRING(shift)
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116
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117 @DOCSTRING(shiftdim)
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118
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119 @DOCSTRING(sort)
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120
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121 @DOCSTRING(sortrows)
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122
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123 @DOCSTRING(issorted)
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124
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125 @DOCSTRING(nth_element)
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126
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127 @DOCSTRING(tril)
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128
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129 @DOCSTRING(triu)
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130
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131 @DOCSTRING(vec)
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133 @DOCSTRING(vech)
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134
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135 @DOCSTRING(prepad)
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136
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137 @DOCSTRING(postpad)
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138
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139 @DOCSTRING(diag)
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140
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141 @DOCSTRING(blkdiag)
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142
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143 @node Special Utility Matrices
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144 @section Special Utility Matrices
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145
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146 @DOCSTRING(eye)
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147
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148 @DOCSTRING(ones)
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150 @DOCSTRING(zeros)
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151
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152 @DOCSTRING(repmat)
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153
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154 @DOCSTRING(repelems)
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155
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156 @DOCSTRING(repelem)
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157
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158 The functions @code{linspace} and @code{logspace} make it very easy to
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159 create vectors with evenly or logarithmically spaced elements.
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160 @xref{Ranges}.
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161
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162 @DOCSTRING(linspace)
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163
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164 @DOCSTRING(logspace)
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165
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166 @DOCSTRING(rand)
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167
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168 @DOCSTRING(randi)
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169
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170 @DOCSTRING(randn)
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171
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172 @DOCSTRING(rande)
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173
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174 @DOCSTRING(randp)
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175
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176 @DOCSTRING(randg)
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177
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178 @DOCSTRING(rng)
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179
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180 The generators operate in the new or old style together, it is not
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181 possible to mix the two. Initializing any generator with
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182 @qcode{"state"} or @qcode{"seed"} causes the others to switch to the
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183 same style for future calls.
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184
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185 The state of each generator is independent and calls to different
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186 generators can be interleaved without affecting the final result. For
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187 example,
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188
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189 @example
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190 @group
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191 rand ("state", [11, 22, 33]);
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192 randn ("state", [44, 55, 66]);
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193 u = rand (100, 1);
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194 n = randn (100, 1);
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195 @end group
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196 @end example
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197
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198 @noindent
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199 and
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200
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201 @example
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202 @group
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203 rand ("state", [11, 22, 33]);
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204 randn ("state", [44, 55, 66]);
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205 u = zeros (100, 1);
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206 n = zeros (100, 1);
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207 for i = 1:100
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208 u(i) = rand ();
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209 n(i) = randn ();
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210 end
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211 @end group
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212 @end example
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213
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214 @noindent
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215 produce equivalent results. When the generators are initialized in
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216 the old style with @qcode{"seed"} only @code{rand} and @code{randn} are
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217 independent, because the old @code{rande}, @code{randg} and
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218 @code{randp} generators make calls to @code{rand} and @code{randn}.
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219
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220 The generators are initialized with random states at start-up, so
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221 that the sequences of random numbers are not the same each time you run
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222 Octave.@footnote{The old versions of @code{rand} and @code{randn}
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223 obtain their initial seeds from the system clock.} If you really do
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224 need to reproduce a sequence of numbers exactly, you can set the state
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225 or seed to a specific value.
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226
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227 If invoked without arguments, @code{rand} and @code{randn} return a
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228 single element of a random sequence.
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229
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230 The original @code{rand} and @code{randn} functions use Fortran code from
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231 @sc{ranlib}, a library of Fortran routines for random number generation,
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232 compiled by Barry W. Brown and @nospell{James Lovato} of the Department of
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233 Biomathematics at The University of Texas, M.D. Anderson Cancer Center,
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234 Houston, TX 77030.
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235
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236 @DOCSTRING(randperm)
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237
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238 @node Famous Matrices
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239 @section Famous Matrices
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240
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241 The following functions return famous matrix forms.
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242
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243 @DOCSTRING(gallery)
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244
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245 @DOCSTRING(hadamard)
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246
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247 @DOCSTRING(hankel)
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248
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249 @DOCSTRING(hilb)
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250
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251 @DOCSTRING(invhilb)
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252
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253 @DOCSTRING(magic)
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254
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255 @DOCSTRING(pascal)
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256
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257 @DOCSTRING(rosser)
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258
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259 @DOCSTRING(toeplitz)
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260
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261 @DOCSTRING(vander)
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262
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263 @DOCSTRING(wilkinson)