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Added tag rc-4-0-0-3 for changeset 065f933ef083
author John W. Eaton <jwe@octave.org>
date Fri, 10 Apr 2015 14:41:21 -0400
parents 4197fc428c7d
children
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4197fc428c7d maint: Update copyright notices for 2015.
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1 @c Copyright (C) 1996-2015 John W. Eaton
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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 the
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7 @c Free Software Foundation; either version 3 of the License, or (at
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8 @c 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 WITHOUT
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11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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13 @c 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 <http://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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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 @anchor{XREFtriu}
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128 @DOCSTRING(tril)
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129
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130 @DOCSTRING(vec)
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132 @DOCSTRING(vech)
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133
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134 @DOCSTRING(prepad)
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135
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136 @DOCSTRING(postpad)
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137
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138 @DOCSTRING(diag)
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139
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140 @DOCSTRING(blkdiag)
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141
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142 @node Special Utility Matrices
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143 @section Special Utility Matrices
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144
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145 @DOCSTRING(eye)
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147 @DOCSTRING(ones)
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149 @DOCSTRING(zeros)
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151 @DOCSTRING(repmat)
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152
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153 @DOCSTRING(repelems)
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154
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155 The functions @code{linspace} and @code{logspace} make it very easy to
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156 create vectors with evenly or logarithmically spaced elements.
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157 @xref{Ranges}.
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158
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159 @DOCSTRING(linspace)
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160
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161 @DOCSTRING(logspace)
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162
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163 @DOCSTRING(rand)
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164
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165 @DOCSTRING(randi)
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166
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167 @DOCSTRING(randn)
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168
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169 @DOCSTRING(rande)
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170
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171 @DOCSTRING(randp)
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172
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173 @DOCSTRING(randg)
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174
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175 The generators operate in the new or old style together, it is not
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176 possible to mix the two. Initializing any generator with
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177 @qcode{"state"} or @qcode{"seed"} causes the others to switch to the
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178 same style for future calls.
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179
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180 The state of each generator is independent and calls to different
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181 generators can be interleaved without affecting the final result. For
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182 example,
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183
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184 @example
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185 @group
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186 rand ("state", [11, 22, 33]);
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187 randn ("state", [44, 55, 66]);
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188 u = rand (100, 1);
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189 n = randn (100, 1);
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190 @end group
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191 @end example
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192
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193 @noindent
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194 and
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195
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196 @example
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197 @group
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198 rand ("state", [11, 22, 33]);
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199 randn ("state", [44, 55, 66]);
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200 u = zeros (100, 1);
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201 n = zeros (100, 1);
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202 for i = 1:100
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203 u(i) = rand ();
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204 n(i) = randn ();
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205 end
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206 @end group
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207 @end example
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208
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209 @noindent
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210 produce equivalent results. When the generators are initialized in
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211 the old style with @qcode{"seed"} only @code{rand} and @code{randn} are
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212 independent, because the old @code{rande}, @code{randg} and
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213 @code{randp} generators make calls to @code{rand} and @code{randn}.
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214
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215 The generators are initialized with random states at start-up, so
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216 that the sequences of random numbers are not the same each time you run
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217 Octave.@footnote{The old versions of @code{rand} and @code{randn}
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218 obtain their initial seeds from the system clock.} If you really do
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219 need to reproduce a sequence of numbers exactly, you can set the state
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220 or seed to a specific value.
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221
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222 If invoked without arguments, @code{rand} and @code{randn} return a
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223 single element of a random sequence.
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224
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225 The original @code{rand} and @code{randn} functions use Fortran code from
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226 @sc{ranlib}, a library of Fortran routines for random number generation,
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227 compiled by Barry W. Brown and James Lovato of the Department of
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228 Biomathematics at The University of Texas, M.D. Anderson Cancer Center,
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229 Houston, TX 77030.
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230
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231 @DOCSTRING(randperm)
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232
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233 @node Famous Matrices
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234 @section Famous Matrices
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235
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236 The following functions return famous matrix forms.
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237
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238 @DOCSTRING(gallery)
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239
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240 @DOCSTRING(hadamard)
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241
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242 @DOCSTRING(hankel)
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243
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244 @DOCSTRING(hilb)
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245
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246 @DOCSTRING(invhilb)
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247
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248 @DOCSTRING(magic)
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249
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250 @DOCSTRING(pascal)
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251
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252 @DOCSTRING(rosser)
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253
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254 @DOCSTRING(toeplitz)
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255
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256 @DOCSTRING(vander)
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257
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258 @DOCSTRING(wilkinson)