Mercurial > hg > octave-nkf
annotate doc/interpreter/matrix.txi @ 13017:aaf6fbb2512f stable
doc: Add cross references to "status of variables" in sections for predicates
* matrix.txi: Cross reference to Status of Variables
* numbers.txi: Ditto.
| author | Jordi Gutiérrez Hermoso <jordigh@gmail.com> |
|---|---|
| date | Sat, 27 Aug 2011 13:37:31 -0500 |
| parents | 4d777e05d47c |
| children | 1653d3a86fca |
| rev | line source |
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| 11523 | 1 @c Copyright (C) 1996-2011 John W. Eaton |
| 7018 | 2 @c |
| 3 @c This file is part of Octave. | |
| 4 @c | |
| 5 @c Octave is free software; you can redistribute it and/or modify it | |
| 6 @c under the terms of the GNU General Public License as published by the | |
| 7 @c Free Software Foundation; either version 3 of the License, or (at | |
| 8 @c your option) any later version. | |
| 9 @c | |
| 10 @c Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 13 @c for more details. | |
| 14 @c | |
| 15 @c You should have received a copy of the GNU General Public License | |
| 16 @c along with Octave; see the file COPYING. If not, see | |
| 17 @c <http://www.gnu.org/licenses/>. | |
| 3294 | 18 |
| 4167 | 19 @node Matrix Manipulation |
| 3294 | 20 @chapter Matrix Manipulation |
| 21 | |
| 22 There are a number of functions available for checking to see if the | |
| 23 elements of a matrix meet some condition, and for rearranging the | |
| 24 elements of a matrix. For example, Octave can easily tell you if all | |
| 25 the elements of a matrix are finite, or are less than some specified | |
| 26 value. Octave can also rotate the elements, extract the upper- or | |
| 27 lower-triangular parts, or sort the columns of a matrix. | |
| 28 | |
| 29 @menu | |
| 30 * Finding Elements and Checking Conditions:: | |
| 31 * Rearranging Matrices:: | |
| 6550 | 32 * Applying a Function to an Array:: |
| 3294 | 33 * Special Utility Matrices:: |
| 34 * Famous Matrices:: | |
| 35 @end menu | |
| 36 | |
| 4167 | 37 @node Finding Elements and Checking Conditions |
| 3294 | 38 @section Finding Elements and Checking Conditions |
| 39 | |
| 40 The functions @code{any} and @code{all} are useful for determining | |
| 41 whether any or all of the elements of a matrix satisfy some condition. | |
| 42 The @code{find} function is also useful in determining which elements of | |
| 43 a matrix meet a specified condition. | |
| 44 | |
| 3369 | 45 @DOCSTRING(any) |
| 3294 | 46 |
| 3369 | 47 @DOCSTRING(all) |
| 3294 | 48 |
| 49 Since the comparison operators (@pxref{Comparison Ops}) return matrices | |
| 50 of ones and zeros, it is easy to test a matrix for many things, not just | |
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51 whether the elements are nonzero. For example, |
| 3294 | 52 |
| 53 @example | |
| 54 @group | |
| 55 all (all (rand (5) < 0.9)) | |
| 56 @result{} 0 | |
| 57 @end group | |
| 58 @end example | |
| 59 | |
| 60 @noindent | |
| 61 tests a random 5 by 5 matrix to see if all of its elements are less | |
| 62 than 0.9. | |
| 63 | |
| 64 Note that in conditional contexts (like the test clause of @code{if} and | |
| 65 @code{while} statements) Octave treats the test as if you had typed | |
| 66 @code{all (all (condition))}. | |
| 67 | |
| 3428 | 68 @DOCSTRING(xor) |
| 69 | |
| 3369 | 70 @DOCSTRING(diff) |
| 3294 | 71 |
| 3369 | 72 @DOCSTRING(isinf) |
| 3294 | 73 |
| 3369 | 74 @DOCSTRING(isnan) |
| 3294 | 75 |
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76 @DOCSTRING(isfinite) |
| 3294 | 77 |
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78 @DOCSTRING(common_size) |
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79 |
| 3369 | 80 @DOCSTRING(find) |
| 3294 | 81 |
| 9367 | 82 @DOCSTRING(lookup) |
| 3428 | 83 |
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84 If you wish to check if a variable exists at all, instead of properties |
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85 its elements may have, consult @ref{Status of variables}. |
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86 |
| 4167 | 87 @node Rearranging Matrices |
| 3294 | 88 @section Rearranging Matrices |
| 89 | |
| 3369 | 90 @DOCSTRING(fliplr) |
| 3294 | 91 |
| 3369 | 92 @DOCSTRING(flipud) |
| 3294 | 93 |
| 4869 | 94 @DOCSTRING(flipdim) |
| 95 | |
| 3369 | 96 @DOCSTRING(rot90) |
| 3294 | 97 |
| 4869 | 98 @DOCSTRING(rotdim) |
| 99 | |
| 4845 | 100 @DOCSTRING(cat) |
| 101 | |
| 102 @DOCSTRING(horzcat) | |
| 103 | |
| 104 @DOCSTRING(vertcat) | |
| 105 | |
| 106 @DOCSTRING(permute) | |
| 107 | |
| 108 @DOCSTRING(ipermute) | |
| 109 | |
| 3369 | 110 @DOCSTRING(reshape) |
| 3294 | 111 |
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112 @DOCSTRING(resize) |
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113 |
| 4894 | 114 @DOCSTRING(circshift) |
| 115 | |
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116 @DOCSTRING(shift) |
| 4894 | 117 |
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118 @DOCSTRING(shiftdim) |
| 3294 | 119 |
| 3369 | 120 @DOCSTRING(sort) |
| 3294 | 121 |
| 6550 | 122 @DOCSTRING(sortrows) |
| 123 | |
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124 @DOCSTRING(issorted) |
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125 |
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126 @DOCSTRING(nth_element) |
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127 |
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128 @anchor{doc-triu} |
| 3369 | 129 @DOCSTRING(tril) |
| 3294 | 130 |
| 3369 | 131 @DOCSTRING(vec) |
| 3294 | 132 |
| 3369 | 133 @DOCSTRING(vech) |
| 3294 | 134 |
| 3428 | 135 @DOCSTRING(prepad) |
| 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 |
| 6550 | 141 @DOCSTRING(blkdiag) |
| 142 | |
| 143 @node Applying a Function to an Array | |
| 144 @section Applying a Function to an Array | |
| 145 | |
| 146 @DOCSTRING(arrayfun) | |
| 147 | |
| 6868 | 148 @DOCSTRING(bsxfun) |
| 149 | |
| 4167 | 150 @node Special Utility Matrices |
| 3294 | 151 @section Special Utility Matrices |
| 152 | |
| 3369 | 153 @DOCSTRING(eye) |
| 3294 | 154 |
| 3369 | 155 @DOCSTRING(ones) |
| 3294 | 156 |
| 3369 | 157 @DOCSTRING(zeros) |
| 3294 | 158 |
| 3920 | 159 @DOCSTRING(repmat) |
| 160 | |
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161 @DOCSTRING(repelems) |
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162 |
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163 The functions @code{linspace} and @code{logspace} make it very easy to |
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164 create vectors with evenly or logarithmically spaced elements. |
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165 @xref{Ranges}. |
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166 |
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167 @DOCSTRING(linspace) |
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168 |
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169 @DOCSTRING(logspace) |
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170 |
| 3369 | 171 @DOCSTRING(rand) |
| 3294 | 172 |
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173 @DOCSTRING(randi) |
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174 |
| 3369 | 175 @DOCSTRING(randn) |
| 3294 | 176 |
| 5730 | 177 @DOCSTRING(rande) |
| 178 | |
| 179 @DOCSTRING(randp) | |
| 180 | |
| 181 @DOCSTRING(randg) | |
| 182 | |
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183 The generators operate in the new or old style together, it is not |
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184 possible to mix the two. Initializing any generator with |
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185 @code{"state"} or @code{"seed"} causes the others to switch to the |
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186 same style for future calls. |
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187 |
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188 The state of each generator is independent and calls to different |
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189 generators can be interleaved without affecting the final result. For |
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190 example, |
| 3294 | 191 |
| 192 @example | |
| 193 @group | |
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194 rand ("state", [11, 22, 33]); |
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195 randn ("state", [44, 55, 66]); |
| 3294 | 196 u = rand (100, 1); |
| 197 n = randn (100, 1); | |
| 198 @end group | |
| 199 @end example | |
| 200 | |
| 201 @noindent | |
| 202 and | |
| 203 | |
| 204 @example | |
| 205 @group | |
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206 rand ("state", [11, 22, 33]); |
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207 randn ("state", [44, 55, 66]); |
| 3294 | 208 u = zeros (100, 1); |
| 209 n = zeros (100, 1); | |
| 210 for i = 1:100 | |
| 211 u(i) = rand (); | |
| 212 n(i) = randn (); | |
| 213 end | |
| 214 @end group | |
| 215 @end example | |
| 216 | |
| 217 @noindent | |
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218 produce equivalent results. When the generators are initialized in |
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219 the old style with @code{"seed"} only @code{rand} and @code{randn} are |
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220 independent, because the old @code{rande}, @code{randg} and |
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221 @code{randp} generators make calls to @code{rand} and @code{randn}. |
| 3294 | 222 |
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223 The generators are initialized with random states at start-up, so |
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224 that the sequences of random numbers are not the same each time you run |
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225 Octave.@footnote{The old versions of @code{rand} and @code{randn} |
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226 obtain their initial seeds from the system clock.} If you really do |
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227 need to reproduce a sequence of numbers exactly, you can set the state |
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228 or seed to a specific value. |
| 3294 | 229 |
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230 If invoked without arguments, @code{rand} and @code{randn} return a |
| 3294 | 231 single element of a random sequence. |
| 232 | |
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233 The original @code{rand} and @code{randn} functions use Fortran code from |
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234 @sc{ranlib}, a library of Fortran routines for random number generation, |
| 3294 | 235 compiled by Barry W. Brown and James Lovato of the Department of |
| 236 Biomathematics at The University of Texas, M.D. Anderson Cancer Center, | |
| 237 Houston, TX 77030. | |
| 238 | |
| 3428 | 239 @DOCSTRING(randperm) |
| 240 | |
| 4167 | 241 @node Famous Matrices |
| 3294 | 242 @section Famous Matrices |
| 243 | |
| 244 The following functions return famous matrix forms. | |
| 245 | |
| 6502 | 246 @DOCSTRING(hadamard) |
| 247 | |
| 3369 | 248 @DOCSTRING(hankel) |
| 3294 | 249 |
| 3369 | 250 @DOCSTRING(hilb) |
| 3294 | 251 |
| 3369 | 252 @DOCSTRING(invhilb) |
| 3294 | 253 |
| 6502 | 254 @DOCSTRING(magic) |
| 255 | |
| 256 @DOCSTRING(pascal) | |
| 257 | |
| 258 @DOCSTRING(rosser) | |
| 259 | |
| 3369 | 260 @DOCSTRING(sylvester_matrix) |
| 3294 | 261 |
| 3369 | 262 @DOCSTRING(toeplitz) |
| 3294 | 263 |
| 3369 | 264 @DOCSTRING(vander) |
| 6502 | 265 |
| 266 @DOCSTRING(wilkinson) |