Mercurial > hg > octave-nkf
annotate doc/interpreter/matrix.txi @ 8286:6f2d95255911
fix @seealso references to point to existing anchors
| author | Thorsten Meyer <thorsten.meyier@gmx.de> |
|---|---|
| date | Wed, 29 Oct 2008 17:52:54 -0400 |
| parents | f38997cf9e5b |
| children | c9cb8f0b8b4f |
| rev | line source |
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| 6778 | 1 @c Copyright (C) 1996, 1997, 2007 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 | |
| 51 whether the elements are nonzero. For example, | |
| 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 | |
| 70 @DOCSTRING(is_duplicate_entry) | |
| 3294 | 71 |
| 3369 | 72 @DOCSTRING(diff) |
| 3294 | 73 |
| 3369 | 74 @DOCSTRING(isinf) |
| 3294 | 75 |
| 3369 | 76 @DOCSTRING(isnan) |
| 3294 | 77 |
| 3369 | 78 @DOCSTRING(finite) |
| 3294 | 79 |
| 3369 | 80 @DOCSTRING(find) |
| 3294 | 81 |
| 3428 | 82 @DOCSTRING(common_size) |
| 83 | |
| 4167 | 84 @node Rearranging Matrices |
| 3294 | 85 @section Rearranging Matrices |
| 86 | |
| 3369 | 87 @DOCSTRING(fliplr) |
| 3294 | 88 |
| 3369 | 89 @DOCSTRING(flipud) |
| 3294 | 90 |
| 4869 | 91 @DOCSTRING(flipdim) |
| 92 | |
| 3369 | 93 @DOCSTRING(rot90) |
| 3294 | 94 |
| 4869 | 95 @DOCSTRING(rotdim) |
| 96 | |
| 4845 | 97 @DOCSTRING(cat) |
| 98 | |
| 99 @DOCSTRING(horzcat) | |
| 100 | |
| 101 @DOCSTRING(vertcat) | |
| 102 | |
| 103 @DOCSTRING(permute) | |
| 104 | |
| 105 @DOCSTRING(ipermute) | |
| 106 | |
| 3369 | 107 @DOCSTRING(reshape) |
| 3294 | 108 |
| 4894 | 109 @DOCSTRING(circshift) |
| 110 | |
| 111 @DOCSTRING(shiftdim) | |
| 112 | |
| 3369 | 113 @DOCSTRING(shift) |
| 3294 | 114 |
| 3369 | 115 @DOCSTRING(sort) |
| 3294 | 116 |
| 6550 | 117 @DOCSTRING(sortrows) |
| 118 | |
| 3294 | 119 Since the @code{sort} function does not allow sort keys to be specified, |
| 120 it can't be used to order the rows of a matrix according to the values | |
| 121 of the elements in various columns@footnote{For example, to first sort | |
| 122 based on the values in column 1, and then, for any values that are | |
| 123 repeated in column 1, sort based on the values found in column 2, etc.} | |
| 124 in a single call. Using the second output, however, it is possible to | |
| 125 sort all rows based on the values in a given column. Here's an example | |
| 126 that sorts the rows of a matrix based on the values in the second | |
| 127 column. | |
| 128 | |
| 129 @example | |
| 130 @group | |
| 131 a = [1, 2; 2, 3; 3, 1]; | |
| 132 [s, i] = sort (a (:, 2)); | |
| 133 a (i, :) | |
| 134 @result{} 3 1 | |
| 135 1 2 | |
| 136 2 3 | |
| 137 @end group | |
| 138 @end example | |
| 139 | |
| 6550 | 140 @DOCSTRING(swap) |
| 141 | |
| 142 @DOCSTRING(swapcols) | |
| 143 | |
| 144 @DOCSTRING(swaprows) | |
| 145 | |
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146 @anchor{doc-triu} |
| 3369 | 147 @DOCSTRING(tril) |
| 3294 | 148 |
| 3369 | 149 @DOCSTRING(vec) |
| 3294 | 150 |
| 3369 | 151 @DOCSTRING(vech) |
| 3294 | 152 |
| 3428 | 153 @DOCSTRING(prepad) |
| 154 | |
| 6550 | 155 @DOCSTRING(blkdiag) |
| 156 | |
| 157 @node Applying a Function to an Array | |
| 158 @section Applying a Function to an Array | |
| 159 | |
| 160 @DOCSTRING(arrayfun) | |
| 161 | |
| 6868 | 162 @DOCSTRING(bsxfun) |
| 163 | |
| 4167 | 164 @node Special Utility Matrices |
| 3294 | 165 @section Special Utility Matrices |
| 166 | |
| 3369 | 167 @DOCSTRING(eye) |
| 3294 | 168 |
| 3369 | 169 @DOCSTRING(ones) |
| 3294 | 170 |
| 3369 | 171 @DOCSTRING(zeros) |
| 3294 | 172 |
| 3920 | 173 @DOCSTRING(repmat) |
| 174 | |
| 3369 | 175 @DOCSTRING(rand) |
| 3294 | 176 |
| 3369 | 177 @DOCSTRING(randn) |
| 3294 | 178 |
| 5730 | 179 @DOCSTRING(rande) |
| 180 | |
| 181 @DOCSTRING(randp) | |
| 182 | |
| 183 @DOCSTRING(randg) | |
| 184 | |
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185 The generators operate in the new or old style together, it is not |
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186 possible to mix the two. Initializing any generator with |
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187 @code{"state"} or @code{"seed"} causes the others to switch to the |
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188 same style for future calls. |
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189 |
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190 The state of each generator is independent and calls to different |
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191 generators can be interleaved without affecting the final result. For |
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192 example, |
| 3294 | 193 |
| 194 @example | |
| 195 @group | |
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196 rand ("state", [11, 22, 33]); |
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197 randn ("state", [44, 55, 66]); |
| 3294 | 198 u = rand (100, 1); |
| 199 n = randn (100, 1); | |
| 200 @end group | |
| 201 @end example | |
| 202 | |
| 203 @noindent | |
| 204 and | |
| 205 | |
| 206 @example | |
| 207 @group | |
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208 rand ("state", [11, 22, 33]); |
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209 randn ("state", [44, 55, 66]); |
| 3294 | 210 u = zeros (100, 1); |
| 211 n = zeros (100, 1); | |
| 212 for i = 1:100 | |
| 213 u(i) = rand (); | |
| 214 n(i) = randn (); | |
| 215 end | |
| 216 @end group | |
| 217 @end example | |
| 218 | |
| 219 @noindent | |
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220 produce equivalent results. When the generators are initialized in |
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221 the old style with @code{"seed"} only @code{rand} and @code{randn} are |
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222 independent, because the old @code{rande}, @code{randg} and |
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223 @code{randp} generators make calls to @code{rand} and @code{randn}. |
| 3294 | 224 |
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225 The generators are initialized with random states at start-up, so |
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226 that the sequences of random numbers are not the same each time you run |
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227 Octave.@footnote{The old versions of @code{rand} and @code{randn} |
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228 obtain their initial seeds from the system clock.} If you really do |
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229 need to reproduce a sequence of numbers exactly, you can set the state |
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230 or seed to a specific value. |
| 3294 | 231 |
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232 If invoked without arguments, @code{rand} and @code{randn} return a |
| 3294 | 233 single element of a random sequence. |
| 234 | |
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235 The original @code{rand} and @code{randn} functions use Fortran code from |
| 3294 | 236 @sc{Ranlib}, a library of fortran routines for random number generation, |
| 237 compiled by Barry W. Brown and James Lovato of the Department of | |
| 238 Biomathematics at The University of Texas, M.D. Anderson Cancer Center, | |
| 239 Houston, TX 77030. | |
| 240 | |
| 3428 | 241 @DOCSTRING(randperm) |
| 242 | |
| 3369 | 243 @DOCSTRING(diag) |
| 3294 | 244 |
| 245 The functions @code{linspace} and @code{logspace} make it very easy to | |
| 246 create vectors with evenly or logarithmically spaced elements. | |
| 247 @xref{Ranges}. | |
| 248 | |
| 3369 | 249 @DOCSTRING(linspace) |
| 3294 | 250 |
| 3369 | 251 @DOCSTRING(logspace) |
| 3294 | 252 |
| 4167 | 253 @node Famous Matrices |
| 3294 | 254 @section Famous Matrices |
| 255 | |
| 256 The following functions return famous matrix forms. | |
| 257 | |
| 6502 | 258 @DOCSTRING(hadamard) |
| 259 | |
| 3369 | 260 @DOCSTRING(hankel) |
| 3294 | 261 |
| 3369 | 262 @DOCSTRING(hilb) |
| 3294 | 263 |
| 3369 | 264 @DOCSTRING(invhilb) |
| 3294 | 265 |
| 6502 | 266 @DOCSTRING(magic) |
| 267 | |
| 268 @DOCSTRING(pascal) | |
| 269 | |
| 270 @DOCSTRING(rosser) | |
| 271 | |
| 3369 | 272 @DOCSTRING(sylvester_matrix) |
| 3294 | 273 |
| 3369 | 274 @DOCSTRING(toeplitz) |
| 3294 | 275 |
| 3369 | 276 @DOCSTRING(vander) |
| 6502 | 277 |
| 278 @DOCSTRING(wilkinson) |