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annotate doc/interpreter/expr.txi @ 14033:dfbf6a49847c stable
doc: Update documentation on indexing expressions
* expr.txi, octave.texi: Update documentation on indexing expressions
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sun, 11 Dec 2011 22:15:48 -0800 |
| parents | 990762e784fe |
| children | b0cdd60db5e5 |
| 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 Expressions |
| 3294 | 20 @chapter Expressions |
| 21 @cindex expressions | |
| 22 | |
| 23 Expressions are the basic building block of statements in Octave. An | |
| 24 expression evaluates to a value, which you can print, test, store in a | |
| 25 variable, pass to a function, or assign a new value to a variable with | |
| 26 an assignment operator. | |
| 27 | |
| 28 An expression can serve as a statement on its own. Most other kinds of | |
| 29 statements contain one or more expressions which specify data to be | |
| 30 operated on. As in other languages, expressions in Octave include | |
| 31 variables, array references, constants, and function calls, as well as | |
| 32 combinations of these with various operators. | |
| 33 | |
| 34 @menu | |
| 35 * Index Expressions:: | |
| 36 * Calling Functions:: | |
| 37 * Arithmetic Ops:: | |
| 38 * Comparison Ops:: | |
| 39 * Boolean Expressions:: | |
| 40 * Assignment Ops:: | |
| 41 * Increment Ops:: | |
| 42 * Operator Precedence:: | |
| 43 @end menu | |
| 44 | |
| 4167 | 45 @node Index Expressions |
| 3294 | 46 @section Index Expressions |
| 47 | |
| 48 @opindex ( | |
| 49 @opindex ) | |
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50 @opindex : |
| 3294 | 51 |
| 52 An @dfn{index expression} allows you to reference or extract selected | |
| 53 elements of a matrix or vector. | |
| 54 | |
| 55 Indices may be scalars, vectors, ranges, or the special operator | |
| 56 @samp{:}, which may be used to select entire rows or columns. | |
| 57 | |
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58 Vectors are indexed using a single index expression. Matrices (2-D) |
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59 and higher multi-dimensional arrays are indexed using either one index |
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60 or @math{N} indices where @math{N} is the dimension of the array. |
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61 When using a single index expression to index 2-D or higher data the |
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62 elements of the array are taken in column-first order (like Fortran). |
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63 |
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64 The output from indexing assumes the dimensions of the index |
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65 expression. For example, |
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66 |
| 5679 | 67 @example |
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68 @group |
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69 a(2) # result is a scalar |
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70 a(1:2) # result is a row vector |
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71 a([1; 2]) # result is a column vector |
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72 @end group |
| 5679 | 73 @end example |
| 74 | |
| 75 As a special case, when a colon is used as a single index, the output | |
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76 is a column vector containing all the elements of the vector or |
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77 matrix. For example: |
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78 |
| 5679 | 79 @example |
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80 a(:) # result is a column vector |
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81 a(:)' # result is a row vector |
| 5679 | 82 @end example |
| 83 | |
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84 The above two code idioms are often used in place of @code{reshape} |
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85 when a simple vector, rather than an arbitrarily sized array, is |
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86 needed. |
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87 |
| 3294 | 88 Given the matrix |
| 89 | |
| 90 @example | |
| 91 a = [1, 2; 3, 4] | |
| 92 @end example | |
| 93 | |
| 94 @noindent | |
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95 all of the following expressions are equivalent and select the first |
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96 row of the matrix. |
| 3294 | 97 |
| 98 @example | |
| 99 @group | |
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100 a(1, [1, 2]) # row 1, columns 1 and 2 |
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101 a(1, 1:2) # row 1, columns in range 1-2 |
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102 a(1, :) # row 1, all columns |
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103 @end group |
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104 @end example |
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105 |
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106 @cindex @code{end}, indexing |
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107 @cindex :end |
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108 |
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109 In index expressions the keyword @code{end} automatically refers to |
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110 the last entry for a particular dimension. This magic index can also |
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111 be used in ranges and typically eliminates the needs to call |
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112 @code{size} or @code{length} to gather array bounds before indexing. |
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113 For example: |
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114 |
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115 @example |
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116 @group |
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117 a = [1, 2, 3, 4]; |
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118 |
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119 a(1:end/2) # first half of a => [1, 2] |
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120 a(end + 1) = 5; # append element |
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121 a(end) = []; # delete element |
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122 a(1:2:end) # odd elements of a => [1, 3] |
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123 a(2:2:end) # even elements of a => [2, 4] |
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124 a(end:-1:1) # reversal of a => [4, 3, 2 , 1] |
| 3294 | 125 @end group |
| 126 @end example | |
| 127 | |
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128 @menu |
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129 * Advanced Indexing:: |
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130 @end menu |
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131 |
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132 @node Advanced Indexing |
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133 @subsection Advanced Indexing |
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134 |
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135 An array with @samp{n} dimensions can be indexed using @samp{m} |
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136 indices. More generally, the set of index tuples determining the |
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137 result is formed by the Cartesian product of the index vectors (or |
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138 ranges or scalars). |
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139 |
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140 For the ordinary and most common case, @w{@code{m == n}}, and each |
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141 index corresponds to its respective dimension. If @w{@code{m < n}} |
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142 and every index is less than the size of the array in the |
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143 @math{i^{th}} dimension, @code{m(i) < n(i)}, then the index expression |
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144 is padded with trailing singleton dimensions (@code{[ones (m-n, 1)]}). |
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145 If @w{@code{m < n}} but one of the indices @code{m(i)} is outside the |
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146 size of the current array, then the last @w{@code{n-m+1}} dimensions |
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147 are folded into a single dimension with an extent equal to the product |
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148 of extents of the original dimensions. This is easiest to understand |
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149 with an example. |
| 3294 | 150 |
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151 @example |
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152 @group |
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153 a = reshape (1:8, 2, 2, 2) # Create 3-D array |
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154 a = |
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155 |
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156 ans(:,:,1) = |
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157 |
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158 1 3 |
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159 2 4 |
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160 |
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161 ans(:,:,2) = |
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162 |
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163 5 7 |
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164 6 8 |
| 9159 | 165 |
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166 a(2,1,2); # Case (m == n): ans = 6 |
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167 a(2,1); # Case (m < n), idx within array: |
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168 # equivalent to a(2,1,1), ans = 2 |
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169 a(2,4); # Case (m < n), idx outside array: |
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170 # Dimension 2 & 3 folded into new dimension of size 2x2 = 4 |
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171 # Select 2nd row, 4th element of [2, 4, 6, 8], ans = 8 |
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172 @end group |
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173 @end example |
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175 One advanced use of indexing is to create arrays filled with a single |
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176 value. This can be done by using an index of ones on a scalar value. |
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177 The result is an object with the dimensions of the index expression |
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178 and every element equal to the original scalar. For example, the |
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179 following statements |
| 3294 | 180 |
| 181 @example | |
| 182 @group | |
| 183 a = 13; | |
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184 a(ones (1, 4)) |
| 3294 | 185 @end group |
| 186 @end example | |
| 187 | |
| 188 @noindent | |
| 189 produce a vector whose four elements are all equal to 13. | |
| 190 | |
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191 Similarly, by indexing a scalar with two vectors of ones it is |
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192 possible to create a matrix. The following statements |
| 3294 | 193 |
| 194 @example | |
| 195 @group | |
| 196 a = 13; | |
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197 a(ones (1, 2), ones (1, 3)) |
| 3294 | 198 @end group |
| 199 @end example | |
| 200 | |
| 201 @noindent | |
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202 create a 2x3 matrix with all elements equal to 13. |
| 3294 | 203 |
| 9159 | 204 The last example could also be written as |
| 205 | |
| 206 @example | |
| 207 @group | |
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208 13(ones (2, 3)) |
| 9159 | 209 @end group |
| 210 @end example | |
| 211 | |
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212 It is more efficient to use indexing rather than the code construction |
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213 @code{scalar * ones (N, M, @dots{})} because it avoids the unnecessary |
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214 multiplication operation. Moreover, multiplication may not be |
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215 defined for the object to be replicated whereas indexing an array is |
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216 always defined. The following code shows how to create a 2x3 cell |
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217 array from a base unit which is not itself a scalar. |
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218 |
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219 @example |
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220 @group |
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221 @{"Hello"@}(ones (2, 3)) |
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222 @end group |
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223 @end example |
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224 |
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225 It should be, noted that @code{ones (1, n)} (a row vector of ones) |
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226 results in a range (with zero increment). A range is stored |
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227 internally as a starting value, increment, end value, and total number |
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228 of values; hence, it is more efficient for storage than a vector or |
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229 matrix of ones whenever the number of elements is greater than 4. In |
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230 particular, when @samp{r} is a row vector, the expressions |
| 9159 | 231 |
| 232 @example | |
| 233 r(ones (1, n), :) | |
| 234 @end example | |
| 235 | |
| 236 @example | |
| 237 r(ones (n, 1), :) | |
| 238 @end example | |
| 239 | |
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240 @noindent |
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241 will produce identical results, but the first one will be |
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242 significantly faster, at least for @samp{r} and @samp{n} large enough. |
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243 In the first case the index is held in compressed form as a range |
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244 which allows Octave to choose a more efficient algorithm to handle the |
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245 expression. |
| 9159 | 246 |
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247 A general recommendation, for a user unaware of these subtleties, is |
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248 to use the function @code{repmat} for replicating smaller arrays into |
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249 bigger ones. |
| 3294 | 250 |
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251 A second use of indexing is to speed up code. Indexing is a fast |
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252 operation and judicious use of it can reduce the requirement for |
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253 looping over individual array elements which is a slow operation. |
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254 |
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255 Consider the following example which creates a 10-element row vector |
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256 @math{a} containing the values |
| 6642 | 257 @tex |
| 258 $a_i = \sqrt{i}$. | |
| 259 @end tex | |
| 260 @ifnottex | |
| 261 a(i) = sqrt(i). | |
| 262 @end ifnottex | |
| 263 | |
| 264 @example | |
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265 @group |
| 6642 | 266 for i = 1:10 |
| 267 a(i) = sqrt (i); | |
| 268 endfor | |
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269 @end group |
| 6642 | 270 @end example |
| 271 | |
| 272 @noindent | |
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273 It is quite inefficient to create a vector using a loop like this. In |
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274 this case, it would have been much more efficient to use the |
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275 expression |
| 3294 | 276 |
| 277 @example | |
| 278 a = sqrt (1:10); | |
| 279 @end example | |
| 280 | |
| 281 @noindent | |
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282 which avoids the loop entirely. |
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283 |
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284 In cases where a loop cannot be avoided, or a number of values must be |
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285 combined to form a larger matrix, it is generally faster to set the |
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286 size of the matrix first (pre-allocate storage), and then insert |
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287 elements using indexing commands. For example, given a matrix |
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288 @code{a}, |
| 3294 | 289 |
| 290 @example | |
| 291 @group | |
| 292 [nr, nc] = size (a); | |
| 293 x = zeros (nr, n * nc); | |
| 294 for i = 1:n | |
| 3602 | 295 x(:,(i-1)*nc+1:i*nc) = a; |
| 3294 | 296 endfor |
| 297 @end group | |
| 298 @end example | |
| 299 | |
| 300 @noindent | |
| 301 is considerably faster than | |
| 302 | |
| 303 @example | |
| 304 @group | |
| 305 x = a; | |
| 306 for i = 1:n-1 | |
| 307 x = [x, a]; | |
| 308 endfor | |
| 309 @end group | |
| 310 @end example | |
| 311 | |
| 312 @noindent | |
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313 because Octave does not have to repeatedly resize the intermediate |
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314 result. |
| 3294 | 315 |
| 6549 | 316 @DOCSTRING(sub2ind) |
| 317 | |
| 318 @DOCSTRING(ind2sub) | |
| 319 | |
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320 @DOCSTRING(isindex) |
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321 |
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322 @DOCSTRING(allow_noninteger_range_as_index) |
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323 |
| 4167 | 324 @node Calling Functions |
| 3294 | 325 @section Calling Functions |
| 326 | |
| 327 A @dfn{function} is a name for a particular calculation. Because it has | |
| 328 a name, you can ask for it by name at any point in the program. For | |
| 329 example, the function @code{sqrt} computes the square root of a number. | |
| 330 | |
| 331 A fixed set of functions are @dfn{built-in}, which means they are | |
| 332 available in every Octave program. The @code{sqrt} function is one of | |
| 333 these. In addition, you can define your own functions. | |
| 334 @xref{Functions and Scripts}, for information about how to do this. | |
| 335 | |
| 336 @cindex arguments in function call | |
| 337 The way to use a function is with a @dfn{function call} expression, | |
| 338 which consists of the function name followed by a list of | |
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339 @dfn{arguments} in parentheses. The arguments are expressions which give |
| 3294 | 340 the raw materials for the calculation that the function will do. When |
| 341 there is more than one argument, they are separated by commas. If there | |
| 342 are no arguments, you can omit the parentheses, but it is a good idea to | |
| 343 include them anyway, to clearly indicate that a function call was | |
| 344 intended. Here are some examples: | |
| 345 | |
| 346 @example | |
| 347 @group | |
| 348 sqrt (x^2 + y^2) # @r{One argument} | |
| 349 ones (n, m) # @r{Two arguments} | |
| 350 rand () # @r{No arguments} | |
| 351 @end group | |
| 352 @end example | |
| 353 | |
| 354 Each function expects a particular number of arguments. For example, the | |
| 355 @code{sqrt} function must be called with a single argument, the number | |
| 356 to take the square root of: | |
| 357 | |
| 358 @example | |
| 359 sqrt (@var{argument}) | |
| 360 @end example | |
| 361 | |
| 362 Some of the built-in functions take a variable number of arguments, | |
| 363 depending on the particular usage, and their behavior is different | |
| 364 depending on the number of arguments supplied. | |
| 365 | |
| 366 Like every other expression, the function call has a value, which is | |
| 367 computed by the function based on the arguments you give it. In this | |
| 368 example, the value of @code{sqrt (@var{argument})} is the square root of | |
| 369 the argument. A function can also have side effects, such as assigning | |
| 370 the values of certain variables or doing input or output operations. | |
| 371 | |
| 372 Unlike most languages, functions in Octave may return multiple values. | |
| 373 For example, the following statement | |
| 374 | |
| 375 @example | |
| 376 [u, s, v] = svd (a) | |
| 377 @end example | |
| 378 | |
| 379 @noindent | |
| 380 computes the singular value decomposition of the matrix @code{a} and | |
| 381 assigns the three result matrices to @code{u}, @code{s}, and @code{v}. | |
| 382 | |
| 383 The left side of a multiple assignment expression is itself a list of | |
| 384 expressions, and is allowed to be a list of variable names or index | |
| 385 expressions. See also @ref{Index Expressions}, and @ref{Assignment Ops}. | |
| 386 | |
| 387 @menu | |
| 388 * Call by Value:: | |
| 389 * Recursion:: | |
| 390 @end menu | |
| 391 | |
| 4167 | 392 @node Call by Value |
| 3294 | 393 @subsection Call by Value |
| 394 | |
| 395 In Octave, unlike Fortran, function arguments are passed by value, which | |
| 396 means that each argument in a function call is evaluated and assigned to | |
| 397 a temporary location in memory before being passed to the function. | |
| 398 There is currently no way to specify that a function parameter should be | |
| 399 passed by reference instead of by value. This means that it is | |
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400 impossible to directly alter the value of a function parameter in the |
| 3294 | 401 calling function. It can only change the local copy within the function |
| 402 body. For example, the function | |
| 403 | |
| 404 @example | |
| 405 @group | |
| 406 function f (x, n) | |
| 407 while (n-- > 0) | |
| 408 disp (x); | |
| 409 endwhile | |
| 410 endfunction | |
| 411 @end group | |
| 412 @end example | |
| 413 | |
| 414 @noindent | |
| 415 displays the value of the first argument @var{n} times. In this | |
| 416 function, the variable @var{n} is used as a temporary variable without | |
| 417 having to worry that its value might also change in the calling | |
| 418 function. Call by value is also useful because it is always possible to | |
| 419 pass constants for any function parameter without first having to | |
| 420 determine that the function will not attempt to modify the parameter. | |
| 421 | |
| 422 The caller may use a variable as the expression for the argument, but | |
| 423 the called function does not know this: it only knows what value the | |
| 424 argument had. For example, given a function called as | |
| 425 | |
| 426 @example | |
| 427 @group | |
| 428 foo = "bar"; | |
| 429 fcn (foo) | |
| 430 @end group | |
| 431 @end example | |
| 432 | |
| 433 @noindent | |
| 434 you should not think of the argument as being ``the variable | |
| 435 @code{foo}.'' Instead, think of the argument as the string value, | |
| 436 @code{"bar"}. | |
| 437 | |
| 438 Even though Octave uses pass-by-value semantics for function arguments, | |
| 439 values are not copied unnecessarily. For example, | |
| 440 | |
| 441 @example | |
| 442 @group | |
| 443 x = rand (1000); | |
| 444 f (x); | |
| 445 @end group | |
| 446 @end example | |
| 447 | |
| 448 @noindent | |
| 449 does not actually force two 1000 by 1000 element matrices to exist | |
| 450 @emph{unless} the function @code{f} modifies the value of its | |
| 451 argument. Then Octave must create a copy to avoid changing the | |
| 452 value outside the scope of the function @code{f}, or attempting (and | |
| 453 probably failing!) to modify the value of a constant or the value of a | |
| 454 temporary result. | |
| 455 | |
| 4167 | 456 @node Recursion |
| 3294 | 457 @subsection Recursion |
| 458 @cindex factorial function | |
| 459 | |
| 6939 | 460 With some restrictions@footnote{Some of Octave's functions are |
| 3294 | 461 implemented in terms of functions that cannot be called recursively. |
| 462 For example, the ODE solver @code{lsode} is ultimately implemented in a | |
| 463 Fortran subroutine that cannot be called recursively, so @code{lsode} | |
| 464 should not be called either directly or indirectly from within the | |
| 465 user-supplied function that @code{lsode} requires. Doing so will result | |
| 6642 | 466 in an error.}, recursive function calls are allowed. A |
| 3294 | 467 @dfn{recursive function} is one which calls itself, either directly or |
| 468 indirectly. For example, here is an inefficient@footnote{It would be | |
| 469 much better to use @code{prod (1:n)}, or @code{gamma (n+1)} instead, | |
| 470 after first checking to ensure that the value @code{n} is actually a | |
| 471 positive integer.} way to compute the factorial of a given integer: | |
| 472 | |
| 473 @example | |
| 474 @group | |
| 475 function retval = fact (n) | |
| 476 if (n > 0) | |
| 477 retval = n * fact (n-1); | |
| 478 else | |
| 479 retval = 1; | |
| 480 endif | |
| 481 endfunction | |
| 482 @end group | |
| 483 @end example | |
| 484 | |
| 485 This function is recursive because it calls itself directly. It | |
| 486 eventually terminates because each time it calls itself, it uses an | |
| 487 argument that is one less than was used for the previous call. Once the | |
| 488 argument is no longer greater than zero, it does not call itself, and | |
| 489 the recursion ends. | |
| 490 | |
| 491 The built-in variable @code{max_recursion_depth} specifies a limit to | |
| 492 the recursion depth and prevents Octave from recursing infinitely. | |
| 493 | |
| 3371 | 494 @DOCSTRING(max_recursion_depth) |
| 3294 | 495 |
| 4167 | 496 @node Arithmetic Ops |
| 3294 | 497 @section Arithmetic Operators |
| 498 @cindex arithmetic operators | |
| 499 @cindex operators, arithmetic | |
| 500 @cindex addition | |
| 501 @cindex subtraction | |
| 502 @cindex multiplication | |
| 503 @cindex matrix multiplication | |
| 504 @cindex division | |
| 505 @cindex quotient | |
| 506 @cindex negation | |
| 507 @cindex unary minus | |
| 508 @cindex exponentiation | |
| 509 @cindex transpose | |
| 510 @cindex Hermitian operator | |
| 511 @cindex transpose, complex-conjugate | |
| 512 @cindex complex-conjugate transpose | |
| 513 | |
| 514 The following arithmetic operators are available, and work on scalars | |
| 515 and matrices. | |
| 516 | |
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517 @table @asis |
| 3294 | 518 @item @var{x} + @var{y} |
| 519 @opindex + | |
| 520 Addition. If both operands are matrices, the number of rows and columns | |
| 521 must both agree. If one operand is a scalar, its value is added to | |
| 522 all the elements of the other operand. | |
| 523 | |
| 524 @item @var{x} .+ @var{y} | |
| 525 @opindex .+ | |
| 526 Element by element addition. This operator is equivalent to @code{+}. | |
| 527 | |
| 528 @item @var{x} - @var{y} | |
| 529 @opindex - | |
| 530 Subtraction. If both operands are matrices, the number of rows and | |
| 531 columns of both must agree. | |
| 532 | |
| 533 @item @var{x} .- @var{y} | |
| 534 Element by element subtraction. This operator is equivalent to @code{-}. | |
| 535 | |
| 536 @item @var{x} * @var{y} | |
| 537 @opindex * | |
| 538 Matrix multiplication. The number of columns of @var{x} must agree | |
| 539 with the number of rows of @var{y}. | |
| 540 | |
| 541 @item @var{x} .* @var{y} | |
| 542 @opindex .* | |
| 543 Element by element multiplication. If both operands are matrices, the | |
| 544 number of rows and columns must both agree. | |
| 545 | |
| 546 @item @var{x} / @var{y} | |
| 547 @opindex / | |
| 548 Right division. This is conceptually equivalent to the expression | |
| 549 | |
| 550 @example | |
| 551 (inverse (y') * x')' | |
| 552 @end example | |
| 553 | |
| 554 @noindent | |
| 555 but it is computed without forming the inverse of @var{y'}. | |
| 556 | |
| 557 If the system is not square, or if the coefficient matrix is singular, | |
| 558 a minimum norm solution is computed. | |
| 559 | |
| 560 @item @var{x} ./ @var{y} | |
| 561 @opindex ./ | |
| 562 Element by element right division. | |
| 563 | |
| 564 @item @var{x} \ @var{y} | |
| 565 @opindex \ | |
| 566 Left division. This is conceptually equivalent to the expression | |
| 567 | |
| 568 @example | |
| 569 inverse (x) * y | |
| 570 @end example | |
| 571 | |
| 572 @noindent | |
| 573 but it is computed without forming the inverse of @var{x}. | |
| 574 | |
| 575 If the system is not square, or if the coefficient matrix is singular, | |
| 576 a minimum norm solution is computed. | |
| 577 | |
| 578 @item @var{x} .\ @var{y} | |
| 579 @opindex .\ | |
| 580 Element by element left division. Each element of @var{y} is divided | |
| 581 by each corresponding element of @var{x}. | |
| 582 | |
| 583 @item @var{x} ^ @var{y} | |
| 584 @itemx @var{x} ** @var{y} | |
| 585 @opindex ** | |
| 586 @opindex ^ | |
| 587 Power operator. If @var{x} and @var{y} are both scalars, this operator | |
| 588 returns @var{x} raised to the power @var{y}. If @var{x} is a scalar and | |
| 589 @var{y} is a square matrix, the result is computed using an eigenvalue | |
| 7001 | 590 expansion. If @var{x} is a square matrix, the result is computed by |
| 3294 | 591 repeated multiplication if @var{y} is an integer, and by an eigenvalue |
| 592 expansion if @var{y} is not an integer. An error results if both | |
| 593 @var{x} and @var{y} are matrices. | |
| 594 | |
| 595 The implementation of this operator needs to be improved. | |
| 596 | |
| 597 @item @var{x} .^ @var{y} | |
|
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598 @itemx @var{x} .** @var{y} |
| 3294 | 599 @opindex .** |
| 600 @opindex .^ | |
| 601 Element by element power operator. If both operands are matrices, the | |
| 602 number of rows and columns must both agree. | |
| 603 | |
| 604 @item -@var{x} | |
| 605 @opindex - | |
| 606 Negation. | |
| 607 | |
| 608 @item +@var{x} | |
| 609 @opindex + | |
| 610 Unary plus. This operator has no effect on the operand. | |
| 611 | |
| 612 @item @var{x}' | |
| 613 @opindex ' | |
| 614 Complex conjugate transpose. For real arguments, this operator is the | |
| 615 same as the transpose operator. For complex arguments, this operator is | |
| 616 equivalent to the expression | |
| 617 | |
| 618 @example | |
| 619 conj (x.') | |
| 620 @end example | |
| 621 | |
| 622 @item @var{x}.' | |
| 623 @opindex .' | |
| 624 Transpose. | |
| 625 @end table | |
| 626 | |
| 627 Note that because Octave's element by element operators begin with a | |
| 628 @samp{.}, there is a possible ambiguity for statements like | |
| 629 | |
| 630 @example | |
| 631 1./m | |
| 632 @end example | |
| 633 | |
| 634 @noindent | |
| 635 because the period could be interpreted either as part of the constant | |
| 636 or as part of the operator. To resolve this conflict, Octave treats the | |
| 637 expression as if you had typed | |
| 638 | |
| 639 @example | |
| 640 (1) ./ m | |
| 641 @end example | |
| 642 | |
| 643 @noindent | |
| 644 and not | |
| 645 | |
| 646 @example | |
| 647 (1.) / m | |
| 648 @end example | |
| 649 | |
| 650 @noindent | |
| 651 Although this is inconsistent with the normal behavior of Octave's | |
| 652 lexer, which usually prefers to break the input into tokens by | |
| 653 preferring the longest possible match at any given point, it is more | |
| 654 useful in this case. | |
| 655 | |
|
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656 @opindex ' |
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657 @DOCSTRING(ctranspose) |
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658 |
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659 @opindex .\ |
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660 @DOCSTRING(ldivide) |
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661 |
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662 @opindex - |
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663 @DOCSTRING(minus) |
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664 |
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665 @opindex \ |
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666 @DOCSTRING(mldivide) |
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667 |
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668 @opindex ** |
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669 @opindex ^ |
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670 @DOCSTRING(mpower) |
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671 |
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672 @opindex / |
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673 @DOCSTRING(mrdivide) |
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674 |
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675 @opindex * |
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676 @DOCSTRING(mtimes) |
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677 |
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678 @opindex + |
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679 @DOCSTRING(plus) |
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680 |
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681 @opindex .** |
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682 @opindex .^ |
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683 @DOCSTRING(power) |
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684 |
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685 @opindex ./ |
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686 @DOCSTRING(rdivide) |
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687 |
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688 @opindex .* |
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689 @DOCSTRING(times) |
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690 |
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691 @opindex .' |
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692 @DOCSTRING(transpose) |
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693 |
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694 @opindex - |
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695 @DOCSTRING(uminus) |
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696 |
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697 @opindex + |
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698 @DOCSTRING(uplus) |
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699 |
| 4167 | 700 @node Comparison Ops |
| 3294 | 701 @section Comparison Operators |
| 702 @cindex comparison expressions | |
| 703 @cindex expressions, comparison | |
| 704 @cindex relational operators | |
| 705 @cindex operators, relational | |
| 706 @cindex less than operator | |
| 707 @cindex greater than operator | |
| 708 @cindex equality operator | |
| 709 @cindex tests for equality | |
| 710 @cindex equality, tests for | |
| 711 | |
| 712 @dfn{Comparison operators} compare numeric values for relationships | |
| 713 such as equality. They are written using | |
| 714 @emph{relational operators}. | |
| 715 | |
| 716 All of Octave's comparison operators return a value of 1 if the | |
| 717 comparison is true, or 0 if it is false. For matrix values, they all | |
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718 work on an element-by-element basis. For example: |
| 3294 | 719 |
| 720 @example | |
| 721 @group | |
| 722 [1, 2; 3, 4] == [1, 3; 2, 4] | |
| 723 @result{} 1 0 | |
| 724 0 1 | |
| 725 @end group | |
| 726 @end example | |
| 727 | |
| 728 If one operand is a scalar and the other is a matrix, the scalar is | |
| 729 compared to each element of the matrix in turn, and the result is the | |
| 730 same size as the matrix. | |
| 731 | |
| 732 @table @code | |
| 733 @item @var{x} < @var{y} | |
| 734 @opindex < | |
| 735 True if @var{x} is less than @var{y}. | |
| 736 | |
| 737 @item @var{x} <= @var{y} | |
| 738 @opindex <= | |
| 739 True if @var{x} is less than or equal to @var{y}. | |
| 740 | |
| 741 @item @var{x} == @var{y} | |
| 742 @opindex == | |
| 743 True if @var{x} is equal to @var{y}. | |
| 744 | |
| 745 @item @var{x} >= @var{y} | |
| 746 @opindex >= | |
| 747 True if @var{x} is greater than or equal to @var{y}. | |
| 748 | |
| 749 @item @var{x} > @var{y} | |
| 750 @opindex > | |
| 751 True if @var{x} is greater than @var{y}. | |
| 752 | |
| 753 @item @var{x} != @var{y} | |
| 754 @itemx @var{x} ~= @var{y} | |
| 755 @opindex != | |
| 756 @opindex ~= | |
| 757 True if @var{x} is not equal to @var{y}. | |
| 758 @end table | |
| 759 | |
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760 For complex numbers, the following ordering is defined: |
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761 @var{z1} < @var{z2} |
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762 iff |
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763 |
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764 @example |
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765 @group |
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766 abs(@var{z1}) < abs(@var{z2}) |
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767 || (abs(@var{z1}) == abs(@var{z2}) && arg(@var{z1}) < arg(@var{z2})) |
|
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768 @end group |
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769 @end example |
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770 |
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771 This is consistent with the ordering used by @dfn{max}, @dfn{min} and |
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772 @dfn{sort}, but is not consistent with @sc{matlab}, which only compares the real |
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|
773 parts. |
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774 |
| 3294 | 775 String comparisons may also be performed with the @code{strcmp} |
| 776 function, not with the comparison operators listed above. | |
| 777 @xref{Strings}. | |
| 778 | |
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779 @opindex == |
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780 @DOCSTRING(eq) |
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|
781 |
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782 @opindex >= |
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783 @DOCSTRING(ge) |
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|
784 |
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785 @opindex > |
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786 @DOCSTRING(gt) |
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|
787 |
| 6550 | 788 @DOCSTRING(isequal) |
| 789 | |
| 790 @DOCSTRING(isequalwithequalnans) | |
| 791 | |
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792 @opindex <= |
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793 @DOCSTRING(le) |
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|
794 |
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|
795 @opindex < |
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796 @DOCSTRING(lt) |
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|
797 |
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798 @opindex != |
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|
799 @opindex ~= |
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800 @DOCSTRING(ne) |
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|
801 |
| 4167 | 802 @node Boolean Expressions |
| 3294 | 803 @section Boolean Expressions |
| 804 @cindex expressions, boolean | |
| 805 @cindex boolean expressions | |
| 806 @cindex expressions, logical | |
| 807 @cindex logical expressions | |
| 808 @cindex operators, boolean | |
| 809 @cindex boolean operators | |
| 810 @cindex logical operators | |
| 811 @cindex operators, logical | |
| 812 @cindex and operator | |
| 813 @cindex or operator | |
| 814 @cindex not operator | |
| 815 | |
| 816 @menu | |
| 817 * Element-by-element Boolean Operators:: | |
| 818 * Short-circuit Boolean Operators:: | |
| 819 @end menu | |
| 820 | |
| 4167 | 821 @node Element-by-element Boolean Operators |
| 3294 | 822 @subsection Element-by-element Boolean Operators |
| 823 @cindex element-by-element evaluation | |
| 824 | |
| 825 An @dfn{element-by-element boolean expression} is a combination of | |
| 826 comparison expressions using the boolean | |
| 827 operators ``or'' (@samp{|}), ``and'' (@samp{&}), and ``not'' (@samp{!}), | |
| 828 along with parentheses to control nesting. The truth of the boolean | |
| 829 expression is computed by combining the truth values of the | |
| 830 corresponding elements of the component expressions. A value is | |
| 831 considered to be false if it is zero, and true otherwise. | |
| 832 | |
| 833 Element-by-element boolean expressions can be used wherever comparison | |
| 834 expressions can be used. They can be used in @code{if} and @code{while} | |
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835 statements. However, a matrix value used as the condition in an |
| 3294 | 836 @code{if} or @code{while} statement is only true if @emph{all} of its |
| 837 elements are nonzero. | |
| 838 | |
| 839 Like comparison operations, each element of an element-by-element | |
| 840 boolean expression also has a numeric value (1 if true, 0 if false) that | |
| 841 comes into play if the result of the boolean expression is stored in a | |
| 842 variable, or used in arithmetic. | |
| 843 | |
| 844 Here are descriptions of the three element-by-element boolean operators. | |
| 845 | |
| 846 @table @code | |
| 847 @item @var{boolean1} & @var{boolean2} | |
| 848 @opindex & | |
| 849 Elements of the result are true if both corresponding elements of | |
| 850 @var{boolean1} and @var{boolean2} are true. | |
| 851 | |
| 852 @item @var{boolean1} | @var{boolean2} | |
| 853 @opindex | | |
| 854 Elements of the result are true if either of the corresponding elements | |
| 855 of @var{boolean1} or @var{boolean2} is true. | |
| 856 | |
| 857 @item ! @var{boolean} | |
| 858 @itemx ~ @var{boolean} | |
| 859 @opindex ~ | |
| 860 @opindex ! | |
| 861 Each element of the result is true if the corresponding element of | |
| 862 @var{boolean} is false. | |
| 863 @end table | |
| 864 | |
| 865 For matrix operands, these operators work on an element-by-element | |
| 866 basis. For example, the expression | |
| 867 | |
| 868 @example | |
| 869 [1, 0; 0, 1] & [1, 0; 2, 3] | |
| 870 @end example | |
| 871 | |
| 872 @noindent | |
| 873 returns a two by two identity matrix. | |
| 874 | |
| 875 For the binary operators, the dimensions of the operands must conform if | |
| 876 both are matrices. If one of the operands is a scalar and the other a | |
| 877 matrix, the operator is applied to the scalar and each element of the | |
| 878 matrix. | |
| 879 | |
| 880 For the binary element-by-element boolean operators, both subexpressions | |
| 881 @var{boolean1} and @var{boolean2} are evaluated before computing the | |
| 882 result. This can make a difference when the expressions have side | |
| 883 effects. For example, in the expression | |
| 884 | |
| 885 @example | |
| 886 a & b++ | |
| 887 @end example | |
| 888 | |
| 889 @noindent | |
| 890 the value of the variable @var{b} is incremented even if the variable | |
| 891 @var{a} is zero. | |
| 892 | |
| 893 This behavior is necessary for the boolean operators to work as | |
| 894 described for matrix-valued operands. | |
| 895 | |
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896 @opindex & |
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897 @DOCSTRING(and) |
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898 |
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899 @opindex ~ |
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900 @opindex ! |
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901 @DOCSTRING(not) |
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902 |
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903 @opindex | |
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904 @DOCSTRING(or) |
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905 |
| 4167 | 906 @node Short-circuit Boolean Operators |
| 3294 | 907 @subsection Short-circuit Boolean Operators |
| 908 @cindex short-circuit evaluation | |
| 909 | |
| 910 Combined with the implicit conversion to scalar values in @code{if} and | |
| 911 @code{while} conditions, Octave's element-by-element boolean operators | |
| 912 are often sufficient for performing most logical operations. However, | |
| 913 it is sometimes desirable to stop evaluating a boolean expression as | |
| 914 soon as the overall truth value can be determined. Octave's | |
| 915 @dfn{short-circuit} boolean operators work this way. | |
| 916 | |
| 917 @table @code | |
| 918 @item @var{boolean1} && @var{boolean2} | |
| 919 @opindex && | |
| 920 The expression @var{boolean1} is evaluated and converted to a scalar | |
| 6632 | 921 using the equivalent of the operation @code{all (@var{boolean1}(:))}. |
| 3294 | 922 If it is false, the result of the overall expression is 0. If it is |
| 923 true, the expression @var{boolean2} is evaluated and converted to a | |
| 6632 | 924 scalar using the equivalent of the operation @code{all |
| 925 (@var{boolean1}(:))}. If it is true, the result of the overall expression | |
| 3294 | 926 is 1. Otherwise, the result of the overall expression is 0. |
| 927 | |
| 6632 | 928 @strong{Warning:} there is one exception to the rule of evaluating |
| 929 @code{all (@var{boolean1}(:))}, which is when @code{boolean1} is the | |
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930 empty matrix. The truth value of an empty matrix is always @code{false} |
| 6632 | 931 so @code{[] && true} evaluates to @code{false} even though |
| 932 @code{all ([])} is @code{true}. | |
| 933 | |
| 3294 | 934 @item @var{boolean1} || @var{boolean2} |
| 935 @opindex || | |
| 936 The expression @var{boolean1} is evaluated and converted to a scalar | |
| 6632 | 937 using the equivalent of the operation @code{all (@var{boolean1}(:))}. |
| 3294 | 938 If it is true, the result of the overall expression is 1. If it is |
| 939 false, the expression @var{boolean2} is evaluated and converted to a | |
| 6632 | 940 scalar using the equivalent of the operation @code{all |
| 941 (@var{boolean1}(:))}. If it is true, the result of the overall expression | |
| 3294 | 942 is 1. Otherwise, the result of the overall expression is 0. |
| 6632 | 943 |
| 944 @strong{Warning:} the truth value of an empty matrix is always @code{false}, | |
| 945 see the previous list item for details. | |
| 3294 | 946 @end table |
| 947 | |
| 948 The fact that both operands may not be evaluated before determining the | |
| 949 overall truth value of the expression can be important. For example, in | |
| 950 the expression | |
| 951 | |
| 952 @example | |
| 953 a && b++ | |
| 954 @end example | |
| 955 | |
| 956 @noindent | |
| 957 the value of the variable @var{b} is only incremented if the variable | |
| 958 @var{a} is nonzero. | |
| 959 | |
| 960 This can be used to write somewhat more concise code. For example, it | |
| 961 is possible write | |
| 962 | |
| 963 @example | |
| 964 @group | |
| 965 function f (a, b, c) | |
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966 if (nargin > 2 && ischar (c)) |
| 3294 | 967 @dots{} |
| 968 @end group | |
| 969 @end example | |
| 970 | |
| 971 @noindent | |
| 972 instead of having to use two @code{if} statements to avoid attempting to | |
| 973 evaluate an argument that doesn't exist. For example, without the | |
| 974 short-circuit feature, it would be necessary to write | |
| 975 | |
| 976 @example | |
| 977 @group | |
| 978 function f (a, b, c) | |
| 979 if (nargin > 2) | |
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980 if (ischar (c)) |
| 3294 | 981 @dots{} |
| 982 @end group | |
| 983 @end example | |
| 984 | |
| 6632 | 985 @noindent |
| 3294 | 986 Writing |
| 987 | |
| 988 @example | |
| 989 @group | |
| 990 function f (a, b, c) | |
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991 if (nargin > 2 & ischar (c)) |
| 3294 | 992 @dots{} |
| 993 @end group | |
| 994 @end example | |
| 995 | |
| 996 @noindent | |
| 997 would result in an error if @code{f} were called with one or two | |
| 998 arguments because Octave would be forced to try to evaluate both of the | |
| 999 operands for the operator @samp{&}. | |
| 1000 | |
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1001 @sc{matlab} has special behavior that allows the operators @samp{&} and |
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1002 @samp{|} to short-circuit when used in the truth expression for @code{if} and |
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1003 @code{while} statements. The Octave parser may be instructed to behave in the |
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1004 same manner, but its use is strongly discouraged. |
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1005 |
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1006 @DOCSTRING(do_braindead_shortcircuit_evaluation) |
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1007 |
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1008 Finally, the ternary operator (?:) is not supported in Octave. If |
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1009 short-circuiting is not important, it can be replaced by the @code{ifelse} |
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1010 function. |
| 10308 | 1011 |
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1012 @DOCSTRING(merge) |
| 10308 | 1013 |
| 4167 | 1014 @node Assignment Ops |
| 3294 | 1015 @section Assignment Expressions |
| 1016 @cindex assignment expressions | |
| 1017 @cindex assignment operators | |
| 1018 @cindex operators, assignment | |
| 1019 @cindex expressions, assignment | |
| 1020 | |
| 1021 @opindex = | |
| 1022 | |
| 1023 An @dfn{assignment} is an expression that stores a new value into a | |
| 1024 variable. For example, the following expression assigns the value 1 to | |
| 1025 the variable @code{z}: | |
| 1026 | |
| 1027 @example | |
| 1028 z = 1 | |
| 1029 @end example | |
| 1030 | |
| 6632 | 1031 @noindent |
| 3294 | 1032 After this expression is executed, the variable @code{z} has the value 1. |
| 1033 Whatever old value @code{z} had before the assignment is forgotten. | |
| 1034 The @samp{=} sign is called an @dfn{assignment operator}. | |
| 1035 | |
| 1036 Assignments can store string values also. For example, the following | |
| 1037 expression would store the value @code{"this food is good"} in the | |
| 1038 variable @code{message}: | |
| 1039 | |
| 1040 @example | |
| 1041 @group | |
| 1042 thing = "food" | |
| 1043 predicate = "good" | |
| 1044 message = [ "this " , thing , " is " , predicate ] | |
| 1045 @end group | |
| 1046 @end example | |
| 1047 | |
| 1048 @noindent | |
| 1049 (This also illustrates concatenation of strings.) | |
| 1050 | |
| 1051 @cindex side effect | |
| 1052 Most operators (addition, concatenation, and so on) have no effect | |
| 1053 except to compute a value. If you ignore the value, you might as well | |
| 1054 not use the operator. An assignment operator is different. It does | |
| 1055 produce a value, but even if you ignore the value, the assignment still | |
| 1056 makes itself felt through the alteration of the variable. We call this | |
| 1057 a @dfn{side effect}. | |
| 1058 | |
| 1059 @cindex lvalue | |
| 1060 The left-hand operand of an assignment need not be a variable | |
| 1061 (@pxref{Variables}). It can also be an element of a matrix | |
| 1062 (@pxref{Index Expressions}) or a list of return values | |
| 1063 (@pxref{Calling Functions}). These are all called @dfn{lvalues}, which | |
| 1064 means they can appear on the left-hand side of an assignment operator. | |
| 1065 The right-hand operand may be any expression. It produces the new value | |
| 1066 which the assignment stores in the specified variable, matrix element, | |
| 1067 or list of return values. | |
| 1068 | |
| 1069 It is important to note that variables do @emph{not} have permanent types. | |
| 1070 The type of a variable is simply the type of whatever value it happens | |
| 1071 to hold at the moment. In the following program fragment, the variable | |
| 1072 @code{foo} has a numeric value at first, and a string value later on: | |
| 1073 | |
| 1074 @example | |
| 1075 @group | |
| 1076 octave:13> foo = 1 | |
| 1077 foo = 1 | |
| 1078 octave:13> foo = "bar" | |
| 1079 foo = bar | |
| 1080 @end group | |
| 1081 @end example | |
| 1082 | |
| 1083 @noindent | |
| 1084 When the second assignment gives @code{foo} a string value, the fact that | |
| 1085 it previously had a numeric value is forgotten. | |
| 1086 | |
| 1087 Assignment of a scalar to an indexed matrix sets all of the elements | |
| 1088 that are referenced by the indices to the scalar value. For example, if | |
| 1089 @code{a} is a matrix with at least two columns, | |
| 1090 | |
| 1091 @example | |
| 1092 @group | |
| 1093 a(:, 2) = 5 | |
| 1094 @end group | |
| 1095 @end example | |
| 1096 | |
| 1097 @noindent | |
| 1098 sets all the elements in the second column of @code{a} to 5. | |
| 1099 | |
| 1100 Assigning an empty matrix @samp{[]} works in most cases to allow you to | |
| 1101 delete rows or columns of matrices and vectors. @xref{Empty Matrices}. | |
| 1102 For example, given a 4 by 5 matrix @var{A}, the assignment | |
| 1103 | |
| 1104 @example | |
| 1105 A (3, :) = [] | |
| 1106 @end example | |
| 1107 | |
| 1108 @noindent | |
| 1109 deletes the third row of @var{A}, and the assignment | |
| 1110 | |
| 1111 @example | |
| 1112 A (:, 1:2:5) = [] | |
| 1113 @end example | |
| 1114 | |
| 1115 @noindent | |
| 6672 | 1116 deletes the first, third, and fifth columns. |
| 3294 | 1117 |
| 1118 An assignment is an expression, so it has a value. Thus, @code{z = 1} | |
| 1119 as an expression has the value 1. One consequence of this is that you | |
| 1120 can write multiple assignments together: | |
| 1121 | |
| 1122 @example | |
| 1123 x = y = z = 0 | |
| 1124 @end example | |
| 1125 | |
| 1126 @noindent | |
| 1127 stores the value 0 in all three variables. It does this because the | |
| 1128 value of @code{z = 0}, which is 0, is stored into @code{y}, and then | |
| 1129 the value of @code{y = z = 0}, which is 0, is stored into @code{x}. | |
| 1130 | |
| 1131 This is also true of assignments to lists of values, so the following is | |
| 1132 a valid expression | |
| 1133 | |
| 1134 @example | |
| 1135 [a, b, c] = [u, s, v] = svd (a) | |
| 1136 @end example | |
| 1137 | |
| 1138 @noindent | |
| 1139 that is exactly equivalent to | |
| 1140 | |
| 1141 @example | |
| 1142 @group | |
| 1143 [u, s, v] = svd (a) | |
| 1144 a = u | |
| 1145 b = s | |
| 1146 c = v | |
| 1147 @end group | |
| 1148 @end example | |
| 1149 | |
| 1150 In expressions like this, the number of values in each part of the | |
| 1151 expression need not match. For example, the expression | |
| 1152 | |
| 1153 @example | |
| 1154 [a, b] = [u, s, v] = svd (a) | |
| 1155 @end example | |
| 1156 | |
| 1157 @noindent | |
| 1158 is equivalent to | |
| 1159 | |
| 1160 @example | |
| 1161 @group | |
| 1162 [u, s, v] = svd (a) | |
| 1163 a = u | |
| 1164 b = s | |
| 1165 @end group | |
| 1166 @end example | |
| 1167 | |
| 6632 | 1168 @noindent |
| 1169 The number of values on the left side of the expression can, however, | |
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1170 not exceed the number of values on the right side. For example, the |
| 6632 | 1171 following will produce an error. |
| 1172 | |
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1173 @example |
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1174 @group |
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1175 [a, b, c, d] = [u, s, v] = svd (a); |
| 7031 | 1176 @print{} error: element number 4 undefined in return list |
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1177 @end group |
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1178 @end example |
| 6632 | 1179 |
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1180 The symbol @code{~} may be used as a placeholder in the list of lvalues, |
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1181 indicating that the corresponding return value should be ignored and not stored |
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1182 anywhere: |
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1183 |
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1184 @example |
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1185 @group |
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1186 [~, s, v] = svd (a); |
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1187 @end group |
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1188 @end example |
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1189 |
| 10228 | 1190 This is cleaner and more memory efficient than using a dummy variable. |
| 1191 The @code{nargout} value for the right-hand side expression is not affected. | |
|
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1192 If the assignment is used as an expression, the return value is a |
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1193 comma-separated list with the ignored values dropped. |
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1194 |
| 6642 | 1195 @opindex += |
| 1196 A very common programming pattern is to increment an existing variable | |
| 1197 with a given value, like this | |
| 1198 | |
| 1199 @example | |
| 1200 a = a + 2; | |
| 1201 @end example | |
| 1202 | |
| 1203 @noindent | |
| 1204 This can be written in a clearer and more condensed form using the | |
| 1205 @code{+=} operator | |
| 1206 | |
| 1207 @example | |
| 1208 a += 2; | |
| 1209 @end example | |
| 1210 | |
| 1211 @noindent | |
| 1212 @opindex -= | |
| 1213 @opindex *= | |
| 1214 @opindex /= | |
| 1215 Similar operators also exist for subtraction (@code{-=}), | |
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1216 multiplication (@code{*=}), and division (@code{/=}). An expression |
| 6642 | 1217 of the form |
| 1218 | |
| 1219 @example | |
| 1220 @var{expr1} @var{op}= @var{expr2} | |
| 1221 @end example | |
| 1222 | |
| 1223 @noindent | |
| 1224 is evaluated as | |
| 1225 | |
| 1226 @example | |
| 1227 @var{expr1} = (@var{expr1}) @var{op} (@var{expr2}) | |
| 1228 @end example | |
| 1229 | |
| 1230 @noindent | |
| 1231 where @var{op} can be either @code{+}, @code{-}, @code{*}, or @code{/}. | |
| 1232 So, the expression | |
| 1233 | |
| 1234 @example | |
| 1235 a *= b+1 | |
| 1236 @end example | |
| 1237 | |
| 1238 @noindent | |
| 1239 is evaluated as | |
| 1240 | |
| 1241 @example | |
| 1242 a = a * (b+1) | |
| 1243 @end example | |
| 1244 | |
| 1245 @noindent | |
| 1246 and @emph{not} | |
| 1247 | |
| 1248 @example | |
| 1249 a = a * b + 1 | |
| 1250 @end example | |
| 1251 | |
| 3294 | 1252 You can use an assignment anywhere an expression is called for. For |
| 1253 example, it is valid to write @code{x != (y = 1)} to set @code{y} to 1 | |
| 1254 and then test whether @code{x} equals 1. But this style tends to make | |
| 1255 programs hard to read. Except in a one-shot program, you should rewrite | |
| 1256 it to get rid of such nesting of assignments. This is never very hard. | |
| 1257 | |
| 1258 @cindex increment operator | |
| 1259 @cindex decrement operator | |
| 1260 @cindex operators, increment | |
| 1261 @cindex operators, decrement | |
| 1262 | |
| 4167 | 1263 @node Increment Ops |
| 3294 | 1264 @section Increment Operators |
| 1265 | |
| 1266 @emph{Increment operators} increase or decrease the value of a variable | |
| 1267 by 1. The operator to increment a variable is written as @samp{++}. It | |
| 1268 may be used to increment a variable either before or after taking its | |
| 1269 value. | |
| 1270 | |
| 1271 For example, to pre-increment the variable @var{x}, you would write | |
| 1272 @code{++@var{x}}. This would add one to @var{x} and then return the new | |
| 1273 value of @var{x} as the result of the expression. It is exactly the | |
| 1274 same as the expression @code{@var{x} = @var{x} + 1}. | |
| 1275 | |
| 1276 To post-increment a variable @var{x}, you would write @code{@var{x}++}. | |
| 1277 This adds one to the variable @var{x}, but returns the value that | |
| 1278 @var{x} had prior to incrementing it. For example, if @var{x} is equal | |
| 1279 to 2, the result of the expression @code{@var{x}++} is 2, and the new | |
| 1280 value of @var{x} is 3. | |
| 1281 | |
| 1282 For matrix and vector arguments, the increment and decrement operators | |
| 1283 work on each element of the operand. | |
| 1284 | |
| 1285 Here is a list of all the increment and decrement expressions. | |
| 1286 | |
| 1287 @table @code | |
| 1288 @item ++@var{x} | |
| 1289 @opindex ++ | |
| 1290 This expression increments the variable @var{x}. The value of the | |
| 1291 expression is the @emph{new} value of @var{x}. It is equivalent to the | |
| 1292 expression @code{@var{x} = @var{x} + 1}. | |
| 1293 | |
| 1294 @item --@var{x} | |
| 1295 @opindex @code{--} | |
| 1296 This expression decrements the variable @var{x}. The value of the | |
| 1297 expression is the @emph{new} value of @var{x}. It is equivalent to the | |
| 1298 expression @code{@var{x} = @var{x} - 1}. | |
| 1299 | |
| 1300 @item @var{x}++ | |
| 1301 @opindex ++ | |
| 1302 This expression causes the variable @var{x} to be incremented. The | |
| 1303 value of the expression is the @emph{old} value of @var{x}. | |
| 1304 | |
| 1305 @item @var{x}-- | |
| 1306 @opindex @code{--} | |
| 1307 This expression causes the variable @var{x} to be decremented. The | |
| 1308 value of the expression is the @emph{old} value of @var{x}. | |
| 1309 @end table | |
| 1310 | |
| 4167 | 1311 @node Operator Precedence |
| 3294 | 1312 @section Operator Precedence |
| 1313 @cindex operator precedence | |
| 1314 | |
| 1315 @dfn{Operator precedence} determines how operators are grouped, when | |
| 1316 different operators appear close by in one expression. For example, | |
| 1317 @samp{*} has higher precedence than @samp{+}. Thus, the expression | |
| 1318 @code{a + b * c} means to multiply @code{b} and @code{c}, and then add | |
| 1319 @code{a} to the product (i.e., @code{a + (b * c)}). | |
| 1320 | |
| 1321 You can overrule the precedence of the operators by using parentheses. | |
| 1322 You can think of the precedence rules as saying where the parentheses | |
| 1323 are assumed if you do not write parentheses yourself. In fact, it is | |
| 1324 wise to use parentheses whenever you have an unusual combination of | |
| 1325 operators, because other people who read the program may not remember | |
| 1326 what the precedence is in this case. You might forget as well, and then | |
| 1327 you too could make a mistake. Explicit parentheses will help prevent | |
| 1328 any such mistake. | |
| 1329 | |
| 1330 When operators of equal precedence are used together, the leftmost | |
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1331 operator groups first, except for the assignment operators, which group |
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1332 in the opposite order. Thus, the expression @code{a - b + c} groups as |
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1333 @code{(a - b) + c}, but the expression @code{a = b = c} groups as |
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1334 @code{a = (b = c)}. |
| 3294 | 1335 |
| 1336 The precedence of prefix unary operators is important when another | |
| 1337 operator follows the operand. For example, @code{-x^2} means | |
| 1338 @code{-(x^2)}, because @samp{-} has lower precedence than @samp{^}. | |
| 1339 | |
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1340 Here is a table of the operators in Octave, in order of decreasing |
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1341 precedence. Unless noted, all operators group left to right. |
| 3294 | 1342 |
| 1343 @table @code | |
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1344 @item function call and array indexing, cell array indexing, and structure element indexing |
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1345 @samp{()} @samp{@{@}} @samp{.} |
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1346 |
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1347 @item postfix increment, and postfix decrement |
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1348 @samp{++} @samp{--} |
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1349 |
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1350 These operators group right to left. |
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1351 |
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1352 @item transpose and exponentiation |
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1353 @samp{'} @samp{.'} @samp{^} @samp{**} @samp{.^} @samp{.**} |
| 3294 | 1354 |
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1355 @item unary plus, unary minus, prefix increment, prefix decrement, and logical "not" |
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1356 @samp{+} @samp{-} @samp{++} @samp{--} @samp{~} @samp{!} |
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1357 |
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1358 @item multiply and divide |
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1359 @samp{*} @samp{/} @samp{\} @samp{.\} @samp{.*} @samp{./} |
| 3294 | 1360 |
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1361 @item add, subtract |
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1362 @samp{+} @samp{-} |
| 3294 | 1363 |
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1364 @item colon |
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1365 @samp{:} |
| 3294 | 1366 |
| 1367 @item relational | |
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1368 @samp{<} @samp{<=} @samp{==} @samp{>=} @samp{>} @samp{!=} |
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1369 @samp{~=} |
| 3294 | 1370 |
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1371 @item element-wise "and" |
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1372 @samp{&} |
| 3294 | 1373 |
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1374 @item element-wise "or" |
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1375 @samp{|} |
| 3294 | 1376 |
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1377 @item logical "and" |
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1378 @samp{&&} |
| 3294 | 1379 |
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1380 @item logical "or" |
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1381 @samp{||} |
| 3294 | 1382 |
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1383 @item assignment |
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1384 @samp{=} @samp{+=} @samp{-=} @samp{*=} @samp{/=} @samp{\=} |
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1385 @samp{^=} @samp{.*=} @samp{./=} @samp{.\=} @samp{.^=} @samp{|=} |
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1386 @samp{&=} |
| 3294 | 1387 |
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1388 These operators group right to left. |
| 3294 | 1389 @end table |