Mercurial > octave
annotate doc/interpreter/numbers.txi @ 8015:30629059b72d
Update the manual to reflect the changes in error output
| author | sh@sh-laptop |
|---|---|
| date | Wed, 06 Aug 2008 22:23:54 +0200 |
| parents | 23c248d415b5 |
| children | cd90e2842080 |
| rev | line source |
|---|---|
| 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 Numeric Data Types |
| 3294 | 20 @chapter Numeric Data Types |
| 21 @cindex numeric constant | |
| 22 @cindex numeric value | |
| 23 | |
| 24 A @dfn{numeric constant} may be a scalar, a vector, or a matrix, and it | |
| 25 may contain complex values. | |
| 26 | |
| 27 The simplest form of a numeric constant, a scalar, is a single number | |
| 28 that can be an integer, a decimal fraction, a number in scientific | |
| 6620 | 29 (exponential) notation, or a complex number. Note that by default numeric |
| 3294 | 30 constants are represented within Octave in double-precision floating |
| 31 point format (complex constants are stored as pairs of double-precision | |
| 6620 | 32 floating point values). It is however possible to represent real |
| 33 integers as described in @ref{Integer Data Types}. Here are some examples | |
| 34 of real-valued numeric constants, which all have the same value: | |
| 3294 | 35 |
| 36 @example | |
| 37 @group | |
| 38 105 | |
| 39 1.05e+2 | |
| 40 1050e-1 | |
| 41 @end group | |
| 42 @end example | |
| 43 | |
| 44 To specify complex constants, you can write an expression of the form | |
| 45 | |
| 46 @example | |
| 47 @group | |
| 48 3 + 4i | |
| 49 3.0 + 4.0i | |
| 50 0.3e1 + 40e-1i | |
| 51 @end group | |
| 52 @end example | |
| 53 | |
| 6620 | 54 @noindent |
| 3294 | 55 all of which are equivalent. The letter @samp{i} in the previous example |
| 56 stands for the pure imaginary constant, defined as | |
| 57 @iftex | |
| 58 @tex | |
| 59 $\sqrt{-1}$. | |
| 60 @end tex | |
| 61 @end iftex | |
| 6620 | 62 @ifnottex |
| 3294 | 63 @code{sqrt (-1)}. |
| 6620 | 64 @end ifnottex |
| 3294 | 65 |
| 66 For Octave to recognize a value as the imaginary part of a complex | |
| 67 constant, a space must not appear between the number and the @samp{i}. | |
| 68 If it does, Octave will print an error message, like this: | |
| 69 | |
| 70 @example | |
| 71 @group | |
| 72 octave:13> 3 + 4 i | |
| 73 | |
| 74 parse error: | |
| 75 | |
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76 syntax error |
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77 |
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78 >>> 3 + 4 i |
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79 ^ |
| 3294 | 80 @end group |
| 81 @end example | |
| 82 | |
| 6620 | 83 @noindent |
| 3294 | 84 You may also use @samp{j}, @samp{I}, or @samp{J} in place of the |
| 85 @samp{i} above. All four forms are equivalent. | |
| 86 | |
| 6549 | 87 @DOCSTRING(double) |
| 88 | |
| 89 @DOCSTRING(complex) | |
| 90 | |
| 3294 | 91 @menu |
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92 * Matrices:: |
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93 * Ranges:: |
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94 * Single Precision Data Types:: |
| 6549 | 95 * Integer Data Types:: |
| 6781 | 96 * Bit Manipulations:: |
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97 * Logical Values:: |
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98 * Promotion and Demotion of Data Types:: |
| 3294 | 99 * Predicates for Numeric Objects:: |
| 100 @end menu | |
| 101 | |
| 4167 | 102 @node Matrices |
| 3294 | 103 @section Matrices |
| 104 @cindex matrices | |
| 105 | |
| 106 @opindex [ | |
| 107 @opindex ] | |
| 108 @opindex ; | |
| 109 @opindex , | |
| 110 | |
| 111 It is easy to define a matrix of values in Octave. The size of the | |
| 112 matrix is determined automatically, so it is not necessary to explicitly | |
| 113 state the dimensions. The expression | |
| 114 | |
| 115 @example | |
| 116 a = [1, 2; 3, 4] | |
| 117 @end example | |
| 118 | |
| 119 @noindent | |
| 120 results in the matrix | |
| 121 @iftex | |
| 122 @tex | |
| 123 $$ a = \left[ \matrix{ 1 & 2 \cr 3 & 4 } \right] $$ | |
| 124 @end tex | |
| 125 @end iftex | |
| 6620 | 126 @ifnottex |
| 3294 | 127 |
| 128 @example | |
| 129 @group | |
| 130 | |
| 131 / \ | |
| 132 | 1 2 | | |
| 133 a = | | | |
| 134 | 3 4 | | |
| 135 \ / | |
| 136 | |
| 137 @end group | |
| 138 @end example | |
| 6620 | 139 @end ifnottex |
| 3294 | 140 |
| 141 Elements of a matrix may be arbitrary expressions, provided that the | |
| 142 dimensions all make sense when combining the various pieces. For | |
| 143 example, given the above matrix, the expression | |
| 144 | |
| 145 @example | |
| 146 [ a, a ] | |
| 147 @end example | |
| 148 | |
| 149 @noindent | |
| 150 produces the matrix | |
| 151 | |
| 152 @example | |
| 153 @group | |
| 154 ans = | |
| 155 | |
| 156 1 2 1 2 | |
| 157 3 4 3 4 | |
| 158 @end group | |
| 159 @end example | |
| 160 | |
| 161 @noindent | |
| 162 but the expression | |
| 163 | |
| 164 @example | |
| 165 [ a, 1 ] | |
| 166 @end example | |
| 167 | |
| 168 @noindent | |
| 169 produces the error | |
| 170 | |
| 171 @example | |
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172 error: number of rows must match (1 != 2) near line 13, column 6 |
| 3294 | 173 @end example |
| 174 | |
| 175 @noindent | |
| 176 (assuming that this expression was entered as the first thing on line | |
| 177 13, of course). | |
| 178 | |
| 179 Inside the square brackets that delimit a matrix expression, Octave | |
| 180 looks at the surrounding context to determine whether spaces and newline | |
| 181 characters should be converted into element and row separators, or | |
| 4476 | 182 simply ignored, so an expression like |
| 3294 | 183 |
| 184 @example | |
| 185 @group | |
| 186 a = [ 1 2 | |
| 187 3 4 ] | |
| 188 @end group | |
| 189 @end example | |
| 190 | |
| 191 @noindent | |
| 192 will work. However, some possible sources of confusion remain. For | |
| 193 example, in the expression | |
| 194 | |
| 195 @example | |
| 196 [ 1 - 1 ] | |
| 197 @end example | |
| 198 | |
| 199 @noindent | |
| 200 the @samp{-} is treated as a binary operator and the result is the | |
| 201 scalar 0, but in the expression | |
| 202 | |
| 203 @example | |
| 204 [ 1 -1 ] | |
| 205 @end example | |
| 206 | |
| 207 @noindent | |
| 208 the @samp{-} is treated as a unary operator and the result is the | |
| 4476 | 209 vector @code{[ 1, -1 ]}. Similarly, the expression |
| 210 | |
| 211 @example | |
| 212 [ sin (pi) ] | |
| 213 @end example | |
| 214 | |
| 215 @noindent | |
| 216 will be parsed as | |
| 217 | |
| 218 @example | |
| 219 [ sin, (pi) ] | |
| 220 @end example | |
| 3294 | 221 |
| 4476 | 222 @noindent |
| 223 and will result in an error since the @code{sin} function will be | |
| 224 called with no arguments. To get around this, you must omit the space | |
| 225 between @code{sin} and the opening parenthesis, or enclose the | |
| 226 expression in a set of parentheses: | |
| 227 | |
| 228 @example | |
| 229 [ (sin (pi)) ] | |
| 230 @end example | |
| 231 | |
| 232 Whitespace surrounding the single quote character (@samp{'}, used as a | |
| 233 transpose operator and for delimiting character strings) can also cause | |
| 234 confusion. Given @code{a = 1}, the expression | |
| 3294 | 235 |
| 236 @example | |
| 237 [ 1 a' ] | |
| 238 @end example | |
| 239 | |
| 240 @noindent | |
| 4476 | 241 results in the single quote character being treated as a |
| 3294 | 242 transpose operator and the result is the vector @code{[ 1, 1 ]}, but the |
| 243 expression | |
| 244 | |
| 245 @example | |
| 246 [ 1 a ' ] | |
| 247 @end example | |
| 248 | |
| 249 @noindent | |
| 250 produces the error message | |
| 251 | |
| 252 @example | |
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253 parse error: |
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254 |
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255 syntax error |
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256 |
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257 >>> [ 1 a ' ] |
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258 ^ |
| 3294 | 259 @end example |
| 260 | |
| 261 @noindent | |
| 6620 | 262 because not doing so would cause trouble when parsing the valid expression |
| 3294 | 263 |
| 264 @example | |
| 265 [ a 'foo' ] | |
| 266 @end example | |
| 267 | |
| 268 For clarity, it is probably best to always use commas and semicolons to | |
| 4476 | 269 separate matrix elements and rows. |
| 3294 | 270 |
| 271 When you type a matrix or the name of a variable whose value is a | |
| 272 matrix, Octave responds by printing the matrix in with neatly aligned | |
| 273 rows and columns. If the rows of the matrix are too large to fit on the | |
| 274 screen, Octave splits the matrix and displays a header before each | |
| 275 section to indicate which columns are being displayed. You can use the | |
| 276 following variables to control the format of the output. | |
| 277 | |
| 3321 | 278 @DOCSTRING(output_max_field_width) |
| 3294 | 279 |
| 3321 | 280 @DOCSTRING(output_precision) |
| 3294 | 281 |
| 282 It is possible to achieve a wide range of output styles by using | |
| 283 different values of @code{output_precision} and | |
| 284 @code{output_max_field_width}. Reasonable combinations can be set using | |
| 285 the @code{format} function. @xref{Basic Input and Output}. | |
| 286 | |
| 3321 | 287 @DOCSTRING(split_long_rows) |
| 3294 | 288 |
| 289 Octave automatically switches to scientific notation when values become | |
| 290 very large or very small. This guarantees that you will see several | |
| 291 significant figures for every value in a matrix. If you would prefer to | |
| 292 see all values in a matrix printed in a fixed point format, you can set | |
| 293 the built-in variable @code{fixed_point_format} to a nonzero value. But | |
| 294 doing so is not recommended, because it can produce output that can | |
| 295 easily be misinterpreted. | |
| 296 | |
| 3321 | 297 @DOCSTRING(fixed_point_format) |
| 3294 | 298 |
| 299 @menu | |
| 300 * Empty Matrices:: | |
| 301 @end menu | |
| 302 | |
| 4167 | 303 @node Empty Matrices |
| 3294 | 304 @subsection Empty Matrices |
| 305 | |
| 306 A matrix may have one or both dimensions zero, and operations on empty | |
| 307 matrices are handled as described by Carl de Boor in @cite{An Empty | |
| 308 Exercise}, SIGNUM, Volume 25, pages 2--6, 1990 and C. N. Nett and W. M. | |
| 309 Haddad, in @cite{A System-Theoretic Appropriate Realization of the Empty | |
| 310 Matrix Concept}, IEEE Transactions on Automatic Control, Volume 38, | |
| 311 Number 5, May 1993. | |
| 312 @iftex | |
| 313 @tex | |
| 314 Briefly, given a scalar $s$, an $m\times n$ matrix $M_{m\times n}$, | |
| 315 and an $m\times n$ empty matrix $[\,]_{m\times n}$ (with either one or | |
| 316 both dimensions equal to zero), the following are true: | |
| 317 $$ | |
| 318 \eqalign{% | |
| 319 s \cdot [\,]_{m\times n} = [\,]_{m\times n} \cdot s &= [\,]_{m\times n}\cr | |
| 320 [\,]_{m\times n} + [\,]_{m\times n} &= [\,]_{m\times n}\cr | |
| 321 [\,]_{0\times m} \cdot M_{m\times n} &= [\,]_{0\times n}\cr | |
| 322 M_{m\times n} \cdot [\,]_{n\times 0} &= [\,]_{m\times 0}\cr | |
| 323 [\,]_{m\times 0} \cdot [\,]_{0\times n} &= 0_{m\times n}} | |
| 324 $$ | |
| 325 @end tex | |
| 326 @end iftex | |
| 6620 | 327 @ifnottex |
| 3294 | 328 Briefly, given a scalar @var{s}, an @var{m} by |
| 329 @var{n} matrix @code{M(mxn)}, and an @var{m} by @var{n} empty matrix | |
| 330 @code{[](mxn)} (with either one or both dimensions equal to zero), the | |
| 331 following are true: | |
| 332 | |
| 333 @example | |
| 334 @group | |
| 335 s * [](mxn) = [](mxn) * s = [](mxn) | |
| 336 | |
| 337 [](mxn) + [](mxn) = [](mxn) | |
| 338 | |
| 339 [](0xm) * M(mxn) = [](0xn) | |
| 340 | |
| 341 M(mxn) * [](nx0) = [](mx0) | |
| 342 | |
| 343 [](mx0) * [](0xn) = 0(mxn) | |
| 344 @end group | |
| 345 @end example | |
| 6620 | 346 @end ifnottex |
| 3294 | 347 |
| 348 By default, dimensions of the empty matrix are printed along with the | |
| 349 empty matrix symbol, @samp{[]}. The built-in variable | |
| 350 @code{print_empty_dimensions} controls this behavior. | |
| 351 | |
| 3321 | 352 @DOCSTRING(print_empty_dimensions) |
| 3294 | 353 |
| 354 Empty matrices may also be used in assignment statements as a convenient | |
| 355 way to delete rows or columns of matrices. | |
| 356 @xref{Assignment Ops, ,Assignment Expressions}. | |
| 357 | |
| 358 When Octave parses a matrix expression, it examines the elements of the | |
| 359 list to determine whether they are all constants. If they are, it | |
| 360 replaces the list with a single matrix constant. | |
| 361 | |
| 4167 | 362 @node Ranges |
| 3294 | 363 @section Ranges |
| 364 @cindex range expressions | |
| 365 @cindex expression, range | |
| 366 | |
| 3920 | 367 @opindex colon |
| 3294 | 368 |
| 369 A @dfn{range} is a convenient way to write a row vector with evenly | |
| 370 spaced elements. A range expression is defined by the value of the first | |
| 371 element in the range, an optional value for the increment between | |
| 372 elements, and a maximum value which the elements of the range will not | |
| 373 exceed. The base, increment, and limit are separated by colons (the | |
| 374 @samp{:} character) and may contain any arithmetic expressions and | |
| 375 function calls. If the increment is omitted, it is assumed to be 1. | |
| 376 For example, the range | |
| 377 | |
| 378 @example | |
| 379 1 : 5 | |
| 380 @end example | |
| 381 | |
| 382 @noindent | |
| 383 defines the set of values @samp{[ 1, 2, 3, 4, 5 ]}, and the range | |
| 384 | |
| 385 @example | |
| 386 1 : 3 : 5 | |
| 387 @end example | |
| 388 | |
| 389 @noindent | |
| 390 defines the set of values @samp{[ 1, 4 ]}. | |
| 391 | |
| 392 Although a range constant specifies a row vector, Octave does @emph{not} | |
| 393 convert range constants to vectors unless it is necessary to do so. | |
| 394 This allows you to write a constant like @samp{1 : 10000} without using | |
| 395 80,000 bytes of storage on a typical 32-bit workstation. | |
| 396 | |
| 397 Note that the upper (or lower, if the increment is negative) bound on | |
| 398 the range is not always included in the set of values, and that ranges | |
| 399 defined by floating point values can produce surprising results because | |
| 400 Octave uses floating point arithmetic to compute the values in the | |
| 401 range. If it is important to include the endpoints of a range and the | |
| 402 number of elements is known, you should use the @code{linspace} function | |
| 403 instead (@pxref{Special Utility Matrices}). | |
| 404 | |
| 405 When Octave parses a range expression, it examines the elements of the | |
| 406 expression to determine whether they are all constants. If they are, it | |
| 407 replaces the range expression with a single range constant. | |
| 408 | |
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409 @node Single Precision Data Types |
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410 @section Single Precision Data Types |
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411 |
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412 Octave includes support for single precision data types, and most of the |
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413 functions in Octave accept single precision values and return single |
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414 precion answers. A single precision variable is created with the |
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415 @code{sample} function. |
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416 |
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417 @DOCSTRING(single) |
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418 |
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419 for example |
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420 |
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421 @example |
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422 sngl = single (rand (2, 2)) |
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423 @result{} sngl = 0.37569 0.92982 |
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424 0.11962 0.50876 |
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425 class (sngl) |
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426 @result{} single |
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427 @end example |
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428 |
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429 Many functions can also return single precision values directly. For |
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430 example |
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431 |
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432 @example |
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433 ones (2, 2, "single") |
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434 zeros (2, 2, "single") |
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435 eye (2, 2, "single") |
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436 rand (2, 2, "single") |
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437 NaN (2, 2, "single") |
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438 NA (2, 2, "single") |
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439 Inf (2, 2, "single") |
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440 @end example |
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441 |
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442 @noindent |
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443 will all return single precision matrices. |
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444 |
| 6549 | 445 @node Integer Data Types |
| 446 @section Integer Data Types | |
| 447 | |
| 6620 | 448 Octave supports integer matrices as an alternative to using double |
| 449 precision. It is possible to use both signed and unsigned integers | |
| 450 represented by 8, 16, 32, or 64 bits. It should be noted that most | |
| 451 computations require floating point data, meaning that integers will | |
| 452 often change type when involved in numeric computations. For this | |
| 453 reason integers are most often used to store data, and not for | |
| 454 calculations. | |
| 455 | |
| 456 In general most integer matrices are created by casting | |
| 457 existing matrices to integers. The following example shows how to cast | |
| 458 a matrix into 32 bit integers. | |
| 459 | |
| 460 @example | |
| 461 float = rand (2, 2) | |
| 462 @result{} float = 0.37569 0.92982 | |
| 463 0.11962 0.50876 | |
| 464 integer = int32 (float) | |
| 465 @result{} integer = 0 1 | |
| 466 0 1 | |
| 467 @end example | |
| 468 | |
| 469 @noindent | |
| 470 As can be seen, floating point values are rounded to the nearest integer | |
| 471 when converted. | |
| 472 | |
| 6549 | 473 @DOCSTRING(isinteger) |
| 474 | |
| 475 @DOCSTRING(int8) | |
| 476 | |
| 477 @DOCSTRING(uint8) | |
| 478 | |
| 479 @DOCSTRING(int16) | |
| 480 | |
| 481 @DOCSTRING(uint16) | |
| 482 | |
| 483 @DOCSTRING(int32) | |
| 484 | |
| 485 @DOCSTRING(uint32) | |
| 486 | |
| 487 @DOCSTRING(int64) | |
| 488 | |
| 489 @DOCSTRING(uint64) | |
| 490 | |
| 491 @DOCSTRING(intmax) | |
| 492 | |
| 493 @DOCSTRING(intmin) | |
| 494 | |
| 6624 | 495 @menu |
| 496 * Integer Arithmetic:: | |
| 497 @end menu | |
| 498 | |
| 6620 | 499 @node Integer Arithmetic |
| 500 @subsection Integer Arithmetic | |
| 501 | |
| 502 While many numerical computations can't be carried out in integers, | |
| 503 Octave does support basic operations like addition and multiplication | |
| 504 on integers. The operators @code{+}, @code{-}, @code{.*}, and @code{./} | |
| 505 works on integers of the same type. So, it is possible to add two 32 bit | |
| 506 integers, but not to add a 32 bit integer and a 16 bit integer. | |
| 507 | |
| 6715 | 508 The arithmetic operations on integers are performed by casting the |
| 509 integer values to double precision values, performing the operation, and | |
| 510 then re-casting the values back to the original integer type. As the | |
| 511 double precision type of Octave is only capable of representing integers | |
| 512 with up to 53 bits of precision, it is not possible to perform | |
| 513 arithmetic of the 64 bit integer types. | |
| 514 | |
| 6620 | 515 When doing integer arithmetic one should consider the possibility of |
| 516 underflow and overflow. This happens when the result of the computation | |
| 517 can't be represented using the chosen integer type. As an example it is | |
| 518 not possible to represent the result of @math{10 - 20} when using | |
| 519 unsigned integers. Octave makes sure that the result of integer | |
| 520 computations is the integer that is closest to the true result. So, the | |
| 521 result of @math{10 - 20} when using unsigned integers is zero. | |
| 522 | |
| 523 When doing integer division Octave will round the result to the nearest | |
| 524 integer. This is different from most programming languages, where the | |
| 525 result is often floored to the nearest integer. So, the result of | |
| 526 @code{int32(5)./int32(8)} is @code{1}. | |
| 527 | |
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528 @DOCSTRING(idivide) |
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529 |
| 6781 | 530 @node Bit Manipulations |
| 531 @section Bit Manipulations | |
| 532 | |
| 533 Octave provides a number of functions for the manipulation of numeric | |
| 534 values on a bit by bit basis. The basic functions to set and obtain the | |
| 535 values of individual bits are @code{bitset} and @code{bitget}. | |
| 536 | |
| 537 @DOCSTRING(bitset) | |
| 538 | |
| 539 @DOCSTRING(bitget) | |
| 540 | |
| 541 The arguments to all of Octave's bitwise operations can be scalar or | |
| 542 arrays, except for @code{bitcmp}, whose @var{k} argument must a | |
| 543 scalar. In the case where more than one argument is an array, then all | |
| 544 arguments must have the same shape, and the bitwise operator is applied | |
| 545 to each of the elements of the argument individually. If at least one | |
| 546 argument is a scalar and one an array, then the scalar argument is | |
| 547 duplicated. Therefore | |
| 548 | |
| 549 @example | |
| 550 bitget (100, 8:-1:1) | |
| 551 @end example | |
| 552 | |
| 553 is the same as | |
| 554 | |
| 555 @example | |
| 556 bitget (100 * ones (1, 8), 8:-1:1) | |
| 557 @end example | |
| 558 | |
| 559 It should be noted that all values passed to the bit manipulation | |
| 560 functions of Octave are treated as integers. Therefore, even though the | |
| 561 example for @code{bitset} above passes the floating point value | |
| 562 @code{10}, it is treated as the bits @code{[1, 0, 1, 0]} rather than the | |
| 563 bits of the native floating point format representation of @code{10}. | |
| 564 | |
| 565 As the maximum number that can be represented by a number is important | |
| 566 for bit manipulation, particularly when forming masks, Octave supplies | |
| 567 the function @code{bitmax}. | |
| 568 | |
| 569 @DOCSTRING(bitmax) | |
| 570 | |
| 571 This is the double precision version of the functions @code{intmax}, | |
| 572 previously discussed. | |
| 573 | |
| 574 Octave also include the basic bitwise 'and', 'or' and 'exclusive or' | |
| 575 operators. | |
| 576 | |
| 577 @DOCSTRING(bitand) | |
| 578 | |
| 579 @DOCSTRING(bitor) | |
| 580 | |
| 581 @DOCSTRING(bitxor) | |
| 582 | |
| 583 The bitwise 'not' operator is unary operator that performs a logial | |
| 584 negation of each of the bits of the value. For this to make sense, the | |
| 585 mask against which the value is negated must be defined. Octave's | |
| 586 bitwise 'not' operator is @code{bitcmp}. | |
| 587 | |
| 588 @DOCSTRING(bitcmp) | |
| 589 | |
| 590 Octave also includes the ability to left and right values bitwise. | |
| 591 | |
| 592 @DOCSTRING(bitshift) | |
| 593 | |
| 594 Bits that are shifted out of either end of the value are lost. Octave | |
| 595 also uses arithmetic shifts, where the sign bit of the value is keep | |
| 596 during a right shift. For example | |
| 597 | |
| 598 @example | |
| 599 @group | |
| 600 bitshift (-10, -1) | |
| 601 @result{} -5 | |
| 602 bitshift (int8 (-1), -1) | |
| 603 @result{} -1 | |
| 604 @end group | |
| 605 @end example | |
| 606 | |
| 607 Note that @code{bitshift (int8 (-1), -1)} is @code{-1} since the bit | |
| 608 representation of @code{-1} in the @code{int8} data type is @code{[1, 1, | |
| 609 1, 1, 1, 1, 1, 1]}. | |
| 610 | |
| 4167 | 611 @node Logical Values |
| 3428 | 612 @section Logical Values |
| 613 | |
| 6620 | 614 Octave has built-in support for logical values, i.e. variables that |
| 615 are either @code{true} or @code{false}. When comparing two variables, | |
| 616 the result will be a logical value whose value depends on whether or | |
| 617 not the comparison is true. | |
| 618 | |
| 619 The basic logical operations are @code{&}, @code{|}, and @code{!}, | |
| 620 that corresponds to ``Logical And'', ``Logical Or'', and ``Logical | |
| 621 Negation''. These operations all follow the rules of logic. | |
| 622 | |
| 623 It is also possible to use logical values as part of standard numerical | |
| 624 calculations. In this case @code{true} is converted to @code{1}, and | |
| 625 @code{false} to 0, both represented using double precision floating | |
| 626 point numbers. So, the result of @code{true*22 - false/6} is @code{22}. | |
| 627 | |
| 628 Logical values can also be used to index matrices and cell arrays. | |
| 629 When indexing with a logical array the result will be a vector containing | |
| 630 the values corresponding to @code{true} parts of the logical array. | |
| 631 The following example illustrates this. | |
| 632 | |
| 633 @example | |
| 634 data = [ 1, 2; 3, 4 ]; | |
| 635 idx = (data <= 2); | |
| 636 data(idx) | |
| 637 @result{} ans = [ 1; 4 ] | |
| 638 @end example | |
| 639 | |
| 640 @noindent | |
| 641 Instead of creating the @code{idx} array it is possible to replace | |
| 642 @code{data(idx)} with @code{data( data <= 2 )} in the above code. | |
| 643 | |
| 644 Besides when doing comparisons, logical values can be constructed by | |
| 645 casting numeric objects to logical values, or by using the @code{true} | |
| 646 or @code{false} functions. | |
| 647 | |
| 6549 | 648 @DOCSTRING(logical) |
| 649 | |
| 3428 | 650 @DOCSTRING(true) |
| 651 | |
| 652 @DOCSTRING(false) | |
| 653 | |
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654 @node Promotion and Demotion of Data Types |
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655 @section Promotion and Demotion of Data Types |
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656 |
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657 Many operators and functions can work with mixed data types. For example |
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658 |
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659 @example |
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660 uint8 (1) + 1 |
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661 @result{} 2 |
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662 @end example |
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663 |
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664 @noindent |
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665 where the above operator works with an 8-bit integer and a double precision |
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666 value and returns an 8-bit integer value. Note that the type is demoted |
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667 to an 8-bit integer, rather than promoted to a double precision value as |
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668 might be expected. The reason is that if Octave promoted values in |
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669 expressions like the above with all numerical constants would need to be |
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670 explicitly cast to the appropriate data type type like |
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671 |
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672 @example |
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673 uint8 (1) + uint8 (1) |
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674 @result{} 2 |
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675 @end example |
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676 |
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677 @noindent |
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678 which becomes difficult for the user to apply uniformly and might allow |
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679 hard to find bugs to be introduced. The same applies to single precision |
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680 values where a mixed operation such as |
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681 |
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682 @example |
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683 single (1) + 1 |
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684 @result{} 2 |
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685 @end example |
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686 |
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687 @noindent |
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688 returns a single precision value. The mixed operations that are valid |
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689 and their returned data types are |
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690 |
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691 @multitable @columnfractions .2 .3 .3 .2 |
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692 @item @tab Mixed Operation @tab Result @tab |
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693 @item @tab double OP single @tab single @tab |
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694 @item @tab double OP integer @tab integer @tab |
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695 @item @tab double OP char @tab double @tab |
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696 @item @tab double OP logical @tab double @tab |
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697 @item @tab single OP integer @tab integer @tab |
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698 @item @tab single OP char @tab single @tab |
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699 @item @tab single OP logical @tab single @tab |
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700 @end multitable |
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701 |
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702 The same logic applies to functions with mixed arguments such as |
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703 |
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704 @example |
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705 min (single (1), 0) |
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706 @result{} 0 |
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707 @end example |
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708 |
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709 @noindent |
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710 where the returned value is single precision. |
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711 |
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712 In the case of mixed type indexed assignments, the type is not |
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713 changed. For example |
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714 |
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715 @example |
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716 x = ones (2, 2); |
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717 x (1, 1) = single (2) |
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718 @result{} x = 2 1 |
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719 1 1 |
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720 @end example |
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721 |
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722 @noindent |
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723 where @code{x} remains of the double precision type. |
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724 |
| 4167 | 725 @node Predicates for Numeric Objects |
| 3294 | 726 @section Predicates for Numeric Objects |
| 727 | |
| 6620 | 728 Since the type of a variable may change during the execution of a |
| 729 program, it can be necessary to type checking at run-time. Doing this | |
| 730 also allows you to change the behaviour of a function depending on the | |
| 731 type of the input. As an example, this naive implementation of @code{abs} | |
| 7001 | 732 returns the absolute value of the input if it is a real number, and the |
| 6620 | 733 length of the input if it is a complex number. |
| 734 | |
| 735 @example | |
| 736 function a = abs (x) | |
| 737 if (isreal (x)) | |
| 738 a = sign (x) .* x; | |
| 739 elseif (iscomplex (x)) | |
| 740 a = sqrt (real(x).^2 + imag(x).^2); | |
| 741 endif | |
| 742 endfunction | |
| 743 @end example | |
| 744 | |
| 745 The following functions are available for determining the type of a | |
| 746 variable. | |
| 747 | |
| 3428 | 748 @DOCSTRING(isnumeric) |
| 749 | |
| 750 @DOCSTRING(isreal) | |
| 751 | |
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752 @DOCSTRING(isfloat) |
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753 |
| 4029 | 754 @DOCSTRING(iscomplex) |
| 3428 | 755 |
| 4029 | 756 @DOCSTRING(ismatrix) |
| 3294 | 757 |
| 4029 | 758 @DOCSTRING(isvector) |
| 3294 | 759 |
| 4029 | 760 @DOCSTRING(isscalar) |
| 3294 | 761 |
| 4029 | 762 @DOCSTRING(issquare) |
| 3294 | 763 |
| 4029 | 764 @DOCSTRING(issymmetric) |
| 3428 | 765 |
| 6550 | 766 @DOCSTRING(isdefinite) |
| 767 | |
| 6688 | 768 @DOCSTRING(islogical) |
| 6550 | 769 |
| 770 @DOCSTRING(isprime) |