Mercurial > octave-antonio
annotate doc/interpreter/func.txi @ 7638:2df457529cfa
implement expm1 and log1p functions
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Tue, 25 Mar 2008 19:47:21 -0400 |
| parents | cbedf652a752 |
| children | bbaa5d7d0143 |
| 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 Functions and Scripts |
| 3294 | 20 @chapter Functions and Script Files |
| 21 @cindex defining functions | |
| 22 @cindex user-defined functions | |
| 23 @cindex functions, user-defined | |
| 24 @cindex script files | |
| 25 | |
| 26 Complicated Octave programs can often be simplified by defining | |
| 27 functions. Functions can be defined directly on the command line during | |
| 28 interactive Octave sessions, or in external files, and can be called just | |
| 29 like built-in functions. | |
| 30 | |
| 31 @menu | |
| 32 * Defining Functions:: | |
| 33 * Multiple Return Values:: | |
| 34 * Variable-length Argument Lists:: | |
| 35 * Variable-length Return Lists:: | |
| 36 * Returning From a Function:: | |
| 6510 | 37 * Default Arguments:: |
| 3294 | 38 * Function Files:: |
| 39 * Script Files:: | |
| 6638 | 40 * Function Handles Inline Functions and Anonymous Functions:: |
| 6549 | 41 * Commands:: |
| 3294 | 42 * Organization of Functions:: |
| 43 @end menu | |
| 44 | |
| 4167 | 45 @node Defining Functions |
| 3294 | 46 @section Defining Functions |
| 47 @cindex @code{function} statement | |
| 48 @cindex @code{endfunction} statement | |
| 49 | |
| 50 In its simplest form, the definition of a function named @var{name} | |
| 51 looks like this: | |
| 52 | |
| 53 @example | |
| 54 @group | |
| 55 function @var{name} | |
| 56 @var{body} | |
| 57 endfunction | |
| 58 @end group | |
| 59 @end example | |
| 60 | |
| 61 @noindent | |
| 62 A valid function name is like a valid variable name: a sequence of | |
| 63 letters, digits and underscores, not starting with a digit. Functions | |
| 64 share the same pool of names as variables. | |
| 65 | |
| 66 The function @var{body} consists of Octave statements. It is the | |
| 67 most important part of the definition, because it says what the function | |
| 68 should actually @emph{do}. | |
| 69 | |
| 70 For example, here is a function that, when executed, will ring the bell | |
| 71 on your terminal (assuming that it is possible to do so): | |
| 72 | |
| 73 @example | |
| 74 @group | |
| 75 function wakeup | |
| 76 printf ("\a"); | |
| 77 endfunction | |
| 78 @end group | |
| 79 @end example | |
| 80 | |
| 81 The @code{printf} statement (@pxref{Input and Output}) simply tells | |
| 82 Octave to print the string @code{"\a"}. The special character @samp{\a} | |
| 83 stands for the alert character (ASCII 7). @xref{Strings}. | |
| 84 | |
| 85 Once this function is defined, you can ask Octave to evaluate it by | |
| 86 typing the name of the function. | |
| 87 | |
| 88 Normally, you will want to pass some information to the functions you | |
| 89 define. The syntax for passing parameters to a function in Octave is | |
| 90 | |
| 91 @example | |
| 92 @group | |
| 93 function @var{name} (@var{arg-list}) | |
| 94 @var{body} | |
| 95 endfunction | |
| 96 @end group | |
| 97 @end example | |
| 98 | |
| 99 @noindent | |
| 100 where @var{arg-list} is a comma-separated list of the function's | |
| 101 arguments. When the function is called, the argument names are used to | |
| 102 hold the argument values given in the call. The list of arguments may | |
| 103 be empty, in which case this form is equivalent to the one shown above. | |
| 104 | |
| 105 To print a message along with ringing the bell, you might modify the | |
| 6510 | 106 @code{wakeup} to look like this: |
| 3294 | 107 |
| 108 @example | |
| 109 @group | |
| 110 function wakeup (message) | |
| 111 printf ("\a%s\n", message); | |
| 112 endfunction | |
| 113 @end group | |
| 114 @end example | |
| 115 | |
| 116 Calling this function using a statement like this | |
| 117 | |
| 118 @example | |
| 119 wakeup ("Rise and shine!"); | |
| 120 @end example | |
| 121 | |
| 122 @noindent | |
| 123 will cause Octave to ring your terminal's bell and print the message | |
| 124 @samp{Rise and shine!}, followed by a newline character (the @samp{\n} | |
| 125 in the first argument to the @code{printf} statement). | |
| 126 | |
| 127 In most cases, you will also want to get some information back from the | |
| 128 functions you define. Here is the syntax for writing a function that | |
| 129 returns a single value: | |
| 130 | |
| 131 @example | |
| 132 @group | |
| 133 function @var{ret-var} = @var{name} (@var{arg-list}) | |
| 134 @var{body} | |
| 135 endfunction | |
| 136 @end group | |
| 137 @end example | |
| 138 | |
| 139 @noindent | |
| 140 The symbol @var{ret-var} is the name of the variable that will hold the | |
| 141 value to be returned by the function. This variable must be defined | |
| 142 before the end of the function body in order for the function to return | |
| 143 a value. | |
| 144 | |
| 145 Variables used in the body of a function are local to the | |
| 146 function. Variables named in @var{arg-list} and @var{ret-var} are also | |
| 147 local to the function. @xref{Global Variables}, for information about | |
| 148 how to access global variables inside a function. | |
| 149 | |
| 150 For example, here is a function that computes the average of the | |
| 151 elements of a vector: | |
| 152 | |
| 153 @example | |
| 154 @group | |
| 155 function retval = avg (v) | |
| 156 retval = sum (v) / length (v); | |
| 157 endfunction | |
| 158 @end group | |
| 159 @end example | |
| 160 | |
| 161 If we had written @code{avg} like this instead, | |
| 162 | |
| 163 @example | |
| 164 @group | |
| 165 function retval = avg (v) | |
| 4029 | 166 if (isvector (v)) |
| 3294 | 167 retval = sum (v) / length (v); |
| 168 endif | |
| 169 endfunction | |
| 170 @end group | |
| 171 @end example | |
| 172 | |
| 173 @noindent | |
| 174 and then called the function with a matrix instead of a vector as the | |
| 175 argument, Octave would have printed an error message like this: | |
| 176 | |
| 177 @example | |
| 178 @group | |
| 179 error: `retval' undefined near line 1 column 10 | |
| 180 error: evaluating index expression near line 7, column 1 | |
| 181 @end group | |
| 182 @end example | |
| 183 | |
| 184 @noindent | |
| 185 because the body of the @code{if} statement was never executed, and | |
| 186 @code{retval} was never defined. To prevent obscure errors like this, | |
| 187 it is a good idea to always make sure that the return variables will | |
| 188 always have values, and to produce meaningful error messages when | |
| 189 problems are encountered. For example, @code{avg} could have been | |
| 190 written like this: | |
| 191 | |
| 192 @example | |
| 193 @group | |
| 194 function retval = avg (v) | |
| 195 retval = 0; | |
| 4029 | 196 if (isvector (v)) |
| 3294 | 197 retval = sum (v) / length (v); |
| 198 else | |
| 199 error ("avg: expecting vector argument"); | |
| 200 endif | |
| 201 endfunction | |
| 202 @end group | |
| 203 @end example | |
| 204 | |
| 205 There is still one additional problem with this function. What if it is | |
| 206 called without an argument? Without additional error checking, Octave | |
| 207 will probably print an error message that won't really help you track | |
| 208 down the source of the error. To allow you to catch errors like this, | |
| 209 Octave provides each function with an automatic variable called | |
| 210 @code{nargin}. Each time a function is called, @code{nargin} is | |
| 211 automatically initialized to the number of arguments that have actually | |
| 212 been passed to the function. For example, we might rewrite the | |
| 213 @code{avg} function like this: | |
| 214 | |
| 215 @example | |
| 216 @group | |
| 217 function retval = avg (v) | |
| 218 retval = 0; | |
| 219 if (nargin != 1) | |
| 220 usage ("avg (vector)"); | |
| 221 endif | |
| 4029 | 222 if (isvector (v)) |
| 3294 | 223 retval = sum (v) / length (v); |
| 224 else | |
| 225 error ("avg: expecting vector argument"); | |
| 226 endif | |
| 227 endfunction | |
| 228 @end group | |
| 229 @end example | |
| 230 | |
| 231 Although Octave does not automatically report an error if you call a | |
| 232 function with more arguments than expected, doing so probably indicates | |
| 233 that something is wrong. Octave also does not automatically report an | |
| 234 error if a function is called with too few arguments, but any attempt to | |
| 235 use a variable that has not been given a value will result in an error. | |
| 236 To avoid such problems and to provide useful messages, we check for both | |
| 237 possibilities and issue our own error message. | |
| 238 | |
| 4700 | 239 @DOCSTRING(nargin) |
| 3294 | 240 |
| 6558 | 241 @DOCSTRING(inputname) |
| 242 | |
| 3371 | 243 @DOCSTRING(silent_functions) |
| 3294 | 244 |
| 4167 | 245 @node Multiple Return Values |
| 3294 | 246 @section Multiple Return Values |
| 247 | |
| 248 Unlike many other computer languages, Octave allows you to define | |
| 249 functions that return more than one value. The syntax for defining | |
| 250 functions that return multiple values is | |
| 251 | |
| 252 @example | |
| 253 function [@var{ret-list}] = @var{name} (@var{arg-list}) | |
| 254 @var{body} | |
| 255 endfunction | |
| 256 @end example | |
| 257 | |
| 258 @noindent | |
| 259 where @var{name}, @var{arg-list}, and @var{body} have the same meaning | |
| 260 as before, and @var{ret-list} is a comma-separated list of variable | |
| 261 names that will hold the values returned from the function. The list of | |
| 262 return values must have at least one element. If @var{ret-list} has | |
| 263 only one element, this form of the @code{function} statement is | |
| 264 equivalent to the form described in the previous section. | |
| 265 | |
| 266 Here is an example of a function that returns two values, the maximum | |
| 267 element of a vector and the index of its first occurrence in the vector. | |
| 268 | |
| 269 @example | |
| 270 @group | |
| 271 function [max, idx] = vmax (v) | |
| 272 idx = 1; | |
| 273 max = v (idx); | |
| 274 for i = 2:length (v) | |
| 275 if (v (i) > max) | |
| 276 max = v (i); | |
| 277 idx = i; | |
| 278 endif | |
| 279 endfor | |
| 280 endfunction | |
| 281 @end group | |
| 282 @end example | |
| 283 | |
| 284 In this particular case, the two values could have been returned as | |
| 285 elements of a single array, but that is not always possible or | |
| 286 convenient. The values to be returned may not have compatible | |
| 287 dimensions, and it is often desirable to give the individual return | |
| 288 values distinct names. | |
| 289 | |
| 290 In addition to setting @code{nargin} each time a function is called, | |
| 291 Octave also automatically initializes @code{nargout} to the number of | |
| 292 values that are expected to be returned. This allows you to write | |
| 293 functions that behave differently depending on the number of values that | |
| 294 the user of the function has requested. The implicit assignment to the | |
| 295 built-in variable @code{ans} does not figure in the count of output | |
| 296 arguments, so the value of @code{nargout} may be zero. | |
| 297 | |
| 298 The @code{svd} and @code{lu} functions are examples of built-in | |
| 299 functions that behave differently depending on the value of | |
| 300 @code{nargout}. | |
| 301 | |
| 302 It is possible to write functions that only set some return values. For | |
| 303 example, calling the function | |
| 304 | |
| 305 @example | |
| 306 function [x, y, z] = f () | |
| 307 x = 1; | |
| 308 z = 2; | |
| 309 endfunction | |
| 310 @end example | |
| 311 | |
| 312 @noindent | |
| 313 as | |
| 314 | |
| 315 @example | |
| 316 [a, b, c] = f () | |
| 317 @end example | |
| 318 | |
| 319 @noindent | |
| 320 produces: | |
| 321 | |
| 322 @example | |
| 323 a = 1 | |
| 324 | |
| 325 b = [](0x0) | |
| 326 | |
| 327 c = 2 | |
| 328 @end example | |
| 329 | |
| 330 @noindent | |
| 6501 | 331 along with a warning. |
| 3294 | 332 |
| 4700 | 333 @DOCSTRING(nargout) |
| 3294 | 334 |
| 3371 | 335 @DOCSTRING(nargchk) |
| 3294 | 336 |
| 4167 | 337 @node Variable-length Argument Lists |
| 3294 | 338 @section Variable-length Argument Lists |
| 4933 | 339 @cindex variable-length argument lists |
| 3294 | 340 @cindex @code{...} |
| 6510 | 341 Sometimes the number of input arguments is not known when the function |
| 342 is defined. As an example think of a function that returns the smallest | |
| 343 of all its input arguments. For example, | |
| 344 | |
| 345 @example | |
| 346 a = smallest (1, 2, 3); | |
| 347 b = smallest (1, 2, 3, 4); | |
| 348 @end example | |
| 349 | |
| 350 @noindent | |
| 351 In this example both @code{a} and @code{b} would be 1. One way to write | |
| 352 the @code{smallest} function is | |
| 353 | |
| 354 @example | |
| 355 function val = smallest (arg1, arg2, arg3, arg4, arg5) | |
| 356 @var{body} | |
| 357 endfunction | |
| 358 @end example | |
| 359 | |
| 360 @noindent | |
| 361 and then use the value of @code{nargin} to determine which of the input | |
| 362 arguments should be considered. The problem with this approach is | |
| 363 that it can only handle a limited number of input arguments. | |
| 364 | |
|
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parents:
7031
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changeset
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365 If the special parameter name @code{varargin} appears at the end of a |
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cbedf652a752
doc fix for varargin and varargout change
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parents:
7031
diff
changeset
|
366 function parameter list it indicates that the function takes a variable |
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cbedf652a752
doc fix for varargin and varargout change
John W. Eaton <jwe@octave.org>
parents:
7031
diff
changeset
|
367 number of input arguments. Using @code{varargin} the function |
| 6510 | 368 looks like this |
| 369 | |
| 370 @example | |
| 371 function val = smallest (varargin) | |
| 372 @var{body} | |
| 373 endfunction | |
| 374 @end example | |
| 375 | |
| 376 @noindent | |
| 377 In the function body the input arguments can be accessed through the | |
| 378 variable @code{varargin}. This variable is a cell array containing | |
| 379 all the input arguments. @xref{Cell Arrays}, for details on working | |
| 380 with cell arrays. The @code{smallest} function can now be defined | |
| 381 like this | |
| 382 | |
| 383 @example | |
| 384 function val = smallest (varargin) | |
| 385 val = min ([varargin@{:@}]); | |
| 386 endfunction | |
| 387 @end example | |
| 388 | |
| 389 @noindent | |
| 390 This implementation handles any number of input arguments, but it's also | |
| 391 a very simple solution to the problem. | |
| 392 | |
| 393 A slightly more complex example of @code{varargin} is a function | |
| 394 @code{print_arguments} that prints all input arguments. Such a function | |
| 395 can be defined like this | |
| 396 | |
| 397 @example | |
| 398 function print_arguments (varargin) | |
| 399 for i = 1:length (varargin) | |
| 400 printf ("Input argument %d: ", i); | |
| 401 disp (varargin@{i@}); | |
| 402 endfor | |
| 403 endfunction | |
| 404 @end example | |
| 405 | |
| 406 @noindent | |
| 407 This function produces output like this | |
| 408 | |
| 409 @example | |
| 410 @group | |
| 411 print_arguments (1, "two", 3); | |
| 412 @print{} Input argument 1: 1 | |
| 413 @print{} Input argument 2: two | |
| 414 @print{} Input argument 3: 3 | |
| 415 @end group | |
| 416 @end example | |
| 3294 | 417 |
| 6558 | 418 @DOCSTRING(parseparams) |
| 419 | |
| 4167 | 420 @node Variable-length Return Lists |
| 3294 | 421 @section Variable-length Return Lists |
| 4933 | 422 @cindex variable-length return lists |
| 6510 | 423 It is possible to return a variable number of output arguments from a |
| 424 function using a syntax that's similar to the one used with the | |
|
7588
cbedf652a752
doc fix for varargin and varargout change
John W. Eaton <jwe@octave.org>
parents:
7031
diff
changeset
|
425 special @code{varargin} parameter name. To let a function return a |
|
cbedf652a752
doc fix for varargin and varargout change
John W. Eaton <jwe@octave.org>
parents:
7031
diff
changeset
|
426 variable number of output arguments the special output parameter name |
|
cbedf652a752
doc fix for varargin and varargout change
John W. Eaton <jwe@octave.org>
parents:
7031
diff
changeset
|
427 @code{varargout} is used. As with @code{varargin}, @code{varargout} is |
|
cbedf652a752
doc fix for varargin and varargout change
John W. Eaton <jwe@octave.org>
parents:
7031
diff
changeset
|
428 a cell array that will contain the requested output arguments. |
| 6510 | 429 |
| 430 As an example the following function sets the first output argument to | |
| 431 1, the second to 2, and so on. | |
| 432 | |
| 433 @example | |
| 434 function varargout = one_to_n () | |
| 435 for i = 1:nargout | |
| 436 varargout@{i@} = i; | |
| 437 endfor | |
| 438 endfunction | |
| 439 @end example | |
| 440 | |
| 441 @noindent | |
| 442 When called this function returns values like this | |
| 443 | |
| 444 @example | |
| 445 @group | |
| 446 [a, b, c] = one_to_n () | |
| 447 @result{} a = 1 | |
| 448 @result{} b = 2 | |
| 449 @result{} c = 3 | |
| 450 @end group | |
| 451 @end example | |
| 3294 | 452 |
|
7588
cbedf652a752
doc fix for varargin and varargout change
John W. Eaton <jwe@octave.org>
parents:
7031
diff
changeset
|
453 If @code{varargin} (@code{varargout}) does not appear as the last |
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cbedf652a752
doc fix for varargin and varargout change
John W. Eaton <jwe@octave.org>
parents:
7031
diff
changeset
|
454 element of the input (output) parameter list, then it is not special, |
|
cbedf652a752
doc fix for varargin and varargout change
John W. Eaton <jwe@octave.org>
parents:
7031
diff
changeset
|
455 and is handled the same as any other parameter name. |
|
cbedf652a752
doc fix for varargin and varargout change
John W. Eaton <jwe@octave.org>
parents:
7031
diff
changeset
|
456 |
| 6558 | 457 @DOCSTRING(deal) |
| 458 | |
| 4167 | 459 @node Returning From a Function |
| 3294 | 460 @section Returning From a Function |
| 461 | |
| 462 The body of a user-defined function can contain a @code{return} statement. | |
| 463 This statement returns control to the rest of the Octave program. It | |
| 464 looks like this: | |
| 465 | |
| 466 @example | |
| 467 return | |
| 468 @end example | |
| 469 | |
| 470 Unlike the @code{return} statement in C, Octave's @code{return} | |
| 471 statement cannot be used to return a value from a function. Instead, | |
| 472 you must assign values to the list of return variables that are part of | |
| 473 the @code{function} statement. The @code{return} statement simply makes | |
| 474 it easier to exit a function from a deeply nested loop or conditional | |
| 475 statement. | |
| 476 | |
| 477 Here is an example of a function that checks to see if any elements of a | |
| 478 vector are nonzero. | |
| 479 | |
| 480 @example | |
| 481 @group | |
| 482 function retval = any_nonzero (v) | |
| 483 retval = 0; | |
| 484 for i = 1:length (v) | |
| 485 if (v (i) != 0) | |
| 486 retval = 1; | |
| 487 return; | |
| 488 endif | |
| 489 endfor | |
| 490 printf ("no nonzero elements found\n"); | |
| 491 endfunction | |
| 492 @end group | |
| 493 @end example | |
| 494 | |
| 495 Note that this function could not have been written using the | |
| 496 @code{break} statement to exit the loop once a nonzero value is found | |
| 497 without adding extra logic to avoid printing the message if the vector | |
| 498 does contain a nonzero element. | |
| 499 | |
| 5763 | 500 @deffn {Keyword} return |
| 3294 | 501 When Octave encounters the keyword @code{return} inside a function or |
| 5016 | 502 script, it returns control to the caller immediately. At the top level, |
| 3294 | 503 the return statement is ignored. A @code{return} statement is assumed |
| 504 at the end of every function definition. | |
| 5763 | 505 @end deffn |
| 3294 | 506 |
| 3371 | 507 @DOCSTRING(return_last_computed_value) |
| 3294 | 508 |
| 6510 | 509 @node Default Arguments |
| 510 @section Default Arguments | |
| 511 @cindex default arguments | |
| 512 | |
| 513 Since Octave supports variable number of input arguments, it is very useful | |
| 514 to assign default values to some input arguments. When an input argument | |
| 515 is declared in the argument list it is possible to assign a default | |
| 516 value to the argument like this | |
| 517 | |
| 518 @example | |
| 519 function @var{name} (@var{arg1} = @var{val1}, @dots{}) | |
| 520 @var{body} | |
| 521 endfunction | |
| 522 @end example | |
| 523 | |
| 524 @noindent | |
| 525 If no value is assigned to @var{arg1} by the user, it will have the | |
| 526 value @var{val1}. | |
| 527 | |
| 528 As an example, the following function implements a variant of the classic | |
| 529 ``Hello, World'' program. | |
| 530 @example | |
| 531 function hello (who = "World") | |
| 532 printf ("Hello, %s!\n", who); | |
| 533 endfunction | |
| 534 @end example | |
| 535 | |
| 536 @noindent | |
| 537 When called without an input argument the function prints the following | |
| 538 @example | |
| 539 @group | |
| 540 hello (); | |
| 541 @print{} Hello, World! | |
| 542 @end group | |
| 543 @end example | |
| 544 | |
| 545 @noindent | |
| 546 and when it's called with an input argument it prints the following | |
| 547 @example | |
| 548 @group | |
| 549 hello ("Beautiful World of Free Software"); | |
| 550 @print{} Hello, Beautiful World of Free Software! | |
| 551 @end group | |
| 552 @end example | |
| 553 | |
| 554 Sometimes it is useful to explicitly tell Octave to use the default value | |
| 555 of an input argument. This can be done writing a @samp{:} as the value | |
| 556 of the input argument when calling the function. | |
| 557 @example | |
| 558 @group | |
| 559 hello (:); | |
| 560 @print{} Hello, World! | |
| 561 @end group | |
| 562 @end example | |
| 563 | |
| 4167 | 564 @node Function Files |
| 3294 | 565 @section Function Files |
| 566 @cindex function file | |
| 567 | |
| 568 Except for simple one-shot programs, it is not practical to have to | |
| 569 define all the functions you need each time you need them. Instead, you | |
| 570 will normally want to save them in a file so that you can easily edit | |
| 571 them, and save them for use at a later time. | |
| 572 | |
| 573 Octave does not require you to load function definitions from files | |
| 574 before using them. You simply need to put the function definitions in a | |
| 575 place where Octave can find them. | |
| 576 | |
| 577 When Octave encounters an identifier that is undefined, it first looks | |
| 578 for variables or functions that are already compiled and currently | |
| 579 listed in its symbol table. If it fails to find a definition there, it | |
| 6556 | 580 searches a list of directories (the @dfn{path}) for files ending in |
| 6554 | 581 @file{.m} that have the same base name as the undefined |
| 582 identifier.@footnote{The @samp{.m} suffix was chosen for compatibility | |
| 583 with @sc{Matlab}.} Once Octave finds a file with a name that matches, | |
| 584 the contents of the file are read. If it defines a @emph{single} | |
| 585 function, it is compiled and executed. @xref{Script Files}, for more | |
| 586 information about how you can define more than one function in a single | |
| 587 file. | |
| 3294 | 588 |
| 589 When Octave defines a function from a function file, it saves the full | |
| 6554 | 590 name of the file it read and the time stamp on the file. If the time |
| 591 stamp on the file changes, Octave may reload the file. When Octave is | |
| 592 running interactively, time stamp checking normally happens at most once | |
| 593 each time Octave prints the prompt. Searching for new function | |
| 594 definitions also occurs if the current working directory changes. | |
| 3294 | 595 |
| 596 Checking the time stamp allows you to edit the definition of a function | |
| 597 while Octave is running, and automatically use the new function | |
| 6554 | 598 definition without having to restart your Octave session. |
| 3294 | 599 |
| 600 To avoid degrading performance unnecessarily by checking the time stamps | |
| 601 on functions that are not likely to change, Octave assumes that function | |
| 602 files in the directory tree | |
| 603 @file{@var{octave-home}/share/octave/@var{version}/m} | |
| 604 will not change, so it doesn't have to check their time stamps every time the | |
| 605 functions defined in those files are used. This is normally a very good | |
| 606 assumption and provides a significant improvement in performance for the | |
| 607 function files that are distributed with Octave. | |
| 608 | |
| 609 If you know that your own function files will not change while you are | |
| 6554 | 610 running Octave, you can improve performance by calling |
| 611 @code{ignore_function_time_stamp ("all")}, so that Octave will | |
| 612 ignore the time stamps for all function files. Passing | |
| 613 @code{"system"} to this function resets the default behavior. | |
| 3294 | 614 |
| 5775 | 615 @c FIXME -- note about time stamps on files in NFS environments? |
| 3294 | 616 |
| 6549 | 617 @DOCSTRING(mfilename) |
| 618 | |
| 6638 | 619 @DOCSTRING(ignore_function_time_stamp) |
| 620 | |
| 621 @menu | |
| 622 * Manipulating the load path:: | |
| 623 * Subfunctions:: | |
| 624 * Overloading and Autoloading:: | |
| 625 * Function Locking:: | |
| 626 @end menu | |
| 627 | |
| 628 @node Manipulating the load path | |
| 629 @subsection Manipulating the load path | |
| 630 | |
| 631 When a function is called Octave searches a list of directories for | |
| 632 a file that contains the function declaration. This list of directories | |
| 633 is known as the load path. By default the load path contains | |
| 634 a list of directories distributed with Octave plus the current | |
| 635 working directory. To see your current load path call the @code{path} | |
| 636 function without any input or output arguments. | |
| 637 | |
| 638 It is possible to add or remove directories to or from the load path | |
| 639 using the @code{addpath} and @code{rmpath}. As an example, the following | |
| 640 code adds @samp{~/Octave} to the load path. | |
| 641 | |
| 642 @example | |
| 643 addpath("~/Octave") | |
| 644 @end example | |
| 645 | |
| 646 @noindent | |
| 647 After this the directory @samp{~/Octave} will be searched for functions. | |
| 648 | |
| 6502 | 649 @DOCSTRING(addpath) |
| 650 | |
| 651 @DOCSTRING(genpath) | |
| 652 | |
| 653 @DOCSTRING(rmpath) | |
| 654 | |
| 655 @DOCSTRING(savepath) | |
| 656 | |
| 6477 | 657 @DOCSTRING(path) |
| 3294 | 658 |
| 6502 | 659 @DOCSTRING(pathdef) |
| 660 | |
| 661 @DOCSTRING(pathsep) | |
| 662 | |
| 3428 | 663 @DOCSTRING(rehash) |
| 664 | |
| 665 @DOCSTRING(file_in_loadpath) | |
| 666 | |
|
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668 |
| 6556 | 669 @node Subfunctions |
| 670 @subsection Subfunctions | |
| 671 | |
| 672 A function file may contain secondary functions called | |
| 673 @dfn{subfunctions}. These secondary functions are only visible to the | |
| 674 other functions in the same function file. For example, a file | |
| 675 @file{f.m} containing | |
| 676 | |
| 677 @example | |
| 678 @group | |
| 679 function f () | |
| 680 printf ("in f, calling g\n"); | |
| 681 g () | |
| 682 endfunction | |
| 683 function g () | |
| 684 printf ("in g, calling h\n"); | |
| 6638 | 685 h () |
| 6556 | 686 endfunction |
| 687 function h () | |
| 688 printf ("in h\n") | |
| 689 endfunction | |
| 690 @end group | |
| 691 @end example | |
| 692 | |
| 693 @noindent | |
| 694 defines a main function @code{f} and two subfunctions. The | |
| 695 subfunctions @code{g} and @code{h} may only be called from the main | |
| 696 function @code{f} or from the other subfunctions, but not from outside | |
| 697 the file @file{f.m}. | |
| 698 | |
| 6635 | 699 @node Overloading and Autoloading |
| 700 @subsection Overloading and Autoloading | |
| 701 | |
| 702 The @code{dispatch} function can be used to alias one function name to | |
| 703 another. It can be used to alias all calls to a particular function name | |
| 704 to another function, or the alias can be limited to only a particular | |
| 705 variable type. Consider the example | |
| 706 | |
| 707 @example | |
| 708 @group | |
| 709 function y = spsin (x) | |
| 710 printf ("Calling spsin\n"); | |
| 711 fflush(stdout); | |
| 712 y = spfun ("sin", x); | |
| 713 endfunction | |
| 714 | |
| 715 dispatch ("sin", "spsin", "sparse matrix"); | |
| 716 y0 = sin(eye(3)); | |
| 717 y1 = sin(speye(3)); | |
| 718 @end group | |
| 719 @end example | |
| 720 | |
| 721 @noindent | |
| 722 Which aliases the @code{spsin} to @code{sin}, but only for real sparse | |
| 723 matrices. Note that the builtin @code{sin} already correctly treats | |
| 724 sparse matrices and so this example is only illustrative. | |
| 725 | |
| 726 @DOCSTRING(dispatch) | |
| 727 | |
| 728 @DOCSTRING(builtin) | |
| 729 | |
| 730 A single dynamically linked file might define several | |
| 731 functions. However, as Octave searches for functions based on the | |
| 732 functions filename, Octave needs a manner in which to find each of the | |
| 733 functions in the dynamically linked file. On operating systems that | |
| 734 support symbolic links, it is possible to create a symbolic link to the | |
| 735 original file for each of the functions which it contains. | |
| 736 | |
| 737 However, there is at least one well known operating system that doesn't | |
| 738 support symbolic links. Making copies of the original file for each of | |
| 739 the functions is also possible, but is undesirable as it multiples the | |
| 740 amount of disk space used by Octave. Instead Octave supplies the | |
| 741 @code{autoload} function, that permits the user to define in which | |
| 742 file a certain function will be found. | |
| 743 | |
| 744 @DOCSTRING(autoload) | |
| 745 | |
| 746 @node Function Locking | |
| 747 @subsection Function Locking | |
| 748 | |
| 749 It is sometime desirable to lock a function into memory with the | |
| 750 @code{mlock} function. This is typically used for dynamically linked | |
| 6899 | 751 functions in Oct-files or mex-files that contain some initialization, |
| 752 and it is desirable that calling @code{clear} does not remove this | |
| 6635 | 753 initialization. |
| 754 | |
| 6899 | 755 As an example, |
| 756 | |
| 757 @example | |
| 758 mlock ("my_function"); | |
| 759 @end example | |
| 760 | |
| 761 @noindent | |
| 762 prevents @code{my_function} from being removed from memory, even if | |
| 763 @code{clear} is called. It is possible to determine if a function is | |
| 764 locked into memory with the @code{mislocked}, and to unlock a function | |
| 765 with @code{munlock}, which the following illustrates. | |
| 766 | |
| 767 @example | |
| 768 @group | |
| 769 mlock ("my_function"); | |
| 770 mislocked ("my_function") | |
| 771 @result{} ans = 1 | |
| 772 munlock ("my_function"); | |
| 773 mislocked ("my_function") | |
| 774 @result{} ans = 0 | |
| 775 @end group | |
| 776 @end example | |
| 777 | |
| 778 A common use of @code{mlock} is to prevent persistent variables from | |
| 779 being removed from memory, as the following example shows. | |
| 780 | |
| 781 @example | |
| 782 @group | |
| 783 function count_calls() | |
| 784 persistent calls = 0; | |
| 7031 | 785 printf ("'count_calls' has been called %d times\n", |
| 786 ++calls); | |
| 6899 | 787 endfunction |
| 788 mlock ("count_calls"); | |
| 789 | |
| 790 count_calls (); | |
| 791 @print{} 'count_calls' has been called 1 times | |
| 792 | |
| 793 clear count_calls | |
| 794 count_calls (); | |
| 795 @print{} 'count_calls' has been called 2 times | |
| 796 @end group | |
| 797 @end example | |
| 798 | |
| 799 @noindent | |
| 800 It is, however, often inconvenient to lock a function from the prompt, | |
| 801 so it is also possible to lock a function from within its body. This | |
| 802 is simply done by calling @code{mlock} from within the function. | |
| 803 | |
| 804 @example | |
| 805 @group | |
| 806 function count_calls () | |
| 807 mlock (); | |
| 808 persistent calls = 0; | |
| 7031 | 809 printf ("'count_calls' has been called %d times\n", |
| 810 ++calls); | |
| 6899 | 811 endfunction |
| 812 @end group | |
| 813 @end example | |
| 814 | |
| 815 @code{mlock} might equally be used to prevent changes to a function from having | |
| 6635 | 816 effect in Octave, though a similar effect can be had with the |
| 817 @code{ignore_function_time_stamp} function. | |
| 818 | |
| 819 @DOCSTRING(mlock) | |
| 820 | |
| 821 @DOCSTRING(munlock) | |
| 822 | |
| 823 @DOCSTRING(mislocked) | |
| 824 | |
| 4167 | 825 @node Script Files |
| 3294 | 826 @section Script Files |
| 827 | |
| 828 A script file is a file containing (almost) any sequence of Octave | |
| 829 commands. It is read and evaluated just as if you had typed each | |
| 830 command at the Octave prompt, and provides a convenient way to perform a | |
| 831 sequence of commands that do not logically belong inside a function. | |
| 832 | |
| 833 Unlike a function file, a script file must @emph{not} begin with the | |
| 834 keyword @code{function}. If it does, Octave will assume that it is a | |
| 835 function file, and that it defines a single function that should be | |
| 836 evaluated as soon as it is defined. | |
| 837 | |
| 838 A script file also differs from a function file in that the variables | |
| 839 named in a script file are not local variables, but are in the same | |
| 840 scope as the other variables that are visible on the command line. | |
| 841 | |
| 842 Even though a script file may not begin with the @code{function} | |
| 843 keyword, it is possible to define more than one function in a single | |
| 844 script file and load (but not execute) all of them at once. To do | |
| 845 this, the first token in the file (ignoring comments and other white | |
| 846 space) must be something other than @code{function}. If you have no | |
| 847 other statements to evaluate, you can use a statement that has no | |
| 848 effect, like this: | |
| 849 | |
| 850 @example | |
| 851 @group | |
| 852 # Prevent Octave from thinking that this | |
| 853 # is a function file: | |
| 854 | |
| 855 1; | |
| 856 | |
| 857 # Define function one: | |
| 858 | |
| 859 function one () | |
| 860 ... | |
| 861 @end group | |
| 862 @end example | |
| 863 | |
| 864 To have Octave read and compile these functions into an internal form, | |
| 6638 | 865 you need to make sure that the file is in Octave's load path |
| 6477 | 866 (accessible through the @code{path} function), then simply type the |
| 867 base name of the file that contains the commands. (Octave uses the | |
| 868 same rules to search for script files as it does to search for | |
| 869 function files.) | |
| 3294 | 870 |
| 871 If the first token in a file (ignoring comments) is @code{function}, | |
| 872 Octave will compile the function and try to execute it, printing a | |
| 873 message warning about any non-whitespace characters that appear after | |
| 874 the function definition. | |
| 875 | |
| 876 Note that Octave does not try to look up the definition of any identifier | |
| 877 until it needs to evaluate it. This means that Octave will compile the | |
| 878 following statements if they appear in a script file, or are typed at | |
| 879 the command line, | |
| 880 | |
| 881 @example | |
| 882 @group | |
| 883 # not a function file: | |
| 884 1; | |
| 885 function foo () | |
| 886 do_something (); | |
| 887 endfunction | |
| 888 function do_something () | |
| 889 do_something_else (); | |
| 890 endfunction | |
| 891 @end group | |
| 892 @end example | |
| 893 | |
| 894 @noindent | |
| 895 even though the function @code{do_something} is not defined before it is | |
| 896 referenced in the function @code{foo}. This is not an error because | |
| 897 Octave does not need to resolve all symbols that are referenced by a | |
| 898 function until the function is actually evaluated. | |
| 899 | |
| 900 Since Octave doesn't look for definitions until they are needed, the | |
| 901 following code will always print @samp{bar = 3} whether it is typed | |
| 902 directly on the command line, read from a script file, or is part of a | |
| 903 function body, even if there is a function or script file called | |
| 6477 | 904 @file{bar.m} in Octave's path. |
| 3294 | 905 |
| 906 @example | |
| 907 @group | |
| 908 eval ("bar = 3"); | |
| 909 bar | |
| 910 @end group | |
| 911 @end example | |
| 912 | |
| 913 Code like this appearing within a function body could fool Octave if | |
| 914 definitions were resolved as the function was being compiled. It would | |
| 915 be virtually impossible to make Octave clever enough to evaluate this | |
| 916 code in a consistent fashion. The parser would have to be able to | |
| 917 perform the call to @code{eval} at compile time, and that would be | |
| 918 impossible unless all the references in the string to be evaluated could | |
| 919 also be resolved, and requiring that would be too restrictive (the | |
| 920 string might come from user input, or depend on things that are not | |
| 921 known until the function is evaluated). | |
| 922 | |
| 923 Although Octave normally executes commands from script files that have | |
| 924 the name @file{@var{file}.m}, you can use the function @code{source} to | |
| 925 execute commands from any file. | |
| 926 | |
| 3371 | 927 @DOCSTRING(source) |
| 3294 | 928 |
| 6638 | 929 @node Function Handles Inline Functions and Anonymous Functions |
| 930 @section Function Handles, Inline Functions, and Anonymous Functions | |
| 4933 | 931 @cindex handle, function handles |
| 932 @cindex inline, inline functions | |
| 6638 | 933 @cindex anonymous functions |
| 4933 | 934 |
| 6638 | 935 It can be very convenient store a function in a variable so that it |
| 936 can be passed to a different function. For example, a function that | |
| 937 performs numerical minimisation needs access to the function that | |
| 938 should be minimised. | |
| 4933 | 939 |
| 940 @menu | |
| 941 * Function Handles:: | |
| 6554 | 942 * Anonymous Functions:: |
| 4933 | 943 * Inline Functions:: |
| 944 @end menu | |
| 945 | |
| 946 @node Function Handles | |
| 947 @subsection Function Handles | |
| 948 | |
| 6554 | 949 A function handle is a pointer to another function and is defined with |
| 950 the syntax | |
| 951 | |
| 952 @example | |
| 953 @@@var{function-name} | |
| 954 @end example | |
| 955 | |
| 956 @noindent | |
| 957 For example | |
| 958 | |
| 959 @example | |
| 6556 | 960 f = @@sin; |
| 6554 | 961 @end example |
| 962 | |
| 963 @noindent | |
| 6570 | 964 Creates a function handle called @code{f} that refers to the |
| 6554 | 965 function @code{sin}. |
| 966 | |
| 967 Function handles are used to call other functions indirectly, or to pass | |
| 968 a function as an argument to another function like @code{quad} or | |
| 969 @code{fsolve}. For example | |
| 970 | |
| 971 @example | |
| 6556 | 972 f = @@sin; |
| 6554 | 973 quad (f, 0, pi) |
| 6929 | 974 @result{} 2 |
| 6554 | 975 @end example |
| 976 | |
| 977 You may use @code{feval} to call a function using function handle, or | |
| 6570 | 978 simply write the name of the function handle followed by an argument |
| 6554 | 979 list. If there are no arguments, you must use an empty argument list |
| 980 @samp{()}. For example | |
| 981 | |
| 982 @example | |
| 6556 | 983 f = @@sin; |
| 6554 | 984 feval (f, pi/4) |
| 6570 | 985 @result{} 0.70711 |
| 6554 | 986 f (pi/4) |
| 6570 | 987 @result{} 0.70711 |
| 6554 | 988 @end example |
| 989 | |
| 4933 | 990 @DOCSTRING(functions) |
| 991 | |
| 992 @DOCSTRING(func2str) | |
| 993 | |
| 994 @DOCSTRING(str2func) | |
| 995 | |
| 6570 | 996 @node Anonymous Functions |
| 6554 | 997 @subsection Anonymous Functions |
| 998 | |
| 999 Anonymous functions are defined using the syntax | |
| 1000 | |
| 1001 @example | |
| 1002 @@(@var{argument-list}) @var{expression} | |
| 1003 @end example | |
| 1004 | |
| 1005 @noindent | |
| 1006 Any variables that are not found in the argument list are inherited from | |
| 1007 the enclosing scope. Anonymous functions are useful for creating simple | |
| 1008 unnamed functions from expressions or for wrapping calls to other | |
| 1009 functions to adapt them for use by functions like @code{quad}. For | |
| 1010 example, | |
| 1011 | |
| 1012 @example | |
| 1013 f = @@(x) x.^2; | |
| 1014 quad (f, 0, 10) | |
| 6570 | 1015 @result{} 333.33 |
| 6554 | 1016 @end example |
| 1017 | |
| 1018 @noindent | |
| 1019 creates a simple unnamed function from the expression @code{x.^2} and | |
| 1020 passes it to @code{quad}, | |
| 1021 | |
| 1022 @example | |
| 1023 quad (@@(x) sin (x), 0, pi) | |
| 6933 | 1024 @result{} 2 |
| 6554 | 1025 @end example |
| 1026 | |
| 1027 @noindent | |
| 1028 wraps another function, and | |
| 1029 | |
| 1030 @example | |
| 1031 a = 1; | |
| 1032 b = 2; | |
| 1033 quad (@@(x) betainc (x, a, b), 0, 0.4) | |
| 6929 | 1034 @result{} 0.13867 |
| 6554 | 1035 @end example |
| 1036 | |
| 1037 @noindent | |
| 1038 adapts a function with several parameters to the form required by | |
| 1039 @code{quad}. In this example, the values of @var{a} and @var{b} that | |
| 1040 are passed to @code{betainc} are inherited from the current | |
| 1041 environment. | |
| 1042 | |
| 4933 | 1043 @node Inline Functions |
| 1044 @subsection Inline Functions | |
| 1045 | |
| 6638 | 1046 An inline function is created from a string containing the function |
| 1047 body using the @code{inline} function. The following code defines the | |
| 1048 function @math{f(x) = x^2 + 2}. | |
| 1049 | |
| 1050 @example | |
| 1051 f = inline("x^2 + 2"); | |
| 1052 @end example | |
| 1053 | |
| 1054 @noindent | |
| 1055 After this it is possible to evaluate @math{f} at any @math{x} by | |
| 1056 writing @code{f(x)}. | |
| 1057 | |
| 4933 | 1058 @DOCSTRING(inline) |
| 1059 | |
| 1060 @DOCSTRING(argnames) | |
| 1061 | |
| 1062 @DOCSTRING(formula) | |
| 1063 | |
| 1064 @DOCSTRING(vectorize) | |
| 1065 | |
| 6549 | 1066 @node Commands |
| 1067 @section Commands | |
| 1068 | |
| 6638 | 1069 Commands are a special class of functions that only accept string |
| 1070 input arguments. A command can be called as an ordinary function, but | |
| 1071 it can also be called without the parentheses like the following example | |
| 1072 shows | |
| 1073 | |
| 1074 @example | |
| 1075 my_command hello world | |
| 1076 @end example | |
| 1077 | |
| 1078 @noindent | |
| 1079 which is the same as | |
| 1080 | |
| 1081 @example | |
| 1082 my_command("hello", "world") | |
| 1083 @end example | |
| 1084 | |
| 1085 The general form of a command call is | |
| 1086 | |
| 1087 @example | |
| 1088 @var{name} @var{arg1} @var{arg2} @dots{} | |
| 1089 @end example | |
| 1090 | |
| 1091 @noindent | |
| 1092 which translates directly to | |
| 1093 | |
| 1094 @example | |
| 1095 @var{name} ("@var{arg1}", "@var{arg2}", @dots{}) | |
| 1096 @end example | |
| 1097 | |
| 7001 | 1098 A function can be used as a command if it accepts string input arguments. |
| 6638 | 1099 To do this, the function must be marked as a command, which can be done |
| 1100 with the @code{mark_as_command} command like this | |
| 1101 | |
| 1102 @example | |
| 1103 mark_as_command name | |
| 1104 @end example | |
| 1105 | |
| 1106 @noindent | |
| 1107 where @code{name} is the function to be marked as a command. | |
| 1108 | |
| 1109 One difficulty of commands occurs when one of the string input arguments | |
| 1110 are stored in a variable. Since Octave can't tell the difference between | |
| 1111 a variable name, and an ordinary string, it is not possible to pass a | |
| 1112 variable as input to a command. In such a situation a command must be | |
| 1113 called as a function. | |
| 1114 | |
| 6549 | 1115 @DOCSTRING(mark_as_command) |
| 1116 | |
| 1117 @DOCSTRING(unmark_command) | |
| 1118 | |
| 1119 @DOCSTRING(iscommand) | |
| 1120 | |
| 1121 @DOCSTRING(mark_as_rawcommand) | |
| 1122 | |
| 1123 @DOCSTRING(unmark_rawcommand) | |
| 1124 | |
| 1125 @DOCSTRING(israwcommand) | |
| 1126 | |
| 4167 | 1127 @node Organization of Functions |
| 3294 | 1128 @section Organization of Functions Distributed with Octave |
| 1129 | |
| 1130 Many of Octave's standard functions are distributed as function files. | |
| 1131 They are loosely organized by topic, in subdirectories of | |
| 1132 @file{@var{octave-home}/lib/octave/@var{version}/m}, to make it easier | |
| 1133 to find them. | |
| 1134 | |
| 1135 The following is a list of all the function file subdirectories, and the | |
| 1136 types of functions you will find there. | |
| 1137 | |
| 1138 @table @file | |
| 1139 @item audio | |
| 1140 Functions for playing and recording sounds. | |
| 1141 | |
| 1142 @item control | |
| 1143 Functions for design and simulation of automatic control systems. | |
| 1144 | |
| 1145 @item elfun | |
| 1146 Elementary functions. | |
| 1147 | |
| 6554 | 1148 @item finance |
| 1149 Functions for computing interest payments, investment values, and rates | |
| 1150 of return. | |
| 1151 | |
| 3294 | 1152 @item general |
| 1153 Miscellaneous matrix manipulations, like @code{flipud}, @code{rot90}, | |
| 1154 and @code{triu}, as well as other basic functions, like | |
| 4029 | 1155 @code{ismatrix}, @code{nargchk}, etc. |
| 3294 | 1156 |
| 1157 @item image | |
| 1158 Image processing tools. These functions require the X Window System. | |
| 1159 | |
| 1160 @item io | |
| 1161 Input-ouput functions. | |
| 1162 | |
| 1163 @item linear-algebra | |
| 1164 Functions for linear algebra. | |
| 1165 | |
| 1166 @item miscellaneous | |
| 1167 Functions that don't really belong anywhere else. | |
| 1168 | |
| 6554 | 1169 @item optimization |
| 1170 Minimization of functions. | |
| 1171 | |
| 1172 @item path | |
| 1173 Functions to manage the directory path Octave uses to find functions. | |
| 1174 | |
| 1175 @item pkg | |
| 1176 Install external packages of functions in Octave. | |
| 1177 | |
| 3294 | 1178 @item plot |
| 6556 | 1179 Functions for displaying and printing two- and three-dimensional graphs. |
| 3294 | 1180 |
| 1181 @item polynomial | |
| 1182 Functions for manipulating polynomials. | |
| 1183 | |
| 1184 @item set | |
| 1185 Functions for creating and manipulating sets of unique values. | |
| 1186 | |
| 1187 @item signal | |
| 1188 Functions for signal processing applications. | |
| 1189 | |
| 6554 | 1190 @item sparse |
| 1191 Functions for handling sparse matrices. | |
| 1192 | |
| 3294 | 1193 @item specfun |
| 1194 Special functions. | |
| 1195 | |
| 1196 @item special-matrix | |
| 1197 Functions that create special matrix forms. | |
| 1198 | |
| 1199 @item startup | |
| 1200 Octave's system-wide startup file. | |
| 1201 | |
| 1202 @item statistics | |
| 1203 Statistical functions. | |
| 1204 | |
| 1205 @item strings | |
| 1206 Miscellaneous string-handling functions. | |
| 1207 | |
| 6554 | 1208 @item testfun |
| 1209 Perform unit tests on other functions. | |
| 1210 | |
| 3294 | 1211 @item time |
| 1212 Functions related to time keeping. | |
| 1213 @end table |