This is Info file octave.info, produced by Makeinfo-1.55 from the input file octave.texi. Copyright (C) 1993, 1994, 1995 John W. Eaton. Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions. File: octave.info, Node: The while Statement, Next: The for Statement, Prev: The if Statement, Up: Statements The `while' Statement ===================== In programming, a "loop" means a part of a program that is (or at least can be) executed two or more times in succession. The `while' statement is the simplest looping statement in Octave. It repeatedly executes a statement as long as a condition is true. As with the condition in an `if' statement, the condition in a `while' statement is considered true if its value is non-zero, and false if its value is zero. If the value of the conditional expression in an `if' statement is a vector or a matrix, it is considered true only if *all* of the elements are non-zero. Octave's `while' statement looks like this: while (CONDITION) BODY endwhile Here BODY is a statement or list of statements that we call the "body" of the loop, and CONDITION is an expression that controls how long the loop keeps running. The first thing the `while' statement does is test CONDITION. If CONDITION is true, it executes the statement BODY. After BODY has been executed, CONDITION is tested again, and if it is still true, BODY is executed again. This process repeats until CONDITION is no longer true. If CONDITION is initially false, the body of the loop is never executed. This example creates a variable `fib' that contains the elements of the Fibonacci sequence. fib = ones (1, 10); i = 3; while (i <= 10) fib (i) = fib (i-1) + fib (i-2); i++; endwhile Here the body of the loop contains two statements. The loop works like this: first, the value of `i' is set to 3. Then, the `while' tests whether `i' is less than or equal to 10. This is the case when `i' equals 3, so the value of the `i'-th element of `fib' is set to the sum of the previous two values in the sequence. Then the `i++' increments the value of `i' and the loop repeats. The loop terminates when `i' reaches 11. A newline is not required between the condition and the body; but using one makes the program clearer unless the body is very simple. File: octave.info, Node: The for Statement, Next: The break Statement, Prev: The while Statement, Up: Statements The `for' Statement =================== The `for' statement makes it more convenient to count iterations of a loop. The general form of the `for' statement looks like this: for VAR = EXPRESSION BODY endfor The assignment expression in the `for' statement works a bit differently than Octave's normal assignment statement. Instead of assigning the complete result of the expression, it assigns each column of the expression to VAR in turn. If EXPRESSION is either a row vector or a scalar, the value of VAR will be a scalar each time the loop body is executed. If VAR is a column vector or a matrix, VAR will be a column vector each time the loop body is executed. The following example shows another way to create a vector containing the first ten elements of the Fibonacci sequence, this time using the `for' statement: fib = ones (1, 10); for i = 3:10 fib (i) = fib (i-1) + fib (i-2); endfor This code works by first evaluating the expression `3:10', to produce a range of values from 3 to 10 inclusive. Then the variable `i' is assigned the first element of the range and the body of the loop is executed once. When the end of the loop body is reached, the next value in the range is assigned to the variable `i', and the loop body is executed again. This process continues until there are no more elements to assign. In the `for' statement, BODY stands for any statement or list of statements. Although it is possible to rewrite all `for' loops as `while' loops, the Octave language has both statements because often a `for' loop is both less work to type and more natural to think of. Counting the number of iterations is very common in loops and it can be easier to think of this counting as part of looping rather than as something to do inside the loop. File: octave.info, Node: The break Statement, Next: The continue Statement, Prev: The for Statement, Up: Statements The `break' Statement ===================== The `break' statement jumps out of the innermost `for' or `while' loop that encloses it. The `break' statement may only be used within the body of a loop. The following example finds the smallest divisor of a given integer, and also identifies prime numbers: num = 103; div = 2; while (div*div <= num) if (rem (num, div) == 0) break; endif div++; endwhile if (rem (num, div) == 0) printf ("Smallest divisor of %d is %d\n", num, div) else printf ("%d is prime\n", num); endif When the remainder is zero in the first `while' statement, Octave immediately "breaks out" of the loop. This means that Octave proceeds immediately to the statement following the loop and continues processing. (This is very different from the `exit' statement which stops the entire Octave program.) Here is another program equivalent to the previous one. It illustrates how the CONDITION of a `while' statement could just as well be replaced with a `break' inside an `if': num = 103; div = 2; while (1) if (rem (num, div) == 0) printf ("Smallest divisor of %d is %d\n", num, div); break; endif div++; if (div*div > num) printf ("%d is prime\n", num); break; endif endwhile File: octave.info, Node: The continue Statement, Next: The unwind_protect Statement, Prev: The break Statement, Up: Statements The `continue' Statement ======================== The `continue' statement, like `break', is used only inside `for' or `while' loops. It skips over the rest of the loop body, causing the next cycle around the loop to begin immediately. Contrast this with `break', which jumps out of the loop altogether. Here is an example: # print elements of a vector of random # integers that are even. # first, create a row vector of 10 random # integers with values between 0 and 100: vec = round (rand (1, 10) * 100); # print what we're interested in: for x = vec if (rem (x, 2) != 0) continue; endif printf ("%d\n", x); endfor If one of the elements of VEC is an odd number, this example skips the print statement for that element, and continues back to the first statement in the loop. This is not a practical example of the `continue' statement, but it should give you a clear understanding of how it works. Normally, one would probably write the loop like this: for x = vec if (rem (x, 2) == 0) printf ("%d\n", x); endif endfor File: octave.info, Node: The unwind_protect Statement, Next: Continuation Lines, Prev: The continue Statement, Up: Statements The `unwind_protect' Statement ============================== Octave supports a limited form of exception handling modelled after the unwind-protect form of Lisp. The general form of an `unwind_protect' block looks like this: unwind_protect BODY unwind_protect_cleanup CLEANUP end_unwind_protect Where BODY and CLEANUP are both optional and may contain any Octave expressions or commands. The statements in CLEANUP are guaranteed to be executed regardless of how control exits BODY. This is useful to protect temporary changes to global variables from possible errors. For example, the following code will always restore the original value of the built-in variable `do_fortran_indexing' even if an error occurs while performing the indexing operation. save_do_fortran_indexing = do_fortran_indexing; unwind_protect do_fortran_indexing = "true"; elt = a (idx) unwind_protect_cleanup do_fortran_indexing = save_do_fortran_indexing; end_unwind_protect Without `unwind_protect', the value of DO_FORTRAN_INDEXING would not be restored if an error occurs while performing the indexing operation because evaluation would stop at the point of the error and the statement to restore the value would not be executed. File: octave.info, Node: Continuation Lines, Prev: The unwind_protect Statement, Up: Statements Continuation Lines ================== In the Octave language, most statements end with a newline character and you must tell Octave to ignore the newline character in order to continue a statement from one line to the next. Lines that end with the characters `...' or `\' are joined with the following line before they are divided into tokens by Octave's parser. For example, the lines x = long_variable_name ... + longer_variable_name \ - 42 form a single statement. The backslash character on the second line above is interpreted a continuation character, *not* as a division operator. For continuation lines that do not occur inside string constants, whitespace and comments may appear between the continuation marker and the newline character. For example, the statement x = long_variable_name ... % comment one + longer_variable_name \ % comment two - 42 % last comment is equivalent to the one shown above. In some cases, Octave will allow you to continue lines without having to specify continuation characters. For example, it is possible to write statements like if (big_long_variable_name == other_long_variable_name || not_so_short_variable_name > 4 && y > x) some (code, here); endif without having to clutter up the if statement with continuation characters. File: octave.info, Node: Functions and Scripts, Next: Built-in Variables, Prev: Statements, Up: Top Functions and Script Files ************************** Complicated Octave programs can often be simplified by defining functions. Functions can be defined directly on the command line during interactive Octave sessions, or in external files, and can be called just like built-in ones. * Menu: * Defining Functions:: * Multiple Return Values:: * Variable-length Argument Lists:: * Variable-length Return Lists:: * Returning From a Function:: * Function Files:: * Script Files:: * Dynamically Linked Functions:: * Organization of Functions:: File: octave.info, Node: Defining Functions, Next: Multiple Return Values, Prev: Functions and Scripts, Up: Functions and Scripts Defining Functions ================== In its simplest form, the definition of a function named NAME looks like this: function NAME BODY endfunction A valid function name is like a valid variable name: a sequence of letters, digits and underscores, not starting with a digit. Functions share the same pool of names as variables. The function BODY consists of Octave statements. It is the most important part of the definition, because it says what the function should actually *do*. For example, here is a function that, when executed, will ring the bell on your terminal (assuming that it is possible to do so): function wakeup printf ("\a"); endfunction The `printf' statement (*note Input and Output::.) simply tells Octave to print the string `"\a"'. The special character `\a' stands for the alert character (ASCII 7). *Note String Constants::. Once this function is defined, you can ask Octave to evaluate it by typing the name of the function. Normally, you will want to pass some information to the functions you define. The syntax for passing parameters to a function in Octave is function NAME (ARG-LIST) BODY endfunction where ARG-LIST is a comma-separated list of the function's arguments. When the function is called, the argument names are used to hold the argument values given in the call. The list of arguments may be empty, in which case this form is equivalent to the one shown above. To print a message along with ringing the bell, you might modify the `beep' to look like this: function wakeup (message) printf ("\a%s\n", message); endfunction Calling this function using a statement like this wakeup ("Rise and shine!"); will cause Octave to ring your terminal's bell and print the message `Rise and shine!', followed by a newline character (the `\n' in the first argument to the `printf' statement). In most cases, you will also want to get some information back from the functions you define. Here is the syntax for writing a function that returns a single value: function RET-VAR = NAME (ARG-LIST) BODY endfunction The symbol RET-VAR is the name of the variable that will hold the value to be returned by the function. This variable must be defined before the end of the function body in order for the function to return a value. For example, here is a function that computes the average of the elements of a vector: function retval = avg (v) retval = sum (v) / length (v); endfunction If we had written `avg' like this instead, function retval = avg (v) if (is_vector (v)) retval = sum (v) / length (v); endif endfunction and then called the function with a matrix instead of a vector as the argument, Octave would have printed an error message like this: error: `retval' undefined near line 1 column 10 error: evaluating index expression near line 7, column 1 because the body of the `if' statement was never executed, and `retval' was never defined. To prevent obscure errors like this, it is a good idea to always make sure that the return variables will always have values, and to produce meaningful error messages when problems are encountered. For example, `avg' could have been written like this: function retval = avg (v) retval = 0; if (is_vector (v)) retval = sum (v) / length (v); else error ("avg: expecting vector argument"); endif endfunction There is still one additional problem with this function. What if it is called without an argument? Without additional error checking, Octave will probably print an error message that won't really help you track down the source of the error. To allow you to catch errors like this, Octave provides each function with an automatic variable called `nargin'. Each time a function is called, `nargin' is automatically initialized to the number of arguments that have actually been passed to the function. For example, we might rewrite the `avg' function like this: function retval = avg (v) retval = 0; if (nargin != 1) error ("usage: avg (vector)"); endif if (is_vector (v)) retval = sum (v) / length (v); else error ("avg: expecting vector argument"); endif endfunction Although Octave does not consider it an error if you call a function with more arguments than were expected, doing so is probably an error, so we check for that possibility too, and issue the error message if either too few or too many arguments have been provided. The body of a user-defined function can contain a `return' statement. This statement returns control to the rest of the Octave program. A `return' statement is assumed at the end of every function definition. File: octave.info, Node: Multiple Return Values, Next: Variable-length Argument Lists, Prev: Defining Functions, Up: Functions and Scripts Multiple Return Values ====================== Unlike many other computer languages, Octave allows you to define functions that return more than one value. The syntax for defining functions that return multiple values is function [RET-LIST] = NAME (ARG-LIST) BODY endfunction where NAME, ARG-LIST, and BODY have the same meaning as before, and RET-LIST is a comma-separated list of variable names that will hold the values returned from the function. The list of return values must have at least one element. If RET-LIST has only one element, this form of the `function' statement is equivalent to the form described in the previous section. Here is an example of a function that returns two values, the maximum element of a vector and the index of its first occurrence in the vector. function [max, idx] = vmax (v) idx = 1; max = v (idx); for i = 2:length (v) if (v (i) > max) max = v (i); idx = i; endif endfor endfunction In this particular case, the two values could have been returned as elements of a single array, but that is not always possible or convenient. The values to be returned may not have compatible dimensions, and it is often desirable to give the individual return values distinct names. In addition to setting `nargin' each time a function is called, Octave also automatically initializes `nargout' to the number of values that are expected to be returned. This allows you to write functions that behave differently depending on the number of values that the user of the function has requested. The implicit assignment to the built-in variable `ans' does not figure in the count of output arguments, so the value of `nargout' may be zero. The `svd' and `lu' functions are examples of built-in functions that behave differently depending on the value of `nargout'. It is possible to write functions that only set some return values. For example, calling the function function [x, y, z] = f () x = 1; z = 2; endfunction [a, b, c] = f () produces: a = 1 b = [](0x0) c = 2 File: octave.info, Node: Variable-length Argument Lists, Next: Variable-length Return Lists, Prev: Multiple Return Values, Up: Functions and Scripts Variable-length Argument Lists ============================== Octave has a real mechanism for handling functions that take an unspecified number of arguments, so it is not necessary to place an upper bound on the number of optional arguments that a function can accept. Here is an example of a function that uses the new syntax to print a header followed by an unspecified number of values: function foo (heading, ...) disp (heading); va_start (); while (--nargin) disp (va_arg ()); endwhile endfunction The ellipsis that marks the variable argument list may only appear once and must be the last element in the list of arguments. Calling `va_start()' positions an internal pointer to the first unnamed argument and allows you to cycle through the arguments more than once. It is not necessary to call `va_start()' if you do not plan to cycle through the arguments more than once. The function `va_arg()' returns the value of the next available argument and moves the internal pointer to the next argument. It is an error to call `va_arg()' when there are no more arguments available. Sometimes it is useful to be able to pass all unnamed arguments to another function. The keyword ALL_VA_ARGS makes this very easy to do. For example, given the functions function f (...) while (nargin--) disp (va_arg ()) endwhile endfunction function g (...) f ("begin", all_va_args, "end") endfunction the statement g (1, 2, 3) prints begin 1 2 3 end The keyword `all_va_args' always stands for the entire list of optional argument, so it is possible to use it more than once within the same function without having to call `var_start ()'. It can only be used within functions that take a variable number of arguments. It is an error to use it in other contexts. File: octave.info, Node: Variable-length Return Lists, Next: Returning From a Function, Prev: Variable-length Argument Lists, Up: Functions and Scripts Variable-length Return Lists ============================ Octave also has a real mechanism for handling functions that return an unspecified number of values, so it is no longer necessary to place an upper bound on the number of outputs that a function can produce. Here is an example of a function that uses the new syntax to produce N values: function [...] = foo (n, x) for i = 1:n vr_val (i * x); endfor endfunction Each time `vr_val()' is called, it places the value of its argument at the end of the list of values to return from the function. Once `vr_val()' has been called, there is no way to go back to the beginning of the list and rewrite any of the return values. As with variable argument lists, the ellipsis that marks the variable return list may only appear once and must be the last element in the list of returned values. File: octave.info, Node: Returning From a Function, Next: Function Files, Prev: Variable-length Return Lists, Up: Functions and Scripts Returning From a Function ========================= The body of a user-defined function can contain a `return' statement. This statement returns control to the rest of the Octave program. It looks like this: return Unlike the `return' statement in C, Octave's `return' statement cannot be used to return a value from a function. Instead, you must assign values to the list of return variables that are part of the `function' statement. The `return' statement simply makes it easier to exit a function from a deeply nested loop or conditional statement. Here is an example of a function that checks to see if any elements of a vector are nonzero. function retval = any_nonzero (v) retval = 0; for i = 1:length (v) if (v (i) != 0) retval = 1; return; endif endfor printf ("no nonzero elements found\n"); endfunction Note that this function could not have been written using the `break' statement to exit the loop once a nonzero value is found without adding extra logic to avoid printing the message if the vector does contain a nonzero element. File: octave.info, Node: Function Files, Next: Script Files, Prev: Returning From a Function, Up: Functions and Scripts Function Files ============== Except for simple one-shot programs, it is not practical to have to define all the functions you need each time you need them. Instead, you will normally want to save them in a file so that you can easily edit them, and save them for use at a later time. Octave does not require you to load function definitions from files before using them. You simply need to put the function definitions in a place where Octave can find them. When Octave encounters an identifier that is undefined, it first looks for variables or functions that are already compiled and currently listed in its symbol table. If it fails to find a definition there, it searches the list of directories specified by the built-in variable `LOADPATH' for files ending in `.m' that have the same base name as the undefined identifier.(1) *Note User Preferences:: for a description of `LOADPATH'. Once Octave finds a file with a name that matches, the contents of the file are read. If it defines a *single* function, it is compiled and executed. *Note Script Files::, for more information about how you can define more than one function in a single file. When Octave defines a function from a function file, it saves the full name of the file it read and the time stamp on the file. After that, it checks the time stamp on the file every time it needs the function. If the time stamp indicates that the file has changed since the last time it was read, Octave reads it again. Checking the time stamp allows you to edit the definition of a function while Octave is running, and automatically use the new function definition without having to restart your Octave session. Checking the time stamp every time a function is used is rather inefficient, but it has to be done to ensure that the correct function definition is used. Octave assumes that function files in the `/usr/local/lib/octave/1.1.1' directory tree will not change, so it doesn't have to check their time stamps every time the functions defined in those files are used. This is normally a very good assumption and provides a significant improvement in performance for the function files that are distributed with Octave. If you know that your own function files will not change while you are running Octave, you can improve performance by setting the variable `ignore_function_time_stamp' to `"all"', so that Octave will ignore the time stamps for all function files. Setting it to `"system"' gives the default behavior. If you set it to anything else, Octave will check the time stamps on all function files. ---------- Footnotes ---------- (1) The `.m' suffix was chosen for compatibility with MATLAB. File: octave.info, Node: Script Files, Next: Dynamically Linked Functions, Prev: Function Files, Up: Functions and Scripts Script Files ============ A script file is a file containing (almost) any sequence of Octave commands. It is read and evaluated just as if you had typed each command at the Octave prompt, and provides a convenient way to perform a sequence of commands that do not logically belong inside a function. Unlike a function file, a script file must *not* begin with the keyword `function'. If it does, Octave will assume that it is a function file, and that it defines a single function that should be evaluated as soon as it is defined. A script file also differs from a function file in that the variables named in a script file are not local variables, but are in the same scope as the other variables that are visible on the command line. Even though a script file may not begin with the `function' keyword, it is possible to define more than one function in a single script file and load (but not execute) all of them at once. To do this, the first token in the file (ignoring comments and other white space) must be something other than `function'. If you have no other statements to evaluate, you can use a statement that has no effect, like this: # Prevent Octave from thinking that this # is a function file: 1; # Define function one: function one () ... To have Octave read and compile these functions into an internal form, you need to make sure that the file is in Octave's `LOADPATH', then simply type the base name of the file that contains the commands. (Octave uses the same rules to search for script files as it does to search for function files.) If the first token in a file (ignoring comments) is `function', Octave will compile the function and try to execute it, printing a message warning about any non-whitespace characters that appear after the function definition. Note that Octave does not try to lookup the definition of any identifier until it needs to evaluate it. This means that Octave will compile the following statements if they appear in a script file, or are typed at the command line, # not a function file: 1; function foo () do_something (); endfunction function do_something () do_something_else (); endfunction even though the function `do_something' is not defined before it is referenced in the function `foo'. This is not an error because the Octave does not need to resolve all symbols that are referenced by a function until the function is actually evaluated. Since Octave doesn't look for definitions until they are needed, the following code will always print `bar = 3' whether it is typed directly on the command line, read from a script file, or is part of a function body, even if there is a function or script file called `bar.m' in Octave's `LOADPATH'. eval ("bar = 3"); bar Code like this appearing within a function body could fool Octave if definitions were resolved as the function was being compiled. It would be virtually impossible to make Octave clever enough to evaluate this code in a consistent fashion. The parser would have to be able to perform the `eval ()' statement at compile time, and that would be impossible unless all the references in the string to be evaluated could also be resolved, and requiring that would be too restrictive (the string might come from user input, or depend on things that are not known until the function is evaluated). File: octave.info, Node: Dynamically Linked Functions, Next: Organization of Functions, Prev: Script Files, Up: Functions and Scripts Dynamically Linked Functions ============================ On some systems, Octave can dynamically load and execute functions written in C++ or other compiled languages. This currently only works on systems that have a working version of the GNU dynamic linker, `dld'. Unfortunately, `dld' does not work on very many systems, but someone is working on making `dld' use the GNU Binary File Descriptor library, `BFD', so that may soon change. In any case, it should not be too hard to make Octave's dynamic linking features work on other systems using system-specific dynamic linking facilities. Here is an example of how to write a C++ function that Octave can load. #include #include "defun-dld.h" #include "tree-const.h" DEFUN_DLD ("hello", Fhello, Shello, -1, -1, "hello (...)\n\ \n\ Print greeting followed by the values of all the arguments passed.\n\ Returns all the arguments passed.") { Octave_object retval; cerr << "Hello, world!\n"; int nargin = args.length (); for (int i = 1; i < nargin; i++) retval (nargin-i-1) = args(i).eval (1); return retval; } Octave's dynamic linking features currently have the following limitations. * Dynamic linking only works on systems that support the GNU dynamic linker, `dld'. * Clearing dynamically linked functions doesn't work. * Configuring Octave with `--enable-lite-kernel' seems to mostly work to make nonessential built-in functions dynamically loaded, but there also seem to be some problems. For example, fsolve seems to always return `info == 3'. This is difficult to debug since `gdb' won't seem to allow breakpoints to be set inside dynamically loaded functions. * Octave uses a lot of memory if the dynamically linked functions are compiled to include debugging symbols. This appears to be a limitation with `dld', and can be avoided by not using `-g' to compile functions that will be linked dynamically. If you would like to volunteer to help improve Octave's ability to dynamically link externally compiled functions, please contact `bug-octave@che.utexas.edu'. File: octave.info, Node: Organization of Functions, Prev: Dynamically Linked Functions, Up: Functions and Scripts Organization of Functions Distributed with Octave ================================================= Many of Octave's standard functions are distributed as function files. They are loosely organized by topic, in subdirectories of `OCTAVE_HOME/lib/octave/VERSION/m', to make it easier to find them. The following is a list of all the function file subdirectories, and the types of functions you will find there. `control' Functions for design and simulation of automatic control systems. `elfun' Elementary functions. `general' Miscellaneous matrix manipulations, like `flipud', `rot90', and `triu', as well as other basic functions, like `is_matrix', `nargchk', etc. `image' Image processing tools. These functions require the X Window System. `linear-algebra' Functions for linear algebra. `miscellaneous' Functions that don't really belong anywhere else. `plot' A set of functions that implement the MATLAB-like plotting functions. `polynomial' Functions for manipulating polynomials. `set' Functions for creating and manipulating sets of unique values. `signal' Functions for signal processing applications. `specfun' Special functions. `special-matrix' Functions that create special matrix forms. `startup' Octave's system-wide startup file. `statistics' Statistical functions. `strings' Miscellaneous string-handling functions. *Note User Preferences:: for an explanation of the built-in variable `LOADPATH', and *Note Function Files:: for a description of the way Octave resolves undefined variable and function names. File: octave.info, Node: Built-in Variables, Next: Arithmetic, Prev: Functions and Scripts, Up: Top Built-in Variables ****************** Most Octave variables are available for you to use for your own purposes; they never change except when your program assigns values to them, and never affect anything except when your program examines them. A few variables have special built-in meanings. Some of them, like `pi' and `eps' provide useful predefined constant values. Others, like `do_fortran_indexing' and `page_screen_output' are examined automatically by Octave, so that you can to tell Octave how to do certain things. There are also two special variables, `ans' and `PWD', that are set automatically by Octave and carry information from the internal workings of Octave to your program. This chapter documents all the built-in variables of Octave. Most of them are also documented in the chapters that describe functions that use them, or are affected by their values. * Menu: * Predefined Constants:: * User Preferences:: * Other Built-in Variables:: * Summary of Preference Variables:: File: octave.info, Node: Predefined Constants, Next: User Preferences, Prev: Built-in Variables, Up: Built-in Variables Predefined Constants ==================== `I, i, J, j' A pure imaginary number, defined as `sqrt (-1)'. The `I' and `J' forms are true constants, and cannot be modified. The `i' and `j' forms are like ordinary variables, and may be used for other purposes. However, unlike other variables, they once again assume their special predefined values if they are cleared *Note Miscellaneous Utilities::. `Inf, inf' Infinity. This is the result of an operation like 1/0, or an operation that results in a floating point overflow. `NaN, nan' Not a number. This is the result of an operation like `0/0', or `Inf - Inf', or any operation with a NaN. `SEEK_SET' `SEEK_CUR' `SEEK_END' These variables may be used as the optional third argument for the function `fseek'. `eps' The machine precision. More precisely, `eps' is the smallest value such that `1+eps' is not equal to 1. This number is system-dependent. On machines that support 64 bit IEEE floating point arithmetic, `eps' is approximately 2.2204e-16. The ratio of the circumference of a circle to its diameter. Internally, `pi' is computed as `4.0 * atan (1.0)'. `realmax' The largest floating point number that is representable. The actual value is system-dependent. On machines that support 64 bit IEEE floating point arithmetic, `realmax' is approximately 1.7977e+308 `realmin' The smallest floating point number that is representable. The actual value is system-dependent. On machines that support 64 bit IEEE floating point arithmetic, `realmin' is approximately 2.2251e-308 `stdin' `stdout' `stderr' These variables are the file numbers corresponding to the standard input, standard output, and standard error streams. These streams are preconnected and available when Octave starts.