C RCS $Id: gnuplot.doc,v 1.40.2.14 2000/10/31 14:48:18 joze Exp $

C 3 December 1998

C Copyright (C) 1986 - 1993, 1998 Thomas Williams, Colin Kelley

C

^ <h2> An Interactive Plotting Program </h2><p>

^ <h2> Thomas Williams & Colin Kelley</h2><p>

^ <h2> Version 3.7 organized by: David Denholm </h2><p>

^ <h2>Major contributors (alphabetic order):</h2>

^<ul><h3>

^<li> Hans-Bernhard Broeker

^<li> John Campbell

^<li> Robert Cunningham

^<li> David Denholm

^<li> Gershon Elber

^<li> Roger Fearick

^<li> Carsten Grammes

^<li> Lucas Hart

^<li> Lars Hecking

^<li> Thomas Koenig

^<li> David Kotz

^<li> Ed Kubaitis

^<li> Russell Lang

^<li> Alexander Lehmann

^<li> Alexander Mai

^<li> Carsten Steger

^<li> Tom Tkacik

^<li> Jos Van der Woude

^<li> James R. Van Zandt

^<li> Alex Woo

^</h3></ul> <p>

^<h2> Copyright (C) 1986 - 1993, 1998 Thomas Williams, Colin Kelley<p>

^ Mailing list for comments: [email protected] <p>

^ Mailing list for bug reports: [email protected]<p>

^</h2><p>

^<h3> This manual was prepared by Dick Crawford</h3><p>

^<h3> 3 December 1998</h3><p>

^<hr>

1 gnuplot

2 Copyright

?copyright

?license

Copyright (C) 1986 - 1993, 1998 Thomas Williams, Colin Kelley

Permission to use, copy, and distribute this software and its

documentation for any purpose with or without fee is hereby granted,

provided that the above copyright notice appear in all copies and

that both that copyright notice and this permission notice appear

in supporting documentation.

Permission to modify the software is granted, but not the right to

distribute the complete modified source code. Modifications are to

be distributed as patches to the released version. Permission to

distribute binaries produced by compiling modified sources is granted,

provided you

1. distribute the corresponding source modifications from the

released version in the form of a patch file along with the binaries,

2. add special version identification to distinguish your version

in addition to the base release version number,

3. provide your name and address as the primary contact for the

support of your modified version, and

4. retain our contact information in regard to use of the base

software.

Permission to distribute the released version of the source code along

with corresponding source modifications in the form of a patch file is

granted with same provisions 2 through 4 for binary distributions.

This software is provided "as is" without express or implied warranty

to the extent permitted by applicable law.

AUTHORS

Original Software:

Thomas Williams, Colin Kelley.

Gnuplot 2.0 additions:

Russell Lang, Dave Kotz, John Campbell.

Gnuplot 3.0 additions:

Gershon Elber and many others.

2 Introduction

?introduction

?

`gnuplot` is a command-driven interactive function and data plotting program.

It is case sensitive (commands and function names written in lowercase are

not the same as those written in CAPS). All command names may be abbreviated

as long as the abbreviation is not ambiguous. Any number of commands may

appear on a line (with the exception that `load` or `call` must be the final

command), separated by semicolons (;). Strings are indicated with quotes.

They may be either single or double quotation marks, e.g.,

load "filename"

cd 'dir'

although there are some subtle differences (see `syntax` for more details).

Any command-line arguments are assumed to be names of files containing

`gnuplot` commands, with the exception of standard X11 arguments, which are

processed first. Each file is loaded with the `load` command, in the order

specified. `gnuplot` exits after the last file is processed. When no load

files are named, `gnuplot` enters into an interactive mode. The special

filename "-" is used to denote standard input. See "help batch/interactive"

for more details.

Many `gnuplot` commands have multiple options. These options must appear in

the proper order, although unwanted ones may be omitted in most cases. Thus

if the entire command is "command a b c", then "command a c" will probably

work, but "command c a" will fail.

Commands may extend over several input lines by ending each line but the last

with a backslash (\). The backslash must be the _last_ character on each

line. The effect is as if the backslash and newline were not there. That

is, no white space is implied, nor is a comment terminated. Therefore,

commenting out a continued line comments out the entire command (see

`comment`). But note that if an error occurs somewhere on a multi-line

command, the parser may not be able to locate precisely where the error is

and in that case will not necessarily point to the correct line.

In this document, curly braces ({}) denote optional arguments and a vertical

bar (|) separates mutually exclusive choices. `gnuplot` keywords or `help`

topics are indicated by backquotes or `boldface` (where available). Angle

brackets (<>) are used to mark replaceable tokens. In many cases, a default

value of the token will be taken for optional arguments if the token is

omitted, but these cases are not always denoted with braces around the angle

brackets.

For on-line help on any topic, type `help` followed by the name of the topic

or just `help` or `?` to get a menu of available topics.

The new `gnuplot` user should begin by reading about `plotting` (if on-line,

type `help plotting`).

^ <a href="http://www.nas.nasa.gov/~woo/gnuplot/simple/simple.html"> Simple Plots Demo </a>

2 Seeking-assistance

?seeking-assistance

There is a mailing list for `gnuplot` users. Note, however, that the

newsgroup

comp.graphics.apps.gnuplot

is identical to the mailing list (they both carry the same set of messages).

We prefer that you read the messages through the newsgroup rather than

subscribing to the mailing list. Administrative requests should be sent to

[email protected]

Send a message with the body (not the subject) consisting of the single word

"help" (without the quotes) for more details.

The address for mailing to list members is:

[email protected]

Bug reports and code contributions should be mailed to:

[email protected]

The list of those interested in beta-test versions is:

[email protected]

There is also a World Wide Web page with up-to-date information, including

known bugs:

^ <a href="http://www.cs.dartmouth.edu/gnuplot_info.html">

http://www.cs.dartmouth.edu/gnuplot_info.html

^ </a>

Before seeking help, please check the

^ <a href="http://www.uni-karlsruhe.de/~ig25/gnuplot-faq.html">

FAQ (Frequently Asked Questions) list.

^ </a>

If you do not have a copy of the FAQ, you may request a copy by email from

the Majordomo address above, ftp a copy from

ftp://ftp.dartmouth.edu/pub/gnuplot

or see the WWW `gnuplot` page.

When posting a question, please include full details of the version of

`gnuplot`, the machine, and operating system you are using. A _small_ script

demonstrating the problem may be useful. Function plots are preferable to

datafile plots. If email-ing to info-gnuplot, please state whether or not

you are subscribed to the list, so that users who use news will know to email

a reply to you. There is a form for such postings on the WWW site.

2 What's New in version 3.7

?new-features

Gnuplot version 3.7 contains many new features. This section gives a partial

list and links to the new items in no particular order.

1. `fit f(x) 'file' via` uses the Marquardt-Levenberg method to fit data.

(This is only slightly different from the `gnufit` patch available for 3.5.)

2. Greatly expanded `using` command. See `plot using`.

3. `set timefmt` allows for the use of dates as input and output for time

series plots. See `Time/Date data` and

^ <a href="http://www.nas.nasa.gov/~woo/gnuplot/timefmt/timefmt.html">

timedat.dem.

^ </a>

4. Multiline labels and font selection in some drivers.

5. Minor (unlabeled) tics. See `set mxtics`.

6. `key` options for moving the key box in the page (and even outside of the

plot), putting a title on it and a box around it, and more. See `set key`.

7. Multiplots on a single logical page with `set multiplot`.

8. Enhanced `postscript` driver with super/subscripts and font changes.

(This was a separate driver (`enhpost`) that was available as a patch for

3.5.)

9. Second axes: use the top and right axes independently of the bottom and

left, both for plotting and labels. See `plot`.

10. Special datafile names `'-'` and `""`. See `plot special-filenames`.

11. Additional coordinate systems for labels and arrows. See `coordinates`.

12. `set size` can try to plot with a specified aspect ratio.

13. `set missing` now treats missing data correctly.

14. The `call` command: `load` with arguments.

15. More flexible `range` commands with `reverse`, `writeback`, and `restore`

keywords.

16. `set encoding` for multi-lingual encoding.

17. New `x11` driver with persistent and multiple windows.

18. New plotting styles: `xerrorbars`, `errorlines`, `yerrorlines`,

`xerrorlines`, `xyerrorlines`, `histeps`, `financebars` and more.

See `set style`.

19. New tic label formats, including `"%l %L"` which uses the mantissa and

exponents to a given base for labels. See `set format`.

20. New drivers, including `cgm` for inclusion into MS-Office applications

and `gif` for serving plots to the WEB.

21. Smoothing and spline-fitting options for `plot`. See `plot smooth`.

22. `set margin` and `set origin` give much better control over where a

graph appears on the page.

23. `set border` now controls each border individually.

24. The new commands `if` and `reread` allow command loops.

25. Point styles and sizes, line types and widths can be specified on the

`plot` command. Line types and widths can also be specified for grids,

borders, tics and arrows. See `plot with`. Furthermore these types may be

combined and stored for further use. See `set style line`.

26. Text (labels, tic labels, and the time stamp) can be written vertically

by those terminals capable of doing so.

2 bind

?commands bind

?bind

The `bind` command allows to (re-)define a sequence of gnuplot commands

which will be executed when a certain key or key sequence is pressed

while the driver's window has the input focus.

Note that `bind` is only available if gnuplot was compiled with mouse

support and it is used by all mouse-capable terminals.

Bindings overwrite the builtin bindings (like in every real editor),

except <space> and 'q' which cannot be rebound.

Mouse Buttons cannot be rebound.

Note that multikey-bindings with modifiers have to be quoted.

Syntax:

bind [<key-sequence>] ["<gnuplot commands>"]

bind!

Examples:

- set bindings:

bind a "replot"

bind "ctrl-a" "plot x*x"

bind "ctrl-alt-a" 'print "great"'

bind Home "set view 60,30; replot"

- show bindings:

bind "ctrl-a" # shows the binding for ctrl-a

bind # shows all bindings

- remove bindings:

bind "ctrl-alt-a" "" # removes binding for ctrl-alt-a

(note that builtins cannot be removed)

bind! # installs default (builtin) bindings

- bind a key to toggle something:

v=0

bind "ctrl-r" "v=v+1;if(v%2)set term x11 noraise; else set term x11 raise"

Modifiers (ctrl / alt) are case insensitive, keys not:

ctrl-alt-a == CtRl-alT-a

ctrl-alt-a != ctrl-alt-A

List of modifiers (alt == meta):

ctrl, alt

List of supported special keys:

"BackSpace", "Tab", "Linefeed", "Clear", "Return", "Pause", "Scroll_Lock",

"Sys_Req", "Escape", "Delete", "Home", "Left", "Up", "Right", "Down",

"PageUp", "PageDown", "End", "Begin",

"KP_Space", "KP_Tab", "KP_Enter", "KP_F1", "KP_F2", "KP_F3", "KP_F4",

"KP_Home", "KP_Left", "KP_Up", "KP_Right", "KP_Down", "KP_PageUp",

"KP_PageDown", "KP_End", "KP_Begin", "KP_Insert", "KP_Delete", "KP_Equal",

"KP_Multiply", "KP_Add", "KP_Separator", "KP_Subtract", "KP_Decimal",

"KP_Divide",

"KP_1" - "KP_9", "F1" - "F12"

see also `help mouse` and `help if`.

2 Batch/Interactive Operation

?batch/interactive

`gnuplot` may be executed in either batch or interactive modes, and the two

may even be mixed together on many systems.

Any command-line arguments are assumed to be names of files containing

`gnuplot` commands (with the exception of standard X11 arguments, which are

processed first). Each file is loaded with the `load` command, in the order

specified. `gnuplot` exits after the last file is processed. When no load

files are named, `gnuplot` enters into an interactive mode. The special

filename "-" is used to denote standard input.

Both the `exit` and `quit` commands terminate the current command file and

`load` the next one, until all have been processed.

Examples:

To launch an interactive session:

gnuplot

To launch a batch session using two command files "input1" and "input2":

gnuplot input1 input2

To launch an interactive session after an initialization file "header" and

followed by another command file "trailer":

gnuplot header - trailer

2 Command-line-editing

?line-editing

?editing

?command-line-editing

Command-line editing is supported by the Unix, Atari, VMS, MS-DOS and OS/2

versions of `gnuplot`. Also, a history mechanism allows previous commands to

be edited and re-executed. After the command line has been edited, a newline

or carriage return will enter the entire line without regard to where the

cursor is positioned.

(The readline function in `gnuplot` is not the same as the readline used in

GNU Bash and GNU Emacs. If the GNU version is desired, it may be selected

instead of the `gnuplot` version at compile time.)

The editing commands are as follows:

@start table - first is interactive cleartext form

`Line-editing`:

^B moves back a single character.

^F moves forward a single character.

^A moves to the beginning of the line.

^E moves to the end of the line.

^H and DEL delete the previous character.

^D deletes the current character.

^K deletes from current position to the end of line.

^L,^R redraws line in case it gets trashed.

^U deletes the entire line.

^W deletes the last word.

`History`:

^P moves back through history.

^N moves forward through history.

#\begin{tabular}{|cl|} \hline

#\multicolumn{2}{|c|}{Command-line Editing Commands} \\ \hline \hline

#Character & Function \\ \hline

# & \multicolumn{1}{|c|}{Line Editing}\\ \cline{2-2}

#\verb~^B~ & move back a single character.\\

#\verb~^F~ & move forward a single character.\\

#\verb~^A~ & move to the beginning of the line.\\

#\verb~^E~ & move to the end of the line.\\

#\verb~^H, DEL~ & delete the previous character.\\

#\verb~^D~ & delete the current character.\\

#\verb~^K~ & delete from current position to the end of line.\\

#\verb~^L, ^R~ & redraw line in case it gets trashed.\\

#\verb~^U~ & delete the entire line. \\

#\verb~^W~ & delete from the current word to the end of line. \\ \hline

# & \multicolumn{1}{|c|}{History} \\ \cline{2-2}

#\verb~^P~ & move back through history.\\

#\verb~^N~ & move forward through history.\\

%c l .

%Character@Function

%_

%@Line Editing

%^B@move back a single character.

%^F@move forward a single character.

%^A@move to the beginning of the line.

%^E@move to the end of the line.

%^H, DEL@delete the previous character.

%^D@delete the current character.

%^K@delete from current position to the end of line.

%^L, ^R@redraw line in case it gets trashed.

%^U@delete the entire line.

%^W@delete from the current word to the end of line.

%_

%@History

%^P@move back through history.

%^N@move forward through history.

@end table

On the IBM PC, the use of a TSR program such as DOSEDIT or CED may be desired

for line editing. The default makefile assumes that this is the case; by

default `gnuplot` will be compiled with no line-editing capability. If you

want to use `gnuplot`'s line editing, set READLINE in the makefile and add

readline.obj to the link file. The following arrow keys may be used on the

IBM PC and Atari versions if readline is used:

@start table - first is interactive cleartext form

Left Arrow - same as ^B.

Right Arrow - same as ^F.

Ctrl Left Arrow - same as ^A.

Ctrl Right Arrow - same as ^E.

Up Arrow - same as ^P.

Down Arrow - same as ^N.

#\begin{tabular}{|cl|} \hline

#Arrow key & Function \\ \hline

#Left & same as \verb~^B~. \\

#Right & same as \verb~^F~. \\

#Ctrl Left & same as \verb~^A~. \\

#Ctrl Right & same as \verb~^E~. \\

#Up & same as \verb~^P~. \\

#Down & same as \verb~^N~. \\

%c l .

%Arrow key@Function

%_

%Left Arrow@same as ^B.

%Right Arrow@same as ^F.

%Ctrl Left Arrow@same as ^A.

%Ctrl Right Arrow@same as ^E.

%Up Arrow@same as ^P.

%Down Arrow@same as ^N.

%_

@end table

The Atari version of readline defines some additional key aliases:

@start table - first is interactive cleartext form

Undo - same as ^L.

Home - same as ^A.

Ctrl Home - same as ^E.

Esc - same as ^U.

Help - `help` plus return.

Ctrl Help - `help `.

#\begin{tabular}{|cl|} \hline

#Arrow key & Function \\ \hline

#Undo & same as \verb~^L~. \\

#Home & same as \verb~^A~. \\

#Ctrl Home & same as \verb~^E~. \\

#Esc & same as \verb~^U~. \\

#Help & `{\bf help}` plus return. \\

#Ctrl Help & `{\bf help}`. \\

%c l .

%Arrow key@Function

%_

%Undo@same as ^L.

%Home@same as ^A.

%Ctrl Home@same as ^E.

%Esc@same as ^U.

%Help@help plus return.

%Ctrl Help@help .

%_

@end table

2 Comments

?comments

Comments are supported as follows: a `#` may appear in most places in a line

and `gnuplot` will ignore the rest of the line. It will not have this effect

inside quotes, inside numbers (including complex numbers), inside command

substitutions, etc. In short, it works anywhere it makes sense to work.

2 Coordinates

?coordinates

The commands `set arrow`, `set key`, and `set label` allow you to draw

something at an arbitrary position on the graph. This position is specified

by the syntax:

{<system>} <x>, {<system>} <y> {,{<system>} <z>}

Each <system> can either be `first`, `second`, `graph` or `screen`.

`first` places the x, y, or z coordinate in the system defined by the left

and bottom axes; `second` places it in the system defined by the second axes

(top and right); `graph` specifies the area within the axes---0,0 is bottom

left and 1,1 is top right (for splot, 0,0,0 is bottom left of plotting area;

use negative z to get to the base---see `set ticslevel`); and `screen`

specifies the screen area (the entire area---not just the portion selected by

`set size`), with 0,0 at bottom left and 1,1 at top right.

If the coordinate system for x is not specified, `first` is used. If the

system for y is not specified, the one used for x is adopted.

If one (or more) axis is timeseries, the appropriate coordinate should

be given as a quoted time string according to the `timefmt` format string.

See `set xdata` and `set timefmt`. `gnuplot` will also accept an integer

expression, which will be interpreted as seconds from 1 January 2000.

2 Environment

?environment

A number of shell environment variables are understood by `gnuplot`. None of

these are required, but may be useful.

If GNUTERM is defined, it is used as the name of the terminal type to be

used. This overrides any terminal type sensed by `gnuplot` on start-up, but

is itself overridden by the .gnuplot (or equivalent) start-up file (see

`start-up`) and, of course, by later explicit changes.

On Unix, AmigaOS, AtariTOS, MS-DOS and OS/2, GNUHELP may be defined to be the

pathname of the HELP file (gnuplot.gih).

On VMS, the logical name GNUPLOT$HELP should be defined as the name of the

help library for `gnuplot`. The `gnuplot` help can be put inside any system

help library, allowing access to help from both within and outside `gnuplot`

if desired.

On Unix, HOME is used as the name of a directory to search for a .gnuplot

file if none is found in the current directory. On AmigaOS, AtariTOS,

MS-DOS and OS/2, gnuplot is used. On VMS, SYS$LOGIN: is used. See `help

start-up`.

On Unix, PAGER is used as an output filter for help messages.

On Unix, AtariTOS and AmigaOS, SHELL is used for the `shell` command. On

MS-DOS and OS/2, COMSPEC is used for the `shell` command.

On MS-DOS, if the BGI or Watcom interface is used, PCTRM is used to tell

the maximum resolution supported by your monitor by setting it to

S<max. horizontal resolution>. E.g. if your monitor's maximum resolution is

800x600, then use:

set PCTRM=S800

If PCTRM is not set, standard VGA is used.

FIT_SCRIPT may be used to specify a `gnuplot` command to be executed when a

fit is interrupted---see `fit`. FIT_LOG specifies the filename of the

logfile maintained by fit.

GNUPLOT_LIB may be used to define additional search directories for data

and command files. The variable may contain a single directory name, or

a list of directories separated by a platform-specific path separator,

eg. ':' on Unix, or ';' on DOS/Windows/OS/2/Amiga platforms. The contents

of GNUPLOT_LIB are appended to the `loadpath` variable, but not saved

with the `save` and `save set` commands.

2 Expressions

?expressions

In general, any mathematical expression accepted by C, FORTRAN, Pascal, or

BASIC is valid. The precedence of these operators is determined by the

specifications of the C programming language. White space (spaces and tabs)

is ignored inside expressions.

Complex constants are expressed as {<real>,<imag>}, where <real> and <imag>

must be numerical constants. For example, {3,2} represents 3 + 2i; {0,1}

represents 'i' itself. The curly braces are explicitly required here.

Note that gnuplot uses both "real" and "integer" arithmetic, like FORTRAN and

C. Integers are entered as "1", "-10", etc; reals as "1.0", "-10.0", "1e1",

3.5e-1, etc. The most important difference between the two forms is in

division: division of integers truncates: 5/2 = 2; division of reals does

not: 5.0/2.0 = 2.5. In mixed expressions, integers are "promoted" to reals

before evaluation: 5/2e0 = 2.5. The result of division of a negative integer

by a positive one may vary among compilers. Try a test like "print -5/2" to

determine if your system chooses -2 or -3 as the answer.

The integer expression "1/0" may be used to generate an "undefined" flag,

which causes a point to ignored; the `ternary` operator gives an example.

The real and imaginary parts of complex expressions are always real, whatever

the form in which they are entered: in {3,2} the "3" and "2" are reals, not

integers.

3 Functions

?expressions functions

?functions

The functions in `gnuplot` are the same as the corresponding functions in

the Unix math library, except that all functions accept integer, real, and

complex arguments, unless otherwise noted.

For those functions that accept or return angles that may be given in either

degrees or radians (sin(x), cos(x), tan(x), asin(x), acos(x), atan(x),

atan2(x) and arg(z)), the unit may be selected by `set angles`, which

defaults to radians.

@start table

#\begin{tabular}{|ccl|} \hline

#\multicolumn{3}{|c|}{Math library functions} \\ \hline \hline

#Function & Arguments & Returns \\ \hline

%c c l .

%Function@Arguments@Returns

%_

4 abs

?expressions functions abs

?functions abs

?abs

#abs(x) & any & absolute value of $x$, $|x|$; same type \\

#abs(x) & complex & length of $x$, $\sqrt{{\mbox{real}(x)^{2} +

#\mbox{imag}(x)^{2}}}$ \\

%abs(x)@any@absolute value of $x$, $|x|$; same type

%abs(x)@complex@length of $x$, $sqrt{roman real (x) sup 2 + roman imag (x) sup 2}$

The `abs(x)` function returns the absolute value of its argument. The

returned value is of the same type as the argument.

For complex arguments, abs(x) is defined as the length of x in the complex

plane [i.e., sqrt(real(x)**2 + imag(x)**2) ].

4 acos

?expressions functions acos

?functions acos

?acos

#acos(x) & any & $\cos^{-1} x$ (inverse cosine) \\

%acos(x)@any@$cos sup -1 x$ (inverse cosine)

The `acos(x)` function returns the arc cosine (inverse cosine) of its

argument. `acos` returns its argument in radians or degrees, as selected by

`set angles`.

4 acosh

?expressions functions acosh

?functions acosh

?acosh

#acosh(x) & any & $\cosh^{-1} x$ (inverse hyperbolic cosine) in radians \\

%acosh(x)@any@$cosh sup -1 x$ (inverse hyperbolic cosine) in radians

The `acosh(x)` function returns the inverse hyperbolic cosine of its argument

in radians.

4 arg

?expressions functions arg

?functions arg

?arg

#arg(x) & complex & the phase of $x$ \\

%arg(x)@complex@the phase of $x$

The `arg(x)` function returns the phase of a complex number in radians or

degrees, as selected by `set angles`.

4 asin

?expressions functions asin

?functions asin

?asin

#asin(x) & any & $\sin^{-1} x$ (inverse sin) \\

%asin(x)@any@$sin sup -1 x$ (inverse sin)

The `asin(x)` function returns the arc sin (inverse sin) of its argument.

`asin` returns its argument in radians or degrees, as selected by `set

angles`.

4 asinh

?expressions functions asinh

?functions asinh

?asinh

#asinh(x) & any & $\sinh^{-1} x$ (inverse hyperbolic sin) in radians \\

%asinh(x)@any@$sinh sup -1 x$ (inverse hyperbolic sin) in radians

The `asinh(x)` function returns the inverse hyperbolic sin of its argument in

radians.

4 atan

?expressions functions atan

?functions atan

?atan

#atan(x) & any & $\tan^{-1} x$ (inverse tangent) \\

%atan(x)@any@$tan sup -1 x$ (inverse tangent)

The `atan(x)` function returns the arc tangent (inverse tangent) of its

argument. `atan` returns its argument in radians or degrees, as selected by

`set angles`.

4 atan2

?expressions functions atan2

?functions atan2

?atan2

#atan2(y,x) & int or real & $\tan^{-1} (y/x)$ (inverse tangent) \\

%atan2(y,x)@int or real@$tan sup -1 (y/x)$ (inverse tangent)

The `atan2(y,x)` function returns the arc tangent (inverse tangent) of the

ratio of the real parts of its arguments. `atan2` returns its argument in

radians or degrees, as selected by `set angles`, in the correct quadrant.

4 atanh

?expressions functions atanh

?functions atanh

?atanh

#atanh(x) & any & $\tanh^{-1} x$ (inverse hyperbolic tangent) in radians \\

%atanh(x)@any@$tanh sup -1 x$ (inverse hyperbolic tangent) in radians

The `atanh(x)` function returns the inverse hyperbolic tangent of its

argument in radians.

4 besj0

?expressions functions besj0

?functions besj0

?besj0

#besj0(x) & int or real & $j_{0}$ Bessel function of $x$, in radians \\

%besj0(x)@int or real@$j sub 0$ Bessel function of $x$, in radians

The `besj0(x)` function returns the j0th Bessel function of its argument.

`besj0` expects its argument to be in radians.

4 besj1

?expressions functions besj1

?functions besj1

?besj1

#besj1(x) & int or real & $j_{1}$ Bessel function of $x$, in radians \\

%besj1(x)@int or real@$j sub 1$ Bessel function of $x$, in radians

The `besj1(x)` function returns the j1st Bessel function of its argument.

`besj1` expects its argument to be in radians.

4 besy0

?expressions functions besy0

?functions besy0

?besy0

#besy0(x) & int or real & $y_{0}$ Bessel function of $x$, in radians \\

%besy0(x)@int or real@$y sub 0$ Bessel function of $x$, in radians

The `besy0` function returns the y0th Bessel function of its argument.

`besy0` expects its argument to be in radians.

4 besy1

?expressions functions besy1

?functions besy1

?besy1

#besy1(x) & int or real & $y_{1}$ Bessel function of $x$, in radians \\

%besy1(x)@int or real@$y sub 1$ Bessel function of $x$, in radians

The `besy1(x)` function returns the y1st Bessel function of its argument.

`besy1` expects its argument to be in radians.

4 ceil

?expressions functions ceil

?functions ceil

?ceil

#ceil(x) & any & $\lceil x \rceil$, smallest integer not less than $x$

#(real part) \\

%ceil(x)@any@$left ceiling x right ceiling$, smallest integer not less than $x$ (real part)

The `ceil(x)` function returns the smallest integer that is not less than its

argument. For complex numbers, `ceil` returns the smallest integer not less

than the real part of its argument.

4 cos

?expressions functions cos

?functions cos

?cos

#cos(x) & any & $\cos x$, cosine of $x$ \\

%cos(x)@radians@$cos~x$, cosine of $x$

The `cos(x)` function returns the cosine of its argument. `cos` accepts its

argument in radians or degrees, as selected by `set angles`.

4 cosh

?expressions functions cosh

?functions cosh

?cosh

#cosh(x) & any & $\cosh x$, hyperbolic cosine of $x$ in radians \\

%cosh(x)@any@$cosh~x$, hyperbolic cosine of $x$ in radians

The `cosh(x)` function returns the hyperbolic cosine of its argument. `cosh`

expects its argument to be in radians.

4 erf

?expressions functions erf

?functions erf

?erf

#erf(x) & any & $\mbox{erf}(\mbox{real}(x))$, error function of real($x$) \\

%erf(x)@any@$erf ( roman real (x))$, error function of real ($x$)

The `erf(x)` function returns the error function of the real part of its

argument. If the argument is a complex value, the imaginary component is

ignored.

4 erfc

?expressions functions erfc

?functions erfc

?erfc

#erfc(x) & any & $\mbox{erfc}(\mbox{real}(x))$, 1.0 - error function of real($x$) \\

%erfc(x)@any@$erfc ( roman real (x))$, 1.0 - error function of real ($x$)

The `erfc(x)` function returns 1.0 - the error function of the real part of

its argument. If the argument is a complex value, the imaginary component is

ignored.

4 exp

?expressions functions exp

?functions exp

?exp

#exp(x) & any & $e^{x}$, exponential function of $x$ \\

%exp(x)@any@$e sup x$, exponential function of $x$

The `exp(x)` function returns the exponential function of its argument (`e`

raised to the power of its argument). On some implementations (notably

suns), exp(-x) returns undefined for very large x. A user-defined function

like safe(x) = x<-100 ? 0 : exp(x) might prove useful in these cases.

4 floor

?expressions functions floor

?functions floor

?floor

#floor(x) & any & $\lfloor x \rfloor$, largest integer not greater

#than $x$ (real part) \\

%floor(x)@any@$left floor x right floor$, largest integer not greater than $x$ (real part)

The `floor(x)` function returns the largest integer not greater than its

argument. For complex numbers, `floor` returns the largest integer not

greater than the real part of its argument.

4 gamma

?expressions functions gamma

?functions gamma

?gamma

#gamma(x) & any & $\mbox{gamma}(\mbox{real}(x))$, gamma function of real($x$) \\

%gamma(x)@any@$GAMMA ( roman real (x))$, gamma function of real ($x$)

The `gamma(x)` function returns the gamma function of the real part of its

argument. For integer n, gamma(n+1) = n!. If the argument is a complex

value, the imaginary component is ignored.

4 ibeta

?expressions functions ibeta

?functions ibeta

?ibeta

#ibeta(p,q,x) & any & $\mbox{ibeta}(\mbox{real}(p,q,x))$, ibeta function of real($p$,$q$,$x$) \\

%ibeta(p,q,x)@any@$ibeta ( roman real (p,q,x))$, ibeta function of real ($p$,$q$,$x$)

The `ibeta(p,q,x)` function returns the incomplete beta function of the real

parts of its arguments. p, q > 0 and x in [0:1]. If the arguments are

complex, the imaginary components are ignored.

4 inverf

?expressions functions inverf

?functions inverf

?inverf

#inverf(x) & any & inverse error function of real($x$) \\

%inverf(x)@any@inverse error function real($x$)

The `inverf(x)` function returns the inverse error function of the real part

of its argument.

4 igamma

?expressions functions igamma

?functions igamma

?igamma

#igamma(a,x) & any & $\mbox{igamma}(\mbox{real}(a,x))$, igamma function of real($a$,$x$) \\

%igamma(a,x)@any@$igamma ( roman real (a,x))$, igamma function of real ($a$,$x$)

The `igamma(a,x)` function returns the incomplete gamma function of the real

parts of its arguments. a > 0 and x >= 0. If the arguments are complex,

the imaginary components are ignored.

4 imag

?expressions functions imag

?functions imag

?imag

#imag(x) & complex & imaginary part of $x$ as a real number \\

%imag(x)@complex@imaginary part of $x$ as a real number

The `imag(x)` function returns the imaginary part of its argument as a real

number.

4 invnorm

?expressions functions invnorm

?functions invnorm

?invnorm

#invnorm(x) & any & inverse normal distribution function of real($x$) \\

%invnorm(x)@any@inverse normal distribution function real($x$)

The `invnorm(x)` function returns the inverse normal distribution function of

the real part of its argument.

4 int

?expressions functions int

?functions int

?int

#int(x) & real & integer part of $x$, truncated toward zero \\

%int(x)@real@integer part of $x$, truncated toward zero

The `int(x)` function returns the integer part of its argument, truncated

toward zero.

4 lgamma

?expressions functions lgamma

?functions lgamma

?lgamma

#lgamma(x) & any & $\mbox{lgamma}(\mbox{real}(x))$, lgamma function of real($x$) \\

%lgamma(x)@any@$lgamma ( roman real (x))$, lgamma function of real ($x$)

The `lgamma(x)` function returns the natural logarithm of the gamma function

of the real part of its argument. If the argument is a complex value, the

imaginary component is ignored.

4 log

?expressions functions log

?functions log

?log

#log(x) & any & $\log_{e} x$, natural logarithm (base $e$) of $x$ \\

%log(x)@any@$ln~x$, natural logarithm (base $e$) of $x$

The `log(x)` function returns the natural logarithm (base `e`) of its

argument.

4 log10

?expressions functions log10

?functions log10

?log10

#log10(x) & any & $\log_{10} x$, logarithm (base $10$) of $x$ \\

%log10(x)@any@${log sub 10}~x$, logarithm (base $10$) of $x$

The `log10(x)` function returns the logarithm (base 10) of its argument.

4 norm

?expressions functions norm

?functions norm

?norm

#norm(x) & any & normal distribution (Gaussian) function of real($x$) \\

%norm(x)@any@$norm(x)$, normal distribution function of real($x$)

The `norm(x)` function returns the normal distribution function (or Gaussian)

of the real part of its argument.

4 rand

?expressions functions rand

?functions rand

?rand

#rand(x) & any & $\mbox{rand}(\mbox{real}(x))$, pseudo random number generator \\

%rand(x)@any@$rand ( roman real (x))$, pseudo random number generator

The `rand(x)` function returns a pseudo random number in the interval [0:1]

using the real part of its argument as a seed. If seed < 0, the sequence

is (re)initialized. If the argument is a complex value, the imaginary

component is ignored.

4 real

?expressions functions real

?functions real

?real

#real(x) & any & real part of $x$ \\

%real(x)@any@real part of $x$

The `real(x)` function returns the real part of its argument.

4 sgn

?expressions functions sgn

?functions sgn

?sgn

#sgn(x) & any & 1 if $x>0$, -1 if $x<0$, 0 if $x=0$. imag($x$) ignored \\

%sgn(x)@any@1 if $x > 0$, -1 if $x < 0$, 0 if $x = 0$. $roman imag (x)$ ignored

The `sgn(x)` function returns 1 if its argument is positive, -1 if its

argument is negative, and 0 if its argument is 0. If the argument is a

complex value, the imaginary component is ignored.

4 sin

?expressions functions sin

?functions sin

?sin

#sin(x) & any & $\sin x$, sine of $x$ \\

%sin(x)@any@$sin~x$, sine of $x$

The `sin(x)` function returns the sine of its argument. `sin` expects its

argument to be in radians or degrees, as selected by `set angles`.

4 sinh

?expressions functions sinh

?functions sinh

?sinh

#sinh(x) & any & $\sinh x$, hyperbolic sine $x$ in radians \\

%sinh(x)@any@$sinh~x$, hyperbolic sine $x$ in radians

The `sinh(x)` function returns the hyperbolic sine of its argument. `sinh`

expects its argument to be in radians.

4 sqrt

?expressions functions sqrt

?functions sqrt

?sqrt

#sqrt(x) & any & $\sqrt{x}$, square root of $x$ \\

%sqrt(x)@any@$sqrt x $, square root of $x$

The `sqrt(x)` function returns the square root of its argument.

4 tan

?expressions functions tan

?functions tan

?tan

#tan(x) & any & $\tan x$, tangent of $x$ \\

%tan(x)@any@$tan~x$, tangent of $x$

The `tan(x)` function returns the tangent of its argument. `tan` expects

its argument to be in radians or degrees, as selected by `set angles`.

4 tanh

?expressions functions tanh

?functions tanh

?tanh

#tanh(x) & any & $\tanh x$, hyperbolic tangent of $x$ in radians\\

%tanh(x)@any@$tanh~x$, hyperbolic tangent of $x$ in radians

The `tanh(x)` function returns the hyperbolic tangent of its argument. `tanh`

expects its argument to be in radians.

@end table

A few additional functions are also available.

@start table

#\begin{tabular}{|ccl|} \hline

#\multicolumn{3}{|c|}{other {\bf gnuplot} functions} \\ \hline \hline

#Function & Arguments & Returns \\ \hline

%c c l .

%Function@Arguments@Returns

%_

4 column

?expressions functions column

?functions column

?column

#column(x) & int & column $x$ during datafile manipulation. \\

%column(x)@int@ column $x$ during datafile manipulation.

`column(x)` may be used only in expressions as part of `using` manipulations

to fits or datafile plots. See `plot datafile using`.

4 tm_hour

?expressions tm_hour

?functions tm_hour

#tm\_hour(x) & int & the hour \\

%tm_hour(x)@int@the hour

The `tm_hour` function interprets its argument as a time, in seconds from

1 Jan 2000. It returns the hour (an integer in the range 0--23) as a real.

4 tm_mday

?expressions tm_mday

?functions tm_mday

#tm\_mday(x) & int & the day of the month \\

%tm_mday(x)@int@the day of the month

The `tm_mday` function interprets its argument as a time, in seconds from

1 Jan 2000. It returns the day of the month (an integer in the range 1--31)

as a real.

4 tm_min

?expressions tm_min

?functions tm_min

#tm\_min(x) & int & the minute \\

%tm_min(x)@int@the minute

The `tm_min` function interprets its argument as a time, in seconds from

1 Jan 2000. It returns the minute (an integer in the range 0--59) as a real.

4 tm_mon

?expressions tm_mon

?functions tm_mon

#tm\_mon(x) & int & the month \\

%tm_mon(x)@int@the month

The `tm_mon` function interprets its argument as a time, in seconds from

1 Jan 2000. It returns the month (an integer in the range 0--11) as a real.

4 tm_sec

?expressions tm_sec

?functions tm_sec

#tm\_sec(x) & int & the second \\

%tm_sec(x)@int@the second

The `tm_sec` function interprets its argument as a time, in seconds from

1 Jan 2000. It returns the second (an integer in the range 0--59) as a real.

4 tm_wday

?expressions tm_wday

?functions tm_wday

#tm\_wday(x) & int & the day of the week \\

%tm_wday(x)@int@the day of the week

The `tm_wday` function interprets its argument as a time, in seconds from

1 Jan 2000. It returns the day of the week (an integer in the range 0--6) as

a real.

4 tm_yday

?expressions tm_yday

?functions tm_yday

#tm\_yday(x) & int & the day of the year \\

%tm_yday(x)@int@the day of the year

The `tm_yday` function interprets its argument as a time, in seconds from

1 Jan 2000. It returns the day of the year (an integer in the range 1--366)

as a real.

4 tm_year

?expressions tm_year