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C RCS $Id: gnuplot.doc,v 1.568 2009/05/17 22:31:55 sfeam Exp $

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

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

^ <h2> Version 4.2 organized by Hans-Bernhard Broeker and others</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> Ethan A Merritt

^<li> Petr Mikulik

^<li> Carsten Steger

^<li> Tom Tkacik

^<li> Jos Van der Woude

^<li> Alex Woo

^<li> James R. Van Zandt

^<li> Johannes Zellner

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

^ Mailing list for comments: gnuplot-info@lists.sourceforge.net <p>

^ Mailing list for bug reports: gnuplot-bugs@lists.sourceforge.net <p>

^</h2><p>

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

^<h3> Last revised: March 2009</h3><p>

^<hr>

1 gnuplot

2 Copyright

?copyright

?license

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.

Gnuplot 4.0 additions:

See list of contributors at head of this document.

2 Introduction

?introduction

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

syntax:

gnuplot {X11OPTIONS} {OPTIONS} file1 file2 ...

Generic X11 options, if any, must come first. See your X11 documentation.

If you are not using X11, ignore this. Options interpreted by gnuplot

may come anywhere on the line. Files are executed in the order specified, as

are commands supplied by the -e option.

Example:

gnuplot file1.in -e "reset" file2.in

The special filename "-" is used to force reading from stdin. `gnuplot` exits

after the last file is processed. If no load files are named, `gnuplot` takes

interactive input from stdin. See help `batch/interactive` for more details.

The options specific to gnuplot can be listed by typing

gnuplot --help

`gnuplot` 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, separated by semicolons (;). Strings may be

set off by either single or double quotes, although there are some subtle

differences. See `syntax` and `quotes` for more details. Examples:

load "filename"

cd 'dir'

Many `gnuplot` commands have multiple options. Version 4 is less sensitive

to the order of these options than earlier versions, but some order-dependence

remains. If you see error messages about unrecognized options, please try

again using the exact order listed in the documentation.

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 `comments`). 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 built-in help on any topic, type `help` followed by the name of the topic

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

The new `gnuplot` user should begin by reading about `plotting` (if in an

interactive session, type `help plotting`).

See the simple.dem demo, also available together with other demos on the web page

^ <a href="http://www.gnuplot.info/demo/">

http://www.gnuplot.info/demo/

^ </a>

2 Seeking-assistance

?help-desk

?seeking-assistance

^ <a name="Seeking-assistance"></a>

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. Instructions for subscribing to gnuplot

mailing lists may be found via the gnuplot development website on SourceForge

^ <a href="http://sourceforge.net/projects/gnuplot">

http://sourceforge.net/projects/gnuplot

^ </a>

The address for mailing to list members is:

gnuplot-info@lists.sourceforge.net

Bug reports and code contributions should be uploaded to the trackers at

http://sourceforge.net/projects/gnuplot

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

gnuplot-beta@lists.sourceforge.net

There is also the canonical (if occasionally out-of-date) gnuplot web page at

^ <a href="http://www.gnuplot.info">

http://www.gnuplot.info

^ </a>

Before seeking help, please check the

^ <a href="http://www.gnuplot.info/faq/">

FAQ (Frequently Asked Questions) list.

^ </a>

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 gnuplot-info, 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 New features introduced in version 4.3

?new-features

Gnuplot version 4.3 offers many new features introduced since the preceding

official version 4.2. This section lists major additions and gives a partial

list of changes and minor new features. For a more exhaustive list, see the

NEWS file.

3 Internationalization

Gnuplot 4.3 contains significantly improved support for locale settings and for

UTF-8 character encodings. See `set locale`, `set encoding`, `set decimalsign`.

3 Transparency

Gnuplot now supports transparent objects in several ways. Any object or plot

element that uses a fill style can be assigned a value from fully opaque to

fully transparent. Image or matrix data can be plotted with an alpha channel

using the new plot style `with rgbalpha`. See `fillstyle`, `rgbalpha`.

3 Volatile Data

The new command `refresh` is similar to `replot` except that it uses the

previously-stored input data values rather than rereading the input data file.

Mouse operations (zoom, rotate) will automatically use `refresh` rather than

`replot` if the input data stream is marked `volatile`. Piped or in-line data

is automatically treated as volatile. See `refresh`, `plot datafile volatile`.

3 Canvas size

?canvas size

?canvas

?set term size

In earlier versions of gnuplot, some terminal types used the values from

`set size` to control also the size of the output canvas; others did not.

The use of 'set size' for this purpose was deprecated in version 4.2.

In version 4.3 almost all terminals now behave as follows:

`set term <terminal_type> size <XX>, <YY>` controls the size of the output

file, or "canvas". Please see individual terminal documentation for allowed

values of the size parameters. By default, the plot will fill this canvas.

`set size <XX>, <YY>` scales the plot itself relative to the size of the

canvas. Scale values less than 1 will cause the plot to not fill the entire

canvas. Scale values larger than 1 will cause only a portion of the plot to

fit on the canvas. Please be aware that setting scale values larger than 1

may cause problems on some terminal types.

The major exception to this convention is the PostScript driver, which

by default continues to act as it has in earlier versions. Be warned that

the next version of gnuplot may change the default behaviour of the

PostScript driver as well.

Example:

set size 0.5, 0.5

set term png size 600, 400

set output "figure.png"

plot "data" with lines

These commands will produce an output file "figure.png" that is 600 pixels

wide and 400 pixels tall. The plot will fill the lower left quarter of this

canvas. This is consistent with the way multiplot mode has always worked,

however it is a change in the way the png driver worked for single plots in

version 4.0.

3 New plot elements

=circles

=ellipse

=polygon

The `set object` command can now be used to define fixed circles, ellipses, and

polygons as well as rectangles. There is a corresponding new plot style

`plot with circles`. See `circle` `ellipse` `polygon`.

3 New or revised terminal drivers

Two new drivers based on the cairo and pango libraries are included,

`pngcairo` and `pdfcairo`. These are alternatives to the older libgd-based

png driver and the older PDFLib-based pdf driver. The figures in the pdf

version of this manual were prepared using the pdfcairo terminal driver.

3 New smoothing algorithms

=kdensity

=cumulative

New smoothing algorithms have been added for both 2- and 3-dimensional plots.

`smooth kdensity` and `smooth cumul` can be used with `plot` to draw

smooth histograms and cumulative distribution functions, resp. For use

with `splot` several new smoothing kernels have been added to `dgrid3d`.

See `smooth` `dgrid3d`.

2 Backwards compatibility

?backwards compatibility

?compatibility

Gnuplot version 4.0 deprecated certain syntax used in earlier versions, but

continued to recognize it. This is now under the control of a configuration

option, and can be disabled as follows:

./configure --disable-backwards-compatibility

Notice: Deprecated syntax items may be disabled permanently in some future

version of gnuplot.

One major difference is the introduction of keywords to disambiguate complex

commands, particularly commands containing string variables. A notable issue

was the use of bare numbers to specify offsets, line and point types.

Illustrative examples:

Deprecated:

set title "Old" 0,-1

set data linespoints

plot 1 2 4 # horizontal line at y=1

New:

TITLE = "New"

set title TITLE offset char 0, char -1

set style data linespoints

plot 1 linetype 2 pointtype 4

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 either program options (first

character is -) or names of files containing `gnuplot` commands. The option

-e "command" may be used to force execution of a gnuplot command. Each file

or command string will be executed in the order specified. The special

filename "-" is indicates that commands are to be read from stdin.

`gnuplot` exits after the last file is processed. If no load files and no

command strings are specified, `gnuplot` accepts interactive input from

stdin.

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

To give `gnuplot` commands directly in the command line, using the "-persist"

option so that the plot remains on the screen afterwards:

gnuplot -persist -e "set title 'Sine curve'; plot sin(x)"

To set user-defined variables a and s prior to executing commands from a file:

gnuplot -e "a=2; s='file.png'" input.gpl

2 Command-line-editing

?line-editing

?editing

?command-line-editing

Command-line editing and command history are supported using either an

external gnu readline library, an external BSD libedit library, or a

built-in equivalent. This choice is a configuration option at the time

gnuplot is built.

The editing commands of the built-in version are given below. The gnu

readline and BSD libedit libraries have their own documentation.

@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 from the current word to the end of line.

`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

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.

See also `set datafile commentschars` for specifying comment characters in

data files. Note that if a comment line ends in '\' then the subsequent

line is also treated as a comment.

2 Coordinates

?coordinates

=axes

The commands `set arrow`, `set key`, `set label` and `set object` 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`, `screen`, or

`character`.

`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`); `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; and `character`

gives the position in character widths and heights from the bottom left of

the screen area (screen 0,0), `character` coordinates depend on the chosen

font size.

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.

In some cases, the given coordinate is not an absolute position but a

relative value (e.g., the second position in `set arrow` ... `rto`). In

most cases, the given value serves as difference to the first position.

If the given coordinate resides in a logarithmic axis the value is

interpreted as factor. For example,

set logscale x

set arrow 100,5 rto 10,2

plots an arrow from position 100,5 to position 1000,7 since the x axis is

logarithmic while the y axis is linear.

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 Datastrings

?datastrings

Data files may contain string data consisting of either an arbitrary string

of printable characters containing no whitespace or an arbitrary string of

characters, possibly including whitespace, delimited by double quotes.

The following sample line from a datafile is interpreted to contain four

columns, with a text field in column 3:

1.000 2.000 "Third column is all of this text" 4.00

Text fields can be positioned within a 2-D or 3-D plot using the commands:

plot 'datafile' using 1:2:4 with labels

splot 'datafile using 1:2:3:4 with labels

A column of text data can also be used to label the ticmarks along one or more

of the plot axes. The example below plots a line through a series of points

with (X,Y) coordinates taken from columns 3 and 4 of the input datafile.

However, rather than generating regularly spaced tics along the x axis

labeled numerically, gnuplot will position a tic mark along the x axis at the

X coordinate of each point and label the tic mark with text taken from column

1 of the input datafile.

set xtics

plot 'datafile' using 3:4:xticlabels(1) with linespoints

=columnheader

There is also an option that will interpret the first entry in a column of

input data (i.e. the column heading) as a text field, and use it as the key

title for data plotted from that column. The example given below will use the

first entry in column 2 to generate a title in the key box, while processing

the remainder of columns 2 and 4 to draw the required line:

plot 'datafile' using 1:(f($2)/$4) with lines title columnhead(2)

See `set style labels`, `using xticlabels`, `plot title`, `using`.

2 Enhanced text mode

?enhanced text

?enhanced

Many terminal types support an enhanced text mode in which additional

formatting information is embedded in the text string. For example, "x^2"

will write x-squared as we are used to seeing it, with a superscript 2.

This mode is normally selected when you set the terminal, e.g.

"set term png enhanced", but may also be toggled afterward using

"set termoption enhanced", or by marking individual strings as in

"set label 'x_2' noenhanced".

@start table - first is interactive cleartext form

Control Examples Explanation

^ a^x superscript

_ a_x subscript

@ @x or a@^b_{cd} phantom box (occupies no width)

& &{space} inserts space of specified length

~ ~a{.8-} overprints '-' on 'a', raised by .8

times the current fontsize

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

#\multicolumn{4}{|c|}{Enhanced Text Control Codes} \\ \hline

#Control & Example & Result & Explanation \\ \hline

#\verb~^~ & \verb~a^x~ & $a^x$ & superscript\\

#\verb~_~ & \verb~a_x~ & $a_x$ & subscript\\

#\verb~@~ & \verb~a@^b_{cd}~ & $a^b_{cd}$ &phantom box (occupies no width)\\

#\verb~&~ & \verb~d&{space}b~ & d\verb*+ +b & inserts space of specified length\\

#\verb|~| & \verb|~a{.8-}| & $\tilde{a}$ & overprints '-' on 'a', raised by .8\\

#\verb~ ~ & \verb~ ~ & ~ ~ & times the current fontsize\\

%c c l .

%.TE", /* ugly - doc2ms uses @ for column separator, but here we */

%.TS", /* need @ in table, so end and restart the table ! */

%center box tab ($) ;

%c c l .

%Control$Examples$Explanation

%^$a^x$superscript

%\&_$a\&_x$subscript

% @ $ @x or a\&@^b\&_{cd}$phantom box (occupies no width)

% & $ &{space}$inserts space of specified length

% ~ $ ~a{.8-}$overprints '-' on 'a', raised by .8

% $ $times the current fontsize

@end table

Braces can be used to place multiple-character text where a single character

is expected (e.g., 2^{10}). To change the font and/or size, use the full form:

{/[fontname][=fontsize | *fontscale] text}. Thus {/Symbol=20 G} is a 20 pt

GAMMA and {/*0.75 K} is a K at three-quarters of whatever fontsize is currently

in effect. (The '/' character MUST be the first character after the '{'.)

The phantom box is useful for a@^b_c to align superscripts and subscripts

but does not work well for overwriting an accent on a letter. For the latter,

it is much better to use an encoding (e.g. iso_8859_1 or utf8) that contains

a large variety of letters with accents or other diacritical marks. See

`set encoding`. Since the box is non-spacing, it is sensible to put the shorter

of the subscript or superscript in the box (that is, after the @).

Space equal in length to a string can be inserted using the '&' character.

Thus

'abc&{def}ghi'

would produce

'abc ghi'.

The '~' character causes the next character or bracketed text to be

overprinted by the following character or bracketed text. The second text

will be horizontally centered on the first. Thus '~a/' will result in an 'a'

with a slash through it. You can also shift the second text vertically by

preceding the second text with a number, which will define the fraction of the

current fontsize by which the text will be raised or lowered. In this case

the number and text must be enclosed in brackets because more than one

character is necessary. If the overprinted text begins with a number, put a

space between the vertical offset and the text ('~{abc}{.5 000}'); otherwise

no space is needed ('~{abc}{.5---}'). You can change the font for one or

both strings ('~a{.5 /*.2 o}'---an 'a' with a one-fifth-size 'o' on top---and

the space between the number and the slash is necessary), but you can't

change it after the beginning of the string. Neither can you use any other

special syntax within either string. You can, of course, use control

characters by escaping them (see below), such as '~a{\^}'

You can access special symbols numerically by specifying \character-code (in

octal), e.g., {/Symbol \245} is the symbol for infinity. This does not work

for multibyte encodings like UTF-8, however. In a UTF-8 environment, you

should be able to enter multibyte sequences implicitly by typing or otherwise

selecting the character you want.

You can escape control characters using \, e.g., \\, \{, and so on.

But be aware that strings in double-quotes are parsed differently than those

enclosed in single-quotes. The major difference is that backslashes may need

to be doubled when in double-quoted strings.

Examples (these are hard to describe in words---try them!):

set xlabel 'Time (10^6 {/Symbol m}s)'

set title '{/Symbol=18 \\362@_{/=9.6 0}^{/=12 x}} \\

{/Helvetica e^{-{/Symbol m}^2/2} d}{/Symbol m}'

The file "ps_guide.ps" in the /docs/psdoc subdirectory of the gnuplot source

distribution contains more examples of the enhanced syntax.

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.

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,

MS-DOS, Windows and OS/2, GNUPLOT is used. On Windows, the NT-specific

variable USERPROFILE is tried, too. VMS, SYS$LOGIN: is used. Type `help

start-up`.

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

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

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

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

fit is interrupted---see `fit`. FIT_LOG specifies the default 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.

Several gnuplot terminal drivers access TrueType fonts via the gd library.

For these drivers the font search path is controlled by the environmental

variable GDFONTPATH. Furthermore, a default font for these drivers may be

set via the environmental variable GNUPLOT_DEFAULT_GDFONT.

The postscript terminal uses its own font search path. It is controlled by

the environmental variable GNUPLOT_FONTPATH. The format is the same as for

GNUPLOT_LIB. The contents of GNUPLOT_FONTPATH are appended to the `fontpath`

variable, but not saved with the `save` and `save set` commands.

GNUPLOT_PS_DIR is used by the postscript driver to use external prologue

files. Depending on the build process, gnuplot contains either a builtin

copy of those files or simply a default hardcoded path. Use this variable

to test the postscript terminal with custom prologue files. See

`postscript prologue`.

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.

=division

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.

Or you can use the pre-defined variable NaN to achieve the same result.

=NaN

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.

Gnuplot can also perform simple operations on strings and string variables.

For example, the expression ("A" . "B" eq "AB") evaluates as true, illustrating

the string concatenation operator and the string equality operator.

A string which contains a numerical value is promoted to the corresponding

integer or real value if used in a numerical expression. Thus ("3" + "4" == 7)

and (6.78 == "6.78") both evaluate to true. An integer, but not a real or

complex value, is promoted to a string if used in string concatenation.

A typical case is the use of integers to construct file names or other strings;

e.g. ("file" . 4 eq "file4") is true.

Substrings can be specified using a postfixed range descriptor [beg:end].

For example, "ABCDEF"[3:4] == "CD" and "ABCDEF"[4:*] == "DEF"

The syntax "string"[beg:end] is exactly equivalent to calling the built-in

string-valued function substr("string",beg,end), except that you cannot

omit either beg or end from the function call.

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 EllipticK

#EllipticK(k) & real k $\in$ (-1:1) & $K(k)$ complete elliptic integral of the first kind \\

%EllipticK(k)@real k in (-1:1)@$K k$ complete elliptic integral of the first kind

See `elliptic integrals`.

4 EllipticE

#EllipticE(k) & real k $\in$ [-1:1] & $E(k)$ complete elliptic integral of the second kind \\

%EllipticE(k)@real k in [-1:1]@ $E k$ complete elliptic integral of the second kind

See `elliptic integrals`.

4 EllipticPi

#EllipticPi(n,k) & real n$<$1, real k $\in$ (-1:1) & $\Pi(n,k)$ complete elliptic integral of the third kind \\

%EllipticPi(n,k)@ real n<1, real k in (-1:1)@ $Pi n,k$ complete elliptic integral of the third kind

See `elliptic integrals`.

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(x)` 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. See `erfc`, `inverf`, and `norm`.

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. See `erf`, `inverf`, and `norm`.

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. See `erf` and `invnorm`.

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 normalized incomplete gamma

function of the real parts of its arguments, where a > 0 and x >= 0.

The standard notation is P(a,x), e.g. Abramowitz and Stegun (6.5.1),

with limiting value of 1 as x approaches infinity. 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 cumulative normal (Gaussian)

distribution function of the real part of its argument. See `norm`.

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 lambertw

?expressions functions lambertw

?functions lambertw

?lambertw

#lambertw(x) & real & Lambert W function \\

%lambertw(x)@real@Lambert W function

The lambertw function returns the value of the principal branch of

Lambert's W function, which is defined by the equation (W(z)*exp(W(z))=z.

z must be a real number with z >= -exp(-1).

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. See `log10`.

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

View remainder of file in raw view

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