C RCS $Id: gnuplot.doc,v 1.916 2014/09/20 11:31:13 markisch Exp $

C

C Copyright (C) 1986 - 1993, 1998, 1999, 2000, 2001, 2004 Thomas Williams, Colin Kelley et al.

C

1 gnuplot

?gnuplot

^<h2 align="center"> An Interactive Plotting Program </h2>

^<p align="center"> Thomas Williams & Colin Kelley</p>

^<p align="center"> Version 5.0 organized by Ethan A Merritt and others</p>

^<p align="center">Major contributors (alphabetic order):<br>

^<br>

^ Hans-Bernhard Broeker, John Campbell,<br>

^ Robert Cunningham, David Denholm,<br>

^ Gershon Elber, Roger Fearick,<br>

^ Carsten Grammes, Lucas Hart,<br>

^ Lars Hecking, Péter Juhász,<br>

^ Thomas Koenig, David Kotz,<br>

^ Ed Kubaitis, Russell Lang,<br>

^ Timothée Lecomte, Alexander Lehmann,<br>

^ Alexander Mai, Bastian Märkisch,<br>

^ Ethan A Merritt, Petr Mikulík,<br>

^ Carsten Steger, Shigeharu Takeno,<br>

^ Tom Tkacik, Jos Van der Woude,<br>

^ James R. Van Zandt, Alex Woo, Johannes Zellner<br>

^</p>

^<p align="center"> Copyright (C) 1986 - 1993, 1998 - 2004 Thomas Williams, Colin Kelley<br>

^ Copyright (C) 2004 - 2014 various authors</p>

^<p align="center"> Mailing list for comments: <tt>gnuplot-info@lists.sourceforge.net</tt><br>

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

^ Web access (preferred): <tt>http://sourceforge.net/projects/gnuplot</tt></p>

^<p align="center"> This manual was originally prepared by Dick Crawford</p>

2 Copyright

?copyright

?license

Copyright (C) 1986 - 1993, 1998, 2004, 2007 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.

Gnuplot 4.0 and 5.0 additions:

See list of contributors at head of this document.

2 Introduction

?introduction

?

`Gnuplot` is a portable command-line driven graphing utility for Linux, OS/2,

MS Windows, OSX, VMS, and many other platforms. The source code is copyrighted

but freely distributed (i.e., you don't have to pay for it). It was originally

created to allow scientists and students to visualize mathematical functions

and data interactively, but has grown to support many non-interactive uses

such as web scripting. It is also used as a plotting engine by third-party

applications like Octave. Gnuplot has been supported and under active

development since 1986.

Gnuplot supports many types of plots in either 2D and 3D. It can draw using

lines, points, boxes, contours, vector fields, surfaces, and various

associated text. It also supports various specialized plot types.

Gnuplot supports many different types of output: interactive screen terminals

(with mouse and hotkey input), direct output to pen plotters or modern

printers, and output to many file formats (eps, emf, fig, jpeg, LaTeX, pdf, png,

postscript, ...). Gnuplot is easily extensible to include new output modes.

Recent additions include interactive terminals based on wxWidgets (usable

on multiple platforms), and Qt. Mouseable plots embedded in web pages

can be generated using the svg or HTML5 canvas terminal drivers.

The command language of `gnuplot` is case sensitive, i.e. commands and

function names written in lowercase are not the same as those written in

capitals. 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. Example:

set title "My First Plot"; plot 'data'; print "all done!"

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.

A large set of demo plots is available on the web page

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

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

^ </a>

When run from command line, gnuplot is invoked using the syntax

gnuplot {OPTIONS} file1 file2 ...

where file1, file2, etc. are input file as in the `load` command.

On X11-based systems, you can use

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

see your X11 documentation and `x11` in this document.

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,

for 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

See `command line options` for more details.

In sessions with an interactive plot window you can hit 'h' anywhere on the

plot for help about `hotkeys` and `mousing` features.

Section `seeking-assistance` will help you to find further information, help

and FAQ.

2 Seeking-assistance

?help-desk

?faq

?FAQ

?seeking-assistance

The canonical gnuplot web page can be found at

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

http://www.gnuplot.info

^ </a>

Before seeking help, please check file FAQ.pdf or the above website for

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

FAQ (Frequently Asked Questions) list.

^ </a>

If you need help as a gnuplot user, please use the newsgroup

comp.graphics.apps.gnuplot

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

subscribing to the mailing list which is also available and carries the same

set of messages. 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/support

Please check previous bug reports if the bug you want to report has not been

already fixed in a newer version.

A mailing list for those interested in development version of gnuplot is:

gnuplot-beta@lists.sourceforge.net

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

the terminal type, and the operating system you are using. A _small_ script

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

datafile plots.

2 New features in version 5

?new-features

* The dot-dash pattern of a line can now be specified independent of other

line properties. See `dashtype`, `set dashtype`, `set linetype`.

* Text markup now supports bold and italic font settings in addition to

subscript, superscript, font size and other previously available properties.

Enhanced text mode is now enabled by default. See `enhanced text`.

* Interactive terminals support hypertext labels that only appear when the

mouse hovers over the label's anchor point.

* New coordinate system (Degrees, Minutes, Seconds). See `set xdata geographic`.

* The default format for axis labels is "% h" ("$%h$" for LaTeX terminals).

This format is like the C standard format %g except that the exponential term,

if present, is written using a superscript. E.g. 1.2 x 10^5 rather than 1.2E05.

* Command scripts may place in-line data in a named data block for repeated

plotting. See `inline data`.

* Support for 32-bit Alpha channel + RGB color #AARRGGBB. See `colorspec`.

* Support for HSV color space via a translation function hsv2rgb(H,S,V).

* Secondary axes (x2, y2) may be locked to the primary axis via a mapping

function. In the simplest case this guarantees that the primary and secondary

axis ranges are identical. In the general case it allows you to define a

non-linear axis, something that previously was possible only for log scaling.

See `set link`.

* Each function in a plot command may optionally be preceded by a sampling

range. This does not affect the overall range of the plot, only the range

over which this function is sampled. See `plot` and `piecewise.dem`.

* If the external library libcerf is available, it is used to provide complex

math routines cerf, cdawson, erfi, faddeeva, and the Voigt profile

VP(x,sigma,gamma).

* The `import` command attaches a user-defined function name to a function

provided by an external shared object (support is operating-system dependent).

A template header and example source and make files for creating a suitable

external shared object are provided in the demo collection.

* Previous commands in the history list of an interactive session can be

reexecuted by number. For example, `history !5` will reexecute the command

numbered 5 in the `history` list.

* Bit-shift operators >> and <<.

* New plot styles: `with parallelaxes`, `with table`, labeled contours.

* Shell invocation of gnuplot can pass parameters to a gnuplot script.

gnuplot -c scriptfile.gp ARG1 ARG2 ARG3 ...

3 New commands

#start

# import f(x) from "plugin.so" # load function from shared library

# set history {quiet|numers} {full|trim} # controls output of history command

# history !N # re-execute prior command by number

# plot <datafile> skip N # skip lines at start of ascii data file

# plot ... smooth mcsplines # monotonic cubic spline fit to data

# reset session # restore initial state of current session

# set arrow <tag> from <start> length <len> angle <ang>

# set colorsequence default|classic|podo # colors used by successive plot elements

# set dashtype <tag> <dash-spec> # user-defined dash patterns

# set link x2 via f(x) inverse g(x) # allows non-linear axis scaling

# set fit quiet|results|brief|verbose # control the amount of fit output

# set contours; splot ... with labels # label contour lines with numeric values

# set style textbox # text elements can be enclosed in a box

# set view map {scale} # allows resizing a 3D projection plot

# set multiplot {next|previous} # navigate within the auto-layout grid

#end

2 Changes in version 5

?changes

These changes introduced in version 5 may cause certain scripts written

for earlier versions of gnuplot to behave differently.

* Revised handling of input data containing NaN, inconsistent number of data

columns, or other unexpected content. See Note under `missing` for examples

and figures.

* Time coordinates are stored internally as the number of seconds relative to

the standard unix epoch 1-Jan-1970. Earlier versions of gnuplot used a

different epoch internally (1-Jan-2000). This change resolves inconsistencies

introduced whenever time in seconds was generated externally. The epoch

convention used by a particular gnuplot installation can be determined using

the command `print strftime("%F",0)`. Time is now stored to at least

millisecond precision.

* The function `timecolumn(N,"timeformat")` now has 2 parameters. Because the

required second parameter is not associated with any particular data axis, this

allows using the `timecolumn` function to read time data for reasons other than

specifying the x or y coordinate.

* The `reverse` keyword of the `set [axis]range` command affects only

autoscaling. It does not invert or otherwise alter the meaning of a command

such as `set xrange [0:1]`. If you want to reverse the direction of the

x axis in such a case, say instead `set xrange [1:0]`.

* The `call` command is implemented by providing a set of variables ARGC,

ARG0, ..., ARG9. ARG0 holds the name of the script file being executed.

ARG1 to ARG9 are string variables and thus may either be referenced directly

or expanded as macros, e.g. @ARG1. The older convention for referencing

call parameters as tokens $0 ... $9 is deprecated.

* The optional bandwidth for the kernel density smoothing option is taken from

a keyword rather than a data column. See `smooth kdensity`.

* `unset xrange` (and other axis ranges) restores the original default range.

* `unset terminal` restores the original terminal of the gnuplot session.

2 Deprecated syntax

?deprecated syntax

?backwards compatibility

?compatibility

Gnuplot version 4 deprecated certain syntax used in earlier versions but

provided a configuration option that allowed backward compatibility.

Support for the old syntax has now been removed.

Deprecated in version 4 and removed in version 5:

set title "Old" 0,-1

set data linespoints

plot 1 2 4 # horizontal line at y=1

Current equivalent:

TITLE = "New"

set title TITLE offset char 0, char -1

set style data linespoints

plot 1 linetype 2 pointtype 4

Deprecated but present in version 5 if configured --enable-backwards-compatibility

if (defined(VARNAME)) ...

set style increment user

plot 'file' thru f(x)

call 'script' 1.23 ABC

(in script: print $0, "$1", "number of args = $#")

Current equivalent:

if (exists("VARNAME")) ...

set linetype

plot 'file' using 1:(f(column(2)))

call 'script' 1.23 "ABC"

(in script: print ARG1, ARG2, "number of args = ", ARGC

2 Batch/Interactive Operation

?batch/interactive

?command line options

`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 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.

Almost all terminals now behave as follows:

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

file, or "canvas". 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

some future 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.

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. Please note that

the action of the DEL key is system-dependent. 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 deletes the previous character.

DEL deletes the current character.

^D deletes current character, sends EOF if the line is empty.

^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 previous 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~ & delete the previous character.\\

#\verb~DEL~ & delete the current character.\\

#\verb~^D~ & delete current character. EOF if line is empty.\\

#\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 previous word. \\ \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@delete the previous character.

%DEL@delete the current character.

%^D@delete current character. EOF if line is empty.

%^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 previous word.

%_

%@History

%^P@move back through history.

%^N@move forward through history.

@end table

^<table align="center" border="1" rules="groups" frame="hsides" cellpadding="3">

^<colgroup>

^ <col align="center">

^ <col align="left">

^</colgroup>

^<thead>

^<tr> <th>Character</th> <th>Function</th></tr>

^</thead>

^<tbody>

^<tr> <td></td> <th>Line Editing</th></tr>

^<tr> <td><tt>^B</tt></td> <td>move back a single character.</td></tr>

^<tr> <td><tt>^F</tt></td> <td>move forward a single character.</td></tr>

^<tr> <td><tt>^A</tt></td> <td>move to the beginning of the line.</td></tr>

^<tr> <td><tt>^E</tt></td> <td>move to the end of the line.</td></tr>

^<tr> <td><tt>^H</tt></td> <td>delete the previous character.</td></tr>

^<tr> <td><tt>DEL</tt></td> <td>delete the current character.</td></tr>

^<tr> <td><tt>^D</tt></td> <td>delete current character. EOF if line is empty</td></tr>

^<tr> <td><tt>^K</tt></td> <td>delete from current position to the end of line.</td></tr>

^<tr> <td><tt>^L, ^R</tt></td> <td>redraw line in case it gets trashed.</td></tr>

^<tr> <td><tt>^U</tt></td> <td>delete the entire line.</td></tr>

^<tr> <td><tt>^W</tt></td> <td>delete previous word.</td></tr>

^</tbody>

^<tbody>

^<tr> <th></th> <th>History</th></tr>

^<tr> <td><tt>^P</tt></td> <td>move back through history.</td></tr>

^<tr> <td><tt>^N</tt></td> <td>move forward through history.</td></tr>

^</tbody>

^</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 x2,y2 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 xyplane`); `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 belongs to a log-scaled axis, a relative value is

interpreted as multiplier. 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 relative to 1 January 1970.

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 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)

Another example:

plot for [i=2:6] 'datafile' using i title "Results for ".columnhead(i)

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

2 Enhanced text mode

?enhanced text

?enhanced

?text_markup

?markup

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 selected by default when you set the terminal, but may be

toggled afterward using "set termoption [no]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

{/Times abc} print abc in font Times at current size

{/Times*2 abc} print abc in font Times at twice current size

{/Times:Italic abc} print abc in font Times with style italic

{/Arial:Bold=20 abc} print abc in boldface Arial font size 20

#\begin{tabular}{|clll|} \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\\

#\verb| | & \verb|{/Times abc}| & {\rm abc} & print abc in font Times at current size\\

#\verb| | & \verb|{/Times*2 abc}| & \Large{\rm abc} & print abc in font Times at twice current size\\

#\verb| | & \verb|{/Times:Italic abc}| & {\it abc} & print abc in font Times with style italic\\

#\verb| | & \verb|{/Arial:Bold=20 abc}| & \Large\textsf{\textbf{abc}} & print abc in boldface Arial font size 20\\

%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

^<table align="center" border="1" rules="groups" frame="hsides" cellpadding="3">

^<colgroup>

^ <col align="center">

^ <col align="center">

^ <col align="left">

^</colgroup>

^<thead>

^<tr> <th>Control</th> <th>Examples</th> <th>Explanation</th></tr>

^</thead>

^<tbody>

^<tr> <td><tt> ^ </tt></td> <td><tt>a^x</tt></td> <td>superscript</td></tr>

^<tr> <td><tt> _ </tt></td> <td><tt>a_x</tt></td> <td>subscript</td></tr>

^<tr> <td><tt> @ </tt></td> <td><tt> @x</tt> or <tt>a@^b_{cd}</tt></td> <td>phantom box (occupies no width)</td></tr>

^<tr> <td><tt> &amp;</tt></td> <td><tt> &amp;{space}</tt></td> <td>inserts space of specified length</td></tr>

^<tr> <td><tt> ~ </tt></td> <td><tt> ~a{.8-}</tt></td> <td>overprints '-' on 'a', raised by .8<br>times the current fontsize</td></tr>

^</tbody>

^</table>

The markup control characers act on the following single character or

bracketed clause. The bracketed clause may contain a string of characters with

no additional markup, e.g. 2^{10}, or it may contain additional markup that

changes font properties. This example illustrates nesting one bracketed clause

inside another to produce a boldface A with an italic subscript i, all in the

current font. If the clause introduced by :Normal were omitted the subscript

would be both italic and boldface.

{/:Bold A_{/:Normal{/:Italic i}}}

Font specifiers MUST be preceeded by a '/' character that immediately follows

the opening '{'.

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 specify special symbols numerically by giving a character code in

octal, e.g. {/Symbol \245} is the symbol for infinity in the Adobe Symbol font.

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.

Note 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.

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

distribution contains more examples of the enhanced syntax, as does the demo

^ <a href="http://www.gnuplot.info/demo/enhanced_utf8.html">

`enhanced_utf8.dem`

^ </a>

2 Environment

?environment

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

these are required, but may be useful.

GNUTERM, if defined, is used as the default terminal type on start-up.

This can be overridden by the ~/.gnuplot (or equivalent) start-up file

(see `startup`) and of course by later explicit `set term` commands.

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 VMS

system help library.

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 MS-DOS, Windows and OS/2,

GNUPLOT is used. On Windows, the NT-specific variable USERPROFILE is also

tried. VMS, SYS$LOGIN: is used. Type `help startup`.

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

On Unix, 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 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 search for external

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

built-in copy of those files or a default hardcoded path. You can use this

variable have the postscript terminal use custom prologue files rather than

the default 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. Or you can use the pre-defined variable NaN

to achieve the same result. See `using` for an example.

=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

Arguments to math functions in `gnuplot` can be integer, real, or complex

unless otherwise noted. Functions that accept or return angles (e.g. sin(x))

treat angle values as radians, but this may be changed to degrees using the

command `set angles`.

^<table align="center" border="1" rules="groups" frame="hsides" cellpadding="3" width="90%">

^<colgroup>

^ <col align="center">

^ <col align="center">

^ <col align="left">

^</colgroup>

^<thead>

^<tr> <th colspan="3"> Math library functions </th></tr>

^<tr> <th>Function</th> <th>Arguments</th> <th>Returns</th></tr>

^</thead>

^<tbody>

^<tr> <td>abs(x)</td> <td>any</td> <td>|<i>x</i>|, absolute value of <i>x</i>; same type</td></tr>

^<tr> <td>abs(x)</td> <td>complex</td> <td>length of <i>x</i>, &radic;( Re(<i>x</i>)² + Im(<i>x</i>)² )</td></tr>

^<tr> <td>acos(x)</td> <td>any</td> <td>cos^-1 <i>x</i> (inverse cosine)</td></tr>

^<tr> <td>acosh(x)</td> <td>any</td> <td>cosh^-1 <i>x</i> (inverse hyperbolic cosine) in radians</td></tr>

^<tr> <td>airy(x)</td> <td>any</td> <td>Airy function Ai(<i>x</i>)</td></tr>

^<tr> <td>arg(x)</td> <td>complex</td> <td>the phase of <i>x</i></td></tr>

^<tr> <td>asin(x)</td> <td>any</td> <td>sin^-1 <i>x</i> (inverse sin)</td></tr>

^<tr> <td>asinh(x)</td> <td>any</td> <td>sinh^-1 <i>x</i> (inverse hyperbolic sin) in radians</td></tr>

^<tr> <td>atan(x)</td> <td>any</td> <td>tan^-1 <i>x</i> (inverse tangent)</td></tr>

^<tr> <td>atan2(y,x)</td> <td>int or real</td> <td>tan^-1(<i>y/x</i>) (inverse tangent)</td></tr>

^<tr> <td>atanh(x)</td> <td>any</td> <td>tanh^-1 <i>x</i> (inverse hyperbolic tangent) in radians</td></tr>

^<tr> <td>EllipticK(k)</td> <td>real k in (-1:1)</td> <td><i>K(k)</i> complete elliptic integral of the first kind</td></tr>

^<tr> <td>EllipticE(k)</td> <td>real k in [-1:1]</td> <td><i>E(k)</i> complete elliptic integral of the second kind</td></tr>

^<tr> <td>EllipticPi(n,k)</td> <td> real n&lt;1, real k in (-1:1)</td> <td> &Pi;(<i>n,k</i>) complete elliptic integral of the third kind</td></tr>

^<tr> <td>besj0(x)</td> <td>int or real</td> <td><i>J</i>₀ Bessel function of <i>x</i>, in radians</td></tr>

^<tr> <td>besj1(x)</td> <td>int or real</td> <td><i>J</i>₁ Bessel function of <i>x</i>, in radians</td></tr>

^<tr> <td>besy0(x)</td> <td>int or real</td> <td><i>Y</i>₀ Bessel function of <i>x</i>, in radians</td></tr>

^<tr> <td>besy1(x)</td> <td>int or real</td> <td><i>Y</i>₁ Bessel function of <i>x</i>, in radians</td></tr>

^<tr> <td>ceil(x)</td> <td>any</td> <td>&lceil;<i>x</i>&rceil;, smallest integer not less than <i>x</i> (real part)</td></tr>

^<tr> <td>cos(x)</td> <td>radians</td> <td>cos <i>x</i>, cosine of <i>x</i></td></tr>

^<tr> <td>cosh(x)</td> <td>any</td> <td>cosh <i>x</i>, hyperbolic cosine of <i>x</i> in radians</td></tr>

^<tr> <td>erf(x)</td> <td>any</td> <td>erf(Re(<i>x</i>)), error function of real(<i>x</i>)</td></tr>

^<tr> <td>erfc(x)</td> <td>any</td> <td>erfc(Re(<i>x</i>)), 1.0 - error function of real(<i>x</i>)</td></tr>

^<tr> <td>exp(x)</td> <td>any</td> <td><i>e^x</i>, exponential function of <i>x</i></td></tr>

^<tr> <td>expint(n,x)</td> <td>any</td> <td><i>E_n</i>(<i>x</i>), exponential integral function of <i>x</i></td></tr>

^<tr> <td>floor(x)</td> <td>any</td> <td>&lfloor;<i>x</i>&rfloor;, largest integer not greater than <i>x</i> (real part)</td></tr>

^<tr> <td>gamma(x)</td> <td>any</td> <td>&Gamma;(Re(<i>x</i>)), gamma function of real(<i>x</i>)</td></tr>

^<tr> <td>ibeta(p,q,x)</td> <td>any</td> <td>ibeta(Re(<i>p,q,x</i>)), ibeta function of real(<i>p</i>,<i>q</i>,<i>x</i>)</td></tr>

^<tr> <td>inverf(x)</td> <td>any</td> <td>inverse error function real(<i>x</i>)</td></tr>

^<tr> <td>igamma(a,x)</td> <td>any</td> <td>igamma(Re(<i>a,x</i>)), igamma function of real(<a>a</a>,<i>x</i>)</td></tr>

^<tr> <td>imag(x)</td> <td>complex</td> <td>Im(<i>x</i>), imaginary part of <i>x</i> as a real number</td></tr>

^<tr> <td>invnorm(x)</td> <td>any</td> <td>inverse normal distribution function real(<i>x</i>)</td></tr>

^<tr> <td>int(x)</td> <td>real</td> <td>integer part of <i>x</i>, truncated toward zero</td></tr>

^<tr> <td>lambertw(x)</td> <td>real</td> <td>Lambert <i>W</i> function</td></tr>

^<tr> <td>lgamma(x)</td> <td>any</td> <td>lgamma(Re(<i>x</i>)), lgamma function of real(<i>x</i>)</td></tr>

^<tr> <td>log(x)</td> <td>any</td> <td>ln <i>x</i>, natural logarithm (base <i>e</i>) of <i>x</i></td></tr>

^<tr> <td>log10(x)</td> <td>any</td> <td>log₁₀ <i>x</i>, logarithm (base 10) of <i>x</i></td></tr>

^<tr> <td>norm(x)</td> <td>any</td> <td>norm(<i>x</i>), normal distribution function of real(<i>x</i>)</td></tr>

^<tr> <td>rand(x)</td> <td>int</td> <td>pseudo random number in the interval [0:1]</td></tr>

^<tr> <td>real(x)</td> <td>any</td> <td>Re(<i>x</i>), real part of <i>x</i></td></tr>

^<tr> <td>sgn(x)</td> <td>any</td> <td>1 if <i>x</i> &gt; 0, -1 if <i>x</i> &lt; 0, 0 if <i>x</i> = 0. &image;(<i>x</i>) ignored</td></tr>

^<tr> <td>sin(x)</td> <td>any</td> <td>sin <i>x</i>, sine of <i>x</i></td></tr>

^<tr> <td>sinh(x)</td> <td>any</td> <td>sinh <i>x</i>, hyperbolic sine of <i>x</i> in radians</td></tr>

^<tr> <td>sqrt(x)</td> <td>any</td> <td>&radic;<i>x</i>, square root of <i>x</i></td></tr>

^<tr> <td>tan(x)</td> <td>any</td> <td>tan <i>x</i>, tangent of <i>x</i></td></tr>

^<tr> <td>tanh(x)</td> <td>any</td> <td>tanh <i>x</i>, hyperbolic tangent of <i>x</i> in radians</td></tr>

^<tr> <td>voigt(x,y)</td> <td>real</td> <td>convolution of Gaussian and Lorentzian</td></tr>

^</tbody>

^</table>

^<p>&nbsp;</p>

^<table align="center" border="1" rules="groups" frame="hsides" cellpadding="3" width="90%">

^<colgroup>

^ <col align="center">

^ <col align="center">

^ <col align="left">

^</colgroup>

^<thead>

^<tr> <th colspan="3">Special functions from libcerf (only if available)</th></tr>

^<tr> <th>Function</th> <th>Arguments</th> <th>Returns</th></tr>

^</thead>

^<tbody>

^<tr> <td>cerf(z)</td> <td>complex</td> <td>complex error function</td></tr>

^<tr> <td>cdawson(z)</td> <td>complex</td> <td>complex Dawson's integral</td></tr>

^<tr> <td>faddeeva(z)</td> <td>complex</td> <td>rescaled complex error function <i>w</i>(<i>z</i>) = exp(-<i>z</i>²) × erfc(-i<i>z</i>)</td></tr>

^<tr> <td>erfi(x)</td> <td>real</td> <td>imaginary error function erfi(<i>x</i>) = -i × erf(i<i>x</i>)</td></tr>

^<tr> <td>VP(x,sigma,gamma)</td> <td>real</td> <td>Voigt profile</td></tr>

^</tbody>

^</table>

^<p>&nbsp;</p>

^<table align="center" border="1" rules="groups" frame="hsides" cellpadding="3" width="90%">

^<colgroup>

^ <col align="center">

^ <col align="center">

^ <col align="left">

^</colgroup>

^<thead>

^<tr> <th colspan="3"> String functions </th></tr>

^<tr> <th>Function</th> <th>Arguments</th> <th>Returns</th></tr>

^</thead>

^<tbody>

^<tr> <td>gprintf("format",x,...)</td> <td>any</td> <td>string result from applying gnuplot's format parser</td></tr>

^<tr> <td>sprintf("format",x,...)</td> <td>multiple</td> <td>string result from C-language sprintf</td></tr>

^<tr> <td>strlen("string")</td> <td>string</td> <td>int length of string in bytes</td></tr>

^<tr> <td>strstrt("string","key")</td> <td>strings</td> <td>int index of first character of substring "key"</td></tr>

^<tr> <td>substr("string",beg,end)</td> <td>multiple</td> <td>string "string"[beg:end]</td></tr>

^<tr> <td>strftime("timeformat",t)</td> <td>any</td> <td>string result from applying gnuplot's time parser</td></tr>

^<tr> <td>strptime("timeformat",s)</td> <td>string</td> <td>seconds since year 1970 as given in string s</td></tr>

^<tr> <td>system("command")</td> <td>string</td> <td>string containing output stream of shell command</td></tr>

^<tr> <td>word("string",n)</td> <td>string, int</td> <td>returns the nth word in "string"</td></tr>

^<tr> <td>words("string")</td> <td>string</td> <td>returns the number of words in "string"</td></tr>

^</tbody>

^</table>

^<p>&nbsp;</p>

^<table align="center" border="1" rules="groups" frame="hsides" cellpadding="3" width="90%">

^<colgroup>

^ <col align="center">

^ <col align="center">

^ <col align="left">

^</colgroup>

^<thead>

^<tr> <th colspan="3"> other gnuplot functions </th></tr>

^<tr> <th>Function</th> <th>Arguments</th> <th>Returns</th></tr>

^</thead>

^<tbody>

^<tr> <td>column(x)</td> <td>int or string</td> <td> contents of column <i>x</i> during data input.</td></tr>

^<tr> <td>columnhead(x)</td> <td>int</td> <td> string containing first entry of column <i>x</i> in datafile.</td></tr>

^<tr> <td>exists("X")</td> <td>string</td> <td> returns 1 if a variable named X is defined, 0 otherwise.</td></tr>

^<tr> <td>hsv2rgb(h,s,v)</td> <td>h,s,v in [0:1]</td> <td> converts HSV color to 24bit RGB color.</td></tr>

^<tr> <td>stringcolumn(x)</td> <td>int</td> <td> content column <i>x</i> as a string.</td></tr>

^<tr> <td>timecolumn(N,format)</td> <td>int, string</td> <td> time data in column <i>N</i> during data input</td></tr>

^<tr> <td>tm_hour(x)</td> <td>int</td> <td>the hour</td></tr>

^<tr> <td>tm_mday(x)</td> <td>int</td> <td>the day of the month</td></tr>

^<tr> <td>tm_min(x)</td> <td>int</td> <td>the minute</td></tr>

^<tr> <td>tm_mon(x)</td> <td>int</td> <td>the month</td></tr>

^<tr> <td>tm_sec(x)</td> <td>int</td> <td>the second</td></tr>

^<tr> <td>tm_wday(x)</td> <td>int</td> <td>the day of the week</td></tr>

^<tr> <td>tm_yday(x)</td> <td>int</td> <td>the day of the year</td></tr>

^<tr> <td>tm_year(x)</td> <td>int</td> <td>the year</td></tr>

^<tr> <td>time(x)</td> <td>any</td> <td>the current system time</td></tr>

^<tr> <td>valid(x)</td> <td>int</td> <td> test validity of column(<i>x</i>) during datafile manip.</td></tr>

^<tr> <td>value("name")</td> <td>string</td> <td> returns the current value of the named variable.</td></tr>

^</tbody>

^</table>

C For TeX and troff output a table replaces the help sections below.

C For the HTML help we want both, table and sections, so the magic

C marker below is used to signal this to doc2html:

^<!-- INCLUDE_NEXT_TABLE -->

@start table

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

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

#Function & Arguments & Returns \\ \hline

#\endhead \hline \endfoot

%c c l .

%Function@Arguments@Returns

%_

4 abs

?expressions 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.

=norm

=modulus

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) ]. This is also known as the norm