gnuplot

An Interactive Plotting Program

Thomas Williams & Colin Kelley

Version 3.7 organized by: David Denholm

Major contributors (alphabetic order):

Hans-Bernhard Broeker

John Campbell

Robert Cunningham

David Denholm

Gershon Elber

Roger Fearick

Carsten Grammes

Lucas Hart

Lars Hecking

Thomas Koenig

David Kotz

Ed Kubaitis

Russell Lang

Alexander Lehmann

Alexander Mai

Carsten Steger

Tom Tkacik

Jos Van der Woude

James R. Van Zandt

Alex Woo

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

Mailing list for comments: info-gnuplot@dartmouth.edu

Mailing list for bug reports: bug-gnuplot@dartmouth.edu

This manual was prepared by Dick Crawford

3 December 1998

gnuplot
Commands
Graphical User Interfaces
Bugs

Copyright
Introduction
Seeking-assistance
What's New in version 3.7
Batch/Interactive Operation
Command-line-editing
Comments
Coordinates
Environment
Expressions
Glossary
Plotting
Start-up
Substitution
Syntax
Time/Date data

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

  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.

      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 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). Simple Plots Demo

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

      majordomo@dartmouth.edu

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:

      info-gnuplot@dartmouth.edu

Bug reports and code contributions should be mailed to:

      bug-gnuplot@dartmouth.edu

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

      info-gnuplot-beta@dartmouth.edu

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

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

Before seeking help, please check the FAQ (Frequently Asked Questions) list. 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.ucc.ie/pub/gnuplot/faq,
      ftp://ftp.gnuplot.vt.edu/pub/gnuplot/faq,

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. 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 timedat.dem.

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 and writeback keywords.

16. set encoding for multi-lingual encoding.

17. New x11 driver with persistent and multiple windows.

18. New plotting styles: xerrorbars, 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 linestyle.

26. Text (labels, tic labels, and the time stamp) can be written vertically by those terminals capable of doing so.

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

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:

      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.

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:

      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.

The Atari version of readline defines some additional key aliases:

      Undo            - same as ^L.
      Home            - same as ^A.
      Ctrl Home       - same as ^E.
      Esc             - same as ^U.
      Help            - help plus return.
      Ctrl Help       - help .

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.

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.

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.

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.

Functions
Operators
User-defined

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.

abs
acos
acosh
arg
asin
asinh
atan
atan2
atanh
besj0
besj1
besy0
besy1
ceil
cos
cosh
erf
erfc
exp
floor
gamma
ibeta
inverf
igamma
imag
invnorm
int
lgamma
log
log10
norm
rand
real
sgn
sin
sinh
sqrt
tan
tanh
column
tm_hour
tm_mday
tm_min
tm_mon
tm_sec
tm_wday
tm_yday
tm_year
valid

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.

The arg(x) function returns the phase of a complex number in radians or degrees, as selected by set angles.

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.

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.

The cos(x) function returns the cosine of its argument. cos accepts its argument in radians or degrees, as selected by set angles.

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.

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.

column(x) may be used only in expressions as part of using manipulations to fits or datafile plots. See plot datafile using.

valid(x) may be used only in expressions as part of using manipulations to fits or datafile plots. See plot datafile using. Use of functions and complex variables for airfoils

The operators in gnuplot are the same as the corresponding operators in the C programming language, except that all operators accept integer, real, and complex arguments, unless otherwise noted. The ** operator (exponentiation) is supported, as in FORTRAN.

Parentheses may be used to change order of evaluation.

Unary
Binary
Ternary

    Symbol      Example    Explanation
      -           -a          unary minus
      +           +a          unary plus (no-operation)
      ~           ~a        * one's complement
      !           !a        * logical negation
      !           a!        * factorial
      $           $3        * call arg/column during using manipulation

(*) Starred explanations indicate that the operator requires an integer argument.

Operator precedence is the same as in Fortran and C. As in those languages, parentheses may be used to change the order of operation. Thus -2**2 = -4, but (-2)**2 = 4.

The factorial operator returns a real number to allow a greater range.

    Symbol       Example      Explanation
      **          a**b          exponentiation
      *           a*b           multiplication
      /           a/b           division
      %           a%b         * modulo
      +           a+b           addition
      -           a-b           subtraction
      ==          a==b          equality
      !=          a!=b          inequality
      <           a<b           less than
      <=          a<=b          less than or equal to
      >           a>b           greater than
      >=          a>=b          greater than or equal to
      &           a&b         * bitwise AND
      ^           a^b         * bitwise exclusive OR
      |           a|b         * bitwise inclusive OR
      &&          a&&b        * logical AND
      ||          a||b        * logical OR

    Symbol       Example      Explanation
      ?:          a?b:c     ternary operation

      f(x) = 0<=x && x<1 ? sin(x) : 1<=x && x<2 ? 1/x : 1/0
      plot f(x)
 

Note that gnuplot quietly ignores undefined values, so the final branch of the function (1/0) will produce no plottable points. Note also that f(x) will be plotted as a continuous function across the discontinuity if a line style is used. To plot it discontinuously, create separate functions for the two pieces. (Parametric functions are also useful for this purpose.)

For data in a file, plot the average of the data in columns 2 and 3 against the datum in column 1, but only if the datum in column 4 is non-negative:

      plot 'file' using 1:( $4<0 ? 1/0 : ($2+$3)/2 )

Please see plot data-file using for an explanation of the using syntax.

New user-defined variables and functions of one through five variables may be declared and used anywhere, including on the plot command itself.

User-defined function syntax:

      <func-name>( <dummy1> {,<dummy2>} ... {,<dummy5>} ) = <expression>

where <expression> is defined in terms of <dummy1> through <dummy5>.

User-defined variable syntax:

      <variable-name> = <constant-expression>

Examples:

      w = 2
      q = floor(tan(pi/2 - 0.1))
      f(x) = sin(w*x)
      sinc(x) = sin(pi*x)/(pi*x)
      delta(t) = (t == 0)
      ramp(t) = (t > 0) ? t : 0
      min(a,b) = (a < b) ? a : b
      comb(n,k) = n!/(k!*(n-k)!)
      len3d(x,y,z) = sqrt(x*x+y*y+z*z)
      plot f(x) = sin(x*a), a = 0.2, f(x), a = 0.4, f(x)

Note that the variable pi is already defined. But it is in no way magic; you may redefine it to be whatever you like.

Valid names are the same as in most programming languages: they must begin with a letter, but subsequent characters may be letters, digits, "$", or "_". Note, however, that the fit mechanism uses several variables with names that begin "FIT_". It is safest to avoid using such names. "FIT_LIMIT", however, is one that you may wish to redefine. See the documentation on fit for details.

See show functions, show variables, and fit.

Throughout this document an attempt has been made to maintain consistency of nomenclature. This cannot be wholly successful because as gnuplot has evolved over time, certain command and keyword names have been adopted that preclude such perfection. This section contains explanations of the way some of these terms are used.

A "page" or "screen" is the entire area addressable by gnuplot. On a monitor, it is the full screen; on a plotter, it is a single sheet of paper.

A screen may contain one or more "plots". A plot is defined by an abscissa and an ordinate, although these need not actually appear on it, as well as the margins and any text written therein.

A plot contains one "graph". A graph is defined by an abscissa and an ordinate, although these need not actually appear on it.

A graph may contain one or more "lines". A line is a single function or data set. "Line" is also a plotting style. The word will also be used in sense "a line of text". Presumably the context will remove any ambiguity.

The lines on a graph may have individual names. These may be listed together with a sample of the plotting style used to represent them in the "key", sometimes also called the "legend".

The word "title" occurs with multiple meanings in gnuplot. In this document, it will always be preceded by the adjective "plot", "line", or "key" to differentiate among them.

A graph may have up to four labelled axes. Various commands have the name of an axis built into their names, such as set xlabel. Other commands have one or more axis names as options, such as set logscale xy. The names of the four axes for these usages are "x" for the axis along the bottom border of the plot, "y" for the left border, "x2" for the top border, and "y2" for the right border. "z" also occurs in commands used with 3-d plotting.

When discussing data files, the term "record" will be resurrected and used to denote a single line of text in the file, that is, the characters between newline or end-of-record characters. A "point" is the datum extracted from a single record. A "datablock" is a set of points from consecutive records, delimited by blank records. A line, when referred to in the context of a data file, is a subset of a datablock.

There are three gnuplot commands which actually create a plot: plot, splot and replot. plot generates 2-d plots, splot generates 3-d plots (actually 2-d projections, of course), and replot appends its arguments to the previous plot or splot and executes the modified command.

Much of the general information about plotting can be found in the discussion of plot; information specific to 3-d can be found in the splot section.

plot operates in either rectangular or polar coordinates -- see set polar for details of the latter. splot operates only in rectangular coordinates, but the set mapping command allows for a few other coordinate systems to be treated. In addition, the using option allows both plot and splot to treat almost any coordinate system you'd care to define.

splot can plot surfaces and contours in addition to points and/or lines. In addition to splot, see set isosamples for information about defining the grid for a 3-d function; splot datafile for information about the requisite file structure for 3-d data values; and set contour and set cntrparam for information about contours.

When gnuplot is run, it looks for an initialization file to load. This file is called .gnuplot on Unix and AmigaOS systems, and GNUPLOT.INI on other systems. If this file is not found in the current directory, the program will look for it in the home directory (under AmigaOS, Atari(single)TOS, MS-DOS and OS/2, the environment variable gnuplot should contain the name of this directory). Note: if NOCWDRC is defined during the installation, gnuplot will not read from the current directory.

If the initialization file is found, gnuplot executes the commands in it. These may be any legal gnuplot commands, but typically they are limited to setting the terminal and defining frequently-used functions or variables.

Command-line substitution is specified by a system command enclosed in backquotes. This command is spawned and the output it produces replaces the name of the command (and backquotes) on the command line. Some implementations also support pipes; see plot data-file special-filenames.

Newlines in the output produced by the spawned command are replaced with blanks.

Command-line substitution can be used anywhere on the gnuplot command line.

Example:

This will run the program leastsq and replace leastsq (including backquotes) on the command line with its output:

      f(x) = leastsq

or, in VMS

      f(x) = run leastsq

The general rules of syntax and punctuation in gnuplot are that keywords and options are order-dependent. Options and any accompanying parameters are separated by spaces whereas lists and coordinates are separated by commas. Ranges are separated by colons and enclosed in brackets [], text and file names are enclosed in quotes, and a few miscellaneous things are enclosed in parentheses. Braces {} are used for a few special purposes.

Commas are used to separate coordinates on the set commands arrow, key, and label; the list of variables being fitted (the list after the via keyword on the fit command); lists of discrete contours or the loop parameters which specify them on the set cntrparam command; the arguments of the set commands dgrid3d, dummy, isosamples, offsets, origin, samples, size, time, and view; lists of tics or the loop parameters which specify them; the offsets for titles and axis labels; parametric functions to be used to calculate the x, y, and z coordinates on the plot, replot and splot commands; and the complete sets of keywords specifying individual plots (data sets or functions) on the plot, replot and splot commands.

Parentheses are used to delimit sets of explicit tics (as opposed to loop parameters) and to indicate computations in the using filter of the fit, plot, replot and splot commands.

(Parentheses and commas are also used as usual in function notation.)

Brackets are used to delimit ranges, whether they are given on set, plot or splot commands.

Colons are used to separate extrema in range specifications (whether they are given on set, plot or splot commands) and to separate entries in the using filter of the plot, replot, splot and fit commands.

Semicolons are used to separate commands given on a single command line.

Braces are used in text to be specially processed by some terminals, like postscript. They are also used to denote complex numbers: {3,2} = 3 + 2i.

Text may be enclosed in single- or double-quotes. Backslash processing of sequences like \n (newline) and \345 (octal character code) is performed for double-quoted strings, but not for single-quoted strings.

The justification is the same for each line of a multi-line string. Thus the center-justified string

      "This is the first line of text.\nThis is the second line."

will produce

                       This is the first line of text.
                          This is the second line.

but

      'This is the first line of text.\nThis is the second line.'

will produce

          This is the first line of text.\nThis is the second line.

Filenames may be entered with either single- or double-quotes. In this manual the command examples generally single-quote filenames and double-quote other string tokens for clarity.

At present you should not embed \n inside {} when using the enhanced option of the postscript terminal.

The EEPIC, Imagen, Uniplex, LaTeX, and TPIC drivers allow a newline to be specified by \\ in a single-quoted string or \\\\ in a double-quoted string.

Back-quotes are used to enclose system commands for substitution.

gnuplot supports the use of time and/or date information as input data. This feature is activated by the commands set xdata time, set ydata time, etc.

Internally all times and dates are converted to the number of seconds from the year 2000. The command set timefmt defines the format for all inputs: data files, ranges, tics, label positions---in short, anything that accepts a data value must receive it in this format. Since only one input format can be in force at a given time, all time/date quantities being input at the same time must be presented in the same format. Thus if both x and y data in a file are time/date, they must be in the same format.

The conversion to and from seconds assumes Universal Time (which is the same as Greenwich Standard Time). There is no provision for changing the time zone or for daylight savings. If all your data refer to the same time zone (and are all either daylight or standard) you don't need to worry about these things. But if the absolute time is crucial for your application, you'll need to convert to UT yourself.

Commands like show xrange will re-interpret the integer according to timefmt. If you change timefmt, and then show the quantity again, it will be displayed in the new timefmt. For that matter, if you give the deactivation command (like set xdata), the quantity will be shown in its numerical form.

The command set format defines the format that will be used for tic labels, whether or not the specified axis is time/date.

If time/date information is to be plotted from a file, the using option _must_ be used on the plot or splot command. These commands simply use white space to separate columns, but white space may be embedded within the time/date string. If you use tabs as a separator, some trial-and-error may be necessary to discover how your system treats them.

The following example demonstrates time/date plotting.

Suppose the file "data" contains records like

      03/21/95 10:00  6.02e23

This file can be plotted by

      set xdata time
      set timefmt "%m/%d/%y"
      set xrange ["03/21/95":"03/22/95"]
      set format x "%m/%d"
      set timefmt "%m/%d/%y %H:%M"
      plot "data" using 1:3

which will produce xtic labels that look like "03/21".

See the descriptions of each command for more details.

This section lists the commands acceptable to gnuplot in alphabetical order. Printed versions of this document contain all commands; on-line versions may not be complete. Indeed, on some systems there may be no commands at all listed under this heading.

Note that in most cases unambiguous abbreviations for command names and their options are permissible, i.e., "p f(x) w l" instead of "plot f(x) with lines".

In the syntax descriptions, braces ({}) denote optional arguments and a vertical bar (|) separates mutually exclusive choices.

cd
call
clear
exit
fit
help
if
load
pause
plot
print
pwd
quit
replot
reread
reset
save
set-show
shell
splot
test
update

      cd '<directory-name>'

      cd 'subdir'
      cd ".."

      cd "c:\newdata"

      cd 'c:\newdata'

The call command is identical to the load command with one exception: you can have up to ten additional parameters to the command (delimited according to the standard parser rules) which can be substituted into the lines read from the file. As each line is read from the called input file, it is scanned for the sequence $ (dollar-sign) followed by a digit (0--9). If found, the sequence is replaced by the corresponding parameter from the call command line. If the parameter was specified as a string in the call line, it is substituted without its enclosing quotes. $ followed by any character other than a digit will be that character. E.g. use $$ to get a single $. Providing more than ten parameters on the call command line will cause an error. A parameter that was not provided substitutes as nothing. Files being called may themselves contain call or load commands.

The call command _must_ be the last command on a multi-command line.

Syntax:

      call "<input-file>" <parameter-0> <parm-1> ... <parm-9>

The name of the input file must be enclosed in quotes, and it is recommended that parameters are similarly enclosed in quotes (future versions of gnuplot may treat quoted and unquoted arguments differently).

Example:

If the file 'calltest.gp' contains the line:

      print "p0=$0 p1=$1 p2=$2 p3=$3 p4=$4 p5=$5 p6=$6 p7=x$7x"

entering the command:

      call 'calltest.gp' "abcd" 1.2 + "'quoted'" -- "$2"

will display:

      p0=abcd p1=1.2 p2=+ p3='quoted' p4=- p5=- p6=$2 p7=xx

NOTE: there is a clash in syntax with the datafile using callback operator. Use $$n or column(n) to access column n from a datafile inside a called datafile plot.

The clear command erases the current screen or output device as specified by set output. This usually generates a formfeed on hardcopy devices. Use set terminal to set the device type.

For some terminals clear erases only the portion of the plotting surface defined by set size, so for these it can be used in conjunction with set multiplot to create an inset.

Example:

      set multiplot
      plot sin(x)
      set origin 0.5,0.5
      set size 0.4,0.4
      clear
      plot cos(x)
      set nomultiplot

Please see set multiplot, set size, and set origin for details of these commands.

The commands exit and quit and the END-OF-FILE character will exit the current gnuplot command file and load the next one. See "help batch/interactive" for more details.

Each of these commands will clear the output device (as does the clear command) before exiting.

      fit {[xrange] {[yrange]}} <function> '<datafile>'
          {datafile-modifiers}
          via '<parameter file>' | <var1>{,<var2>,...}

      [{dummy_variable=}{<min>}{:<max>}],

analogous to plot; see plot ranges.

<function> is any valid gnuplot expression, although it is usual to use a previously user-defined function of the form f(x) or f(x,y).

<datafile> is treated as in the plot command. All the plot datafile modifiers (using, every,...) except smooth are applicable to fit. See plot datafile.

The default data formats for fitting functions with a single independent variable, y=f(x), are {x:}y or x:y:s; those formats can be changed with the datafile using qualifier. The third item, (a column number or an expression), if present, is interpreted as the standard deviation of the corresponding y value and is used to compute a weight for the datum, 1/s**2. Otherwise, all data points are weighted equally, with a weight of one.

To fit a function with two independent variables, z=f(x,y), the required format is using with four items, x:y:z:s. The complete format must be given---no default columns are assumed for a missing token. Weights for each data point are evaluated from 's' as above. If error estimates are not available, a constant value can be specified as a constant expression (see plot datafile using), e.g., using 1:2:3:(1).

Multiple datasets may be simultaneously fit with functions of one independent variable by making y a 'pseudo-variable', e.g., the dataline number, and fitting as two independent variables. See fit multibranch.

The via qualifier specifies which parameters are to be adjusted, either directly, or by referencing a parameter file.

Examples:

      f(x) = a*x**2 + b*x + c
      g(x,y) = a*x**2 + b*y**2 + c*x*y
      FIT_LIMIT = 1e-6
      fit f(x) 'measured.dat' via 'start.par'
      fit f(x) 'measured.dat' using 3:($7-5) via 'start.par'
      fit f(x) './data/trash.dat' using 1:2:3 via a, b, c
      fit g(x,y) 'surface.dat' using 1:2:3:(1) via a, b, c

After each iteration step, detailed information about the current state of the fit is written to the display. The same information about the initial and final states is written to a log file, "fit.log". This file is always appended to, so as to not lose any previous fit history; it should be deleted or renamed as desired.

The fit may be interrupted by pressing Ctrl-C (any key but Ctrl-C under MSDOS and Atari Multitasking Systems). After the current iteration completes, you have the option to (1) stop the fit and accept the current parameter values, (2) continue the fit, (3) execute a gnuplot command as specified by the environment variable FIT_SCRIPT. The default for FIT_SCRIPT is replot, so if you had previously plotted both the data and the fitting function in one graph, you can display the current state of the fit.

Once fit has finished, the update command may be used to store final values in a file for subsequent use as a parameter file. See update for details.

adjustable parameters
beginner's guide
error estimates
fit controlling
multi-branch
starting values
tips

      varname = value

      varname = value       # FIXED

means that the variable is treated as a 'fixed parameter', initialized by the parameter file, but not adjusted by fit. For clarity, it may be useful to designate variables as fixed parameters so that their values are reported by fit. The keyword # FIXED has to appear in exactly this form.

fit is used to find a set of parameters that 'best' fits your data to your user-defined function. The fit is judged on the basis of the the sum of the squared differences or 'residuals' (SSR) between the input data points and the function values, evaluated at the same places. This quantity is often called 'chisquare' (i.e., the Greek letter chi, to the power of 2). The algorithm attempts to minimize SSR, or more precisely, WSSR, as the residuals are 'weighted' by the input data errors (or 1.0) before being squared; see fit error_estimates for details.

That's why it is called 'least-squares fitting'. Let's look at an example to see what is meant by 'non-linear', but first we had better go over some terms. Here it is convenient to use z as the dependent variable for user-defined functions of either one independent variable, z=f(x), or two independent variables, z=f(x,y). A parameter is a user-defined variable that fit will adjust, i.e., an unknown quantity in the function declaration. Linearity/non-linearity refers to the relationship of the dependent variable, z, to the parameters which fit is adjusting, not of z to the independent variables, x and/or y. (To be technical, the second {and higher} derivatives of the fitting function with respect to the parameters are zero for a linear least-squares problem).

For linear least-squares (LLS), the user-defined function will be a sum of simple functions, not involving any parameters, each multiplied by one parameter. NLLS handles more complicated functions in which parameters can be used in a large number of ways. An example that illustrates the difference between linear and nonlinear least-squares is the Fourier series. One member may be written as

     z=a*sin(c*x) + b*cos(c*x).

If a and b are the unknown parameters and c is constant, then estimating values of the parameters is a linear least-squares problem. However, if c is an unknown parameter, the problem is nonlinear.

In the linear case, parameter values can be determined by comparatively simple linear algebra, in one direct step. However LLS is a special case which is also solved along with more general NLLS problems by the iterative procedure that gnuplot uses. fit attempts to find the minimum by doing a search. Each step (iteration) calculates WSSR with a new set of parameter values. The Marquardt-Levenberg algorithm selects the parameter values for the next iteration. The process continues until a preset criterium is met, either (1) the fit has "converged" (the relative change in WSSR is less than FIT_LIMIT), or (2) it reaches a preset iteration count limit, FIT_MAXITER (see fit control variables). The fit may also be interrupted and subsequently halted from the keyboard (see fit).

Often the function to be fitted will be based on a model (or theory) that attempts to describe or predict the behaviour of the data. Then fit can be used to find values for the free parameters of the model, to determine how well the data fits the model, and to estimate an error range for each parameter. See fit error_estimates.

Alternatively, in curve-fitting, functions are selected independent of a model (on the basis of experience as to which are likely to describe the trend of the data with the desired resolution and a minimum number of parameters*functions.) The fit solution then provides an analytic representation of the curve.

However, if all you really want is a smooth curve through your data points, the smooth option to plot may be what you've been looking for rather than fit.

In fit, the term "error" is used in two different contexts, data error estimates and parameter error estimates.

Data error estimates are used to calculate the relative weight of each data point when determining the weighted sum of squared residuals, WSSR or chisquare. They can affect the parameter estimates, since they determine how much influence the deviation of each data point from the fitted function has on the final values. Some of the fit output information, including the parameter error estimates, is more meaningful if accurate data error estimates have been provided.

The 'statistical overview' describes some of the fit output and gives some background for the 'practical guidelines'.

statistical overview
practical guidelines

At the conclusion fit reports 'stdfit', the standard deviation of the fit, which is the rms of the residuals, and the variance of the residuals, also called 'reduced chisquare' when the data points are weighted. The number of degrees of freedom (the number of data points minus the number of fitted parameters) is used in these estimates because the parameters used in calculating the residuals of the datapoints were obtained from the same data.

To estimate confidence levels for the parameters, one can use the minimum chisquare obtained from the fit and chisquare statistics to determine the value of chisquare corresponding to the desired confidence level, but considerably more calculation is required to determine the combinations of parameters which produce such values.

Rather than determine confidence intervals, fit reports parameter error estimates which are readily obtained from the variance-covariance matrix after the final iteration. By convention, these estimates are called "standard errors" or "asymptotic standard errors", since they are calculated in the same way as the standard errors (standard deviation of each parameter) of a linear least-squares problem, even though the statistical conditions for designating the quantity calculated to be a standard deviation are not generally valid for the NLLS problem. The asymptotic standard errors are generally over-optimistic and should not be used for determining confidence levels, but are useful for qualitative purposes.

The final solution also produces a correlation matrix, which gives an indication of the correlation of parameters in the region of the solution; if one parameter is changed, increasing chisquare, does changing another compensate? The main diagonal elements, autocorrelation, are all 1; if all parameters were independent, all other elements would be nearly 0. Two variables which completely compensate each other would have an off-diagonal element of unit magnitude, with a sign depending on whether the relation is proportional or inversely proportional. The smaller the magnitudes of the off-diagonal elements, the closer the estimates of the standard deviation of each parameter would be to the asymptotic standard error.

Weighting the data provides a basis for interpreting the additional fit output after the last iteration. Even if you weight each point equally, estimating an average standard deviation rather than using a weight of 1 makes WSSR a dimensionless variable, as chisquare is by definition.

Each fit iteration will display information which can be used to evaluate the progress of the fit. (An '*' indicates that it did not find a smaller WSSR and is trying again.) The 'sum of squares of residuals', also called 'chisquare', is the WSSR between the data and your fitted function; fit has minimized that. At this stage, with weighted data, chisquare is expected to approach the number of degrees of freedom (data points minus parameters). The WSSR can be used to calculate the reduced chisquare (WSSR/ndf) or stdfit, the standard deviation of the fit, sqrt(WSSR/ndf). Both of these are reported for the final WSSR.

If the data are unweighted, stdfit is the rms value of the deviation of the data from the fitted function, in user units.

If you supplied valid data errors, the number of data points is large enough, and the model is correct, the reduced chisquare should be about unity. (For details, look up the 'chi-squared distribution' in your favourite statistics reference.) If so, there are additional tests, beyond the scope of this overview, for determining how well the model fits the data.

A reduced chisquare much larger than 1.0 may be due to incorrect data error estimates, data errors not normally distributed, systematic measurement errors, 'outliers', or an incorrect model function. A plot of the residuals, e.g., plot 'datafile' using 1:($2-f($1)), may help to show any systematic trends. Plotting both the data points and the function may help to suggest another model.

Similarly, a reduced chisquare less than 1.0 indicates WSSR is less than that expected for a random sample from the function with normally distributed errors. The data error estimates may be too large, the statistical assumptions may not be justified, or the model function may be too general, fitting fluctuations in a particular sample in addition to the underlying trends. In the latter case, a simpler function may be more appropriate.

You'll have to get used to both fit and the kind of problems you apply it to before you can relate the standard errors to some more practical estimates of parameter uncertainties or evaluate the significance of the correlation matrix.

Note that fit, in common with most NLLS implementations, minimizes the weighted sum of squared distances (y-f(x))**2. It does not provide any means to account for "errors" in the values of x, only in y. Also, any "outliers" (data points outside the normal distribution of the model) will have an exaggerated effect on the solution.

There are a number of gnuplot variables that can be defined to affect fit. Those which can be defined once gnuplot is running are listed under 'control_variables' while those defined before starting gnuplot are listed under 'environment_variables'.

control variables
environment variables

      FIT_LIMIT

      FIT_MAXITER

      FIT_START_LAMBDA

      FIT_LAMBDA_FACTOR

Oher variables with the FIT_ prefix may be added to fit, so it is safer not to use that prefix for user-defined variables.

The variables FIT_SKIP and FIT_INDEX were used by earlier releases of gnuplot with a 'fit' patch called gnufit and are no longer available. The datafile every modifier provides the functionality of FIT_SKIP. FIT_INDEX was used for multi-branch fitting, but multi-branch fitting of one independent variable is now done as a pseudo-3D fit in which the second independent variable and using are used to specify the branch. See fit multi-branch.

The environment variables must be defined before gnuplot is executed; how to do so depends on your operating system.

      FIT_LOG

changes the name (and/or path) of the file to which the fit log will be written from the default of "fit.log" in the working directory.

      FIT_SCRIPT

specifies a command that may be executed after an user interrupt. The default is replot, but a plot or load command may be useful to display a plot customized to highlight the progress of the fit.

     f(x,y) = (y==0) ? a*exp(-x/tau) : b*exp(-x/tau)
     fit f(x,y) 'datafile' using  1:-1:2:3  via a, b, tau

fit may, and often will get "lost" if started far from a solution, where SSR is large and changing slowly as the parameters are varied, or it may reach a numerically unstable region (e.g., too large a number causing a floating point overflow) which results in an "undefined value" message or gnuplot halting.

To improve the chances of finding the global optimum, you should set the starting values at least roughly in the vicinity of the solution, e.g., within an order of magnitude, if possible. The closer your starting values are to the solution, the less chance of stopping at another minimum. One way to find starting values is to plot data and the fitting function on the same graph and change parameter values and replot until reasonable similarity is reached. The same plot is also useful to check whether the fit stopped at a minimum with a poor fit.

Of course, a reasonably good fit is not proof there is not a "better" fit (in either a statistical sense, characterized by an improved goodness-of-fit criterion, or a physical sense, with a solution more consistent with the model.) Depending on the problem, it may be desirable to fit with various sets of starting values, covering a reasonable range for each parameter.

Here are some tips to keep in mind to get the most out of fit. They're not very organized, so you'll have to read them several times until their essence has sunk in.

The two forms of the via argument to fit serve two largely distinct purposes. The via "file" form is best used for (possibly unattended) batch operation, where you just supply the startup values in a file and can later use update to copy the results back into another (or the same) parameter file.

The via var1, var2, ... form is best used interactively, where the command history mechanism may be used to edit the list of parameters to be fitted or to supply new startup values for the next try. This is particularly useful for hard problems, where a direct fit to all parameters at once won't work without good starting values. To find such, you can iterate several times, fitting only some of the parameters, until the values are close enough to the goal that the final fit to all parameters at once will work.

Make sure that there is no mutual dependency among parameters of the function you are fitting. For example, don't try to fit a*exp(x+b), because a*exp(x+b)=a*exp(b)*exp(x). Instead, fit either a*exp(x) or exp(x+b).

A technical issue: the parameters must not be too different in magnitude. The larger the ratio of the largest and the smallest absolute parameter values, the slower the fit will converge. If the ratio is close to or above the inverse of the machine floating point precision, it may take next to forever to converge, or refuse to converge at all. You will have to adapt your function to avoid this, e.g., replace 'parameter' by '1e9*parameter' in the function definition, and divide the starting value by 1e9.

If you can write your function as a linear combination of simple functions weighted by the parameters to be fitted, by all means do so. That helps a lot, because the problem is no longer nonlinear and should converge with only a small number of iterations, perhaps just one.

Some prescriptions for analysing data, given in practical experimentation courses, may have you first fit some functions to your data, perhaps in a multi-step process of accounting for several aspects of the underlying theory one by one, and then extract the information you really wanted from the fitting parameters of those functions. With fit, this may often be done in one step by writing the model function directly in terms of the desired parameters. Transforming data can also quite often be avoided, though sometimes at the cost of a more difficult fit problem. If you think this contradicts the previous paragraph about simplifying the fit function, you are correct.

A "singular matrix" message indicates that this implementation of the Marquardt-Levenberg algorithm can't calculate parameter values for the next iteration. Try different starting values, writing the function in another form, or a simpler function.

Finally, a nice quote from the manual of another fitting package (fudgit), that kind of summarizes all these issues: "Nonlinear fitting is an art!"

      help {<topic>}

If <topic> is not specified, a short message is printed about gnuplot. After help for the requested topic is given, a menu of subtopics is given; help for a subtopic may be requested by typing its name, extending the help request. After that subtopic has been printed, the request may be extended again or you may go back one level to the previous topic. Eventually, the gnuplot command line will return.

If a question mark (?) is given as the topic, the list of topics currently available is printed on the screen.

      if (<condition>) <command-line>

      pi=3
      if (pi!=acos(-1)) print "?Fixing pi!"; pi=acos(-1); print pi

      ?Fixing pi!
      3.14159265358979

      if (1==2) print "Never see this"; print "Or this either"

See reread for an example of how if and reread can be used together to perform a loop.

The load command executes each line of the specified input file as if it had been typed in interactively. Files created by the save command can later be loaded. Any text file containing valid commands can be created and then executed by the load command. Files being loaded may themselves contain load or call commands. See comment for information about comments in commands. To load with arguments, see call.

The load command _must_ be the last command on a multi-command line.

Syntax:

      load "<input-file>"

The name of the input file must be enclosed in quotes.

The special filename "-" may be used to load commands from standard input. This allows a gnuplot command file to accept some commands from standard input. Please see "help batch/interactive" for more details.

Examples:

      load 'work.gnu'
      load "func.dat"

The load command is performed implicitly on any file names given as arguments to gnuplot. These are loaded in the order specified, and then gnuplot exits.

The pause command displays any text associated with the command and then waits a specified amount of time or until the carriage return is pressed. pause is especially useful in conjunction with load files.

Syntax:

      pause <time> {"<string>"}

<time> may be any integer constant or expression. Choosing -1 will wait until a carriage return is hit, zero (0) won't pause at all, and a positive integer will wait the specified number of seconds. pause 0 is synonymous with print.

Note: Since pause communicates with the operating system rather than the graphics, it may behave differently with different device drivers (depending upon how text and graphics are mixed).

Examples:

      pause -1    # Wait until a carriage return is hit
      pause 3     # Wait three seconds
      pause -1  "Hit return to continue"
      pause 10  "Isn't this pretty?  It's a cubic spline."

plot is the primary command for drawing plots with gnuplot. It creates plots of functions and data in many, many ways. plot is used to draw 2-d functions and data; splot draws 2-d projections of 3-d surfaces and data. plot and splot contain many common features; see splot for differences. Note specifically that splot's binary and matrix options do not exist for plot.

Syntax:

      plot {<ranges>}
           {<function> | {"<datafile>" {datafile-modifiers}}}
           {axes <axes>} {<title-spec>} {with <style>}
           {, {definitions,} <function> ...}

where either a <function> or the name of a data file enclosed in quotes is supplied. A function is a mathematical expression or a pair of mathematical expressions in parametric mode. The expressions may be defined completely or in part earlier in the stream of gnuplot commands (see user-defined).

It is also possible to define functions and parameters on the plot command itself. This is done merely by isolating them from other items with commas.

There are four possible sets of axes available; the keyword <axes> is used to select the axes for which a particular line should be scaled. x1y1 refers to the axes on the bottom and left; x2y2 to those on the top and right; x1y2 to those on the bottom and right; and x2y1 to those on the top and left. Ranges specified on the plot command apply only to the first set of axes (bottom left).

Examples:

      plot sin(x)
      plot f(x) = sin(x*a), a = .2, f(x), a = .4, f(x)
      plot [t=1:10] [-pi:pi*2] tan(t), \
           "data.1" using (tan($2)):($3/$4) smooth csplines \
                    axes x1y2 notitle with lines 5

data-file
errorbars
parametric
ranges
title
with

Discrete data contained in a file can be displayed by specifying the name of the data file (enclosed in single or double quotes) on the plot command line.

Syntax:

      plot '<file_name>' {index <index list>}
                            {every <every list>}
                            {thru <thru expression>}
                            {using <using list>}
                            {smooth <option>}

The modifiers index, every, thru, using, and smooth are discussed separately. In brief, index selects which data sets in a multi-data-set file are to be plotted, every specifies which points within a single data set are to be plotted, using determines how the columns within a single record are to be interpreted (thru is a special case of using), and smooth allows for simple interpolation and approximation. ('splot' has a similar syntax, but does not support the smooth and thru options.)

Data files should contain at least one data point per record (using can select one data point from the record). Records beginning with # (and also with ! on VMS) will be treated as comments and ignored. Each data point represents an (x,y) pair. For plots with error bars (see set style errorbars), each data point is (x,y,ydelta), (x,y,ylow,yhigh), (x,y,xdelta), (x,y,xlow,xhigh), or (x,y,xlow,xhigh,ylow,yhigh). In all cases, the numbers on each record of a data file must be separated by white space (one or more blanks or tabs), unless a format specifier is provided by the using option. This white space divides each record into columns.

Data may be written in exponential format with the exponent preceded by the letter e, E, d, D, q, or Q.

Only one column (the y value) need be provided. If x is omitted, gnuplot provides integer values starting at 0.

In datafiles, blank records (records with no characters other than blanks and a newline and/or carriage return) are significant---pairs of blank records separate indexes (see plot datafile index). Data separated by double blank records are treated as if they were in separate data files.

Single blank records designate discontinuities in a plot; no line will join points separated by a blank records (if they are plotted with a line style).

If autoscaling has been enabled (set autoscale), the axes are automatically extended to include all datapoints, with a whole number of tic marks if tics are being drawn. This has two consequences: i) For splot, the corner of the surface may not coincide with the corner of the base. In this case, no vertical line is drawn. ii) When plotting data with the same x range on a dual-axis graph, the x coordinates may not coincide if the x2tics are not being drawn. This is because the x axis has been autoextended to a whole number of tics, but the x2 axis has not. The following example illustrates the problem:

      reset; plot '-', '-'
      1 1
      19 19
      e
      1 1
      19 19
      e

every
example datafile
index
smooth
special-filenames
thru
using

In the discussion a "point" is a datum defined by a single record in the file; "block" here will mean the same thing as "datablock" (see glossary).

Syntax:

      plot 'file' every {<point_incr>}
                          {:{<block_incr>}
                            {:{<start_point>}
                              {:{<start_block>}
                                {:{<end_point>}
                                  {:<end_block>}}}}}

The data points to be plotted are selected according to a loop from <start_point> to <end_point> with increment <point_incr> and the blocks according to a loop from <start_block> to <end_block> with increment <block_incr>.

The first datum in each block is numbered '0', as is the first block in the file.

Note that records containing unplottable information are counted.

Any of the numbers can be omitted; the increments default to unity, the start values to the first point or block, and the end values to the last point or block. If every is not specified, all points in all lines are plotted.

Examples:

      every :::3::3    # selects just the fourth block ('0' is first)
      every :::::9     # selects the first 10 blocks
      every 2:2        # selects every other point in every other block
      every ::5::15    # selects points 5 through 15 in each block
 Simple Plot Demos ,
 Non-parametric splot demos , and
 Parametric splot demos.

      pop(x) = 103*exp((1965-x)/10)
      plot [1960:1990] 'population.dat', pop(x)

      # Gnu population in Antarctica since 1965
         1965   103
         1970   55
         1975   34
         1980   24
         1985   10

      plot 'file' index <m>{{:<n>}:<p>}

      plot 'file' index 4:5
  splot with indices demo. 

gnuplot includes a few general-purpose routines for interpolation and approximation of data; these are grouped under the smooth option. More sophisticated data processing may be performed by preprocessing the data externally or by using fit with an appropriate model.

Syntax:

      smooth {unique | csplines | acsplines | bezier | sbezier}

unique plots the data after making them monotonic. Each of the other routines uses the data to determine the coefficients of a continuous curve between the endpoints of the data. This curve is then plotted in the same manner as a function, that is, by finding its value at uniform intervals along the abscissa (see set samples) and connecting these points with straight line segments (if a line style is chosen).

If autoscale is in effect, the ranges will be computed such that the plotted curve lies within the borders of the graph.

If too few points are available to allow the selected option to be applied, an error message is produced. The minimum number is one for unique, four for acsplines, and three for the others.

The smooth options have no effect on function plots.

acsplines
bezier
csplines
sbezier
unique

The acsplines option approximates the data with a "natural smoothing spline". After the data are made monotonic in x (see smooth unique), a curve is piecewise constructed from segments of cubic polynomials whose coefficients are found by the weighting the data points; the weights are taken from the third column in the data file. That default can be modified by the third entry in the using list, e.g.,

      plot 'data-file' using 1:2:(1.0) smooth acsplines

Qualitatively, the absolute magnitude of the weights determines the number of segments used to construct the curve. If the weights are large, the effect of each datum is large and the curve approaches that produced by connecting consecutive points with natural cubic splines. If the weights are small, the curve is composed of fewer segments and thus is smoother; the limiting case is the single segment produced by a weighted linear least squares fit to all the data. The smoothing weight can be expressed in terms of errors as a statistical weight for a point divided by a "smoothing factor" for the curve so that (standard) errors in the file can be used as smoothing weights.

Example:

      sw(x,S)=1/(x*x*S)
      plot 'data_file' using 1:2:(sw($3,100)) smooth acsplines

The csplines option connects consecutive points by natural cubic splines after rendering the data monotonic (see smooth unique).

The sbezier option first renders the data monotonic (unique) and then applies the bezier algorithm.

The unique option makes the data monotonic in x; points with the same x-value are replaced by a single point having the average y-value. The resulting points are then connected by straight line segments. See demos.

A special filename of '-' specifies that the data are inline; i.e., they follow the command. Only the data follow the command; plot options like filters, titles, and line styles remain on the 'plot' command line. This is similar to << in unix shell script, and $DECK in VMS DCL. The data are entered as though they are being read from a file, one data point per record. The letter "e" at the start of the first column terminates data entry. The using option can be applied to these data---using it to filter them through a function might make sense, but selecting columns probably doesn't!

'-' is intended for situations where it is useful to have data and commands together, e.g., when gnuplot is run as a sub-process of some front-end application. Some of the demos, for example, might use this feature. While plot options such as index and every are recognized, their use forces you to enter data that won't be used. For example, while

      plot '-' index 0, '-' index 1
      2
      4
      6

      10
      12
      14
      e
      2
      4
      6

      10
      12
      14
      e

does indeed work,

      plot '-', '-'
      2
      4
      6
      e
      10
      12
      14
      e

is a lot easier to type.

If you use '-' with replot, you may need to enter the data more than once (see replot).

A blank filename ('') specifies that the previous filename should be reused. This can be useful with things like

      plot 'a/very/long/filename' using 1:2, '' using 1:3, '' using 1:4

(If you use both '-' and '' on the same plot command, you'll need to have two sets of inline data, as in the example above.)

On some computer systems with a popen function (Unix), the datafile can be piped through a shell command by starting the file name with a '<'. For example,

      pop(x) = 103*exp(-x/10)
      plot "< awk '{print $1-1965, $2}' population.dat", pop(x)

would plot the same information as the first population example but with years since 1965 as the x axis. If you want to execute this example, you have to delete all comments from the data file above or substitute the following command for the first part of the command above (the part up to the comma):

      plot "< awk '$0 !~ /^#/ {print $1-1965, $2}' population.dat"

While this approach is most flexible, it is possible to achieve simple filtering with the using or thru keywords.

      plot 'file' thru f(x)

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

      plot 'file' thru f(y)

thru is parsed for splot and fit but has no effect.

      plot 'file' using {<entry> {:<entry> {:<entry> ...}}} {'format'}

N.B.---the call command also uses $'s as a special character. See call for details about how to include a column number in a call argument list.

If the using list has but a single entry, that <entry> will be used for y and the data point number is used for x; for example, "plot 'file' using 1" is identical to "plot 'file' using 0:1". If the using list has two entries, these will be used for x and y. Additional entries are usually errors in x and/or y. See set style for details about plotting styles that make use of error information, and fit for use of error information in curve fitting.

'scanf' accepts several numerical specifications but gnuplot requires all inputs to be double-precision floating-point variables, so lf is the only permissible specifier. 'scanf' expects to see white space---a blank, tab ("\t"), newline ("\n"), or formfeed ("\f")---between numbers; anything else in the input stream must be explicitly skipped.

Note that the use of "\t", "\n", or "\f" or requires use of double-quotes rather than single-quotes.

Examples:

This creates a plot of the sum of the 2nd and 3rd data against the first: (The format string specifies comma- rather than space-separated columns.)

      plot 'file' using 1:($2+$3) '%lf,%lf,%lf'

In this example the data are read from the file "MyData" using a more complicated format:

      plot 'MyData' using "%*lf%lf%*20[^\n]%lf"

The meaning of this format is:

      %*lf        ignore a number
      %lf         read a double-precision number (x by default)
      %*20[^\n]   ignore 20 non-newline characters
      %lf         read a double-precision number (y by default)

One trick is to use the ternary ?: operator to filter data:

      plot 'file' using 1:($3>10 ? $2 : 1/0)

which plots the datum in column two against that in column one provided the datum in column three exceeds ten. 1/0 is undefined; gnuplot quietly ignores undefined points, so unsuitable points are suppressed.

In fact, you can use a constant expression for the column number, provided it doesn't start with an opening parenthesis; constructs like using 0+(complicated expression) can be used. The crucial point is that the expression is evaluated once if it doesn't start with a left parenthesis, or once for each data point read if it does.

If timeseries data are being used, the time can span multiple columns. The starting column should be specified. Note that the spaces within the time must be included when calculating starting columns for other data. E.g., if the first element on a line is a time with an embedded space, the y value should be specified as column three.

It should be noted that plot 'file', plot 'file' using 1:2, and plot 'file' using ($1):($2) can be subtly different: 1) if file has some lines with one column and some with two, the first will invent x values when they are missing, the second will quietly ignore the lines with one column, and the third will store an undefined value for lines with one point (so that in a plot with lines, no line joins points across the bad point); 2) if a line contains text at the first column, the first will abort the plot on an error, but the second and third should quietly skip the garbage.

In fact, it is often possible to plot a file with lots of lines of garbage at the top simply by specifying

      plot 'file' using 1:2

However, if you want to leave text in your data files, it is safer to put the comment character (#) in the first column of the text lines. Feeble using demos.

Error bars are supported for 2-d data file plots by reading one to four additional columns (or using entries); these additional values are used in different ways by the various errorbar styles.

In the default situation, gnuplot expects to see three, four, or six numbers on each line of the data file---either

      (x, y, ydelta),
      (x, y, ylow, yhigh),
      (x, y, xdelta),
      (x, y, xlow, xhigh),
      (x, y, xdelta, ydelta), or
      (x, y, xlow, xhigh, ylow, yhigh).

The x coordinate must be specified. The order of the numbers must be exactly as given above, though the using qualifier can manipulate the order and provide values for missing columns. For example,

      plot 'file' with errorbars
      plot 'file' using 1:2:(sqrt($1)) with xerrorbars
      plot 'file' using 1:2:($1-$3):($1+$3):4:5 with xyerrorbars

The last example is for a file containing an unsupported combination of relative x and absolute y errors. The using entry generates absolute x min and max from the relative error.

The y error bar is a vertical line plotted from (x, ylow) to (x, yhigh). If ydelta is specified instead of ylow and yhigh, ylow = y - ydelta and yhigh = y + ydelta are derived. If there are only two numbers on the record, yhigh and ylow are both set to y. The x error bar is a horizontal line computed in the same fashion. To get lines plotted between the data points, plot the data file twice, once with errorbars and once with lines (but remember to use the notitle option on one to avoid two entries in the key).

The error bars have crossbars at each end unless set bar is used (see set bar for details).

If autoscaling is on, the ranges will be adjusted to include the error bars. Errorbar demos.

See plot using, plot with, and set style for more information.

When in parametric mode (set parametric) mathematical expressions must be given in pairs for plot and in triplets for splot.

Examples:

      plot sin(t),t**2
      splot cos(u)*cos(v),cos(u)*sin(v),sin(u)

Data files are plotted as before, except any preceding parametric function must be fully specified before a data file is given as a plot. In other words, the x parametric function (sin(t) above) and the y parametric function (t**2 above) must not be interrupted with any modifiers or data functions; doing so will generate a syntax error stating that the parametric function is not fully specified.

Other modifiers, such as with and title, may be specified only after the parametric function has been completed:

      plot sin(t),t**2 title 'Parametric example' with linespoints
  Parametric Mode Demos. 

      [{<dummy-var>=}{{<min>}:{<max>}}]
      [{{<min>}:{<max>}}]

The first form applies to the independent variable (xrange or trange, if in parametric mode). The second form applies to the dependent variable yrange (and xrange, too, if in parametric mode). <dummy-var> is a new name for the independent variable. (The defaults may be changed with set dummy.) The optional <min> and <max> terms can be constant expressions or *.

In non-parametric mode, the order in which ranges must be given is xrange and yrange.

In parametric mode, the order for the plot command is trange, xrange, and yrange. The following plot command shows setting the trange to [-pi:pi], the xrange to [-1.3:1.3] and the yrange to [-1:1] for the duration of the graph:

      plot [-pi:pi] [-1.3:1.3] [-1:1] sin(t),t**2

Note that the x2range and y2range cannot be specified here---set x2range and set y2range must be used.

Ranges are interpreted in the order listed above for the appropriate mode. Once all those needed are specified, no further ones must be listed, but unneeded ones cannot be skipped---use an empty range [] as a placeholder.

* can be used to allow autoscaling of either of min and max. See also set autoscale.

Ranges specified on the plot or splot command line affect only that graph; use the set xrange, set yrange, etc., commands to change the default ranges for future graphs.

With time data, you must provide the range (in the same manner as the time appears in the datafile) within quotes. gnuplot uses the timefmt string to read the value---see set timefmt.

Examples:

This uses the current ranges:

      plot cos(x)

This sets the x range only:

      plot [-10:30] sin(pi*x)/(pi*x)

This is the same, but uses t as the dummy-variable:

      plot [t = -10 :30]  sin(pi*t)/(pi*t)

This sets both the x and y ranges:

      plot [-pi:pi] [-3:3]  tan(x), 1/x

This sets only the y range, and turns off autoscaling on both axes:

      plot [ ] [-2:sin(5)*-8] sin(x)**besj0(x)

This sets xmax and ymin only:

      plot [:200] [-pi:]  exp(sin(x))

This sets the x range for a timeseries:

      set timefmt "%d/%m/%y %H:%M"
      plot ["1/6/93 12:00":"5/6/93 12:00"] 'timedata.dat'

See Demo.

      title "<title>" | notitle

By default the line title is the function or file name as it appears on the plot command. If it is a file name, any datafile modifiers specified will be included in the default title.

The layout of the key itself (position, title justification, etc.) can be controlled by set key. Please see set key for details.

Examples:

This plots y=x with the title 'x':

      plot x

This plots x squared with title "x^2" and file "data.1" with title "measured data":

      plot x**2 title "x^2", 'data.1' t "measured data"

This puts an untitled circular border around a polar graph:

      set polar; plot my_function(t), 1 notitle

      with <style> { {linestyle | ls <line_style>}
                     | {{linetype | lt <line_type>}
                        {linewidth | lw <line_width>}
                        {pointtype | pt <point_type>}
                        {pointsize | ps <point_size>}} }

where <style> is either lines, points, linespoints, impulses, dots, steps, fsteps, histeps, errorbars, xerrorbars, yerrorbars, xyerrorbars, boxes, boxerrorbars, boxxyerrorbars, financebars, candlesticks or vector. Some of these styles require additional information. See set style <style> for details of each style.

Default styles are chosen with the set function style and set data style commands.

By default, each function and data file will use a different line type and point type, up to the maximum number of available types. All terminal drivers support at least six different point types, and re-use them, in order, if more are required. The LaTeX driver supplies an additional six point types (all variants of a circle), and thus will only repeat after 12 curves are plotted with points. The PostScript drivers (postscript) supplies a total of 64.

If you wish to choose the line or point type for a single plot, <line_type> and <point_type> may be specified. These are positive integer constants (or expressions) that specify the line type and point type to be used for the plot. Use test to display the types available for your terminal.

You may also scale the line width and point size for a plot by using <line_width> and <point_size>, which are specified relative to the default values for each terminal. The pointsize may also be altered globally---see set pointsize for details. But note that both <point_size> as set here and as set by set pointsize multiply the default point size---their effects are not cumulative. That is, set pointsize 2; plot x w p ps 3 will use points three times default size, not six.

If you have defined specific line type/width and point type/size combinations with set linestyle, one of these may be selected by setting <line_style> to the index of the desired style.

The keywords may be abbreviated as indicated.

Note that the linewidth and pointsize options are not supported by all terminals.

Examples:

This plots sin(x) with impulses:

      plot sin(x) with impulses

This plots x with points, x**2 with the default:

      plot x*y w points, x**2 + y**2

This plots tan(x) with the default function style, file "data.1" with lines:

      plot [ ] [-2:5] tan(x), 'data.1' with l

This plots "leastsq.dat" with impulses:

      plot 'leastsq.dat' w i

This plots the data file "population" with boxes:

      plot 'population' with boxes

This plots "exper.dat" with errorbars and lines connecting the points (errorbars require three or four columns):

      plot 'exper.dat' w lines, 'exper.dat' notitle w errorbars

This plots sin(x) and cos(x) with linespoints, using the same line type but different point types:

      plot sin(x) with linesp lt 1 pt 3, cos(x) with linesp lt 1 pt 4

This plots file "data" with points of type 3 and twice usual size:

      plot 'data' with points pointtype 3 pointsize 2

This plots two data sets with lines differing only by weight:

      plot 'd1' t "good" w l lt 2 lw 3, 'd2' t "bad" w l lt 2 lw 1

See set style to change the default styles. Styles demos.

The print command prints the value of <expression> to the screen. It is synonymous with pause 0. <expression> may be anything that gnuplot can evaluate that produces a number, or it can be a string.

Syntax:

      print <expression> {, <expression>, ...}

See expressions.

The exit and quit commands and END-OF-FILE character will exit gnuplot. Each of these commands will clear the output device (as does the clear command) before exiting.

The replot command without arguments repeats the last plot or splot command. This can be useful for viewing a plot with different set options, or when generating the same plot for several devices.

Arguments specified after a replot command will be added onto the last plot or splot command (with an implied ',' separator) before it is repeated. replot accepts the same arguments as the plot and splot commands except that ranges cannot be specified. Thus you can use replot to plot a function against the second axes if the previous command was plot but not if it was splot, and similarly you can use replot to add a plot from a binary file only if the previous command was splot.

N.B.---use of

      plot '-' ; ... ; replot

is not recommended. gnuplot does not store the inline data internally, so since replot appends new information to the previous plot and then executes the modified command, the '-' from the initial plot will expect to read inline data again.

Note that replot does not work in multiplot mode, since it reproduces only the last plot rather than the entire screen.

See also command-line-editing for ways to edit the last plot (splot) command.

The reread command causes the current gnuplot command file, as specified by a load command or on the command line, to be reset to its starting point before further commands are read from it. This essentially implements an endless loop of the commands from the beginning of the command file to the reread command. (But this is not necessarily a disaster---reread can be very useful when used in conjunction with if. See if for details.) The reread command has no effect if input from standard input.

Examples:

Suppose the file "looper" contains the commands

      a=a+1
      plot sin(x*a)
      pause -1
      if(a<5) reread

and from within gnuplot you submit the commands

      a=0
      load 'looper'

The result will be four plots (separated by the pause message).

Suppose the file "data" contains six columns of numbers with a total yrange from 0 to 10; the first is x and the next are five different functions of x. Suppose also that the file "plotter" contains the commands

      c_p = c_p+1
      plot "$0" using 1:c_p with lines linetype c_p
      if(c_p <  n_p) reread

and from within gnuplot you submit the commands

      n_p=6
      c_p=1
      set nokey
      set yrange [0:10]
      set multiplot
      call 'plotter' 'data'
      set nomultiplot

The result is a single graph consisting of five plots. The yrange must be set explicitly to guarantee that the five separate graphs (drawn on top of each other in multiplot mode) will have exactly the same axes. The linetype must be specified; otherwise all the plots would be drawn with the same type. Reread Animation Demo

The reset command causes all options that can be set with the set command to take on their default values. The only exceptions are that the terminal set with set term and the output file set with set output are left unchanged. This command is useful, e.g., to restore the default settings at the end of a command file, or to return to a defined state after lots of settings have been changed within a command file. Please refer to the set command to see the default values that the various options take.

The save command saves user-defined functions, variables, set options, or all three, plus the last plot (splot) command to the specified file.

Syntax:

      save  {<option>} '<filename>'

where <option> is functions, variables or set. If no option is used, gnuplot saves functions, variables, set options and the last plot (splot) command.

saved files are written in text format and may be read by the load command.

The filename must be enclosed in quotes.

Examples:

      save 'work.gnu'
      save functions 'func.dat'
      save var 'var.dat'
      save set 'options.dat'

The set command can be used to sets _lots_ of options. No screen is drawn, however, until a plot, splot, or replot command is given.

The show command shows their settings; show all shows all the settings.

If a variable contains time/date data, show will display it according to the format currently defined by set timefmt, even if that was not in effect when the variable was initially defined.

angles
arrow
autoscale
bar
bmargin
border
boxwidth
clabel
clip
cntrparam
contour
data style
dgrid3d
dummy
encoding
format
function style
functions
grid
hidden3d
isosamples
key
label
linestyle
lmargin
locale
logscale
mapping
margin
missing
multiplot
mx2tics
mxtics
my2tics
mytics
mztics
offsets
origin
output
parametric
pointsize
polar
rmargin
rrange
samples
size
style
surface
terminal<