File: gnuplot.texi

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gnuplot 3.7.2-4
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\input texinfo   @c -*-texinfo-*-

@c %**start of header
@setfilename gnuplot.info
@settitle Gnuplot: An Interactive Plotting Program
@setchapternewpage odd
@c %**end of header

@c define the command and options indeces
@defindex cm
@defindex op
@defindex tm

@direntry
* GNUPLOT: (gnuplot).             An Interactive Plotting Program
@end direntry

@ifnottex
@node Top, gnuplot, (dir), (dir)
@top Master Menu
@end ifnottex

@example
                       GNUPLOT

            An Interactive Plotting Program
             Thomas Williams & Colin Kelley
          Version 3.7 organized by: David Denholm

 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


Major contributors (alphabetic order):
@end example

@c ^ <h2> An Interactive Plotting Program </h2><p>
@c ^ <h2>  Thomas Williams & Colin Kelley</h2><p>
@c ^ <h2>   Version 3.7 organized by: David Denholm </h2><p>
@c ^ <h2>Major contributors (alphabetic order):</h2>

@itemize @bullet
@item
Hans-Bernhard Broeker
@item
John Campbell
@item
Robert Cunningham
@item
David Denholm
@item
Gershon Elber
@item
Roger Fearick
@item
Carsten Grammes
@item
Lucas Hart
@item
Lars Hecking
@item
Thomas Koenig
@item
David Kotz
@item
Ed Kubaitis
@item
Russell Lang
@item
Alexander Lehmann
@item
Alexander Mai
@item
Carsten Steger
@item
Tom Tkacik
@item
Jos Van der Woude
@item
James R. Van Zandt
@item
Alex Woo
@end itemize

@c ^<h2>  Copyright (C) 1986 - 1993, 1998   Thomas Williams, Colin Kelley<p>
@c ^   Mailing list for comments: info-gnuplot@@dartmouth.edu <p>
@c ^   Mailing list for bug reports: bug-gnuplot@@dartmouth.edu<p>
@c ^</h2><p>
@c ^<h3> This manual was prepared by Dick Crawford</h3><p>
@c ^<h3> 3 December 1998</h3><p>
@c ^<hr>

@menu
* gnuplot::                     
* Commands::                    
* Graphical_User_Interfaces::   
* Bugs::                        
* Concept_Index::               
* Command_Index::               
* Options_Index::               
* Function_Index::              
* Terminal_Index::              
@end menu

@node gnuplot, Commands, Top, Top
@chapter gnuplot


@menu
* 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::              
@end menu

@node Copyright, Introduction, gnuplot, gnuplot
@section Copyright

@cindex copyright

@cindex license

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

@end example

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
@example
  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.
@end example

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.


@example
      AUTHORS

@end example

@example
      Original Software:
         Thomas Williams,  Colin Kelley.

@end example

@example
      Gnuplot 2.0 additions:
         Russell Lang, Dave Kotz, John Campbell.

@end example

@example
      Gnuplot 3.0 additions:
         Gershon Elber and many others.

@end example

@node Introduction, Seeking-assistance, Copyright, gnuplot
@section Introduction

@cindex introduction

@c ?
`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 @ref{load} or @ref{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.,

@example
      load "filename"
      cd 'dir'

@end example

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 @ref{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 @ref{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 @ref{help} followed by the name of the topic
or just @ref{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`).
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/simple.html,Simple Plots Demo }

@node Seeking-assistance, What's_New_in_version_3.7, Introduction, gnuplot
@section Seeking-assistance

@cindex seeking-assistance

There is a mailing list for `gnuplot` users.  Note, however, that the
newsgroup
@example
      comp.graphics.apps.gnuplot
@end example

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
@example
      majordomo@@dartmouth.edu
@end example

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:
@example
      info-gnuplot@@dartmouth.edu

@end example

Bug reports and code contributions should be mailed to:
@example
      bug-gnuplot@@dartmouth.edu

@end example

The list of those interested in beta-test versions is:
@example
      info-gnuplot-beta@@dartmouth.edu

@end example

There is also a World Wide Web page with up-to-date information, including
known bugs:
@uref{http://www.cs.dartmouth.edu/gnuplot_info.html,http://www.cs.dartmouth.edu/gnuplot_info.html
}

Before seeking help, please check the
@uref{http://www.ucc.ie/gnuplot/gnuplot-faq.html,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
@example
      ftp://ftp.ucc.ie/pub/gnuplot/faq,
      ftp://ftp.gnuplot.vt.edu/pub/gnuplot/faq,
@end example

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.

@node What's_New_in_version_3.7, Batch/Interactive_Operation, Seeking-assistance, gnuplot
@section What's New in version 3.7

@cindex new-features

Gnuplot version 3.7 contains many new features.  This section gives a partial
list and links to the new items in no particular order.

1. `fit f(x) 'file' via` uses the Marquardt-Levenberg method to fit data.
(This is only slightly different from the `gnufit` patch available for 3.5.)

2. Greatly expanded @ref{using} command.  See @ref{using}.

3. @ref{timefmt} allows for the use of dates as input and output for time
series plots.  See `Time/Date data` and
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/timedat.html,timedat.dem.
}

4. Multiline labels and font selection in some drivers.

5. Minor (unlabeled) tics.  See @ref{mxtics}.

6. @ref{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 @ref{key}.

7. Multiplots on a single logical page with @ref{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 @ref{plot}.

10. Special datafile names `'-'` and `""`.  See @ref{special-filenames}.

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

12. @ref{size} can try to plot with a specified aspect ratio.

13. @ref{missing} now treats missing data correctly.

14. The @ref{call} command: @ref{load} with arguments.

15. More flexible `range` commands with `reverse` and `writeback` keywords.

16. @ref{encoding} for multi-lingual encoding.

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

18. New plotting styles: @ref{xerrorbars}, @ref{histeps}, @ref{financebars} and more.
See @ref{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 @ref{plot}.  See @ref{smooth}.

22. @ref{margin} and @ref{origin} give much better control over where a
graph appears on the page.

23. @ref{border} now controls each border individually.

24. The new commands @ref{if} and @ref{reread} allow command loops.

25. Point styles and sizes, line types and widths can be specified on the
@ref{plot} command.  Line types and widths can also be specified for grids,
borders, tics and arrows.  See @ref{with}.  Furthermore these types may be
combined and stored for further use.  See @ref{linestyle}.

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

@node Batch/Interactive_Operation, Command-line-editing, What's_New_in_version_3.7, gnuplot
@section Batch/Interactive Operation

@cindex batch/interactive

`gnuplot` may be executed in either batch or interactive modes, and the two
may even be mixed together on many systems.

Any command-line arguments are assumed to be names of files containing
`gnuplot` commands (with the exception of standard X11 arguments, which are
processed first).  Each file is loaded with the @ref{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 @ref{exit} and @ref{quit} commands terminate the current command file and
@ref{load} the next one, until all have been processed.

Examples:

To launch an interactive session:
@example
      gnuplot

@end example

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

@end example

To launch an interactive session after an initialization file "header" and
followed by another command file "trailer":
@example
      gnuplot header - trailer

@end example

@node Command-line-editing, Comments, Batch/Interactive_Operation, gnuplot
@section Command-line-editing

@cindex line-editing

@cindex editing

@cindex history

@cindex command-line-editing

Command-line editing is supported by the Unix, Atari, VMS, MS-DOS and OS/2
versions of `gnuplot`.  Also, a history mechanism allows previous commands to
be edited and re-executed.  After the command line has been edited, a newline
or carriage return will enter the entire line without regard to where the
cursor is positioned.

(The readline function in `gnuplot` is not the same as the readline used in
GNU Bash and GNU Emacs.  If the GNU version is desired, it may be selected
instead of the `gnuplot` version at compile time.)


The editing commands are as follows:


@example
      `Line-editing`:

@end example

@example
      ^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.

@end example

@example
      `History`:

@end example

@example
      ^P    moves back through history.
      ^N    moves forward through history.

@end example


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:


@example
      Left  Arrow      - same as ^B.
      Right Arrow      - same as ^F.
      Ctrl Left  Arrow - same as ^A.
      Ctrl Right Arrow - same as ^E.
      Up    Arrow      - same as ^P.
      Down  Arrow      - same as ^N.

@end example


The Atari version of readline defines some additional key aliases:


@example
      Undo            - same as ^L.
      Home            - same as ^A.
      Ctrl Home       - same as ^E.
      Esc             - same as ^U.
      Help            - @ref{help} plus return.
      Ctrl Help       - `help `.

@end example


@node Comments, Coordinates, Command-line-editing, gnuplot
@section Comments

@cindex 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.

@node Coordinates, Environment, Comments, gnuplot
@section Coordinates

@cindex coordinates

The commands @ref{arrow}, @ref{key}, and @ref{label} allow you to draw
something at an arbitrary position on the graph.  This position is specified
by the syntax:

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

@end example

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 @ref{ticslevel}); and `screen`
specifies the screen area (the entire area---not just the portion selected by
@ref{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 @ref{timefmt} format string.
See @ref{xdata} and @ref{timefmt}.  `gnuplot` will also accept an integer
expression, which will be interpreted as seconds from 1 January 2000.

@node Environment, Expressions, Coordinates, gnuplot
@section Environment

@cindex environment

A number of shell environment variables are understood by `gnuplot`.  None of
these are required, but may be useful.

If GNUTERM is defined, it is used as the name of the terminal type to be
used.  This overrides any terminal type sensed by `gnuplot` on start-up, but
is itself overridden by the .gnuplot (or equivalent) start-up file (see
`start-up`) and, of course, by later explicit changes.

On Unix, AmigaOS, AtariTOS, MS-DOS and OS/2, GNUHELP may be defined to be the
pathname of the HELP file (gnuplot.gih).

On VMS, the logical name GNUPLOT$HELP should be defined as the name of the
help library for `gnuplot`.  The `gnuplot` help can be put inside any system
help library, allowing access to help from both within and outside `gnuplot`
if desired.

On Unix, HOME is used as the name of a directory to search for a .gnuplot
file if none is found in the current directory.  On AmigaOS, AtariTOS,
MS-DOS and OS/2, gnuplot is used.  On VMS, SYS$LOGIN: is used. See `help
start-up`.

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

On Unix, AtariTOS and AmigaOS, SHELL is used for the @ref{shell} command.  On
MS-DOS and OS/2, COMSPEC is used for the @ref{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:
@example
      set PCTRM=S800
@end example

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.

@node Expressions, Glossary, Environment, gnuplot
@section Expressions

@cindex expressions

In general, any mathematical expression accepted by C, FORTRAN, Pascal, or
BASIC is valid.  The precedence of these operators is determined by the
specifications of the C programming language.  White space (spaces and tabs)
is ignored inside expressions.

Complex constants are expressed as @{<real>,<imag>@}, where <real> and <imag>
must be numerical constants.  For example, @{3,2@} represents 3 + 2i; @{0,1@}
represents 'i' itself.  The curly braces are explicitly required here.

Note that gnuplot uses both "real" and "integer" arithmetic, like FORTRAN and
C.  Integers are entered as "1", "-10", etc; reals as "1.0", "-10.0", "1e1",
3.5e-1, etc.  The most important difference between the two forms is in
division: division of integers truncates: 5/2 = 2; division of reals does
not: 5.0/2.0 = 2.5.  In mixed expressions, integers are "promoted" to reals
before evaluation: 5/2e0 = 2.5.  The result of division of a negative integer
by a positive one may vary among compilers.  Try a test like "print -5/2" to
determine if your system chooses -2 or -3 as the answer.

The integer expression "1/0" may be used to generate an "undefined" flag,
which causes a point to ignored; the `ternary` operator gives an example.

The real and imaginary parts of complex expressions are always real, whatever
the form in which they are entered: in @{3,2@} the "3" and "2" are reals, not
integers.

@menu
* Functions::                   
* Operators::                   
* User-defined::                
@end menu

@node Functions, Operators, Expressions, Expressions
@subsection Functions

@c ?expressions functions
@cindex functions
@opindex functions


The functions in `gnuplot` are the same as the corresponding functions in
the Unix math library, except that all functions accept integer, real, and
complex arguments, unless otherwise noted.

For those functions that accept or return angles that may be given in either
degrees or radians (sin(x), cos(x), tan(x), asin(x), acos(x), atan(x),
atan2(x) and arg(z)), the unit may be selected by @ref{angles}, which
defaults to radians.



@menu
* 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::                       
@end menu

@node abs, acos, Functions, Functions
@subsubsection abs

@c ?expressions functions abs
@c ?functions abs
@cindex abs
@findex abs


The `abs(x)` function returns the absolute value of its argument.  The
returned value is of the same type as the argument.

For complex arguments, abs(x) is defined as the length of x in the complex
plane [i.e.,  sqrt(real(x)**2 + imag(x)**2) ].

@node acos, acosh, abs, Functions
@subsubsection acos

@c ?expressions functions acos
@c ?functions acos
@cindex acos
@findex acos


The `acos(x)` function returns the arc cosine (inverse cosine) of its
argument.  `acos` returns its argument in radians or degrees, as selected by
@ref{angles}.

@node acosh, arg, acos, Functions
@subsubsection acosh

@c ?expressions functions acosh
@c ?functions acosh
@cindex acosh
@findex acosh


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

@node arg, asin, acosh, Functions
@subsubsection arg

@c ?expressions functions arg
@c ?functions arg
@cindex arg
@findex arg


The `arg(x)` function returns the phase of a complex number in radians or
degrees, as selected by @ref{angles}.

@node asin, asinh, arg, Functions
@subsubsection asin

@c ?expressions functions asin
@c ?functions asin
@cindex asin
@findex asin


The `asin(x)` function returns the arc sin (inverse sin) of its argument.
`asin` returns its argument in radians or degrees, as selected by @ref{angles}.

@node asinh, atan, asin, Functions
@subsubsection asinh

@c ?expressions functions asinh
@c ?functions asinh
@cindex asinh
@findex asinh


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

@node atan, atan2, asinh, Functions
@subsubsection atan

@c ?expressions functions atan
@c ?functions atan
@cindex atan
@findex atan


The `atan(x)` function returns the arc tangent (inverse tangent) of its
argument.  `atan` returns its argument in radians or degrees, as selected by
@ref{angles}.

@node atan2, atanh, atan, Functions
@subsubsection atan2

@c ?expressions functions atan2
@c ?functions atan2
@cindex atan2
@findex atan2


The `atan2(y,x)` function returns the arc tangent (inverse tangent) of the
ratio of the real parts of its arguments.  @ref{atan2} returns its argument in
radians or degrees, as selected by @ref{angles}, in the correct quadrant.

@node atanh, besj0, atan2, Functions
@subsubsection atanh

@c ?expressions functions atanh
@c ?functions atanh
@cindex atanh
@findex atanh


The `atanh(x)` function returns the inverse hyperbolic tangent of its
argument in radians.

@node besj0, besj1, atanh, Functions
@subsubsection besj0

@c ?expressions functions besj0
@c ?functions besj0
@cindex besj0
@findex besj0


The `besj0(x)` function returns the j0th Bessel function of its argument.
@ref{besj0} expects its argument to be in radians.

@node besj1, besy0, besj0, Functions
@subsubsection besj1

@c ?expressions functions besj1
@c ?functions besj1
@cindex besj1
@findex besj1


The `besj1(x)` function returns the j1st Bessel function of its argument.
@ref{besj1} expects its argument to be in radians.

@node besy0, besy1, besj1, Functions
@subsubsection besy0

@c ?expressions functions besy0
@c ?functions besy0
@cindex besy0
@findex besy0


The @ref{besy0} function returns the y0th Bessel function of its argument.
@ref{besy0} expects its argument to be in radians.

@node besy1, ceil, besy0, Functions
@subsubsection besy1

@c ?expressions functions besy1
@c ?functions besy1
@cindex besy1
@findex besy1


The `besy1(x)` function returns the y1st Bessel function of its argument.
@ref{besy1} expects its argument to be in radians.

@node ceil, cos, besy1, Functions
@subsubsection ceil

@c ?expressions functions ceil
@c ?functions ceil
@cindex ceil
@findex ceil


The `ceil(x)` function returns the smallest integer that is not less than its
argument.  For complex numbers, @ref{ceil} returns the smallest integer not less
than the real part of its argument.

@node cos, cosh, ceil, Functions
@subsubsection cos

@c ?expressions functions cos
@c ?functions cos
@cindex cos
@findex cos


The `cos(x)` function returns the cosine of its argument.  `cos` accepts its
argument in radians or degrees, as selected by @ref{angles}.

@node cosh, erf, cos, Functions
@subsubsection cosh

@c ?expressions functions cosh
@c ?functions cosh
@cindex cosh
@findex cosh


The `cosh(x)` function returns the hyperbolic cosine of its argument.  @ref{cosh}
expects its argument to be in radians.

@node erf, erfc, cosh, Functions
@subsubsection erf

@c ?expressions functions erf
@c ?functions erf
@cindex erf
@findex erf


The `erf(x)` function returns the error function of the real part of its
argument.  If the argument is a complex value, the imaginary component is
ignored.

@node erfc, exp, erf, Functions
@subsubsection erfc

@c ?expressions functions erfc
@c ?functions erfc
@cindex erfc
@findex erfc


The `erfc(x)` function returns 1.0 - the error function of the real part of
its argument.  If the argument is a complex value, the imaginary component is
ignored.

@node exp, floor, erfc, Functions
@subsubsection exp

@c ?expressions functions exp
@c ?functions exp
@cindex exp
@findex exp


The `exp(x)` function returns the exponential function of its argument (`e`
raised to the power of its argument).  On some implementations (notably
suns), exp(-x) returns undefined for very large x.  A user-defined function
like safe(x) = x<-100 ? 0 : exp(x) might prove useful in these cases.

@node floor, gamma, exp, Functions
@subsubsection floor

@c ?expressions functions floor
@c ?functions floor
@cindex floor
@findex floor


The `floor(x)` function returns the largest integer not greater than its
argument.  For complex numbers, @ref{floor} returns the largest integer not
greater than the real part of its argument.

@node gamma, ibeta, floor, Functions
@subsubsection gamma

@c ?expressions functions gamma
@c ?functions gamma
@cindex gamma
@findex gamma


The `gamma(x)` function returns the gamma function of the real part of its
argument.  For integer n, gamma(n+1) = n!.  If the argument is a complex
value, the imaginary component is ignored.

@node ibeta, inverf, gamma, Functions
@subsubsection ibeta

@c ?expressions functions ibeta
@c ?functions ibeta
@cindex ibeta
@findex ibeta


The `ibeta(p,q,x)` function returns the incomplete beta function of the real
parts of its arguments. p, q > 0 and x in [0:1].  If the arguments are
complex, the imaginary components are ignored.

@node inverf, igamma, ibeta, Functions
@subsubsection inverf

@c ?expressions functions inverf
@c ?functions inverf
@cindex inverf
@findex inverf


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

@node igamma, imag, inverf, Functions
@subsubsection igamma

@c ?expressions functions igamma
@c ?functions igamma
@cindex igamma
@findex igamma


The `igamma(a,x)` function returns the incomplete gamma function of the real
parts of its arguments.  a > 0 and x >= 0.  If the arguments are complex,
the imaginary components are ignored.

@node imag, invnorm, igamma, Functions
@subsubsection imag

@c ?expressions functions imag
@c ?functions imag
@cindex imag
@findex imag


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

@node invnorm, int, imag, Functions
@subsubsection invnorm

@c ?expressions functions invnorm
@c ?functions invnorm
@cindex invnorm
@findex invnorm


The `invnorm(x)` function returns the inverse normal distribution function of
the real part of its argument.

@node int, lgamma, invnorm, Functions
@subsubsection int

@c ?expressions functions int
@c ?functions int
@cindex int
@findex int


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

@node lgamma, log, int, Functions
@subsubsection lgamma

@c ?expressions functions lgamma
@c ?functions lgamma
@cindex lgamma
@findex lgamma


The `lgamma(x)` function returns the natural logarithm of the gamma function
of the real part of its argument.  If the argument is a complex value, the
imaginary component is ignored.

@node log, log10, lgamma, Functions
@subsubsection log

@c ?expressions functions log
@c ?functions log
@cindex log
@findex log


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

@node log10, norm, log, Functions
@subsubsection log10

@c ?expressions functions log10
@c ?functions log10
@cindex log10
@findex log10


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

@node norm, rand, log10, Functions
@subsubsection norm

@c ?expressions functions norm
@c ?functions norm
@cindex norm
@findex norm


The `norm(x)` function returns the normal distribution function (or Gaussian)
of the real part of its argument.

@node rand, real, norm, Functions
@subsubsection rand

@c ?expressions functions rand
@c ?functions rand
@cindex rand
@findex rand


The `rand(x)` function returns a pseudo random number in the interval [0:1]
using the real part of its argument as a seed.  If seed < 0, the sequence
is (re)initialized.  If the argument is a complex value, the imaginary
component is ignored.

@node real, sgn, rand, Functions
@subsubsection real

@c ?expressions functions real
@c ?functions real
@cindex real
@findex real


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

@node sgn, sin, real, Functions
@subsubsection sgn

@c ?expressions functions sgn
@c ?functions sgn
@cindex sgn
@findex sgn


The `sgn(x)` function returns 1 if its argument is positive, -1 if its
argument is negative, and 0 if its argument is 0.  If the argument is a
complex value, the imaginary component is ignored.

@node sin, sinh, sgn, Functions
@subsubsection sin

@c ?expressions functions sin
@c ?functions sin
@cindex sin
@findex sin


The `sin(x)` function returns the sine of its argument.  `sin` expects its
argument to be in radians or degrees, as selected by @ref{angles}.

@node sinh, sqrt, sin, Functions
@subsubsection sinh

@c ?expressions functions sinh
@c ?functions sinh
@cindex sinh
@findex sinh


The `sinh(x)` function returns the hyperbolic sine of its argument.  @ref{sinh}
expects its argument to be in radians.

@node sqrt, tan, sinh, Functions
@subsubsection sqrt

@c ?expressions functions sqrt
@c ?functions sqrt
@cindex sqrt
@findex sqrt


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

@node tan, tanh, sqrt, Functions
@subsubsection tan

@c ?expressions functions tan
@c ?functions tan
@cindex tan
@findex tan


The `tan(x)` function returns the tangent of its argument.  `tan` expects
its argument to be in radians or degrees, as selected by @ref{angles}.

@node tanh, column, tan, Functions
@subsubsection tanh

@c ?expressions functions tanh
@c ?functions tanh
@cindex tanh
@findex tanh


The `tanh(x)` function returns the hyperbolic tangent of its argument.  @ref{tanh}
expects its argument to be in radians.


A few additional functions are also available.



@node column, tm_hour, tanh, Functions
@subsubsection column

@c ?expressions functions column
@c ?functions column
@cindex column
@findex column


`column(x)` may be used only in expressions as part of @ref{using} manipulations
to fits or datafile plots.  See @ref{using}.

@node tm_hour, tm_mday, column, Functions
@subsubsection tm_hour

@c ?expressions tm_hour
@findex tm_hour
@c ?functions tm_hour
The @ref{tm_hour} function interprets its argument as a time, in seconds from
1 Jan 2000.  It returns the hour (an integer in the range 0--23) as a real.

@node tm_mday, tm_min, tm_hour, Functions
@subsubsection tm_mday

@c ?expressions tm_mday
@findex tm_mday
@c ?functions tm_mday
The @ref{tm_mday} function interprets its argument as a time, in seconds from
1 Jan 2000.  It returns the day of the month (an integer in the range 1--31)
as a real.

@node tm_min, tm_mon, tm_mday, Functions
@subsubsection tm_min

@c ?expressions tm_min
@findex tm_min
@c ?functions tm_min
The @ref{tm_min} function interprets its argument as a time, in seconds from
1 Jan 2000.  It returns the minute (an integer in the range 0--59) as a real.

@node tm_mon, tm_sec, tm_min, Functions
@subsubsection tm_mon

@c ?expressions tm_mon
@findex tm_mon
@c ?functions tm_mon
The @ref{tm_mon} function interprets its argument as a time, in seconds from
1 Jan 2000.  It returns the month (an integer in the range 1--12) as a real.

@node tm_sec, tm_wday, tm_mon, Functions
@subsubsection tm_sec

@c ?expressions tm_sec
@findex tm_sec
@c ?functions tm_sec
The @ref{tm_sec} function interprets its argument as a time, in seconds from
1 Jan 2000.  It returns the second (an integer in the range 0--59) as a real.

@node tm_wday, tm_yday, tm_sec, Functions
@subsubsection tm_wday

@c ?expressions tm_wday
@findex tm_wday
@c ?functions tm_wday
The @ref{tm_wday} function interprets its argument as a time, in seconds from
1 Jan 2000.  It returns the day of the week (an integer in the range 1--7) as
a real.

@node tm_yday, tm_year, tm_wday, Functions
@subsubsection tm_yday

@c ?expressions tm_yday
@findex tm_yday
@c ?functions tm_yday
The @ref{tm_yday} function interprets its argument as a time, in seconds from
1 Jan 2000.  It returns the day of the year (an integer in the range 1--366)
as a real.

@node tm_year, valid, tm_yday, Functions
@subsubsection tm_year

@c ?expressions tm_year
@findex tm_year
@c ?functions tm_year
The @ref{tm_year} function interprets its argument as a time, in seconds from
1 Jan 2000.  It returns the year (an integer) as a real.

@node valid,  , tm_year, Functions
@subsubsection valid

@c ?expressions functions valid
@c ?functions valid
@cindex valid
@findex valid


`valid(x)` may be used only in expressions as part of @ref{using} manipulations
to fits or datafile plots.  See @ref{using}.

@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/airfoil.html,Use of functions and complex variables for airfoils }

@node Operators, User-defined, Functions, Expressions
@subsection Operators

@c ?expressions operators
@cindex operators

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.

@menu
* Unary::                       
* Binary::                      
* Ternary::                     
@end menu

@node Unary, Binary, Operators, Operators
@subsubsection Unary

@c ?expressions operators unary
@c ?operators unary
@cindex unary

The following is a list of all the unary operators and their usages:


@example
    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 @ref{using} manipulation

@end example

(*) 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.

@node Binary, Ternary, Unary, Operators
@subsubsection Binary

@c ?expressions operators binary
@c ?operators binary
@cindex binary

The following is a list of all the binary operators and their usages:


@example
    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

@end example


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

Logical AND (&&) and OR (||) short-circuit the way they do in C.  That is,
the second `&&` operand is not evaluated if the first is false; the second
`||` operand is not evaluated if the first is true.

@node Ternary,  , Binary, Operators
@subsubsection Ternary

@c ?expressions operators ternary
@c ?operators ternary
@cindex ternary

There is a single ternary operator:


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

@end example


The ternary operator behaves as it does in C.  The first argument (a), which
must be an integer, is evaluated.  If it is true (non-zero), the second
argument (b) is evaluated and returned; otherwise the third argument (c) is
evaluated and returned.

The ternary operator is very useful both in constructing piecewise functions
and in plotting points only when certain conditions are met.

Examples:

Plot a function that is to equal sin(x) for 0 <= x < 1, 1/x for 1 <= x < 2,
and undefined elsewhere:
@example
      f(x) = 0<=x && x<1 ? sin(x) : 1<=x && x<2 ? 1/x : 1/0
      plot f(x)
@end example

@c ^ <img align=bottom src="http://www.nas.nasa.gov/~woo/gnuplot/doc/ternary.gif" alt="[ternary.gif]" width=640 height=480>
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:

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

@end example

Please see @ref{using} for an explanation of the @ref{using} syntax.

@node User-defined,  , Operators, Expressions
@subsection User-defined

@c ?expressions user-defined
@cindex user-defined

@cindex variables
@opindex variables


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

User-defined function syntax:
@example
      <func-name>( <dummy1> @{,<dummy2>@} ... @{,<dummy5>@} ) = <expression>

@end example

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

User-defined variable syntax:
@example
      <variable-name> = <constant-expression>

@end example

Examples:
@example
      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)

@end example

@c ^ <img align=bottom src="http://www.nas.nasa.gov/~woo/gnuplot/doc/userdefined.gif" alt="[userdefined.gif]" width=640 height=480>
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 @ref{functions}, @ref{variables}, and `fit`.

@node Glossary, Plotting, Expressions, gnuplot
@section Glossary

@cindex glossary

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 @ref{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.

@node Plotting, Start-up, Glossary, gnuplot
@section Plotting

@cindex plotting

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

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

@ref{plot} operates in either rectangular or polar coordinates -- see `set polar`
for details of the latter.  `splot` operates only in rectangular coordinates,
but the @ref{mapping} command allows for a few other coordinate systems to be
treated.  In addition, the @ref{using} option allows both @ref{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 @ref{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 @ref{contour} and @ref{cntrparam} for information about contours.

@node Start-up, Substitution, Plotting, gnuplot
@section Start-up

@cindex startup

@cindex start

@cindex .gnuplot

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.

@node Substitution, Syntax, Start-up, gnuplot
@section Substitution

@cindex substitution

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 @ref{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:
@example
      f(x) = `leastsq`

@end example

or, in VMS
@example
      f(x) = `run leastsq`

@end example

@node Syntax, Time/Date_data, Substitution, gnuplot
@section Syntax

@cindex syntax

@cindex specify

@cindex punctuation

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 @ref{arrow},
@ref{key}, and @ref{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 @ref{cntrparam} command; the arguments
of the `set` commands @ref{dgrid3d}, @ref{dummy}, @ref{isosamples}, @ref{offsets}, @ref{origin},
@ref{samples}, @ref{size}, `time`, and @ref{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 @ref{plot},
@ref{replot} and `splot` commands; and the complete sets of keywords specifying
individual plots (data sets or functions) on the @ref{plot}, @ref{replot} and `splot`
commands.

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

Colons are used to separate extrema in `range` specifications (whether they
are given on `set`, @ref{plot} or `splot` commands) and to separate entries in
the @ref{using} filter of the @ref{plot}, @ref{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
@example
      "This is the first line of text.\nThis is the second line."
@end example

will produce
@example
                       This is the first line of text.
                          This is the second line.
@end example

but
@example
      'This is the first line of text.\nThis is the second line.'
@end example

will produce
@example
          This is the first line of text.\nThis is the second line.

@end example

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.

@node Time/Date_data,  , Syntax, gnuplot
@section Time/Date data

@cindex time/date

`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 @ref{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 @ref{xrange} will re-interpret the integer according to
@ref{timefmt}.  If you change @ref{timefmt}, and then `show` the quantity again, it
will be displayed in the new @ref{timefmt}.  For that matter, if you give the
deactivation command (like @ref{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 @ref{using} option
_must_ be used on the @ref{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

@example
      03/21/95 10:00  6.02e23

@end example

This file can be plotted by

@example
      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

@end example

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

See the descriptions of each command for more details.

@node Commands, Graphical_User_Interfaces, gnuplot, Top
@chapter Commands

@cindex commands

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.

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

@node cd, call, Commands, Commands
@section cd

@c ?commands cd
@cindex cd
@cmindex cd


The @ref{cd} command changes the working directory.

Syntax:
@example
      cd '<directory-name>'

@end example

The directory name must be enclosed in quotes.

Examples:
@example
      cd 'subdir'
      cd ".."

@end example

DOS users _must_ use single-quotes---backslash [\] has special significance
inside double-quotes.  For example,
@example
      cd "c:\newdata"
@end example

fails, but
@example
      cd 'c:\newdata'
@end example

works as expected.

@node call, clear, cd, Commands
@section call

@c ?commands call
@cindex call
@cmindex call


The @ref{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 @ref{call}ed input file, it is
scanned for the sequence `$` (dollar-sign) followed by a digit (0--9).  If
found, the sequence is replaced by the corresponding parameter from the
@ref{call} command line.  If the parameter was specified as a string in the
@ref{call} line, it is substituted without its enclosing quotes.  `$` 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 @ref{call} command
line will cause an error.  A parameter that was not provided substitutes as
nothing.  Files being @ref{call}ed may themselves contain @ref{call} or @ref{load}
commands.

The @ref{call} command _must_ be the last command on a multi-command line.

Syntax:
@example
      call "<input-file>" <parameter-0> <parm-1> ... <parm-9>

@end example

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

@end example

entering the command:
@example
      call 'calltest.gp' "abcd" 1.2 + "'quoted'" -- "$2"

@end example

will display:
@example
      p0=abcd p1=1.2 p2=+ p3='quoted' p4=- p5=- p6=$2 p7=xx

@end example

NOTE: there is a clash in syntax with the datafile @ref{using} callback
operator.  Use `$$n` or `column(n)` to access column n from a datafile inside
a @ref{call}ed datafile plot.

@node clear, exit, call, Commands
@section clear

@c ?commands clear
@cindex clear
@cmindex clear


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

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

Example:
@example
      set multiplot
      plot sin(x)
      set origin 0.5,0.5
      set size 0.4,0.4
      clear
      plot cos(x)
      set nomultiplot

@end example

Please see @ref{multiplot}, @ref{size}, and @ref{origin} for details of these
commands.

@node exit, fit, clear, Commands
@section exit

@c ?commands exit
@cindex exit
@cmindex exit


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

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

@node fit, help, exit, Commands
@section fit

@c ?commands fit
@cindex fit
@cmindex fit


@cindex least-squares

@cindex Marquardt

The `fit` command can fit a user-defined function to a set of data points
(x,y) or (x,y,z), using an implementation of the nonlinear least-squares
(NLLS) Marquardt-Levenberg algorithm.  Any user-defined variable occurring in
the function body may serve as a fit parameter, but the return type of the
function must be real.

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

@end example

Ranges may be specified to temporarily limit the data which is to be fitted;
any out-of-range data points are ignored. The syntax is
@example
      [@{dummy_variable=@}@{<min>@}@{:<max>@}],
@end example

analogous to @ref{plot}; see @ref{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 @ref{plot} command.  All the `plot datafile`
modifiers (@ref{using}, @ref{every},...) except @ref{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 @ref{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 @ref{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 @ref{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:
@example
      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

@end example

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 @ref{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 @ref{update} command may be used to store final
values in a file for subsequent use as a parameter file.   See @ref{update}
for details.

@menu
* adjustable_parameters::       
* beginner's_guide::            
* error_estimates::             
* fit_controlling::             
* multi-branch::                
* starting_values::             
* tips::                        
@end menu

@node adjustable_parameters, beginner's_guide, fit, fit
@subsection adjustable parameters

@c ?commands fit parameters
@c ?fit parameters
@c ?commands fit adjustable_parameters
@c ?fit adjustable_parameters
@cindex fit_parameters

There are two ways that `via` can specify the parameters to be adjusted,
either directly on the command line or indirectly, by referencing a
parameter file.  The two use different means to set initial values.

Adjustable parameters can be specified by a comma-separated list of variable
names after the `via` keyword.  Any variable that is not already defined is
is created with an initial value of 1.0.  However, the fit is more likely
to converge rapidly if the variables have been previously declared with more
appropriate starting values.

In a parameter file, each parameter to be varied and a corresponding initial
value are specified, one per line, in the form
@example
      varname = value

@end example

Comments, marked by '#', and blank lines are permissible.  The
special form
@example
      varname = value       # FIXED

@end example

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.


@node beginner's_guide, error_estimates, adjustable_parameters, fit
@subsection beginner's guide

@c ?commands fit beginners_guide
@c ?fit beginners_guide
@c ?fit guide
@cindex fitting

`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
@example
     z=a*sin(c*x) + b*cos(c*x).
@end example

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 @ref{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 @ref{smooth} option to @ref{plot} may be what you've been looking for rather
than `fit`.

@node error_estimates, fit_controlling, beginner's_guide, fit
@subsection error estimates

@c ?commands fit error_estimate
@c ?fit error_estimate
@c ?fit errors
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'.

@menu
* statistical_overview::        
* practical_guidelines::        
@end menu

@node statistical_overview, practical_guidelines, error_estimates, error_estimates
@subsubsection statistical overview

@c ?commands fit error statistical_overview
@c ?fit error statistical_overview
@cindex statistical_overview

The theory of non-linear least-squares (NLLS) is generally described in terms
of a normal distribution of errors, that is, the input data is assumed to be
a sample from a population having a given mean and a Gaussian (normal)
distribution about the mean with a given standard deviation.  For a sample of
sufficiently large size, and knowing the population standard deviation, one
can use the statistics of the chisquare distribution to describe a "goodness
of fit" by looking at the variable often called "chisquare".  Here, it is
sufficient to say that a reduced chisquare (chisquare/degrees of freedom,
where degrees of freedom is the number of datapoints less the number of
parameters being fitted) of 1.0 is an indication that the weighted sum of
squared deviations between the fitted function and the data points is the
same as that expected for a random sample from a population characterized by
the function with the current value of the parameters and the given standard
deviations.

If the standard deviation for the population is not constant, as in counting
statistics where variance = counts, then each point should be individually
weighted when comparing the observed sum of deviations and the expected sum
of deviations.

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.

@node practical_guidelines,  , statistical_overview, error_estimates
@subsubsection practical guidelines

@c ?commands fit error practical_guidelines
@c ?fit error practical_guidelines
@cindex practical_guidelines

@cindex guidelines

If you have a basis for assigning weights to each data point, doing so lets
you make use of additional knowledge about your measurements, e.g., take into
account that some points may be more reliable than others.  That may affect
the final values of the parameters.

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.

@node fit_controlling, multi-branch, error_estimates, fit
@subsection fit controlling

@c ?commands fit_control
@cindex fit_control

@c ?fit control
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'.

@menu
* control_variables::           
* environment_variables::       
@end menu

@node control_variables, environment_variables, fit_controlling, fit_controlling
@subsubsection control variables

@c ?commands fit_control variables
@c ?fit_control variables
@c ?fit control variables
The default epsilon limit (1e-5) may be changed by declaring a value for
@example
      FIT_LIMIT
@end example

When the sum of squared residuals changes between two iteration steps by
a factor less than this number (epsilon), the fit is considered to have
'converged'.

The maximum number of iterations may be limited by declaring a value for
@example
      FIT_MAXITER
@end example

A value of 0 (or not defining it at all)  means that there is no limit.

If you need even more control about the algorithm, and know the
Marquardt-Levenberg algorithm well, there are some more variables to
influence it. The startup value of `lambda` is normally calculated
automatically from the ML-matrix, but if you want to, you may provide
your own one with
@example
      FIT_START_LAMBDA
@end example

Specifying FIT_START_LAMBDA as zero or less will re-enable the automatic
selection. The variable
@example
      FIT_LAMBDA_FACTOR
@end example

gives the factor by which `lambda` is increased or decreased whenever
the chi-squared target function increased or decreased significantly.
Setting FIT_LAMBDA_FACTOR to zero re-enables the default factor of
10.0.

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 @ref{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 @ref{using} are used to specify the branch.
See @ref{multi-branch}.

@node environment_variables,  , control_variables, fit_controlling
@subsubsection environment variables

@c ?commands fit_control environment
@c ?fit_control environment
@c ?fit control environment
The environment variables must be defined before `gnuplot` is executed; how
to do so depends on your operating system.

@example
      FIT_LOG
@end example

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.

@example
      FIT_SCRIPT
@end example

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

@node multi-branch, starting_values, fit_controlling, fit
@subsection multi-branch

@c ?commands fit multi-branch
@c ?fit multi-branch
@cindex multi-branch

@cindex branch

In multi-branch fitting, multiple data sets can be simultaneously fit with
functions of one independent variable having common parameters by minimizing
the total WSSR.  The function and parameters (branch) for each data set are
selected by using a 'pseudo-variable', e.g., either the dataline number (a
'column' index of -1) or the datafile index (-2), as the second independent
variable.

Example:  Given two exponential decays of the form, z=f(x), each describing
a different data set but having a common decay time, estimate the values of
the parameters.  If the datafile has the format x:z:s, then
@example
     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

@end example

For a more complicated example, see the file "hexa.fnc" used by the
"fit.dem" demo.

Appropriate weighting may be required since unit weights may cause one
branch to predominate if there is a difference in the scale of the dependent
variable.  Fitting each branch separately, using the multi-branch solution
as initial values, may give an indication as to the relative effect of each
branch on the joint solution.

@node starting_values, tips, multi-branch, fit
@subsection starting values

@c ?commands fit starting_values
@c ?fit starting_values
@cindex starting_values

Nonlinear fitting is not guaranteed to converge to the global optimum (the
solution with the smallest sum of squared residuals, SSR), and can get stuck
at a local minimum.  The routine has no way to determine that;  it is up to
you to judge whether this has happened.

`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 @ref{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.

@node tips,  , starting_values, fit
@subsection tips

@c ?commands fit tips
@c ?fit tips
@cindex tips

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 @ref{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!"

@node help, if, fit, Commands
@section help

@c ?commands help
@cindex help
@cmindex help


The @ref{help} command displays on-line help. To specify information on a
particular topic use the syntax:

@example
      help @{<topic>@}

@end example

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.

@node if, load, help, Commands
@section if

@c ?commands if
@cindex if
@cmindex if


The @ref{if} command allows commands to be executed conditionally.

Syntax:
@example
      if (<condition>) <command-line>

@end example

<condition> will be evaluated.  If it is true (non-zero), then the command(s)
of the <command-line> will be executed.  If <condition> is false (zero), then
the entire <command-line> is ignored.  Note that use of `;` to allow multiple
commands on the same line will _not_ end the conditionalized commands.

Examples:
@example
      pi=3
      if (pi!=acos(-1)) print "?Fixing pi!"; pi=acos(-1); print pi
@end example

will display:
@example
      ?Fixing pi!
      3.14159265358979
@end example

but
@example
      if (1==2) print "Never see this"; print "Or this either"
@end example

will not display anything.

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

@node load, pause, if, Commands
@section load

@c ?commands load
@cindex load
@cmindex load


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

The @ref{load} command _must_ be the last command on a multi-command line.

Syntax:
@example
      load "<input-file>"

@end example

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

The special filename "-" may be used to @ref{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:
@example
      load 'work.gnu'
      load "func.dat"

@end example

The @ref{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.

@node pause, plot, load, Commands
@section pause

@c ?commands pause
@cindex pause
@cmindex pause


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

Syntax:
@example
      pause <time> @{"<string>"@}

@end example

<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 @ref{print}.

Note: Since @ref{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:
@example
      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."

@end example


@node plot, print, pause, Commands
@section plot

@c ?commands plot
@cindex plot
@cmindex plot


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

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

@end example

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 @ref{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 @ref{plot} command apply only to the first set of
axes (bottom left).

Examples:
@example
      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

@end example


@menu
* data-file::                   
* errorbars::                   
* parametric::                  
* ranges::                      
* title::                       
* with::                        
@end menu

@node data-file, errorbars, plot, plot
@subsection data-file

@c ?commands plot datafile
@c ?plot datafile
@cindex data-file

@cindex datafile

@cindex data

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 @ref{plot} command line.

Syntax:
@example
      plot '<file_name>' @{index <index list>@}
                            @{every <every list>@}
                            @{thru <thru expression>@}
                            @{using <using list>@}
                            @{smooth <option>@}

@end example

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

Data files should contain at least one data point per record (@ref{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 @ref{plot}s with error bars (see @ref{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 @ref{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 @ref{index}es (see @ref{index}).  Data separated by double
blank records are treated as if they were in separate data files.

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

If autoscaling has been enabled (@ref{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:

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

@end example

@menu
* every::                       
* example_datafile::            
* index::                       
* smooth::                      
* special-filenames::           
* thru::                        
* using::                       
@end menu

@node every, example_datafile, data-file, data-file
@subsubsection every

@c ?commands plot datafile every
@c ?plot datafile every
@c ?plot every
@c ?data-file every
@c ?datafile every
@cindex every

The @ref{every} keyword allows a periodic sampling of a data set to be plotted.

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

@end example

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 @ref{every} is not specified, all points in all lines are plotted.

Examples:
@example
      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
@end example

@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/simple.html,Simple Plot Demos },
@uref{http://www.nas.nasa.gov/~woo/gnuplot/surfacea/surfacea.html,Non-parametric splot demos }, and
@uref{http://www.nas.nasa.gov/~woo/gnuplot/surfaceb/surfaceb.html,Parametric splot demos.}

@node example_datafile, index, every, data-file
@subsubsection example datafile

@c ?commands plot datafile example
@c ?plot datafile example
@c ?plot example
@c ?datafile example
@c ?data-file example
@cindex example

This example plots the data in the file "population.dat" and a theoretical
curve:

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

@end example

The file "population.dat" might contain:

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

@end example

@c ^ <img align=bottom src="http://www.nas.nasa.gov/~woo/gnuplot/doc/population.gif" alt="[population.gif]" width=640 height=480>

@node index, smooth, example_datafile, data-file
@subsubsection index

@c ?commands plot datafile index
@c ?plot datafile index
@c ?plot index
@c ?data-file index
@c ?datafile index
@cindex index

The @ref{index} keyword allows only some of the data sets in a multi-data-set
file to be plotted.

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

@end example

Data sets are separated by pairs of blank records.  `index <m>` selects only
set <m>; `index <m>:<n>` selects sets in the range <m> to <n>; and `index
<m>:<n>:<p>` selects indices <m>, <m>+<p>, <m>+2<p>, etc., but stopping at
<n>.  Following C indexing, the index 0 is assigned to the first data set in
the file.  Specifying too large an index results in an error message.  If
@ref{index} is not specified, all sets are plotted as a single data set.

Example:
@example
      plot 'file' index 4:5
@end example

@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/multimsh.html,splot with indices demo. }

@node smooth, special-filenames, index, data-file
@subsubsection smooth

@c ?commands plot datafile smooth
@c ?plot datafile smooth
@c ?plot smooth
@c ?data-file smooth
@c ?datafile smooth
@cindex smooth

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

Syntax:
@example
      smooth @{unique | csplines | acsplines | bezier | sbezier@}

@end example

`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 @ref{samples}) and connecting these points with
straight line segments (if a line style is chosen).

If @ref{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 @ref{smooth} options have no effect on function plots.


@noindent --- ACSPLINES ---

@c ?commands plot datafile smooth acsplines
@c ?plot datafile smooth acsplines
@c ?data-file smooth acsplines
@c ?datafile smooth acsplines
@c ?plot smooth acsplines
@c ?plot acsplines
@c ?smooth acsplines
@cindex acsplines

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 @ref{using} list, e.g.,
@example
      plot 'data-file' using 1:2:(1.0) smooth acsplines

@end example

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

@end example


@noindent --- BEZIER ---

@c ?commands plot datafile smooth bezier
@c ?plot datafile smooth bezier
@c ?plot smooth bezier
@c ?data-file smooth bezier
@c ?datafile smooth bezier
@c ?plot bezier
@c ?smooth bezier
@cindex bezier

The `bezier` option approximates the data with a Bezier curve of degree n
(the number of data points) that connects the endpoints.


@noindent --- CSPLINES ---

@c ?commands plot datafile smooth csplines
@c ?plot datafile smooth csplines
@c ?plot smooth csplines
@c ?data-file smooth csplines
@c ?datafile smooth csplines
@c ?plot csplines
@c ?smooth csplines
@cindex csplines

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


@noindent --- SBEZIER ---

@c ?commands plot datafile smooth sbezier
@c ?plot datafile smooth sbezier
@c ?plot smooth sbezier
@c ?data-file smooth sbezier
@c ?datafile smooth sbezier
@c ?plot sbezier
@c ?smooth sbezier
@cindex sbezier

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


@noindent --- UNIQUE ---

@c ?commands plot datafile smooth unique
@c ?plot datafile smooth unique
@c ?plot smooth unique
@c ?data-file smooth unique
@c ?datafile smooth unique
@c ?plot unique
@c ?smooth unique
@cindex unique

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.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/mgr.html,See demos. }

@node special-filenames, thru, smooth, data-file
@subsubsection special-filenames

@c ?commands plot datafile special-filenames
@c ?plot datafile special-filenames
@c ?plot special-filenames
@c ?datafile special-filenames
@cindex special-filenames

A special filename of `'-'` specifies that the data are inline; i.e., they
follow the command.  Only the data follow the command; @ref{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
@ref{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
@ref{plot} options such as @ref{index} and @ref{every} are recognized, their use forces
you to enter data that won't be used.  For example, while

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

@end example


@example
      10
      12
      14
      e
      2
      4
      6

@end example


@example
      10
      12
      14
      e

@end example

does indeed work,

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

@end example

is a lot easier to type.

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

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

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

@end example

(If you use both `'-'` and `''` on the same @ref{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,

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

@end example

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):

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

@end example

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

@node thru, using, special-filenames, data-file
@subsubsection thru

@c ?commands plot datafile thru
@c ?plot datafile thru
@c ?plot thru
@c ?data-file thru
@c ?datafile thru
@cindex thru

The @ref{thru} function is provided for backward compatibility.

Syntax:
@example
      plot 'file' thru f(x)

@end example

It is equivalent to:

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

@end example

While the latter appears more complex, it is much more flexible.  The more
natural

@example
      plot 'file' thru f(y)

@end example

also works (i.e. you can use y as the dummy variable).

@ref{thru} is parsed for `splot` and `fit` but has no effect.

@node using,  , thru, data-file
@subsubsection using

@c ?commands plot datafile using
@c ?plot datafile using
@c ?plot using
@c ?data-file using
@c ?datafile using
@cindex using

The most common datafile modifier is @ref{using}.

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

@end example

If a format is specified, each datafile record is read using the C library's
'scanf' function, with the specified format string.  Otherwise the record is
read and broken into columns at spaces or tabs.  A format cannot be specified
if time-format data is being used (this must be done by `set data time`).

The resulting array of data is then sorted into columns according to the
entries.  Each <entry> may be a simple column number, which selects the
datum, an expression enclosed in parentheses, or empty.  The expression can
use $1 to access the first item read, $2 for the second item, and so on.  It
can also use `column(x)` and `valid(x)` where x is an arbitrary expression
resulting in an integer.  `column(x)` returns the x'th datum; `valid(x)`
tests that the datum in the x'th column is a valid number.  A column number
of 0 generates a number increasing (from zero) with each point, and is reset
upon encountering two blank records.  A column number of -1 gives the
dataline number, which starts at 0, increments at single blank records, and
is reset at double blank records.  A column number of -2 gives the index
number, which is incremented only when two blank records are found.  An empty
<entry> will default to its order in the list of entries.  For example,
`using ::4` is interpreted as `using 1:2:4`.

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

If the @ref{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 @ref{using} list has two
entries, these will be used for x and y.  Additional entries are usually
errors in x and/or y.  See @ref{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.)
@example
      plot 'file' using 1:($2+$3) '%lf,%lf,%lf'

@end example

In this example the data are read from the file "MyData" using a more
complicated format:
@example
      plot 'MyData' using "%*lf%lf%*20[^\n]%lf"

@end example

The meaning of this format is:

@example
      %*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)

@end example

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

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

@end example

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

@example
      plot 'file' using 1:2

@end example

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.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/using.html,Feeble using demos. }

@node errorbars, parametric, data-file, plot
@subsection errorbars

@c ?commands plot errorbars
@c ?commands splot errorbars
@c ?plot errorbars
@c ?splot errorbars
@cindex errorbars

Error bars are supported for 2-d data file plots by reading one to four
additional columns (or @ref{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

@example
      (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).

@end example

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

@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

@end example

The last example is for a file containing an unsupported combination of
relative x and absolute y errors.  The @ref{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,
@ref{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 @ref{bar} is used (see @ref{bar} for details).

If autoscaling is on, the ranges will be adjusted to include the error bars.
@uref{http://www.nas.nasa.gov/~woo/gnuplot/errorbar/errorbar.html,Errorbar demos. }

See @ref{using}, @ref{with}, and @ref{style} for more information.

@node parametric, ranges, errorbars, plot
@subsection parametric

@c ?commands plot parametric
@c ?commands splot parametric
@c ?plot parametric
@c ?splot parametric
@cindex parametric
@opindex parametric


When in parametric mode (`set parametric`) mathematical expressions must be
given in pairs for @ref{plot} and in triplets for `splot`.

Examples:
@example
      plot sin(t),t**2
      splot cos(u)*cos(v),cos(u)*sin(v),sin(u)

@end example

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 @ref{with} and `title`, may be specified only after the
parametric function has been completed:

@example
      plot sin(t),t**2 title 'Parametric example' with linespoints
@end example

@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/param.html,Parametric Mode Demos. }

@node ranges, title, parametric, plot
@subsection ranges

@c ?commands plot ranges
@c ?commands splot ranges
@c ?plot ranges
@c ?splot ranges
@cindex ranges

The optional ranges specify the region of the graph that will be displayed.

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

@end example

The first form applies to the independent variable (@ref{xrange} or @ref{trange}, if
in parametric mode).  The second form applies to the dependent variable
@ref{yrange} (and @ref{xrange}, too, if in parametric mode).  <dummy-var> is a new
name for the independent variable.  (The defaults may be changed with @ref{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 @ref{xrange}
and @ref{yrange}.

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

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

@end example

Note that the x2range and y2range cannot be specified here---@ref{x2range}
and @ref{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
@ref{autoscale}.

Ranges specified on the @ref{plot} or `splot` command line affect only that
graph; use the @ref{xrange}, @ref{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 @ref{timefmt} string
to read the value---see @ref{timefmt}.

Examples:

This uses the current ranges:
@example
      plot cos(x)

@end example

This sets the x range only:
@example
      plot [-10:30] sin(pi*x)/(pi*x)

@end example

This is the same, but uses t as the dummy-variable:
@example
      plot [t = -10 :30]  sin(pi*t)/(pi*t)

@end example

This sets both the x and y ranges:
@example
      plot [-pi:pi] [-3:3]  tan(x), 1/x

@end example

This sets only the y range, and turns off autoscaling on both axes:
@example
      plot [ ] [-2:sin(5)*-8] sin(x)**besj0(x)

@end example

This sets xmax and ymin only:
@example
      plot [:200] [-pi:]  exp(sin(x))

@end example

This sets the x range for a timeseries:
@example
      set timefmt "%d/%m/%y %H:%M"
      plot ["1/6/93 12:00":"5/6/93 12:00"] 'timedata.dat'

@end example

@uref{http://www.nas.nasa.gov/~woo/gnuplot/ranges/ranges.html,See Demo. }

@node title, with, ranges, plot
@subsection title

@c ?commands plot title
@c ?commands splot title
@c ?plot title
@c ?splot title
A line title for each function and data set appears in the key, accompanied
by a sample of the line and/or symbol used to represent it.  It can be
changed by using the `title` option.

Syntax:
@example
      title "<title>" | notitle

@end example

where <title> is the new title of the line and must be enclosed in quotes.
The quotes will not be shown in the key.  A special character may be given as
a backslash followed by its octal value ("\345").  The tab character "\t" is
understood.  Note that backslash processing occurs only for strings enclosed
in double quotes---use single quotes to prevent such processing.  The newline
character "\n" is not processed in key entries in either type of string.

The line title and sample can be omitted from the key by using the keyword
`notitle`.  A null title (`title ''`) is equivalent to `notitle`.  If only
the sample is wanted, use one or more blanks (`title ' '`).

By default the line title is the function or file name as it appears on the
@ref{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 @ref{key}.  Please see @ref{key} for details.

Examples:

This plots y=x with the title 'x':
@example
      plot x

@end example

This plots x squared with title "x^2" and file "data.1" with title
"measured data":
@example
      plot x**2 title "x^2", 'data.1' t "measured data"

@end example

This puts an untitled circular border around a polar graph:
@example
      set polar; plot my_function(t), 1 notitle

@end example

@node with,  , title, plot
@subsection with

@c ?commands plot with
@c ?commands splot with
@c ?commands plot style
@c ?commands splot style
@c ?plot with
@c ?plot style
@c ?splot with
@c ?splot style
@cindex style
@opindex style


@cindex with

Functions and data may be displayed in one of a large number of styles.
The @ref{with} keyword provides the means of selection.

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

@end example

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

Default styles are chosen with the @ref{style} and @ref{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 @ref{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
@ref{pointsize} for details.  But note that both <point_size> as set here and
as set by @ref{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 @ref{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 @ref{pointsize} options are not supported by all
terminals.

Examples:

This plots sin(x) with impulses:
@example
      plot sin(x) with impulses

@end example

This plots x with points, x**2 with the default:
@example
      plot x*y w points, x**2 + y**2

@end example

This plots tan(x) with the default function style, file "data.1" with lines:
@example
      plot [ ] [-2:5] tan(x), 'data.1' with l

@end example

This plots "leastsq.dat" with impulses:
@example
      plot 'leastsq.dat' w i

@end example

This plots the data file "population" with boxes:
@example
      plot 'population' with boxes

@end example

This plots "exper.dat" with errorbars and lines connecting the points
(errorbars require three or four columns):
@example
      plot 'exper.dat' w lines, 'exper.dat' notitle w errorbars

@end example

This plots sin(x) and cos(x) with linespoints, using the same line type but
different point types:
@example
      plot sin(x) with linesp lt 1 pt 3, cos(x) with linesp lt 1 pt 4

@end example

This plots file "data" with points of type 3 and twice usual size:
@example
      plot 'data' with points pointtype 3 pointsize 2

@end example

This plots two data sets with lines differing only by weight:
@example
      plot 'd1' t "good" w l lt 2 lw 3, 'd2' t "bad" w l lt 2 lw 1

@end example

See @ref{style} to change the default styles.
@uref{http://www.nas.nasa.gov/~woo/gnuplot/styles/styles.html,Styles demos. }

@node print, pwd, plot, Commands
@section print

@c ?commands print
@cindex print
@cmindex print


The @ref{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:
@example
      print <expression> @{, <expression>, ...@}

@end example

See `expressions`.

@node pwd, quit, print, Commands
@section pwd

@c ?commands pwd
@cindex pwd
@cmindex pwd


The @ref{pwd} command prints the name of the working directory to the screen.

@node quit, replot, pwd, Commands
@section quit

@c ?commands quit
@cindex quit
@cmindex quit


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

@node replot, reread, quit, Commands
@section replot

@c ?commands replot
@cindex replot
@cmindex replot


The @ref{replot} command without arguments repeats the last @ref{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 @ref{replot} command will be added onto the last
@ref{plot} or `splot` command (with an implied ',' separator) before it is
repeated.  @ref{replot} accepts the same arguments as the @ref{plot} and `splot`
commands except that ranges cannot be specified.  Thus you can use @ref{replot}
to plot a function against the second axes if the previous command was @ref{plot}
but not if it was `splot`, and similarly you can use @ref{replot} to add a plot
from a binary file only if the previous command was `splot`.

N.B.---use of

@example
      plot '-' ; ... ; replot

@end example

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

Note that @ref{replot} does not work in @ref{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 @ref{plot} (`splot`)
command.

@node reread, reset, replot, Commands
@section reread

@c ?commands reread
@cindex reread
@cmindex reread


The @ref{reread} command causes the current `gnuplot` command file, as specified
by a @ref{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 @ref{reread} command.  (But this is not necessarily a disaster---@ref{reread} can
be very useful when used in conjunction with @ref{if}.  See @ref{if} for details.)
The @ref{reread} command has no effect if input from standard input.

Examples:

Suppose the file "looper" contains the commands
@example
      a=a+1
      plot sin(x*a)
      pause -1
      if(a<5) reread
@end example

and from within `gnuplot` you submit the commands
@example
      a=0
      load 'looper'
@end example

The result will be four plots (separated by the @ref{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
@example
      c_p = c_p+1
      plot "$0" using 1:c_p with lines linetype c_p
      if(c_p <  n_p) reread
@end example

and from within `gnuplot` you submit the commands
@example
      n_p=6
      c_p=1
      set nokey
      set yrange [0:10]
      set multiplot
      call 'plotter' 'data'
      set nomultiplot
@end example

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.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/animate.html,Reread Animation Demo}

@node reset, save, reread, Commands
@section reset

@c ?commands reset
@cindex reset
@cmindex reset


The @ref{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 @ref{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.

@node save, set-show, reset, Commands
@section save

@c ?commands save
@cindex save
@cmindex save


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

Syntax:
@example
      save  @{<option>@} '<filename>'

@end example

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

@ref{save}d files are written in text format and may be read by the @ref{load}
command.

The filename must be enclosed in quotes.

Examples:
@example
      save 'work.gnu'
      save functions 'func.dat'
      save var 'var.dat'
      save set 'options.dat'

@end example

@node set-show, shell, save, Commands
@section set-show

@c ?commands set
@c ?commands show
@cindex set

@cindex show

@c ?show all
The `set` command can be used to sets _lots_ of options.  No screen is
drawn, however, until a @ref{plot}, `splot`, or @ref{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 @ref{timefmt}, even if that was not in effect
when the variable was initially defined.

@menu
* 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::                    
* tics::                        
* ticslevel::                   
* ticscale::                    
* timestamp::                   
* timefmt::                     
* title_::                      
* tmargin::                     
* trange::                      
* urange::                      
* variables::                   
* version::                     
* view::                        
* vrange::                      
* x2data::                      
* x2dtics::                     
* x2label::                     
* x2mtics::                     
* x2range::                     
* x2tics::                      
* x2zeroaxis::                  
* xdata::                       
* xdtics::                      
* xlabel::                      
* xmtics::                      
* xrange::                      
* xtics::                       
* xzeroaxis::                   
* y2data::                      
* y2dtics::                     
* y2label::                     
* y2mtics::                     
* y2range::                     
* y2tics::                      
* y2zeroaxis::                  
* ydata::                       
* ydtics::                      
* ylabel::                      
* ymtics::                      
* yrange::                      
* ytics::                       
* yzeroaxis::                   
* zdata::                       
* zdtics::                      
* zero::                        
* zeroaxis::                    
* zlabel::                      
* zmtics::                      
* zrange::                      
* ztics::                       
@end menu

@node angles, arrow, set-show, set-show
@subsection angles

@c ?commands set angles
@c ?commands show angles
@c ?set angles
@c ?show angles
@cindex angles
@opindex angles


@c ?commands set angles degrees
@c ?set angles degrees
@c ?angles degrees
@cindex degrees

By default, `gnuplot` assumes the independent variable in polar graphs is in
units of radians.  If `set angles degrees` is specified before `set polar`,
then the default range is [0:360] and the independent variable has units of
degrees.  This is particularly useful for plots of data files.  The angle
setting also applies to 3-d mapping as set via the @ref{mapping} command.

Syntax:
@example
      set angles @{degrees | radians@}
      show angles

@end example

The angle specified in `set grid polar` is also read and displayed in the
units specified by @ref{angles}.

@ref{angles} also affects the arguments of the machine-defined functions
sin(x), cos(x) and tan(x), and the outputs of asin(x), acos(x), atan(x),
atan2(x), and arg(x).  It has no effect on the arguments of hyperbolic
functions or Bessel functions.  However, the output arguments of inverse
hyperbolic functions of complex arguments are affected; if these functions
are used, `set angles radians` must be in effect to maintain consistency
between input and output arguments.

@example
      x=@{1.0,0.1@}
      set angles radians
      y=sinh(x)
      print y         #prints @{1.16933, 0.154051@}
      print asinh(y)  #prints @{1.0, 0.1@}
@end example

but
@example
      set angles degrees
      y=sinh(x)
      print y         #prints @{1.16933, 0.154051@}
      print asinh(y)  #prints @{57.29578, 5.729578@}
@end example

@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/poldat.html,Polar plot using @ref{angles}. }

@node arrow, autoscale, angles, set-show
@subsection arrow

@c ?commands set arrow
@c ?commands set noarrow
@c ?commands show arrow
@c ?set arrow
@c ?set noarrow
@c ?show arrow
@cindex arrow
@opindex arrow


@cindex noarrow

Arbitrary arrows can be placed on a plot using the @ref{arrow} command.

Syntax:
@example
      set arrow @{<tag>@} @{from <position>@} @{to <position>@} @{@{no@}head@}
                @{ @{linestyle | ls <line_style>@}
                  | @{linetype | lt <line_type>@}
                    @{linewidth | lw <line_width@} @}
      set noarrow @{<tag>@}
      show arrow

@end example

<tag> is an integer that identifies the arrow.  If no tag is given, the
lowest unused tag value is assigned automatically.  The tag can be used to
delete or change a specific arrow.  To change any attribute of an existing
arrow, use the @ref{arrow} command with the appropriate tag and specify the
parts of the arrow to be changed.

The <position>s are specified by either x,y or x,y,z, and may be preceded by
`first`, `second`, `graph`, or `screen` to select the coordinate system.
Unspecified coordinates default to 0.  The endpoints can be specified in
one of four coordinate systems---`first` or `second` axes, `graph` or
`screen`.  See `coordinates` for details.  A coordinate system specifier
does not carry over from the "from" position to the "to" position.  Arrows
outside the screen boundaries are permitted but may cause device errors.

Specifying `nohead` produces an arrow drawn without a head---a line segment.
This gives you yet another way to draw a line segment on the plot.  By
default, arrows have heads.

The line style may be selected from a user-defined list of line styles (see
@ref{linestyle}) or may be defined here by providing values for <line_type>
(an index from the default list of styles) and/or <line_width> (which is a
multiplier for the default width).

Note, however, that if a user-defined line style has been selected, its
properties (type and width) cannot be altered merely by issuing another
@ref{arrow} command with the appropriate index and `lt` or `lw`.

Examples:

To set an arrow pointing from the origin to (1,2) with user-defined style 5,
use:
@example
      set arrow to 1,2 ls 5

@end example

To set an arrow from bottom left of plotting area to (-5,5,3), and tag the
arrow number 3, use:
@example
      set arrow 3 from graph 0,0 to -5,5,3

@end example

To change the preceding arrow to end at 1,1,1, without an arrow head and
double its width, use:
@example
      set arrow 3 to 1,1,1 nohead lw 2

@end example

To draw a vertical line from the bottom to the top of the graph at x=3, use:
@example
      set arrow from 3, graph 0 to 3, graph 1 nohead

@end example

To delete arrow number 2, use:
@example
      set noarrow 2

@end example

To delete all arrows, use:
@example
      set noarrow

@end example

To show all arrows (in tag order), use:
@example
      show arrow
@end example

@uref{http://www.nas.nasa.gov/~woo/gnuplot/arrows/arrows.html,Arrows Demos. }

@node autoscale, bar, arrow, set-show
@subsection autoscale

@c ?commands set autoscale
@c ?commands set noautoscale
@c ?commands show autoscale
@c ?set autoscale
@c ?set noautoscale
@c ?show autoscale
@cindex autoscale
@opindex autoscale


@cindex noautoscale

Autoscaling may be set individually on the x, y or z axis or globally on all
axes. The default is to autoscale all axes.

Syntax:
@example
      set autoscale @{<axes>@{min|max@}@}
      set noautoscale @{<axes>@{min|max@}@}
      show autoscale

@end example

where <axes> is either `x`, `y`, `z`, `x2`, `y2` or `xy`.  A keyword with
`min` or `max` appended (this cannot be done with `xy`) tells `gnuplot` to
autoscale just the minimum or maximum of that axis.  If no keyword is given,
all axes are autoscaled.

When autoscaling, the axis range is automatically computed and the dependent
axis (y for a @ref{plot} and z for `splot`) is scaled to include the range of the
function or data being plotted.

If autoscaling of the dependent axis (y or z) is not set, the current y or z
range is used.

Autoscaling the independent variables (x for @ref{plot} and x,y for `splot`) is a
request to set the domain to match any data file being plotted.  If there are
no data files, autoscaling an independent variable has no effect.  In other
words, in the absence of a data file, functions alone do not affect the x
range (or the y range if plotting z = f(x,y)).

Please see @ref{xrange} for additional information about ranges.

The behavior of autoscaling remains consistent in parametric mode, (see `set
parametric`).  However, there are more dependent variables and hence more
control over x, y, and z axis scales.  In parametric mode, the independent or
dummy variable is t for @ref{plot}s and u,v for `splot`s.  @ref{autoscale} in
parametric mode, then, controls all ranges (t, u, v, x, y, and z) and allows
x, y, and z to be fully autoscaled.

Autoscaling works the same way for polar mode as it does for parametric mode
for @ref{plot}, with the extension that in polar mode @ref{dummy} can be used to
change the independent variable from t (see @ref{dummy}).

When tics are displayed on second axes but no plot has been specified for
those axes, x2range and y2range are inherited from xrange and yrange.  This
is done _before_ xrange and yrange are autoextended to a whole number of
tics, which can cause unexpected results.

Examples:

This sets autoscaling of the y axis (other axes are not affected):
@example
      set autoscale y

@end example

This sets autoscaling only for the minimum of the y axis (the maximum of the
y axis and the other axes are not affected):
@example
      set autoscale ymin

@end example

This sets autoscaling of the x and y axes:
@example
      set autoscale xy

@end example

This sets autoscaling of the x, y, z, x2 and y2 axes:
@example
      set autoscale

@end example

This disables autoscaling of the x, y, z, x2 and y2 axes:
@example
      set noautoscale

@end example

This disables autoscaling of the z axis only:
@example
      set noautoscale z

@end example

@menu
* parametric_mode::             
* polar_mode::                  
@end menu

@node parametric_mode, polar_mode, autoscale, autoscale
@subsubsection parametric mode

@c ?commands set autoscale parametric
@c ?set autoscale parametric
@c ?set autoscale t
When in parametric mode (`set parametric`), the xrange is as fully scalable
as the y range.  In other words, in parametric mode the x axis can be
automatically scaled to fit the range of the parametric function that is
being plotted.  Of course, the y axis can also be automatically scaled just
as in the non-parametric case.  If autoscaling on the x axis is not set, the
current x range is used.

Data files are plotted the same in parametric and non-parametric mode.
However, there is a difference in mixed function and data plots: in
non-parametric mode with autoscaled x, the x range of the datafile controls
the x range of the functions; in parametric mode it has no influence.

For completeness a last command `set autoscale t` is accepted.  However, the
effect of this "scaling" is very minor.  When `gnuplot` determines that the
t range would be empty, it makes a small adjustment if autoscaling is true.
Otherwise, `gnuplot` gives an error.  Such behavior may, in fact, not be very
useful and the command `set autoscale t` is certainly questionable.

`splot` extends the above ideas as you would expect.  If autoscaling is set,
then x, y, and z ranges are computed and each axis scaled to fit the
resulting data.

@node polar_mode,  , parametric_mode, autoscale
@subsubsection polar mode

@c ?commands set autoscale polar
@c ?set autoscale polar
@c ?set autoscale t
When in polar mode (`set polar`), the xrange and the yrange are both found
from the polar coordinates, and thus they can both be automatically scaled.
In other words, in polar mode both the x and y axes can be automatically
scaled to fit the ranges of the polar function that is being plotted.

When plotting functions in polar mode, the rrange may be autoscaled.  When
plotting data files in polar mode, the trange may also be autoscaled.  Note
that if the trange is contained within one quadrant, autoscaling will produce
a polar plot of only that single quadrant.

Explicitly setting one or two ranges but not others may lead to unexpected
results.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/poldat.html,See polar demos }

@node bar, bmargin, autoscale, set-show
@subsection bar

@c ?commands set bar
@c ?commands show bar
@c ?set bar
@c ?show bar
The @ref{bar} command controls the tics at the ends of errorbars.

Syntax:
@example
      set bar @{small | large | <size>@}
      show bar

@end example

`small` is a synonym for 0.0, and `large` for 1.0.
The default is 1.0 if no size is given.

@node bmargin, border, bar, set-show
@subsection bmargin

@c ?commands set bmargin
@c ?set bmargin
@cindex bmargin
@opindex bmargin


The command @ref{bmargin} sets the size of the bottom margin.  Please see
@ref{margin} for details.

@node border, boxwidth, bmargin, set-show
@subsection border

@c ?commands set border
@c ?commands set noborder
@c ?commands show border
@c ?set border
@c ?set noborder
@c ?show border
@cindex border
@opindex border


@cindex noborder

The @ref{border} and `set noborder` commands control the display of the graph
borders for the @ref{plot} and `splot` commands.

Syntax:
@example
      set border @{<integer> @{ @{linestyle | ls <line_style>@}
                              | @{linetype | lt <line_type> @}
                                @{linewidth | lw <line_width>@} @} @}
      set noborder
      show border

@end example

The borders are encoded in a 12-bit integer: the bottom four bits control the
border for @ref{plot} and the sides of the base for `splot`; The next four bits
control the verticals in `splot`; the top four bits control the edges on top
of the `splot`.  In detail, the `<integer>` should be the sum of the
appropriate entries from the following table:


@example
                        plot border     splot         splot
          Side          splot base    verticals        top
      bottom (south)         1            16           256
      left   (west)          2            32           512
      top    (north)         4            64          1024
      right  (east)          8           128          2048

@end example


The default is 31, which is all four sides for @ref{plot}, and base and z axis
for `splot`.

Using the optional <line_style>, <line_type> and <line_width>
specifiers, the way the border lines are drawn can be influenced
(limited by what the current terminal driver supports).  By default,
the border is drawn with twice the usual linewidth.  The <line_width>
specifier scales this default value; for example, `set border 15 lw 2`
will produce a border with four times the usual linewidth.

Various axes or combinations of axes may be added together in the command.

To have tics on edges other than bottom and left, disable the usual tics and
enable the second axes.

Examples:

Draw all borders:
@example
      set border

@end example

Draw only the SOUTHWEST borders:
@example
      set border 3

@end example

Draw a complete box around a `splot`:
@example
      set border 4095

@end example

Draw a partial box, omitting the front vertical:
@example
      set border 127+256+512

@end example

Draw only the NORTHEAST borders:
@example
      set noxtics; set noytics; set x2tics; set y2tics; set border 12

@end example

@uref{http://www.nas.nasa.gov/~woo/gnuplot/borders/borders.html,Borders Demo. }

@node boxwidth, clabel, border, set-show
@subsection boxwidth

@c ?commands set boxwidth
@c ?commands show boxwidth
@c ?set boxwidth
@c ?show boxwidth
@cindex boxwidth
@opindex boxwidth


The @ref{boxwidth} command is used to set the default width of boxes in the
@ref{boxes} and @ref{boxerrorbars} styles.

Syntax:
@example
      set boxwidth @{<width>@}
      show boxwidth

@end example

If a data file is plotted without the width being specified in the third,
fourth, or fifth column (or @ref{using} entry), or if a function is plotted, the
width of each box is set by the @ref{boxwidth} command.  (If a width is given
both in the file and by the @ref{boxwidth} command, the one in the file is
used.)  If the width is not specified in one of these ways, the width of each
box will be calculated automatically so that it touches the adjacent boxes.
In a four-column data set, the fourth column will be interpreted as the box
width unless the width is set to -2.0, in which case the width will be
calculated automatically.  See @ref{boxerrorbars} for more details.

To set the box width to automatic use the command
@example
      set boxwidth
@end example

or, for four-column data,
@example
      set boxwidth -2

@end example

The same effect can be achieved with the @ref{using} keyword in @ref{plot}:
@example
      plot 'file' using 1:2:3:4:(-2)

@end example

@node clabel, clip, boxwidth, set-show
@subsection clabel

@c ?commands set clabel
@c ?commands set noclabel
@c ?commands show clabel
@c ?set clabel
@c ?set noclabel
@c ?show clabel
@cindex clabel
@opindex clabel


@cindex noclabel

`gnuplot` will vary the linetype used for each contour level when clabel is
set.  When this option on (the default), a legend labels each linestyle with
the z level it represents.  It is not possible at present to separate the
contour labels from the surface key.

Syntax:
@example
      set clabel @{'<format>'@}
      set noclabel
      show clabel

@end example

The default for the format string is %8.3g, which gives three decimal places.
This may produce poor label alignment if the key is altered from its default
configuration.

The first contour linetype, or only contour linetype when clabel is off, is
the surface linetype +1; contour points are the same style as surface points.

See also @ref{contour}.

@node clip, cntrparam, clabel, set-show
@subsection clip

@c ?commands set clip
@c ?commands set noclip
@c ?commands show clip
@c ?set clip
@c ?set noclip
@c ?show clip
@cindex clip
@opindex clip


@cindex noclip

`gnuplot` can clip data points and lines that are near the boundaries of a
graph.

Syntax:
@example
      set clip <clip-type>
      set noclip <clip-type>
      show clip

@end example

Three clip types are supported by `gnuplot`: `points`, `one`, and `two`.
One, two, or all three clip types may be active for a single graph.

The `points` clip type forces `gnuplot` to clip (actually, not plot at all)
data points that fall within but too close to the boundaries.  This is done
so that large symbols used for points will not extend outside the boundary
lines.  Without clipping points near the boundaries, the plot may look bad.
Adjusting the x and y ranges may give similar results.

Setting the `one` clip type causes `gnuplot` to draw a line segment which has
only one of its two endpoints within the graph.  Only the in-range portion of
the line is drawn.  The alternative is to not draw any portion of the line
segment.

Some lines may have both endpoints out of range, but pass through the graph.
Setting the `two` clip-type allows the visible portion of these lines to be
drawn.

In no case is a line drawn outside the graph.

The defaults are `noclip points`, `clip one`, and `noclip two`.

To check the state of all forms of clipping, use
@example
      show clip

@end example

For backward compatibility with older versions, the following forms are also
permitted:
@example
      set clip
      set noclip

@end example

@ref{clip} is synonymous with `set clip points`; `set noclip` turns off all
three types of clipping.

@node cntrparam, contour, clip, set-show
@subsection cntrparam

@c ?commands set cntrparam
@c ?commands show cntrparam
@c ?set cntrparam
@c ?show cntrparam
@cindex cntrparam
@opindex cntrparam


@ref{cntrparam} controls the generation of contours and their smoothness for
a contour plot. @ref{contour} displays current settings of @ref{cntrparam} as
well as @ref{contour}.

Syntax:
@example
      set cntrparam @{  @{linear | cubicspline | bspline@}
                      @{ points <n>@} @{ order <n> @}
                      @{ levels   auto @{<n>@} | <n>
                               | discrete <z1> @{,<z2>@{,<z3>...@}@}
                               | incremental <start>, <incr> @{,<end>@}
                       @}
                     @}
      show contour

@end example

This command has two functions.  First, it sets the values of z for which
contour points are to be determined (by linear interpolation between data
points or function isosamples.)  Second, it controls the way contours are
drawn between the points determined to be of equal z.  <n> should be an
integral constant expression and <z1>, <z2> ... any constant expressions.
The parameters are:

`linear`, `cubicspline`, `bspline`---Controls type of approximation or
interpolation.  If `linear`, then straight line segments connect points of
equal z magnitude.  If `cubicspline`, then piecewise-linear contours are
interpolated between the same equal z points to form somewhat smoother
contours, but which may undulate.  If `bspline`, a guaranteed-smoother curve
is drawn, which only approximates the position of the points of equal-z.

`points`---Eventually all drawings are done with piecewise-linear strokes.
This number controls the number of line segments used to approximate the
`bspline` or `cubicspline` curve.  Number of cubicspline or bspline
segments (strokes) = `points` * number of linear segments.

`order`---Order of the bspline approximation to be used.  The bigger this
order is, the smoother the resulting contour.  (Of course, higher order
bspline curves will move further away from the original piecewise linear
data.)  This option is relevant for `bspline` mode only.  Allowed values are
integers in the range from 2 (linear) to 10.

`levels`--- Selection of contour levels,  controlled by `auto` (default),
`discrete`, `incremental`, and <n>, number of contour levels, limited to
@example
 MAX_DISCRETE_LEVELS as defined in plot.h (30 is standard.)

@end example

For `auto`, <n> specifies a nominal number of levels; the actual number will
be adjusted to give simple labels. If the surface is bounded by zmin and zmax,
contours will be generated at integer multiples of dz between zmin and zmax,
where dz is 1, 2, or 5 times some power of ten (like the step between two
tic marks).

For `levels discrete`, contours will be generated at z = <z1>, <z2> ... as
specified; the number of discrete levels sets the number of contour levels.
In `discrete` mode, any `set cntrparms levels <n>` are ignored.

For `incremental`, contours are generated at values of z beginning at <start>
and increasing by <increment>, until the number of contours is reached. <end>
is used to determine the number of contour levels, which will be changed by
any subsequent `set cntrparam levels <n>`.

If the command @ref{cntrparam} is given without any arguments specified,  the
defaults are used: linear, 5 points, order 4, 5 auto levels.

Examples:
@example
      set cntrparam bspline
      set cntrparam points 7
      set cntrparam order 10

@end example

To select levels automatically, 5 if the level increment criteria are met:
@example
      set cntrparam levels auto 5

@end example

To specify discrete levels at .1, .37, and .9:
@example
      set cntrparam levels discrete .1,1/exp(1),.9

@end example

To specify levels from 0 to 4 with increment 1:
@example
      set cntrparam levels incremental  0,1,4

@end example

To set the number of levels to 10 (changing an incremental end or possibly
the number of auto levels):
@example
      set cntrparam levels 10

@end example

To set the start and increment while retaining the number of levels:
@example
      set cntrparam levels incremental 100,50

@end example

See also @ref{contour} for control of where the contours are drawn, and @ref{clabel} for control of the format of the contour labels and linetypes.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/contours.html,Contours Demo} and
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/discrete.html,contours with User Defined Levels.}

@node contour, data_style, cntrparam, set-show
@subsection contour

@c ?commands set contour
@c ?commands set nocontour
@c ?commands show contour
@c ?set contour
@c ?set nocontour
@c ?show contour
@cindex contour
@opindex contour


@cindex nocontour

@ref{contour} enables contour drawing for surfaces. This option is available
for `splot` only.

Syntax:
@example
      set contour @{base | surface | both@}
      set nocontour
      show contour

@end example

The three options specify where to draw the contours: `base` draws the
contours on the grid base where the x/ytics are placed, @ref{surface} draws the
contours on the surfaces themselves, and `both` draws the contours on both
the base and the surface.  If no option is provided, the default is `base`.

See also @ref{cntrparam} for the parameters that affect the drawing of
contours, and @ref{clabel} for control of labelling of the contours.

The surface can be switched off (see @ref{surface}), giving a contour-only
graph.  Though it is possible to use @ref{size} to enlarge the plot to fill
the screen, more control over the output format can be obtained by writing
the contour information to a file, and rereading it as a 2-d datafile plot:

@example
      set nosurface
      set contour
      set cntrparam ...
      set term table
      set out 'filename'
      splot ...
      set out
      # contour info now in filename
      set term <whatever>
      plot 'filename'

@end example

In order to draw contours, the data should be organized as "grid data".  In
such a file all the points for a single y-isoline are listed, then all the
points for the next y-isoline, and so on.  A single blank line (a line
containing no characters other than blank spaces and a carriage return and/or
a line feed) separates one y-isoline from the next.  See also `splot datafile`.

If contours are desired from non-grid data, @ref{dgrid3d} can be used to
create an appropriate grid.  See @ref{dgrid3d} for more information.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/contours.html,Contours Demo} and
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/discrete.html,contours with User Defined Levels.}

@node data_style, dgrid3d, contour, set-show
@subsection data style

@c ?commands set data style
@c ?commands show data style
@c ?set data style
@c ?show data style
@c ?data style
The @ref{style} command changes the default plotting style for data
plots.

Syntax:
@example
      set data style <style-choice>
      show data style

@end example

See @ref{style} for the choices.  If no choice is given, the choices are
listed.  @ref{style} shows the current default data plotting style.

@node dgrid3d, dummy, data_style, set-show
@subsection dgrid3d

@c ?commands set dgrid3d
@c ?commands set nodgrid3d
@c ?commands show dgrid3d
@c ?set dgrid3d
@c ?set nodgrid3d
@c ?show dgrid3d
@cindex dgrid3d
@opindex dgrid3d


@cindex nodgrid3d

The @ref{dgrid3d} command enables, and can set parameters for, non-grid
to grid data mapping.

Syntax:
@example
      set dgrid3d @{<row_size>@} @{,@{<col_size>@} @{,<norm>@}@}
      set nodgrid3d
      show dgrid3d

@end example

By default @ref{dgrid3d} is disabled.  When enabled, 3-d data read from a file
are always treated as a scattered data set.  A grid with dimensions derived
from a bounding box of the scattered data and size as specified by the
row/col_size parameters is created for plotting and contouring.  The grid
is equally spaced in x (rows) and in y (columns); the z values are computed
as weighted averages of the scattered points' z values.

The third parameter, norm, controls the weighting:  Each data point is
weighted inversely by its distance from the grid point raised to the norm
power.  (Actually, the weights are given by the inverse of dx^norm + dy^norm,
where dx and dy are the components of the separation of the grid point from
each data point.  For some norms that are powers of two, specifically 4, 8,
and 16, the computation is optimized by using the Euclidean distance in the
weight calculation, (dx^2+dx^2)^norm/2.  However, any non-negative integer
can be used.)

The closer the data point is to a grid point, the more effect it has on
that grid point and the larger the value of norm the less effect more
distant data points have on that grid point.

The @ref{dgrid3d} option is a simple low pass filter that converts scattered
data to a grid data set.  More sophisticated approaches to this problem
exist and should be used to preprocess the data outside `gnuplot` if this
simple solution is found inadequate.

(The z values are found by weighting all data points, not by interpolating
between nearby data points;  also edge effects may produce unexpected and/or
undesired results.  In some cases, small norm values produce a grid point
reflecting the average of distant data points rather than a local average,
while large values of norm may produce "steps" with several grid points
having the same value as the closest data point, rather than making a smooth
transition between adjacent data points.  Some areas of a grid may be filled
by extrapolation, to an arbitrary boundary condition.  The variables are
not normalized; consequently the units used for x and y will affect the
relative weights of points in the x and y directions.)

Examples:
@example
      set dgrid3d 10,10,1     # defaults
      set dgrid3d ,,4

@end example

The first specifies that a grid of size 10 by 10 is to be constructed using
a norm value of 1 in the weight computation.  The second only modifies the
norm, changing it to 4.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/scatter.html,Dgrid3d Demo.}


@node dummy, encoding, dgrid3d, set-show
@subsection dummy

@c ?commands set dummy
@c ?commands show dummy
@c ?set dummy
@c ?show dummy
@cindex dummy
@opindex dummy


The @ref{dummy} command changes the default dummy variable names.

Syntax:
@example
      set dummy @{<dummy-var>@} @{,<dummy-var>@}
      show dummy

@end example

By default, `gnuplot` assumes that the independent, or "dummy", variable for
the @ref{plot} command is "t" if in parametric or polar mode, or "x" otherwise.
Similarly the independent variables for the `splot` command are "u" and "v"
in parametric mode (`splot` cannot be used in polar mode), or "x" and "y"
otherwise.

It may be more convenient to call a dummy variable by a more physically
meaningful or conventional name.  For example, when plotting time functions:

@example
      set dummy t
      plot sin(t), cos(t)

@end example

At least one dummy variable must be set on the command; @ref{dummy} by itself
will generate an error message.

Examples:
@example
      set dummy u,v
      set dummy ,s

@end example

The second example sets the second variable to s.

@node encoding, format, dummy, set-show
@subsection encoding

@c ?commands set encoding
@c ?commands show encoding
@c ?set encoding
@c ?show encoding
@cindex encoding
@opindex encoding


The @ref{encoding} command selects a character encoding.  Valid values are
`default`, which tells a terminal to use its default; `iso_8859_1` (known in
the PostScript world as `ISO-Latin1`), which is used on many Unix workstations
and with MS-Windows; `cp850`, for OS/2; and `cp437`, for MS-DOS.

Syntax:
@example
      set encoding @{<value>@}
      show encoding

@end example

Note that encoding is not supported by all terminal drivers and that
the device must be able to produce the desired non-standard characters.

@node format, function_style, encoding, set-show
@subsection format

@c ?commands set format
@c ?commands show format
@c ?set format
@c ?show format
@cindex format
@opindex format


The format of the tic-mark labels can be set with the `set format` command.

Syntax:
@example
      set format @{<axes>@} @{"<format-string>"@}
      set format @{<axes>@} @{'<format-string>'@}
      show format

@end example

where <axes> is either `x`, `y`, `z`, `xy`, `x2`, `y2` or nothing (which is
the same as `xy`).  The length of the string representing a tic mark (after
formatting with 'printf') is restricted to 100 characters.  If the format
string is omitted, the format will be returned to the default "%g".  For
LaTeX users, the format "$%g$" is often desirable.  If the empty string "" is
used, no label will be plotted with each tic, though the tic mark will still
be plotted.  To eliminate all tic marks, use `set noxtics` or `set noytics`.

Newline (\n) is accepted in the format string.  Use double-quotes rather than
single-quotes to enable such interpretation.  See also `syntax`.

The default format for both axes is "%g", but other formats such as "%.2f" or
"%3.0em" are often desirable.  Anything accepted by 'printf' when given a
double precision number, and accepted by the terminal, will work.  Some other
options have been added.  If the format string looks like a floating point
format, then `gnuplot` tries to construct a reasonable format.

Characters not preceded by "%" are printed verbatim.  Thus you can include
spaces and labels in your format string, such as "%g m", which will put " m"
after each number.  If you want "%" itself, double it: "%g %%".

See also @ref{xtics} for more information about tic labels.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/electron.html,See demo. }

@menu
* format_specifiers::           
* time/date_specifiers::        
@end menu

@node format_specifiers, time/date_specifiers, format, format
@subsubsection format specifiers

@c ?commands set format specifiers
@c ?set format specifiers
@c ?format specifiers
@cindex format_specifiers

The acceptable formats (if not in time/date mode) are:


@example
      Format       Explanation
      %f           floating point notation
      %e or %E     exponential notation; an "e" or "E" before the power
      %g or %G     the shorter of %e (or %E) and %f
      %x or %X     hex
      %o or %O     octal
      %t           mantissa to base 10
      %l           mantissa to base of current logscale
      %s           mantissa to base of current logscale; scientific power
      %T           power to base 10
      %L           power to base of current logscale
      %S           scientific power
      %c           character replacement for scientific power
      %P           multiple of pi

@end example


A 'scientific' power is one such that the exponent is a multiple of three.
Character replacement of scientific powers (`"%c"`) has been implemented
for powers in the range -18 to +18.  For numbers outside of this range the
format reverts to exponential.

Other acceptable modifiers (which come after the "%" but before the format
specifier) are "-", which left-justifies the number; "+", which forces all
numbers to be explicitly signed; "#", which places a decimal point after
floats that have only zeroes following the decimal point; a positive integer,
which defines the field width; "0" (the digit, not the letter) immediately
preceding the field width, which indicates that leading zeroes are to be used
instead of leading blanks; and a decimal point followed by a non-negative
integer, which defines the precision (the minimum number of digits of an
integer, or the number of digits following the decimal point of a float).

Some releases of 'printf' may not support all of these modifiers but may also
support others; in case of doubt, check the appropriate documentation and
then experiment.

Examples:
@example
      set format y "%t"; set ytics (5,10)          # "5.0" and "1.0"
      set format y "%s"; set ytics (500,1000)      # "500" and "1.0"
      set format y "+-12.3f"; set ytics(12345)     # "+12345.000  "
      set format y "%.2t*10^%+03T"; set ytic(12345)# "1.23*10^+04"
      set format y "%s*10^@{%S@}"; set ytic(12345)   # "12.345*10^@{3@}"
      set format y "%s %cg"; set ytic(12345)       # "12.345 kg"
      set format y "%.0P pi"; set ytic(6.283185)   # "2 pi"
      set format y "%.0P%%"; set ytic(50)          # "50%"

@end example

@example
      set log y 2; set format y '%l'; set ytics (1,2,3)
      #displays "1.0", "1.0" and "1.5" (since 3 is 1.5 * 2^1)

@end example

There are some problem cases that arise when numbers like 9.999 are printed
with a format that requires both rounding and a power.

If the data type for the axis is time/date, the format string must contain
valid codes for the 'strftime' function (outside of `gnuplot`, type "man
strftime").  See @ref{timefmt} for a list of the allowed input format codes.

@node time/date_specifiers,  , format_specifiers, format
@subsubsection time/date specifiers

@c ?commands set format time/date_specifiers
@c ?set format time/date_specifiers
@c ?set time/date_specifiers
@cindex time/date_specifiers

In time/date mode, the acceptable formats are:


@example
      Format       Explanation
      %a           abbreviated name of day of the week
      %A           full name of day of the week
      %b or %h     abbreviated name of the month
      %B           full name of the month
      %d           day of the month, 1--31
      %D           shorthand for "%m/%d/%y"
      %H or %k     hour, 0--24
      %I or %l     hour, 0--12
      %j           day of the year, 1--366
      %m           month, 1--12
      %M           minute, 0--60
      %p           "am" or "pm"
      %r           shorthand for "%I:%M:%S %p"
      %R           shorthand for "%H:%M"
      %S           second, 0--60
      %T           shorthand for "%H:%M:%S"
      %U           week of the year (week starts on Sunday)
      %w           day of the week, 0--6 (Sunday = 0)
      %W           week of the year (week starts on Monday)
      %y           year, 0-99
      %Y           year, 4-digit

@end example


Except for the non-numerical formats, these may be preceded by a "0" ("zero",
not "oh") to pad the field length with leading zeroes, and a positive digit,
to define the minimum field width (which will be overridden if the specified
width is not large enough to contain the number).  There is a 24-character
limit to the length of the printed text; longer strings will be truncated.

Examples:

Suppose the text is "76/12/25 23:11:11".  Then
@example
      set format x                 # defaults to "12/25/76" \n "23:11"
      set format x "%A, %d %b %Y"  # "Saturday, 25 Dec 1976"
      set format x "%r %d"         # "11:11:11 pm 12/25/76"

@end example

Suppose the text is "98/07/06 05:04:03".  Then
@example
      set format x "%1y/%2m/%3d %01H:%02M:%03S"  # "98/ 7/  6 5:04:003"

@end example

@node function_style, functions, format, set-show
@subsection function style

@c ?commands set function style
@c ?commands show function style
@c ?set function style
@c ?show function style
@c ?function style
The @ref{style} command changes the default plotting style for
function plots.

Syntax:
@example
      set function style <style-choice>
      show function style

@end example

See @ref{style} for the choices.  If no choice is given, the choices are
listed.  @ref{style} shows the current default function plotting
style.

@node functions, grid, function_style, set-show
@subsection functions

@c ?commands show functions
@c ?show functions
The @ref{functions} command lists all user-defined functions and their
definitions.

Syntax:
@example
      show functions

@end example

For information about the definition and usage of functions in `gnuplot`,
please see `expressions`.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/spline.html,Splines as User Defined Functions.}
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/airfoil.html,Use of functions and complex variables for airfoils }

@node grid, hidden3d, functions, set-show
@subsection grid

@c ?commands set grid
@c ?commands set nogrid
@c ?commands show grid
@c ?set grid
@c ?set nogrid
@c ?show grid
@cindex grid
@opindex grid


@cindex nogrid

The `set grid` command allows grid lines to be drawn on the plot.

Syntax:
@example
      set grid @{@{no@}@{m@}xtics@} @{@{no@}@{m@}ytics@} @{@{no@}@{m@}ztics@}
               @{@{no@}@{m@}x2tics@} @{@{no@}@{m@}y2tics@}
               @{polar @{<angle>@}@}
               @{ @{linestyle <major_linestyle>@}
                 | @{linetype | lt <major_linetype>@}
                   @{linewidth | lw <major_linewidth>@}
                 @{ , @{linestyle | ls <minor_linestyle>@}
                     | @{linetype | lt <minor_linetype>@}
                       @{linewidth | lw <minor_linewidth>@} @} @}
      set nogrid
      show grid

@end example

The grid can be enabled and disabled for the major and/or minor tic
marks on any axis, and the linetype and linewidth can be specified
for major and minor grid lines, also via a predefined linestyle, as
far as the active terminal driver supports this.

Additionally, a polar grid can be selected for 2-d plots---circles are drawn
to intersect the selected tics, and radial lines are drawn at definable
intervals.  (The interval is given in degrees or radians ,depending on the
@ref{angles} setting.)  Note that a polar grid is no longer automatically
generated in polar mode.

The pertinent tics must be enabled before `set grid` can draw them; `gnuplot`
will quietly ignore instructions to draw grid lines at non-existent tics, but
they will appear if the tics are subsequently enabled.

If no linetype is specified for the minor gridlines, the same linetype as the
major gridlines is used.  The default polar angle is 30 degrees.

By default, grid lines are drawn with half the usual linewidth. The major and
minor linewidth specifiers scale this default value; for example, `set grid
lw .5` will draw grid lines with one quarter the usual linewidth.

Z grid lines are drawn on the back of the plot.  This looks better if a
partial box is drawn around the plot---see @ref{border}.

@node hidden3d, isosamples, grid, set-show
@subsection hidden3d

@c ?commands set hidden3d
@c ?commands set nohidden3d
@c ?commands show hidden3d
@c ?set hidden3d
@c ?set nohidden3d
@c ?show hidden3d
@cindex hidden3d
@opindex hidden3d


@cindex nohidden3d

The @ref{hidden3d} command enables hidden line removal for surface plotting
(see `splot`).  Some optional features of the underlying algorithm can also
be controlled using this command.

Syntax:
@example
      set hidden3d @{defaults@} |
                   @{ @{@{offset <offset>@} | @{nooffset@}@}
                     @{trianglepattern <bitpattern>@}
                     @{@{undefined <level>@} | @{noundefined@}@}
                     @{@{no@}altdiagonal@}
                     @{@{no@}bentover@} @}
      set nohidden3d
      show hidden3d

@end example

In contrast to the usual display in gnuplot, hidden line removal actually
treats the given function or data grids as real surfaces that can't be seen
through, so parts behind the surface will be hidden by it.  For this to be
possible, the surface needs to have 'grid structure' (see `splot datafile`
about this), and it has to be drawn `with lines` or @ref{linespoints}.

When @ref{hidden3d} is set, both the hidden portion of the surface and possibly
its contours drawn on the base (see @ref{contour}) as well as the grid will
be hidden.  Each surface has its hidden parts removed with respect to itself
and to other surfaces, if more than one surface is plotted.  Contours drawn
on the surface (@ref{surface}) don't work.  Labels and arrows are
always visible and are unaffected.  The key is also never hidden by the
surface.

Functions are evaluated at isoline intersections.  The algorithm interpolates
linearly between function points or data points when determining the visible
line segments.  This means that the appearance of a function may be different
when plotted with @ref{hidden3d} than when plotted with `nohidden3d` because in
the latter case functions are evaluated at each sample.  Please see @ref{samples} and @ref{isosamples} for discussion of the difference.

The algorithm used to remove the hidden parts of the surfaces has some
additional features controllable by this command.  Specifying `defaults` will
set them all to their default settings, as detailed below.  If `defaults` is
not given, only explicitly specified options will be influenced: all others
will keep their previous values, so you can turn on/off hidden line removal
via `set @{no@}hidden3d`, without modifying the set of options you chose.

The first option, `offset`, influences the linestyle used for lines on the
'back' side.  Normally, they are drawn in a linestyle one index number higher
than the one used for the front, to make the two sides of the surface
distinguishable.  You can specify a different line style offset to add
instead of the default 1, by `offset <offset>`.  Option `nooffset` stands for
`offset 0`, making the two sides of the surface use the same linestyle.

Next comes the option `trianglepattern <bitpattern>`.  <bitpattern> must be
a number between 0 and 7, interpreted as a bit pattern.  Each bit determines
the visibility of one edge of the triangles each surface is split up into.
Bit 0 is for the 'horizontal' edges of the grid, Bit 1 for the 'vertical'
ones, and Bit 2 for the diagonals that split each cell of the original grid
into two triangles.  The default pattern is 3, making all horizontal and
vertical lines visible, but not the diagonals.  You may want to choose 7 to
see those diagonals as well.

The `undefined <level>` option lets you decide what the algorithm is to do
with data points that are undefined (missing data, or undefined function
values), or exceed the given x-, y- or z-ranges.  Such points can either be
plotted nevertheless, or taken out of the input data set.  All surface
elements touching a point that is taken out will be taken out as well, thus
creating a hole in the surface.  If <level> = 3, equivalent to option
`noundefined`, no points will be thrown away at all.  This may produce all
kinds of problems elsewhere, so you should avoid this.  <level> = 2 will
throw away undefined points, but keep the out-of-range ones.  <level> = 1,
the default, will get rid of out-of-range points as well.

By specifying `noaltdiagonal`, you can override the default handling of a
special case can occur if `undefined` is active (i.e. <level> is not 3).
Each cell of the grid-structured input surface will be divided in two
triangles along one of its diagonals.  Normally, all these diagonals have
the same orientation relative to the grid.  If exactly one of the four cell
corners is excluded by the `undefined` handler, and this is on the usual
diagonal, both triangles will be excluded.  However if the default setting
of `altdiagonal` is active, the other diagonal will be chosen for this cell
instead, minimizing the size of the hole in the surface.

The `bentover` option controls what happens to another special case, this
time in conjunction with the `trianglepattern`.  For rather crumply surfaces,
it can happen that the two triangles a surface cell is divided into are seen
from opposite sides (i.e. the original quadrangle is 'bent over'), as
illustrated in the following ASCII art:

@example
                                                              C----B
    original quadrangle:  A--B      displayed quadrangle:     |\   |
      ("set view 0,0")    | /|    ("set view 75,75" perhaps)  | \  |
                          |/ |                                |  \ |
                          C--D                                |   \|
                                                              A    D

@end example

If the diagonal edges of the surface cells aren't generally made visible by
bit 2 of the <bitpattern> there, the edge CB above wouldn't be drawn at all,
normally, making the resulting display hard to understand.  Therefore, the
default option of `bentover` will turn it visible in this case.  If you don't
want that, you may choose `nobentover` instead.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/hidden.html,Hidden Line Removal Demo} and
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/singulr.html,Complex Hidden Line Demo. }

@node isosamples, key, hidden3d, set-show
@subsection isosamples

@c ?commands set isosamples
@c ?commands show isosamples
@c ?set isosamples
@c ?show isosamples
@cindex isosamples
@opindex isosamples


The isoline density (grid) for plotting functions as surfaces may be changed
by the @ref{isosamples} command.

Syntax:
@example
      set isosamples <iso_1> @{,<iso_2>@}
      show isosamples

@end example

Each function surface plot will have <iso_1> iso-u lines and <iso_2> iso-v
lines.  If you only specify <iso_1>, <iso_2> will be set to the same value
as <iso_1>.  By default, sampling is set to 10 isolines per u or v axis.
A higher sampling rate will produce more accurate plots, but will take longer.
These parameters have no effect on data file plotting.

An isoline is a curve parameterized by one of the surface parameters while
the other surface parameter is fixed.  Isolines provide a simple means to
display a surface.  By fixing the u parameter of surface s(u,v), the iso-u
lines of the form c(v) = s(u0,v) are produced, and by fixing the v parameter,
the iso-v lines of the form c(u) = s(u,v0) are produced.

When a function surface plot is being done without the removal of hidden
lines, @ref{samples}  controls the number of points sampled along each
isoline;  see @ref{samples} and @ref{hidden3d}.  The contour algorithm
assumes that a function sample occurs at each isoline intersection, so
change in @ref{samples} as well as @ref{isosamples} may be desired when changing
the resolution of a function surface/contour.

@node key, label, isosamples, set-show
@subsection key

@c ?commands set key
@c ?commands set nokey
@c ?commands show key
@c ?set key
@c ?set nokey
@c ?show key
@cindex key
@opindex key


@cindex nokey

@cindex legend

The @ref{key} enables a key (or legend) describing plots on a plot.

The contents of the key, i.e., the names given to each plotted data set and
function and samples of the lines and/or symbols used to represent them, are
determined by the `title` and @ref{with} options of the @{`s`@}@ref{plot} command.
Please see `plot title` and @ref{with} for more information.

Syntax:
@example
      set key @{  left | right | top | bottom | outside | below
               | <position>@}
              @{Left | Right@} @{@{no@}reverse@}
              @{samplen <sample_length>@} @{spacing <vertical_spacing>@}
              @{width <width_increment>@}
              @{title "<text>"@}
              @{@{no@}box @{ @{linestyle | ls <line_style>@}
                         | @{linetype | lt <line_type>@}
                           @{linewidth | lw <line_width>@}@}@}
      set nokey
      show key

@end example

By default the key is placed in the upper right corner of the graph.  The
keywords `left`, `right`, `top`, `bottom`, `outside` and `below` may be used
to place the key in the other corners inside the graph or to the right
(outside) or below the graph.  They may be given alone or combined.

Justification of the labels within the key is controlled by `Left` or `Right`
(default is `Right`).  The text and sample can be reversed (`reverse`) and a
box can be drawn around the key (`box @{...@}`) in a specified `linetype`
and `linewidth`, or a user-defined @ref{linestyle}. Note that not all
terminal drivers support linewidth selection, though.

The length of the sample line can be controlled by `samplen`.  The sample
length is computed as the sum of the tic length and <sample_length> times the
character width.  `samplen` also affects the positions of point samples in
the key since these are drawn at the midpoint of the sample line, even if it
is not drawn.  <sample_length> must be an integer.

The vertical spacing between lines is controlled by `spacing`.  The spacing
is set equal to the product of the pointsize, the vertical tic size, and
<vertical_spacing>.  The program will guarantee that the vertical spacing is
no smaller than the character height.

The <width_increment> is a number of character widths to be added to or
subtracted from the length of the string.  This is useful only when you are
putting a box around the key and you are using control characters in the text.
`gnuplot` simply counts the number of characters in the string when computing
the box width; this allows you to correct it.

A title can be put on the key (`title "<text>"`)---see also `syntax` for the
distinction between text in single- or double-quotes.  The key title uses the
same justification as do the plot titles.

The defaults for @ref{key} are `right`, `top`, `Right`, `noreverse`, `samplen
4`, `spacing 1.25`, `title ""`, and `nobox`.  The default <linetype> is the
same as that used for the plot borders.  Entering @ref{key} with no options
returns the key to its default configuration.

The <position> can be a simple x,y,z as in previous versions, but these can
be preceded by one of four keywords (`first`, `second`, `graph`, `screen`)
which selects the coordinate system in which the position is specified.  See
`coordinates` for more details.

The key is drawn as a sequence of lines, with one plot described on each
line.  On the right-hand side (or the left-hand side, if `reverse` is
selected) of each line is a representation that attempts to mimic the way the
curve is plotted.  On the other side of each line is the text description
(the line title), obtained from the @ref{plot} command.  The lines are vertically
arranged so that an imaginary straight line divides the left- and right-hand
sides of the key.  It is the coordinates of the top of this line that are
specified with the @ref{key} command.  In a @ref{plot}, only the x and y
coordinates are used to specify the line position.  For a `splot`, x, y and
z are all used as a 3-d location mapped using the same mapping as the graph
itself to form the required 2-d screen position of the imaginary line.

Some or all of the key may be outside of the graph boundary, although this
may interfere with other labels and may cause an error on some devices.  If
you use the keywords `outside` or `below`, `gnuplot` makes space for the keys
and the graph becomes smaller.  Putting keys outside to the right, they
occupy as few columns as possible, and putting them below, as many columns as
possible (depending of the length of the labels), thus stealing as little
space from the graph as possible.

When using the TeX or PostScript drivers, or similar drivers where formatting
information is embedded in the string, `gnuplot` is unable to calculate
correctly the width of the string for key positioning.  If the key is to be
positioned at the left, it may be convenient to use the combination  `set key
left Left reverse`.  The box and gap in the grid will be the width of the
literal string.

If `splot` is being used to draw contours, the contour labels will be listed
in the key.  If the alignment of these labels is poor or a different number
of decimal places is desired, the label format can be specified.  See @ref{clabel} for details.

Examples:

This places the key at the default location:
@example
      set key

@end example

This disables the key:
@example
      set nokey

@end example

This places a key at coordinates 2,3.5,2 in the default (first) coordinate
system:
@example
      set key 2,3.5,2

@end example

This places the key below the graph:
@example
      set key below

@end example

This places the key in the bottom left corner, left-justifies the text,
gives it a title, and draws a box around it in linetype 3:
@example
      set key left bottom Left title 'Legend' box 3

@end example

@node label, linestyle, key, set-show
@subsection label

@c ?commands set label
@c ?commands set nolabel
@c ?commands show label
@c ?set label
@c ?set nolabel
@c ?show label
@cindex label
@opindex label


@cindex nolabel

Arbitrary labels can be placed on the plot using the @ref{label} command.

Syntax:
@example
      set label @{<tag>@} @{"<label_text>"@} @{at <position>@}
                @{<justification>@} @{@{no@}rotate@} @{font "<name><,size>"@}
      set nolabel @{<tag>@}
      show label

@end example

The <position> is specified by either x,y or x,y,z, and may be preceded by
`first`, `second`, `graph`, or `screen` to select the coordinate system.
See `coordinates` for details.

The tag is an integer that is used to identify the label. If no <tag> is
given, the lowest unused tag value is assigned automatically.  The tag can be
used to delete or modify a specific label.  To change any attribute of an
existing label, use the @ref{label} command with the appropriate tag, and
specify the parts of the label to be changed.

By default, the text is placed flush left against the point x,y,z.  To adjust
the way the label is positioned with respect to the point x,y,z, add the
parameter <justification>, which may be `left`, `right` or `center`,
indicating that the point is to be at the left, right or center of the text.
Labels outside the plotted boundaries are permitted but may interfere with
axis labels or other text.

If `rotate` is given, the label is written vertically (if the terminal can do
so, of course).

If one (or more) axis is timeseries, the appropriate coordinate should be
given as a quoted time string according to the @ref{timefmt} format string.  See
@ref{xdata} and @ref{timefmt}.

The EEPIC, Imagen, LaTeX, and TPIC drivers allow \\ in a string to specify
a newline.

Examples:

To set a label at (1,2) to "y=x", use:
@example
      set label "y=x" at 1,2

@end example

To set a Sigma of size 24, from the Symbol font set, at the center of
the graph, use:
@example
      set label "S" at graph 0.5,0.5 center font "Symbol,24"

@end example

To set a label "y=x^2" with the right of the text at (2,3,4), and tag the
label as number 3, use:
@example
      set label 3 "y=x^2" at 2,3,4 right

@end example

To change the preceding label to center justification, use:
@example
      set label 3 center

@end example

To delete label number 2, use:
@example
      set nolabel 2

@end example

To delete all labels, use:
@example
      set nolabel

@end example

To show all labels (in tag order), use:
@example
      show label

@end example

To set a label on a graph with a timeseries on the x axis, use, for example:
@example
      set timefmt "%d/%m/%y,%H:%M"
      set label "Harvest" at "25/8/93",1

@end example

@node linestyle, lmargin, label, set-show
@subsection linestyle

@c ?commands set linestyle
@c ?commands set nolinestyle
@c ?commands show linestyle
@c ?set linestyle
@c ?set nolinestyle
@c ?show linestyle
@cindex linestyle
@opindex linestyle


Each terminal has a default set of line and point types, which can be seen
by using the command @ref{test}.  @ref{linestyle} defines a set of line types
and widths and point types and sizes so that you can refer to them later by
an index instead of repeating all the information at each invocation.

Syntax:
@example
      set linestyle <index> @{linetype | lt <line_type>@}
                            @{linewidth | lw <line_width>@}
                            @{pointtype | pt <point_type>@}
                            @{pointsize | ps <point_size>@}
      set nolinestyle
      show linestyle

@end example

The line and point types are taken from the default types for the terminal
currently in use.  The line width and point size are multipliers for the
default width and size (but note that <point_size> here is unaffected by
the multiplier given on 'set pointsize').

The defaults for the line and point types is the index.  The defaults for
the width and size are both unity.

Linestyles created by this mechanism do not replace the default styles;
both may be used.

Not all terminals support the `linewidth` and @ref{pointsize} features; if
not supported, the option will be ignored.

Note that this feature is not completely implemented; linestyles defined by
this mechanism may be used with 'plot', 'splot', 'replot', and 'set arrow',
but not by other commands that allow the default index to be used, such as
'set grid'.

Example:
Suppose that the default lines for indices 1, 2, and 3 are red, green, and
blue, respectively, and the default point shapes for the same indices are a
square, a cross, and a triangle, respectively.  Then

@example
      set linestyle 1 lt 2 lw 2 pt 3 ps 0.5

@end example

defines a new linestyle that is green and twice the default width and a new
pointstyle that is a half-sized triangle.  The commands

@example
      set function style lines
      plot f(x) lt 3, g(x) ls 1

@end example

will create a plot of f(x) using the default blue line and a plot of g(x)
using the user-defined wide green line.  Similarly the commands

@example
      set function style linespoints
      plot p(x) lt 1 pt 3, q(x) ls 1

@end example

will create a plot of f(x) using the default triangles connected by a red
line and q(x) using small triangles connected by a green line.

@node lmargin, locale, linestyle, set-show
@subsection lmargin

@c ?commands set lmargin
@c ?set lmargin
@cindex lmargin
@opindex lmargin


The command @ref{lmargin} sets the size of the left margin.  Please see
@ref{margin} for details.

@node locale, logscale, lmargin, set-show
@subsection locale

@c ?commands set locale
@c ?commands show logscale
@c ?set locale
@c ?show logscale
@cindex locale
@opindex locale


The @ref{locale} setting determines the language with which `@{x,y,z@}@{d,m@}tics`
will write the days and months.

Syntax:
@example
      set locale @{"<locale>"@}

@end example

<locale> may be any language designation acceptable to your installation.
See your system documentation for the available options.  The default value
is determined from the LANG environment variable.

@node logscale, mapping, locale, set-show
@subsection logscale

@c ?commands set logscale
@c ?commands set nologscale
@c ?commands show logscale
@c ?set logscale
@c ?set nologscale
@c ?show logscale
@cindex logscale
@opindex logscale


@cindex nologscale

Log scaling may be set on the x, y, z, x2 and/or y2 axes.

Syntax:
@example
      set logscale <axes> <base>
      set nologscale <axes>
      show logscale

@end example

where <axes> may be any combinations of `x`, `y`, and `z`, in any order, or
`x2` or `y2` and where <base> is the base of the log scaling.  If <base> is
not given, then 10 is assumed.  If <axes> is not given, then all axes are
assumed.  `set nologscale` turns off log scaling for the specified axes.

Examples:

To enable log scaling in both x and z axes:
@example
      set logscale xz

@end example

To enable scaling log base 2 of the y axis:
@example
      set logscale y 2

@end example

To disable z axis log scaling:
@example
      set nologscale z

@end example

@node mapping, margin, logscale, set-show
@subsection mapping

@c ?commands set mapping
@c ?commands show mapping
@c ?set mapping
@c ?show mapping
@cindex mapping
@opindex mapping


If data are provided to `splot` in spherical or cylindrical coordinates,
the @ref{mapping} command should be used to instruct `gnuplot` how to
interpret them.

Syntax:
@example
      set mapping @{cartesian | spherical | cylindrical@}

@end example

A cartesian coordinate system is used by default.

For a spherical coordinate system, the data occupy two or three columns (or
@ref{using} entries).  The first two are interpreted as the polar and azimuthal
angles theta and phi (in the units specified by @ref{angles}).  The radius r
is taken from the third column if there is one, or is set to unity if there
is no third column.  The mapping is:

@example
      x = r * cos(theta) * cos(phi)
      y = r * sin(theta) * cos(phi)
      z = r * sin(phi)

@end example

Note that this is a "geographic" spherical system, rather than a "polar" one.

For a cylindrical coordinate system, the data again occupy two or three
columns.  The first two are interpreted as theta (in the units specified by
@ref{angles}) and z.  The radius is either taken from the third column or set
to unity, as in the spherical case.  The mapping is:

@example
      x = r * cos(theta)
      y = r * sin(theta)
      z = z

@end example

The effects of @ref{mapping} can be duplicated with the @ref{using} filter on the
`splot` command, but @ref{mapping} may be more convenient if many data files are
to be processed.  However even if @ref{mapping} is used, @ref{using} may still be
necessary if the data in the file are not in the required order.

@ref{mapping} has no effect on @ref{plot}.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/world.html,Mapping Demos.}

@node margin, missing, mapping, set-show
@subsection margin

@c ?commands set margin
@c ?commands show margin
@c ?set margin
@c ?show margin
@cindex margin
@opindex margin


The computed margins can be overridden by the @ref{margin} commands.  @ref{margin} shows the current settings.

Syntax:
@example
      set bmargin @{<margin>@}
      set lmargin @{<margin>@}
      set rmargin @{<margin>@}
      set tmargin @{<margin>@}
      show margin

@end example

The units of <margin> are character heights or widths, as appropriate.  A
positive value defines the absolute size of the margin.  A negative value
(or none) causes `gnuplot` to revert to the computed value.

Normally the margins of a plot are automatically calculated based on tics,
tic labels, axis labels, the plot title, the timestamp and the size of the
key if it is outside the borders.  If, however, tics are attached to the
axes (`set xtics axis`, for example), neither the tics themselves nor their
labels will be included in either the margin calculation or the calculation
of the positions of other text to be written in the margin.  This can lead
to tic labels overwriting other text if the axis is very close to the border.

@node missing, multiplot, margin, set-show
@subsection missing

@c ?commands set missing
@c ?set missing
@cindex missing
@opindex missing


The @ref{missing} command allows you to tell `gnuplot` what character is
used in a data file to denote missing data.

Syntax:
@example
      set missing @{"<character>"@}
      show missing

@end example

Example:
@example
      set missing "?"

@end example

would mean that, when plotting a file containing

@example
         1 1
         2 ?
         3 2

@end example

the middle line would be ignored.

There is no default character for @ref{missing}.

@node multiplot, mx2tics, missing, set-show
@subsection multiplot

@c ?commands set multiplot
@c ?commands set nomultiplot
@c ?set multiplot
@c ?set nomultiplot
@cindex multiplot
@opindex multiplot


@cindex nomultiplot

The command @ref{multiplot} places `gnuplot` in the multiplot mode, in which
several plots are placed on the same page, window, or screen.

Syntax:
@example
      set multiplot
      set nomultiplot

@end example

For some terminals, no plot is displayed until the command `set nomultiplot`
is given, which causes the entire page to be drawn and then returns `gnuplot`
to its normal single-plot mode.  For other terminals, each separate @ref{plot}
command produces a plot, but the screen may not be cleared between plots.

Any labels or arrows that have been defined will be drawn for each plot
according to the current size and origin (unless their coordinates are
defined in the `screen` system).  Just about everything else that can be
`set` is applied to each plot, too.  If you want something to appear only
once on the page, for instance a single time stamp, you'll need to put a `set
time`/`set notime` pair around one of the @ref{plot}, `splot` or @ref{replot}
commands within the @ref{multiplot}/`set nomultiplot` block.

The commands @ref{origin} and @ref{size} must be used to correctly position
each plot; see @ref{origin} and @ref{size} for details of their usage.

Example:
@example
      set size 0.7,0.7
      set origin 0.1,0.1
      set multiplot
      set size 0.4,0.4
      set origin 0.1,0.1
      plot sin(x)
      set size 0.2,0.2
      set origin 0.5,0.5
      plot cos(x)
      set nomultiplot

@end example

displays a plot of cos(x) stacked above a plot of sin(x).  Note the initial
@ref{size} and @ref{origin}.  While these are not always required, their
inclusion is recommended.  Some terminal drivers require that bounding box
information be available before any plots can be made, and the form given
above guarantees that the bounding box will include the entire plot array
rather than just the bounding box of the first plot.

@ref{size} and @ref{origin} refer to the entire plotting area used for each
plot.  If you want to have the axes themselves line up, you can guarantee
that the margins are the same size with the @ref{margin} commands.  See
@ref{margin} for their use.  Note that the margin settings are absolute,
in character units, so the appearance of the graph in the remaining space
will depend on the screen size of the display device, e.g., perhaps quite
different on a video display and a printer.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/multiplt.html,See demo. }

@node mx2tics, mxtics, multiplot, set-show
@subsection mx2tics

@c ?commands set mx2tics
@c ?commands set nomx2tics
@c ?commands show mx2tics
@c ?set mx2tics
@c ?set nomx2tics
@c ?show mx2tics
@cindex mx2tics
@opindex mx2tics


@cindex nomx2tics

Minor tic marks along the x2 (top) axis are controlled by @ref{mx2tics}.
Please see @ref{mxtics}.

@node mxtics, my2tics, mx2tics, set-show
@subsection mxtics

@c ?commands set mxtics
@c ?commands set nomxtics
@c ?commands show mxtics
@c ?set mxtics
@c ?set nomxtics
@c ?show mxtics
@cindex mxtics
@opindex mxtics


@cindex nomxtics

Minor tic marks along the x axis are controlled by @ref{mxtics}.  They can be
turned off with `set nomxtics`.  Similar commands control minor tics along
the other axes.

Syntax:
@example
      set mxtics @{<freq> | default@}
      set nomxtics
      show mxtics

@end example

The same syntax applies to @ref{mytics}, @ref{mztics}, @ref{mx2tics} and @ref{my2tics}.

<freq> is the number of sub-intervals (NOT the number of minor tics) between
major tics (ten is the default for a linear axis, so there are nine minor
tics between major tics). Selecting `default` will return the number of minor
ticks to its default value.

If the axis is logarithmic, the number of sub-intervals will be set to a
reasonable number by default (based upon the length of a decade).  This will
be overridden if <freq> is given.  However the usual minor tics (2, 3, ...,
8, 9 between 1 and 10, for example) are obtained by setting <freq> to 10,
even though there are but nine sub-intervals.

Minor tics can be used only with uniformly spaced major tics.  Since major
tics can be placed arbitrarily by `set @{x|x2|y|y2|z@}tics`, minor tics cannot
be used if major tics are explicitly `set`.

By default, minor tics are off for linear axes and on for logarithmic axes.
They inherit the settings for `axis|border` and `@{no@}mirror` specified for
the major tics.  Please see @ref{xtics} for information about these.

@node my2tics, mytics, mxtics, set-show
@subsection my2tics

@c ?commands set my2tics
@c ?commands set nomy2tics
@c ?commands show my2tics
@c ?set my2tics
@c ?set nomy2tics
@c ?show my2tics
@cindex my2tics
@opindex my2tics


@cindex nomy2tics

Minor tic marks along the y2 (right-hand) axis are controlled by @ref{my2tics}.  Please see @ref{mxtics}.

@node mytics, mztics, my2tics, set-show
@subsection mytics

@c ?commands set mytics
@c ?commands set nomytics
@c ?commands show mytics
@c ?set mytics
@c ?set nomytics
@c ?show mytics
@cindex mytics
@opindex mytics


@cindex nomytics

Minor tic marks along the y axis are controlled by @ref{mytics}.  Please
see @ref{mxtics}.

@node mztics, offsets, mytics, set-show
@subsection mztics

@c ?commands set mztics
@c ?commands set nomztics
@c ?commands show mztics
@c ?set mztics
@c ?set nomztics
@c ?show mztics
@cindex mztics
@opindex mztics


@cindex nomztics

Minor tic marks along the z axis are controlled by @ref{mztics}.  Please
see @ref{mxtics}.

@node offsets, origin, mztics, set-show
@subsection offsets

@c ?commands set offsets
@c ?commands set nooffsets
@c ?commands show offsets
@c ?set offsets
@c ?set nooffsets
@c ?show offsets
@cindex offsets
@opindex offsets


@cindex nooffsets

Offsets provide a mechanism to put a boundary around the data inside of an
autoscaled graph.

Syntax:
@example
      set offsets <left>, <right>, <top>, <bottom>
      set nooffsets
      show offsets

@end example

Each offset may be a constant or an expression.  Each defaults to 0.  Left
and right offsets are given in units of the x axis, top and bottom offsets in
units of the y axis.  A positive offset expands the graph in the specified
direction, e.g., a positive bottom offset makes ymin more negative.  Negative
offsets, while permitted, can have unexpected interactions with autoscaling
and clipping.

Offsets are ignored in `splot`s.

Example:
@example
      set offsets 0, 0, 2, 2
      plot sin(x)

@end example

This graph of sin(x) will have a y range [-3:3] because the function
will be autoscaled to [-1:1] and the vertical offsets are each two.

@node origin, output, offsets, set-show
@subsection origin

@c ?commands set origin
@c ?commands show origin
@c ?set origin
@c ?show origin
@cindex origin
@opindex origin


The @ref{origin} command is used to specify the origin of a plotting surface
(i.e., the graph and its margins) on the screen.  The coordinates are given
in the `screen` coordinate system (see `coordinates` for information about
this system).

Syntax:
@example
      set origin <x-origin>,<y-origin>

@end example

@node output, parametric_, origin, set-show
@subsection output

@c ?commands set output
@c ?commands show output
@c ?set output
@c ?show output
@cindex output
@opindex output


By default, screens are displayed to the standard output. The @ref{output}
command redirects the display to the specified file or device.

Syntax:
@example
      set output @{"<filename>"@}
      show output

@end example

The filename must be enclosed in quotes.  If the filename is omitted, any
output file opened by a previous invocation of @ref{output} will be closed
and new output will be sent to STDOUT.  (If you give the command `set output
"STDOUT"`, your output may be sent to a file named "STDOUT"!  ["May be", not
"will be", because some terminals, like `x11`, ignore @ref{output}.])

MSDOS users should note that the \ character has special significance in
double-quoted strings, so single-quotes should be used for filenames in
different directories.

When both @ref{terminal} and @ref{output} are used together, it is safest to
give @ref{terminal} first, because some terminals set a flag which is needed
in some operating systems.  This would be the case, for example, if the
operating system needs to know whether or not a file is to be formatted in
order to open it properly.

On machines with popen functions (Unix), output can be piped through a shell
command if the first non-whitespace character of the filename is '|'.
For instance,

@example
      set output "|lpr -Plaser filename"
      set output "|lp -dlaser filename"

@end example

On MSDOS machines, `set output "PRN"` will direct the output to the default
printer.  On VMS, output can be sent directly to any spooled device.  It is
also possible to send the output to DECnet transparent tasks, which allows
some flexibility.

@node parametric_, pointsize, output, set-show
@subsection parametric

@c ?commands set parametric
@c ?commands set noparametric
@c ?commands show parametric
@c ?set parametric
@c ?set noparametric
@c ?show parametric
@cindex parametric
@opindex parametric


@cindex noparametric

The `set parametric` command changes the meaning of @ref{plot} (`splot`) from
normal functions to parametric functions.  The command `set noparametric`
restores the plotting style to normal, single-valued expression plotting.

Syntax:
@example
      set parametric
      set noparametric
      show parametric

@end example

For 2-d plotting, a parametric function is determined by a pair of parametric
functions operating on a parameter.  An example of a 2-d parametric function
would be `plot sin(t),cos(t)`, which draws a circle (if the aspect ratio is
set correctly---see @ref{size}).  `gnuplot` will display an error message if
both functions are not provided for a parametric @ref{plot}.

For 3-d plotting, the surface is described as x=f(u,v), y=g(u,v), z=h(u,v).
Therefore a triplet of functions is required.  An example of a 3-d parametric
function would be `cos(u)*cos(v),cos(u)*sin(v),sin(u)`, which draws a sphere.
`gnuplot` will display an error message if all three functions are not
provided for a parametric `splot`.

The total set of possible plots is a superset of the simple f(x) style plots,
since the two functions can describe the x and y values to be computed
separately.  In fact, plots of the type t,f(t) are equivalent to those
produced with f(x) because the x values are computed using the identity
function.  Similarly, 3-d plots of the type u,v,f(u,v) are equivalent to
f(x,y).

Note that the order the parametric functions are specified is xfunction,
yfunction (and zfunction) and that each operates over the common parametric
domain.

Also, the `set parametric` function implies a new range of values.  Whereas
the normal f(x) and f(x,y) style plotting assume an xrange and yrange (and
zrange), the parametric mode additionally specifies a trange, urange, and
vrange.  These ranges may be set directly with @ref{trange}, @ref{urange},
and @ref{vrange}, or by specifying the range on the @ref{plot} or `splot`
commands.  Currently the default range for these parametric variables is
[-5:5].  Setting the ranges to something more meaningful is expected.

@node pointsize, polar, parametric_, set-show
@subsection pointsize

@c ?commands set pointsize
@c ?commands show pointsize
@c ?set pointsize
@c ?show pointsize
@cindex pointsize
@opindex pointsize


The @ref{pointsize} command scales the size of the points used in plots.

Syntax:
@example
      set pointsize <multiplier>
      show pointsize

@end example

The default is a multiplier of 1.0.  Larger pointsizes may be useful to
make points more visible in bitmapped graphics.

The pointsize of a single plot may be changed on the @ref{plot} command.  See
@ref{with} for details.

Please note that the pointsize setting is not supported by all terminal
types.

@node polar, rmargin, pointsize, set-show
@subsection polar

@c ?commands set polar
@c ?commands set nopolar
@c ?commands show polar
@c ?set polar
@c ?set nopolar
@c ?show polar
@cindex polar
@opindex polar


@cindex nopolar

The `set polar` command changes the meaning of the plot from rectangular
coordinates to polar coordinates.

Syntax:
@example
      set polar
      set nopolar
      show polar

@end example

There have been changes made to polar mode in version 3.7, so that scripts
for `gnuplot` versions 3.5 and earlier will require modification.  The main
change is that the dummy variable t is used for the angle so that the x and
y ranges can be controlled independently.  Other changes are:
1) tics are no longer put along the zero axes automatically
---use `set xtics axis nomirror`; `set ytics axis nomirror`;
2) the grid, if selected, is not automatically polar
---use `set grid polar`;
3) the grid is not labelled with angles
---use @ref{label} as necessary.

In polar coordinates, the dummy variable (t) is an angle.  The default range
of t is [0:2*pi], or, if degree units have been selected, to [0:360] (see
@ref{angles}).

The command `set nopolar` changes the meaning of the plot back to the default
rectangular coordinate system.

The `set polar` command is not supported for `splot`s.  See the @ref{mapping}
command for similar functionality for `splot`s.

While in polar coordinates the meaning of an expression in t is really
r = f(t), where t is an angle of rotation.  The trange controls the domain
(the angle) of the function, and the x and y ranges control the range of the
graph in the x and y directions.  Each of these ranges, as well as the
rrange, may be autoscaled or set explicitly.  See @ref{xrange} for details
of all the `set range` commands.

Example:
@example
      set polar
      plot t*sin(t)
      plot [-2*pi:2*pi] [-3:3] [-3:3] t*sin(t)

@end example

The first @ref{plot} uses the default polar angular domain of 0 to 2*pi.  The
radius and the size of the graph are scaled automatically.  The second @ref{plot}
expands the domain, and restricts the size of the graph to [-3:3] in both
directions.

You may want to `set size square` to have `gnuplot` try to make the aspect
ratio equal to unity, so that circles look circular.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/polar.html,Polar demos }
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/poldat.html,Polar Data Plot. }

@node rmargin, rrange, polar, set-show
@subsection rmargin

@c ?commands set rmargin
@c ?set rmargin
@cindex rmargin
@opindex rmargin


The command @ref{rmargin} sets the size of the right margin.  Please see
@ref{margin} for details.

@node rrange, samples, rmargin, set-show
@subsection rrange

@c ?commands set rrange
@c ?commands show rrange
@c ?set rrange
@c ?show rrange
@cindex rrange
@opindex rrange


The @ref{rrange} command sets the range of the radial coordinate for a
graph in polar mode.  Please see @ref{xrange} for details.

@node samples, size, rrange, set-show
@subsection samples

@c ?commands set samples
@c ?commands show samples
@c ?set samples
@c ?show samples
@cindex samples
@opindex samples


The sampling rate of functions, or for interpolating data, may be changed
by the @ref{samples} command.

Syntax:
@example
      set samples <samples_1> @{,<samples_2>@}
      show samples

@end example

By default, sampling is set to 100 points.  A higher sampling rate will
produce more accurate plots, but will take longer.  This parameter has no
effect on data file plotting unless one of the interpolation/approximation
options is used.  See @ref{smooth} re 2-d data and @ref{cntrparam} and
@ref{dgrid3d} re 3-d data.

When a 2-d graph is being done, only the value of <samples_1> is relevant.

When a surface plot is being done without the removal of hidden lines, the
value of samples specifies the number of samples that are to be evaluated for
the isolines.  Each iso-v line will have <sample_1> samples and each iso-u
line will have <sample_2> samples.  If you only specify <samples_1>,
<samples_2> will be set to the same value as <samples_1>.  See also @ref{isosamples}.

@node size, style, samples, set-show
@subsection size

@c ?commands set size
@c ?commands show size
@c ?set size
@c ?show size
@cindex size
@opindex size


The @ref{size} command scales the displayed size of the plot.

Syntax:
@example
      set size @{@{no@}square | ratio <r> | noratio@} @{<xscale>,<yscale>@}
      show size

@end example

The <xscale> and <yscale> values are the scaling factors for the size of the
plot, which includes the graph and the margins.

`ratio` causes `gnuplot` to try to create a graph with an aspect ratio of <r>
(the ratio of the y-axis length to the x-axis length) within the portion of
the plot specified by <xscale> and <yscale>.

The meaning of a negative value for <r> is different.  If <r>=-1, gnuplot
tries to set the scales so that the unit has the same length on both the x
and y axes (suitable for geographical data, for instance).  If <r>=-2, the
unit on y has twice the length of the unit on x, and so on.

The success of `gnuplot` in producing the requested aspect ratio depends on
the terminal selected.  The graph area will be the largest rectangle of
aspect ratio <r> that will fit into the specified portion of the output
(leaving adequate margins, of course).

`square` is a synonym for `ratio 1`.

Both `noratio` and `nosquare` return the graph to the default aspect ratio
of the terminal, but do not return <xscale> or <yscale> to their default
values (1.0).

`ratio` and `square` have no effect on 3-d plots.

@ref{size} is relative to the default size, which differs from terminal to
terminal.  Since `gnuplot` fills as much of the available plotting area as
possible by default, it is safer to use @ref{size} to decrease the size of
a plot than to increase it.  See @ref{terminal} for the default sizes.

On some terminals, changing the size of the plot will result in text being
misplaced.

Examples:

To set the size to normal size use:
@example
      set size 1,1

@end example

To make the graph half size and square use:
@example
      set size square 0.5,0.5

@end example

To make the graph twice as high as wide use:
@example
      set size ratio 2

@end example

@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/airfoil.html,See demo. }

@node style, surface, size, set-show
@subsection style

@c ?commands set function style
@c ?commands show function style
@c ?commands set data style
@c ?commands show data style
@c ?set function style
@c ?show function style
@c ?set data style
@c ?show data style
@c ?set style
@c ?show style
Default styles are chosen with the @ref{style} and @ref{style}
commands.  See @ref{with} for information about how to override the default
plotting style for individual functions and data sets.

Syntax:
@example
      set function style <style>
      set data style <style>
      show function style
      show data style

@end example

The types used for all line and point styles (i.e., solid, dash-dot, color,
etc. for lines; circles, squares, crosses, etc. for points) will be either
those specified on the @ref{plot} or `splot` command or will be chosen
sequentially from the types available to the terminal in use.  Use the
command @ref{test} to see what is available.

None of the styles requiring more than two columns of information (e.g.,
@ref{errorbars}) can be used with `splot`s or function @ref{plot}s.  Neither @ref{boxes}
nor any of the @ref{steps} styles can be used with `splot`s.  If an inappropriate
style is specified, it will be changed to `points`.

For 2-d data with more than two columns, `gnuplot` is picky about the allowed
`errorbar` styles.  The @ref{using} option on the @ref{plot} command can be used to
set up the correct columns for the style you want.  (In this discussion,
"column" will be used to refer both to a column in the data file and an entry
in the @ref{using} list.)

For three columns, only @ref{xerrorbars}, @ref{yerrorbars} (or @ref{errorbars}), @ref{boxes},
and @ref{boxerrorbars} are allowed.  If another plot style is used, the style
will be changed to @ref{yerrorbars}.  The @ref{boxerrorbars} style will calculate the
boxwidth automatically.

For four columns, only @ref{xerrorbars}, @ref{yerrorbars} (or @ref{errorbars}),
@ref{xyerrorbars}, @ref{boxxyerrorbars}, and @ref{boxerrorbars} are allowed.  An illegal
style will be changed to @ref{yerrorbars}.

Five-column data allow only the @ref{boxerrorbars}, @ref{financebars}, and
@ref{candlesticks} styles.  (The last two of these are primarily used for plots
of financial prices.)  An illegal style will be changed to @ref{boxerrorbars}
before plotting.

Six- and seven-column data only allow the @ref{xyerrorbars} and @ref{boxxyerrorbars}
styles.  Illegal styles will be changed to @ref{xyerrorbars} before plotting.

For more information about error bars, please see @ref{errorbars}.

@menu
* boxerrorbars::                
* boxes::                       
* boxxyerrorbars::              
* candlesticks::                
* dots::                        
* financebars::                 
* fsteps::                      
* histeps::                     
* impulses::                    
* lines::                       
* linespoints::                 
* points::                      
* steps::                       
* vector::                      
* xerrorbars::                  
* xyerrorbars::                 
* yerrorbars::                  
@end menu

@node boxerrorbars, boxes, style, style
@subsubsection boxerrorbars

@c ?commands set style boxerrorbars
@c ?set style boxerrorbars
@c ?style boxerrorbars
@cindex boxerrorbars

The @ref{boxerrorbars} style is only relevant to 2-d data plotting.  It is a
combination of the @ref{boxes} and @ref{yerrorbars} styles.  The boxwidth will come
from the fourth column if the y errors are in the form of "ydelta" and the
boxwidth was not previously set equal to -2.0 (`set boxwidth -2.0`) or from
the fifth column if the y errors are in the form of "ylow yhigh".  The
special case  `boxwidth = -2.0` is for four-column data with y errors in the
form "ylow yhigh".  In this case the boxwidth will be calculated so that each
box touches the adjacent boxes.  The width will also be calculated in cases
where three-column data are used.

The box height is determined from the y error in the same way as it is for
the @ref{yerrorbars} style---either from y-ydelta to y+ydelta or from ylow to
yhigh, depending on how many data columns are provided.
@uref{http://www.nas.nasa.gov/~woo/gnuplot/errorbar/errorbar.html,See Demo. }

@node boxes, boxxyerrorbars, boxerrorbars, style
@subsubsection boxes

@c ?commands set style boxes
@c ?commands set style bargraph
@c ?set style boxes
@c ?set style bargraph
@c ?style boxes
@c ?style bargraph
@cindex boxes

@cindex bargraph

The @ref{boxes} style is only relevant to 2-d plotting.  It draws a box centered
about the given x coordinate from the x axis (not the graph border) to the
given y coordinate.  The width of the box is obtained in one of three ways.
If it is a data plot and the data file has a third column, this will be used
to set the width of the box.  If not, if a width has been set using the @ref{boxwidth} command, this will be used.  If neither of these is available, the
width of each box will be calculated automatically so that it touches the
adjacent boxes.

@node boxxyerrorbars, candlesticks, boxes, style
@subsubsection boxxyerrorbars

@c ?commands set style boxxyerrorbars
@c ?set style boxxyerrorbars
@c ?style boxxyerrorbars
@cindex boxxyerrorbars

The @ref{boxxyerrorbars} style is only relevant to 2-d data plotting.  It is a
combination of the @ref{boxes} and @ref{xyerrorbars} styles.

The box width and height are determined from the x and y errors in the same
way as they are for the @ref{xyerrorbars} style---either from xlow to xhigh and
from ylow to yhigh, or from x-xdelta to x+xdelta and from y-ydelta to
y+ydelta , depending on how many data columns are provided.

@node candlesticks, dots, boxxyerrorbars, style
@subsubsection candlesticks

@c ?commands set style candlesticks
@c ?set style candlesticks
@c ?style candlesticks
@cindex candlesticks

The @ref{candlesticks} style is only relevant for 2-d data plotting of financial
data.  Five columns of data are required; in order, these should be the x
coordinate (most likely a date) and the opening, low, high, and closing
prices.  The symbol is an open rectangle, centered horizontally at the x
coordinate and limited vertically by the opening and closing prices.  A
vertical line segment at the x coordinate extends up from the top of the
rectangle to the high price and another down to the low.  The width of the
rectangle may be changed by @ref{bar}.  The symbol will be unchanged if the
low and high prices are interchanged or if the opening and closing prices
are interchanged.  See @ref{bar} and @ref{financebars}.
@uref{http://www.nas.nasa.gov/~woo/gnuplot/finance/finance.html,See demos.}

@node dots, financebars, candlesticks, style
@subsubsection dots

@c ?commands set style dots
@c ?set style dots
@c ?style dots
@cindex dots

The @ref{dots} style plots a tiny dot at each point; this is useful for scatter
plots with many points.

@node financebars, fsteps, dots, style
@subsubsection financebars

@c ?commands set style financebars
@c ?set style financebars
@c ?style financebars
@cindex financebars

The @ref{financebars} style is only relevant for 2-d data plotting of financial
data.  Five columns of data are required; in order, these should be the x
coordinate (most likely a date) and the opening, low, high, and closing
prices.  The symbol is a vertical line segment, located horizontally at the x
coordinate and limited vertically by the high and low prices.  A horizontal
tic on the left marks the opening price and one on the right marks the
closing price.  The length of these tics may be changed by @ref{bar}.  The
symbol will be unchanged if the high and low prices are interchanged.  See
@ref{bar} and @ref{candlesticks}.
@uref{http://www.nas.nasa.gov/~woo/gnuplot/finance/finance.html,See demos.}

@node fsteps, histeps, financebars, style
@subsubsection fsteps

@c ?commands set style fsteps
@c ?set style fsteps
@c ?style fsteps
@cindex fsteps

The @ref{fsteps} style is only relevant to 2-d plotting.  It connects consecutive
points with two line segments: the first from (x1,y1) to (x1,y2) and the
second from (x1,y2) to (x2,y2).
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/steps.html,See demo. }

@node histeps, impulses, fsteps, style
@subsubsection histeps

@c ?commands set style histeps
@c ?set style histeps
@c ?style histeps
@cindex histeps

The @ref{histeps} style is only relevant to 2-d plotting.  It is intended for
plotting histograms.  Y-values are assumed to be centered at the x-values;
the point at x1 is represented as a horizontal line from ((x0+x1)/2,y1) to
((x1+x2)/2,y1).  The lines representing the end points are extended so that
the step is centered on at x.  Adjacent points are connected by a vertical
line at their average x, that is, from ((x1+x2)/2,y1) to ((x1+x2)/2,y2).

If @ref{autoscale} is in effect, it selects the xrange from the data rather than
the steps, so the end points will appear only half as wide as the others.
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/steps.html,See demo. }

@ref{histeps} is only a plotting style; `gnuplot` does not have the ability to
create bins and determine their population from some data set.

@node impulses, lines, histeps, style
@subsubsection impulses

@c ?commands set style impulses
@c ?set style impulses
@c ?style impulses
@cindex impulses

The @ref{impulses} style displays a vertical line from the x axis (not the graph
border), or from the grid base for `splot`, to each point.

@node lines, linespoints, impulses, style
@subsubsection lines

@c ?commands set style lines
@c ?set style lines
@c ?style lines
@cindex lines

The `lines` style connects adjacent points with straight line segments.

@node linespoints, points, lines, style
@subsubsection linespoints

@c ?commands set style linespoints
@c ?commands set style lp
@c ?set style linespoints
@c ?set style lp
@c ?style linespoints
@c ?style lp
@cindex linespoints

@cindex lp

The @ref{linespoints} style does both `lines` and `points`, that is, it draws a
small symbol at each point and then connects adjacent points with straight
line segments.  The command @ref{pointsize} may be used to change the size of
the points.  See @ref{pointsize} for its usage.

@ref{linespoints} may be abbreviated `lp`.

@node points, steps, linespoints, style
@subsubsection points

@c ?commands set style points
@c ?set style points
@c ?style points
@cindex points

The `points` style displays a small symbol at each point.  The command @ref{pointsize} may be used to change the size of the points.  See @ref{pointsize}
for its usage.

@node steps, vector, points, style
@subsubsection steps

@c ?commands set style steps
@c ?set style steps
@c ?style steps
@cindex steps

The @ref{steps} style is only relevant to 2-d plotting.  It connects consecutive
points with two line segments: the first from (x1,y1) to (x2,y1) and the
second from (x2,y1) to (x2,y2).
@uref{http://www.gnuplot.vt.edu/gnuplot/gpdocs/steps.html,See demo. }

@node vector, xerrorbars, steps, style
@subsubsection vector

@c ?commands set style vector
@c ?set style vector
@c ?style vector
@cindex vector

The @ref{vector} style draws a vector from (x,y) to (x+xdelta,y+ydelta).  Thus
it requires four columns of data.  It also draws a small arrowhead at the
end of the vector.

The @ref{vector} style is still experimental: it doesn't get clipped properly
and other things may also be wrong with it.  Use it at your own risk.

@node xerrorbars, xyerrorbars, vector, style
@subsubsection xerrorbars

@c ?commands set style xerrorbars
@c ?set style xerrorbars
@c ?style xerrorbars
@cindex xerrorbars

The @ref{xerrorbars} style is only relevant to 2-d data plots.  @ref{xerrorbars} is
like @ref{dots}, except that a horizontal error bar is also drawn.  At each point
(x,y), a line is drawn from (xlow,y) to (xhigh,y) or from (x-xdelta,y) to
(x+xdelta,y), depending on how many data columns are provided.  A tic mark
is placed at the ends of the error bar (unless @ref{bar} is used---see @ref{bar} for details).

@node xyerrorbars, yerrorbars, xerrorbars, style
@subsubsection xyerrorbars

@c ?commands set style xyerrorbars
@c ?set style xyerrorbars
@c ?style xyerrorbars
@cindex xyerrorbars

The @ref{xyerrorbars} style is only relevant to 2-d data plots.  @ref{xyerrorbars} is
like @ref{dots}, except that horizontal and vertical error bars are also drawn.
At each point (x,y), lines are drawn from (x,y-ydelta) to (x,y+ydelta) and
from (x-xdelta,y) to (x+xdelta,y) or from (x,ylow) to (x,yhigh) and from
(xlow,y) to (xhigh,y), depending upon the number of data columns provided.  A
tic mark is placed at the ends of the error bar (unless @ref{bar} is
used---see @ref{bar} for details).

If data are provided in an unsupported mixed form, the @ref{using} filter on the
@ref{plot} command should be used to set up the appropriate form.  For example,
if the data are of the form (x,y,xdelta,ylow,yhigh), then you can use

@example
      plot 'data' using 1:2:($1-$3),($1+$3),4,5 with xyerrorbars

@end example

@node yerrorbars,  , xyerrorbars, style
@subsubsection yerrorbars

@c ?commands set style yerrorbars
@c ?commands set style errorbars
@c ?set style yerrorbars
@c ?set style errorbars
@c ?style yerrorbars
@c ?style errorbars
@cindex yerrorbars

@cindex errorbars

The @ref{yerrorbars} (or @ref{errorbars}) style is only relevant to 2-d data plots.
@ref{yerrorbars} is like @ref{dots}, except that a vertical error bar is also drawn.
At each point (x,y), a line is drawn from (x,y-ydelta) to (x,y+ydelta) or
from (x,ylow) to (x,yhigh), depending on how many data columns are provided.
A tic mark is placed at the ends of the error bar (unless @ref{bar} is
used---see @ref{bar} for details).
@uref{http://www.nas.nasa.gov/~woo/gnuplot/errorbar/errorbar.html,See demo. }

@node surface, terminal, style, set-show
@subsection surface

@c ?commands set surface
@c ?commands set nosurface
@c ?commands show surface
@c ?set surface
@c ?set nosurface
@c ?show surface
@cindex surface
@opindex surface


@cindex nosurface

The command @ref{surface} controls the display of surfaces by `splot`.

Syntax:
@example
      set surface
      set nosurface
      show surface

@end example

The surface is drawn with the style specifed by @ref{with}, or else the
appropriate style, data or function.

Whenever `set nosurface` is issued, `splot` will not draw points or lines
corresponding to the function or data file points.  Contours may be still be
drawn on the surface, depending on the @ref{contour} option. `set nosurface;
set contour base` is useful for displaying contours on the grid base.  See
also @ref{contour}.
@c ^ <h2> Terminal Types </h2>

@node terminal, tics, surface, set-show
@subsection terminal

@c ?commands set terminal
@c ?commands show terminal
@c ?set terminal
@c ?set term
@c ?show terminal
@cindex terminal
@opindex terminal


@cindex term

`gnuplot` supports many different graphics devices.  Use @ref{terminal} to
tell `gnuplot` what kind of output to generate. Use @ref{output} to redirect
that output to a file or device.

Syntax:
@example
      set terminal @{<terminal-type>@}
      show terminal

@end example

If <terminal-type> is omitted, `gnuplot` will list the available terminal
types.  <terminal-type> may be abbreviated.

If both @ref{terminal} and @ref{output} are used together, it is safest to
give @ref{terminal} first, because some terminals set a flag which is needed
in some operating systems.

Several terminals have additional options.  For example, see `dumb`,
`iris4d`, `hpljii` or `postscript`.

This document may describe drivers that are not available to you because they
were not installed, or it may not describe all the drivers that are available
to you, depending on its output format.
@@c <4 -- all terminal stuff is pulled from the .trm files

@menu
* aifm::                        
* cgm::                         
* corel::                       
* dumb::                        
* dxf::                         
* eepic::                       
* epson-180dpi::                
* fig::                         
* gif::                         
* gpic::                        
* hp2623a::                     
* hp2648::                      
* hp500c::                      
* hpgl::                        
* hpljii::                      
* hppj::                        
* imagen::                      
* latex::                       
* mf::                          
* mif::                         
* pbm::                         
* png::                         
* postscript::                  
* pslatex_and_pstex::           
* pstricks::                    
* qms::                         
* regis::                       
* sun::                         
* tek410x::                     
* table::                       
* tek40::                       
* texdraw::                     
* tgif::                        
* tkcanvas::                    
* tpic::                        
* x11::                         
* xlib::                        
@end menu

@node aifm, cgm, terminal, terminal
@subsubsection aifm

@c ?commands set terminal aifm
@c ?set terminal aifm
@c ?set term aifm
@c ?terminal aifm
@c ?term aifm
@cindex aifm
@tmindex aifm


Several options may be set in `aifm`---the Adobe Illustrator 3.0+ driver.

Syntax:
@example
      set terminal aifm @{<color>@} @{"<fontname>"@} @{<fontsize>@}

@end example

<color> is either `color` or `monochrome`; "<fontname>" is the name of a
valid PostScript font; <fontsize> is the size of the font in PostScript
points, before scaling by the @ref{size} command.  Selecting `default` sets
all options to their default values: `monochrome`, "Helvetica", and 14pt.

Since AI does not really support multiple pages, multiple graphs will be
drawn directly on top of one another.  However, each graph will be grouped
individually, making it easy to separate them inside AI (just pick them up
and move them).

Examples:
@example
      set term aifm
      set term aifm 22
      set size 0.7,1.4; set term aifm color "Times-Roman" 14"

@end example

@node cgm, corel, aifm, terminal
@subsubsection cgm

@c ?commands set terminal cgm
@c ?set terminal cgm
@c ?set term cgm
@c ?terminal cgm
@c ?term cgm
@cindex cgm
@tmindex cgm


The `cgm` terminal generates a Computer Graphics Metafile.  This file format
is a subset of the ANSI X3.122-1986 standard entitled "Computer Graphics -
Metafile for the Storage and Transfer of Picture Description Information".
Several options may be set in `cgm`.

Syntax:
@example
      set terminal cgm @{<mode>@} @{<color>@} @{<rotation>@} @{solid | dashed@}
                       @{width <plot_width>@} @{linewidth <line_width>@}
                       @{"<font>"@} @{<fontsize>@}

@end example

where <mode> is `landscape`, `portrait`, or `default`;
<color> is either `color` or `monochrome`; 
<rotation> is either `rotate` or `norotate`;
`solid` draws all curves with solid lines, overriding any dashed patterns;
<plot_width> is the width of the page in points; 
<line_width> is the line width in points; 
<font> is the name of a font; and 
`<fontsize>` is the size of the font in points.

By default, `cgm` uses rotated text for the Y axis label.

The first six options can be in any order.  Selecting `default` sets all
options to their default values.

Examples:
@example
      set terminal cgm landscape color rotate dashed width 432 \\
                     linewidth 1  'Arial Bold' 12       # defaults
      set terminal cgm 14 linewidth 2  14  # wider lines & larger font
      set terminal cgm portrait 'Times Roman Italic' 12
      set terminal cgm color solid    # no pesky dashes!

@end example


@noindent --- FONT ---

@c ?commands set terminal cgm font
@c ?set terminal cgm font
@c ?set term cgm font
@c ?cgm font
The first part of a Computer Graphics Metafile, the metafile description,
includes a font table.  In the picture body, a font is designated by an
index into this table.  By default, this terminal generates a table with
the following fonts:

@example
      Arial
      Arial Italic
      Arial Bold
      Arial Bold Italic
      Times Roman
      Times Roman Italic
      Times Roman Bold
      Times Roman Bold Italic
      Helvetica
      Roman

@end example

Case is not distinct, but the modifiers must appear in the above order (that
is, not 'Arial Italic Bold').  'Arial Bold' is the default font.

You may also specify a font name which does not appear in the default font
table.  In that case, a new font table is constructed with the specified
font as its only entry.  You must ensure that the spelling, capitalization,
and spacing of the name are appropriate for the application that will read
the CGM file.


@noindent --- FONTSIZE ---

@c ?commands set terminal cgm fontsize
@c ?set terminal cgm fontsize
@c ?set term cgm fontsize
@c ?cgm fontsize
Fonts are scaled assuming the page is 6 inches wide.  If the @ref{size} command
is used to change the aspect ratio of the page or the CGM file is converted
to a different width (e.g. it is imported into a document in which the
margins are not 6 inches apart), the resulting font sizes will be different.
To change the assumed width, use the `width` option.


@noindent --- LINEWIDTH ---

@c ?commands set terminal cgm linewidth
@c ?set terminal cgm linewidth
@c ?set term cgm linewidth
@c ?cgm linewidth
The `linewidth` option sets the width of lines in pt.  The default width is
1 pt.  Scaling is affected by the actual width of the page, as discussed
under the `fontsize` and `width` options


@noindent --- ROTATE ---

@c ?commands set terminal cgm rotate
@c ?set terminal cgm rotate
@c ?set term cgm rotate
@c ?cgm rotate
The `norotate` option may be used to disable text rotation.  For example,
the CGM input filter for Word for Windows 6.0c can accept rotated text, but
the DRAW editor within Word cannot.  If you edit a graph (for example, to
label a curve), all rotated text is restored to horizontal.  The Y axis
label will then extend beyond the clip boundary.  With `norotate`, the Y
axis label starts in a less attractive location, but the page can be edited
without damage.  The `rotate` option confirms the default behavior.


@noindent --- SOLID ---

@c ?set terminal cgm solid
@c ?set term cgm solid
@c ?cgm solid
The `solid` option may be used to disable dashed line styles in the
plots.  This is useful when color is enabled and the dashing of the lines
detracts from the appearance of the plot. The `dashed` option confirms the
default behavior, which gives a different dash pattern to each curve.


@noindent --- SIZE ---

@c ?commands set terminal cgm size
@c ?set terminal cgm size
@c ?set term cgm size
@c ?scgm size
Default size of a CGM page is 32599 units wide and 23457 units high for
landscape, or 23457 units wide by 32599 units high for portrait.


@noindent --- WIDTH ---

@c ?commands set terminal cgm width
@c ?set terminal cgm width
@c ?set term cgm width
@c ?cgm width
All distances in the CGM file are in abstract units.  The application that
reads the file determines the size of the final page.  By default, the width
of the final page is assumed to be 6 inches (15.24 cm).  This distance is
used to calculate the correct font size, and may be changed with the `width`
option.  The keyword should be followed by the width in points.  (Here, a
point is 1/72 inch, as in PostScript.  This unit is known as a "big point"
in TeX.)  `gnuplot` arithmetic can be used to convert from other units, as
follows:
@example
      set terminal cgm width 432            # default
      set terminal cgm width 6*72           # same as above
      set terminal cgm width 10/2.54*72     # 10 cm wide

@end example


@noindent --- WINWORD6 ---

@c ?commands set terminal cgm winword6
@c ?set terminal cgm winword6
@c ?set term cgm winword6
@c ?cgm winword6
The default font table was chosen to match, where possible, the default font
assignments made by the Computer Graphics Metafile input filter for
Microsoft Word 6.0c, although the filter makes available only 'Arial' and
'Times Roman' fonts and their bold and/or italic variants.  Other fonts such
as 'Helvetica' and 'Roman' are not available.  If the CGM file includes a
font table, the filter mostly ignores it.  However, it changes certain font
assignments so that they disagree with the table.  As a workaround, the
`winword6` option deletes the font table from the CGM file.  In this case,
the filter makes predictable font assignments.  'Arial Bold' is correctly
assigned even with the font table present, which is one reason it was chosen
as the default.

`winword6` disables the color tables for a similar reason---with the color
table included, Microsoft Word displays black for color 7.

Linewidths and pointsizes may be changed with @ref{linestyle}."

@node corel, dumb, cgm, terminal
@subsubsection corel

@c ?commands set terminal corel
@c ?set terminal corel