The commands for graphing data begin with the `g` prefix key. Calc
uses GNUPLOT 2.0 or 3.0 to do graphics. These commands will only work
if GNUPLOT is available on your system. (While GNUPLOT sounds like
a relative of GNU Emacs, it is actually completely unrelated.
However, it is free software and can be obtained from the Free
Software Foundation's machine ``prep.ai.mit.edu'`.)

If you have GNUPLOT installed on your system but Calc is unable to
find it, you may need to set the `calc-gnuplot-name`

variable
in your ``.emacs'` file. You may also need to set some Lisp
variables to show Calc how to run GNUPLOT on your system; these
are described under `g D` and `g O` below. If you are
using the X window system, Calc will configure GNUPLOT for you
automatically. If you have GNUPLOT 3.0 and you are not using X,
Calc will configure GNUPLOT to display graphs using simple character
graphics that will work on any terminal.

The easiest graphics command is `g f` (`calc-graph-fast`

).
This command takes two vectors of equal length from the stack.
The vector at the top of the stack represents the "y" values of
the various data points. The vector in the second-to-top position
represents the corresponding "x" values. This command runs
GNUPLOT (if it has not already been started by previous graphing
commands) and displays the set of data points. The points will
be connected by lines, and there will also be some kind of symbol
to indicate the points themselves.

The "x" entry may instead be an interval form, in which case suitable "x" values are interpolated between the minimum and maximum values of the interval (whether the interval is open or closed is ignored).

The "x" entry may also be a number, in which case Calc uses the sequence of "x" values x, x+1, x+2, etc. (Generally the number 0 or 1 would be used for x in this case.)

The "y" entry may be any formula instead of a vector. Calc effectively
uses `N` (`calc-eval-num`

) to evaluate variables in the formula;
the result of this must be a formula in a single (unassigned) variable.
The formula is plotted with this variable taking on the various "x"
values. Graphs of formulas by default use lines without symbols at the
computed data points. Note that if neither "x" nor "y" is a vector,
Calc guesses at a reasonable number of data points to use. See the
`g N` command below. (The "x" values must be either a vector
or an interval if "y" is a formula.)

If "y" is (or evaluates to) a formula of the form
``xy( x, y)'` then the result is a
parametric plot. The two arguments of the fictitious

`xy`

function
are used as the "x" and "y" coordinates of the curve, respectively.
In this case the "x" vector or interval you specified is not directly
visible in the graph. For example, if "x" is the interval Also, "x" and "y" may each be variable names, in which case Calc looks for suitable vectors, intervals, or formulas stored in those variables.

The "x" and "y" values for the data points (as pulled from the vectors,
calculated from the formulas, or interpolated from the intervals) should
be real numbers (integers, fractions, or floats). If either the "x"
value or the "y" value of a given data point is not a real number, that
data point will be omitted from the graph. The points on either side
of the invalid point will *not* be connected by a line.

See the documentation for `g a` below for a description of the way
numeric prefix arguments affect `g f`.

If you store an empty vector in the variable `PlotRejects`

(i.e., `[ ] s t PlotRejects`), Calc will append information to
this vector for every data point which was rejected because its
"x" or "y" values were not real numbers. The result will be
a matrix where each row holds the curve number, data point number,
"x" value, and "y" value for a rejected data point.
See section The Evaluates-To Operator, for a handy way to keep tabs on the
current value of `PlotRejects`

. See section Other Operations on Variables,
for the `s R` command which is another easy way to examine
`PlotRejects`

.

To clear the graphics display, type `g c` (`calc-graph-clear`

).
If the GNUPLOT output device is an X window, the window will go away.
Effects on other kinds of output devices will vary. You don't need
to use `g c` if you don't want to--if you give another `g f`
or `g p` command later on, it will reuse the existing graphics
window if there is one.

The `g F` (`calc-graph-fast-3d`

) command makes a three-dimensional
graph. It works only if you have GNUPLOT 3.0 or later; with GNUPLOT 2.0,
you will see a GNUPLOT error message if you try this command.

The `g F` command takes three values from the stack, called "x",
"y", and "z", respectively. As was the case for 2D graphs, there
are several options for these values.

In the first case, "x" and "y" are each vectors (not necessarily of
the same length); either or both may instead be interval forms. The
"z" value must be a matrix with the same number of rows as elements
in "x", and the same number of columns as elements in "y". The
result is a surface plot where @c{$z_{ij}$}
z_ij is the height of the point
at coordinate (x_i, y_j) on the surface. The 3D graph will
be displayed from a certain default viewpoint; you can change this
viewpoint by adding a ``set view'` to the ``*Gnuplot Commands*'`
buffer as described later. See the GNUPLOT 3.0 documentation for a
description of the ``set view'` command.

Each point in the matrix will be displayed as a dot in the graph,
and these points will be connected by a grid of lines (**isolines**).

In the second case, "x", "y", and "z" are all vectors of equal length. The resulting graph displays a 3D line instead of a surface, where the coordinates of points along the line are successive triplets of values from the input vectors.

In the third case, "x" and "y" are vectors or interval forms, and "z" is any formula involving two variables (not counting variables with assigned values). These variables are sorted into alphabetical order; the first takes on values from "x" and the second takes on values from "y" to form a matrix of results that are graphed as a 3D surface.

If the "z" formula evaluates to a call to the fictitious function
``xyz( x, y, z)'`, then the result is a
"parametric surface." In this case, the axes of the graph are
taken from the

It is also possible to have a function in a regular `g f` plot
evaluate to an `xyz`

call. Since `g f` plots a line, not
a surface, the result will be a 3D parametric line. For example,
``[[0..720], xyz(sin(x), cos(x), x)]'` will plot two turns of a
helix (a three-dimensional spiral).

As for `g f`, each of "x", "y", and "z" may instead be
variables containing the relevant data.

The `g f` command is really shorthand for the following commands:
`C-u g d g a g p`. Likewise, `g F` is shorthand for
`C-u g d g A g p`. You can gain more control over your graph
by using these commands directly.

The `g a` (`calc-graph-add`

) command adds the "curve"
represented by the two values on the top of the stack to the current
graph. You can have any number of curves in the same graph. When
you give the `g p` command, all the curves will be drawn superimposed
on the same axes.

The `g a` command (and many others that affect the current graph)
will cause a special buffer, ``*Gnuplot Commands*'`, to be displayed
in another window. This buffer is a template of the commands that will
be sent to GNUPLOT when it is time to draw the graph. The first
`g a` command adds a `plot`

command to this buffer. Succeeding
`g a` commands add extra curves onto that `plot`

command.
Other graph-related commands put other GNUPLOT commands into this
buffer. In normal usage you never need to work with this buffer
directly, but you can if you wish. The only constraint is that there
must be only one `plot`

command, and it must be the last command
in the buffer. If you want to save and later restore a complete graph
configuration, you can use regular Emacs commands to save and restore
the contents of the ``*Gnuplot Commands*'` buffer.

If the values on the stack are not variable names, `g a` will invent
variable names for them (of the form ``PlotData n'`) and store
the values in those variables. The "x" and "y" variables are what
go into the

`plot`

command in the template. If you add a curve
that uses a certain variable and then later change that variable, you
can replot the graph without having to delete and re-add the curve.
That's because the variable name, not the vector, interval or formula
itself, is what was added by
A numeric prefix argument on `g a` or `g f` changes the way
stack entries are interpreted as curves. With a positive prefix
argument n, the top n stack entries are "y" values
for n different curves which share a common "x" value in
the n+1st stack entry. (Thus `g a` with no prefix
argument is equivalent to `C-u 1 g a`.)

A prefix of zero or plain `C-u` means to take two stack entries,
"x" and "y" as usual, but to interpret "y" as a vector of
"y" values for several curves that share a common "x".

A negative prefix argument tells Calc to read n vectors from
the stack; each vector [x, y] describes an independent curve.
This is the only form of `g a` that creates several curves at once
that don't have common "x" values. (Of course, the range of "x"
values covered by all the curves ought to be roughly the same if
they are to look nice on the same graph.)

For example, to plot @c{$\sin n x$}
sin(n x) for integers n
from 1 to 5, you could use `v x` to create a vector of integers
(n), then `V M '` or `V M $` to map ``sin(n x)'`
across this vector. The resulting vector of formulas is suitable
for use as the "y" argument to a `C-u g a` or `C-u g f`
command.

The `g A` (`calc-graph-add-3d`

) command adds a 3D curve
to the graph. It is not legal to intermix 2D and 3D curves in a
single graph. This command takes three arguments, "x", "y",
and "z", from the stack. With a positive prefix n, it
takes n+2 arguments (common "x" and "y", plus n
separate "z"s). With a zero prefix, it takes three stack entries
but the "z" entry is a vector of curve values. With a negative
prefix -n, it takes n vectors of the form [x, y, z].
The `g A` command works by adding a `splot`

(surface-plot)
command to the ``*Gnuplot Commands*'` buffer.

(Although `g a` adds a 2D `plot`

command to the
``*Gnuplot Commands*'` buffer, Calc changes this to `splot`

before sending it to GNUPLOT if it notices that the data points are
evaluating to `xyz`

calls. It will not work to mix 2D and 3D
`g a` curves in a single graph, although Calc does not currently
check for this.)

The `g d` (`calc-graph-delete`

) command deletes the most
recently added curve from the graph. It has no effect if there are
no curves in the graph. With a numeric prefix argument of any kind,
it deletes all of the curves from the graph.

The `g H` (`calc-graph-hide`

) command "hides" or "unhides"
the most recently added curve. A hidden curve will not appear in
the actual plot, but information about it such as its name and line and
point styles will be retained.

The `g j` (`calc-graph-juggle`

) command moves the curve
at the end of the list (the "most recently added curve") to the
front of the list. The next-most-recent curve is thus exposed for
`g d` or similar commands to use. With `g j` you can work
with any curve in the graph even though curve-related commands only
affect the last curve in the list.

The `g p` (`calc-graph-plot`

) command uses GNUPLOT to draw
the graph described in the ``*Gnuplot Commands*'` buffer. Any
GNUPLOT parameters which are not defined by commands in this buffer
are reset to their default values. The variables named in the `plot`

command are written to a temporary data file and the variable names
are then replaced by the file name in the template. The resulting
plotting commands are fed to the GNUPLOT program. See the documentation
for the GNUPLOT program for more specific information. All temporary
files are removed when Emacs or GNUPLOT exits.

If you give a formula for "y", Calc will remember all the values that
it calculates for the formula so that later plots can reuse these values.
Calc throws out these saved values when you change any circumstances
that may affect the data, such as switching from Degrees to Radians
mode, or changing the value of a parameter in the formula. You can
force Calc to recompute the data from scratch by giving a negative
numeric prefix argument to `g p`.

Calc uses a fairly rough step size when graphing formulas over intervals.
This is to ensure quick response. You can "refine" a plot by giving
a positive numeric prefix argument to `g p`. Calc goes through
the data points it has computed and saved from previous plots of the
function, and computes and inserts a new data point midway between
each of the existing points. You can refine a plot any number of times,
but beware that the amount of calculation involved doubles each time.

Calc does not remember computed values for 3D graphs. This means the
numerix prefix argument, if any, to `g p` is effectively ignored if
the current graph is three-dimensional.

The `g P` (`calc-graph-print`

) command is like `g p`,
except that it sends the output to a printer instead of to the
screen. More precisely, `g p` looks for ``set terminal'`
or ``set output'` commands in the ``*Gnuplot Commands*'` buffer;
lacking these it uses the default settings. However, `g P`
ignores ``set terminal'` and ``set output'` commands and
uses a different set of default values. All of these values are
controlled by the `g D` and `g O` commands discussed below.
Provided everything is set up properly, `g p` will plot to
the screen unless you have specified otherwise and `g P` will
always plot to the printer.

The `g g` (`calc-graph-grid`

) command turns the "grid"
on and off. It is off by default; tick marks appear only at the
edges of the graph. With the grid turned on, dotted lines appear
across the graph at each tick mark. Note that this command only
changes the setting in ``*Gnuplot Commands*'`; to see the effects
of the change you must give another `g p` command.

The `g b` (`calc-graph-border`

) command turns the border
(the box that surrounds the graph) on and off. It is on by default.
This command will only work with GNUPLOT 3.0 and later versions.

The `g k` (`calc-graph-key`

) command turns the "key"
on and off. The key is a chart in the corner of the graph that
shows the correspondence between curves and line styles. It is
off by default, and is only really useful if you have several
curves on the same graph.

The `g N` (`calc-graph-num-points`

) command allows you
to select the number of data points in the graph. This only affects
curves where neither "x" nor "y" is specified as a vector.
Enter a blank line to revert to the default value (initially 15).
With no prefix argument, this command affects only the current graph.
With a positive prefix argument this command changes or, if you enter
a blank line, displays the default number of points used for all
graphs created by `g a` that don't specify the resolution explicitly.
With a negative prefix argument, this command changes or displays
the default value (initially 5) used for 3D graphs created by `g A`.
Note that a 3D setting of 5 means that a total of 5^2 = 25 points
will be computed for the surface.

Data values in the graph of a function are normally computed to a
precision of five digits, regardless of the current precision at the
time. This is usually more than adequate, but there are cases where
it will not be. For example, plotting 1 + x with x in the
interval ``[0 .. 1e-6]'` will round all the data points down
to 1.0! Putting the command ``set precision n'` in the

The `g h` (`calc-graph-header`

) command sets the title
for the graph. This will show up centered above the graph.
The default title is blank (no title).

The `g n` (`calc-graph-name`

) command sets the title of an
individual curve. Like the other curve-manipulating commands, it
affects the most recently added curve, i.e., the last curve on the
list in the ``*Gnuplot Commands*'` buffer. To set the title of
the other curves you must first juggle them to the end of the list
with `g j`, or edit the ``*Gnuplot Commands*'` buffer by hand.
Curve titles appear in the key; if the key is turned off they are
not used.

The `g t` (`calc-graph-title-x`

) and `g T`
(`calc-graph-title-y`

) commands set the titles on the "x"
and "y" axes, respectively. These titles appear next to the
tick marks on the left and bottom edges of the graph, respectively.
Calc does not have commands to control the tick marks themselves,
but you can edit them into the ``*Gnuplot Commands*'` buffer if
you wish. See the GNUPLOT documentation for details.

The `g r` (`calc-graph-range-x`

) and `g R`
(`calc-graph-range-y`

) commands set the range of values on the
"x" and "y" axes, respectively. You are prompted to enter a
suitable range. This should be either a pair of numbers of the
form, `` min:max'`, or a blank line to revert to the
default behavior of setting the range based on the range of values
in the data, or

The `g l` (`calc-graph-log-x`

) and `g L` (`calc-graph-log-y`

)
commands allow you to set either or both of the axes of the graph to
be logarithmic instead of linear.

For 3D plots, `g C-t`, `g C-r`, and `g C-l` (those are
letters with the Control key held down) are the corresponding commands
for the "z" axis.

The `g z` (`calc-graph-zero-x`

) and `g Z`
(`calc-graph-zero-y`

) commands control whether a dotted line is
drawn to indicate the "x" and/or "y" zero axes. (These are the same
dotted lines that would be drawn there anyway if you used `g g` to
turn the "grid" feature on.) Zero-axis lines are on by default, and
may be turned off only in GNUPLOT 3.0 and later versions. They are
not available for 3D plots.

The `g s` (`calc-graph-line-style`

) command turns the connecting
lines on or off for the most recently added curve, and optionally selects
the style of lines to be used for that curve. Plain `g s` simply
toggles the lines on and off. With a numeric prefix argument, `g s`
turns lines on and sets a particular line style. Line style numbers
start at one and their meanings vary depending on the output device.
GNUPLOT guarantees that there will be at least six different line styles
available for any device.

The `g S` (`calc-graph-point-style`

) command similarly turns
the symbols at the data points on or off, or sets the point style.
If you turn both lines and points off, the data points will show as
tiny dots.

Another way to specify curve styles is with the `LineStyles`

and
`PointStyles`

variables. These variables initially have no stored
values, but if you store a vector of integers in one of these variables,
the `g a` and `g f` commands will use those style numbers
instead of the defaults for new curves that are added to the graph.
An entry should be a positive integer for a specific style, or 0 to let
the style be chosen automatically, or *-1* to turn off lines or points
altogether. If there are more curves than elements in the vector, the
last few curves will continue to have the default styles. Of course,
you can later use `g s` and `g S` to change any of these styles.

For example, `'[2 -1 3] RET s t LineStyles` causes the first curve
to have lines in style number 2, the second curve to have no connecting
lines, and the third curve to have lines in style 3. Point styles will
still be assigned automatically, but you could store another vector in
`PointStyles`

to define them, too.

The `g D` (`calc-graph-device`

) command sets the device name
(or "terminal name" in GNUPLOT lingo) to be used by `g p` commands
on this graph. It does not affect the permanent default device name.
If you enter a blank name, the device name reverts to the default.
Enter ``?'` to see a list of supported devices.

With a positive numeric prefix argument, `g D` instead sets
the default device name, used by all plots in the future which do
not override it with a plain `g D` command. If you enter a
blank line this command shows you the current default. The special
name `default`

signifies that Calc should choose `x11`

if
the X window system is in use (as indicated by the presence of a
`DISPLAY`

environment variable), or otherwise `dumb`

under
GNUPLOT 3.0 and later, or `postscript`

under GNUPLOT 2.0.
This is the initial default value.

The `dumb`

device is an interface to "dumb terminals," i.e.,
terminals with no special graphics facilities. It writes a crude
picture of the graph composed of characters like `-`

and `|`

to a buffer called ``*Gnuplot Trail*'`, which Calc then displays.
The graph is made the same size as the Emacs screen, which on most
dumb terminals will be @c{$80\times24$}
80x24 characters. The graph is displayed in
an Emacs "recursive edit"; type `q` or `M-# M-#` to exit
the recursive edit and return to Calc. Note that the `dumb`

device is present only in GNUPLOT 3.0 and later versions.

The word `dumb`

may be followed by two numbers separated by
spaces. These are the desired width and height of the graph in
characters. Also, the device name `big`

is like `dumb`

but creates a graph four times the width and height of the Emacs
screen. You will then have to scroll around to view the entire
graph. In the ``*Gnuplot Trail*'` buffer, `SPC`, `DEL`,
`<`, and `>` are defined to scroll by one screenful in each
of the four directions.

With a negative numeric prefix argument, `g D` sets or displays
the device name used by `g P` (`calc-graph-print`

). This
is initially `postscript`

. If you don't have a PostScript
printer, you may decide once again to use `dumb`

to create a
plot on any text-only printer.

The `g O` (`calc-graph-output`

) command sets the name of
the output file used by GNUPLOT. For some devices, notably `x11`

,
there is no output file and this information is not used. Many other
"devices" are really file formats like `postscript`

; in these
cases the output in the desired format goes into the file you name
with `g O`. Type `g O stdout RET` to set GNUPLOT to write
to its standard output stream, i.e., to ``*Gnuplot Trail*'`.
This is the default setting.

Another special output name is `tty`

, which means that GNUPLOT
is going to write graphics commands directly to its standard output,
which you wish Emacs to pass through to your terminal. Tektronix
graphics terminals, among other devices, operate this way. Calc does
this by telling GNUPLOT to write to a temporary file, then running a
sub-shell executing the command ``cat tempfile >/dev/tty'`. On
typical Unix systems, this will copy the temporary file directly to
the terminal, bypassing Emacs entirely. You will have to type `C-l`
to Emacs afterwards to refresh the screen.

Once again, `g O` with a positive or negative prefix argument
sets the default or printer output file names, respectively. In each
case you can specify `auto`

, which causes Calc to invent a temporary
file name for each `g p` (or `g P`) command. This temporary file
will be deleted once it has been displayed or printed. If the output file
name is not `auto`

, the file is not automatically deleted.

The default and printer devices and output files can be saved
permanently by the `m m` (`calc-save-modes`

) command. The
default number of data points (see `g N`) and the X geometry
(see `g X`) are also saved. Other graph information is *not*
saved; you can save a graph's configuration simply by saving the contents
of the ``*Gnuplot Commands*'` buffer.

If you are installing Calc you may wish to configure the default and
printer devices and output files for the whole system. The relevant
Lisp variables are `calc-gnuplot-default-device`

and `-output`

,
and `calc-gnuplot-print-device`

and `-output`

. The output
file names must be either strings as described above, or Lisp
expressions which are evaluated on the fly to get the output file names.

Other important Lisp variables are `calc-gnuplot-plot-command`

and
`calc-gnuplot-print-command`

, which give the system commands to
display or print the output of GNUPLOT, respectively. These may be
`nil`

if no command is necessary, or strings which can include
``%s'` to signify the name of the file to be displayed or printed.
Or, these variables may contain Lisp expressions which are evaluated
to display or print the output.

The `g x` (`calc-graph-display`

) command lets you specify
on which X window system display your graphs should be drawn. Enter
a blank line to see the current display name. This command has no
effect unless the current device is `x11`

.

The `g X` (`calc-graph-geometry`

) command is a similar
command for specifying the position and size of the X window.
The normal value is `default`

, which generally means your
window manager will let you place the window interactively.
Entering ``800x500+0+0'` would create an 800-by-500 pixel
window in the upper-left corner of the screen.

The buffer called ``*Gnuplot Trail*'` holds a transcript of the
session with GNUPLOT. This shows the commands Calc has "typed" to
GNUPLOT and the responses it has received. Calc tries to notice when an
error message has appeared here and display the buffer for you when
this happens. You can check this buffer yourself if you suspect
something has gone wrong.

The `g C` (`calc-graph-command`

) command prompts you to
enter any line of text, then simply sends that line to the current
GNUPLOT process. The ``*Gnuplot Trail*'` buffer looks deceptively
like a Shell buffer but you can't type commands in it yourself.
Instead, you must use `g C` for this purpose.

The `g v` (`calc-graph-view-commands`

) and `g V`
(`calc-graph-view-trail`

) commands display the ``*Gnuplot Commands*'`
and ``*Gnuplot Trail*'` buffers, respectively, in another window.
This happens automatically when Calc thinks there is something you
will want to see in either of these buffers. If you type `g v`
or `g V` when the relevant buffer is already displayed, the
buffer is hidden again.

One reason to use `g v` is to add your own commands to the
``*Gnuplot Commands*'` buffer. Press `g v`, then use
`C-x o` to switch into that window. For example, GNUPLOT has
``set label'` and ``set arrow'` commands that allow you to
annotate your plots. Since Calc doesn't understand these commands,
you have to add them to the ``*Gnuplot Commands*'` buffer
yourself, then use `g p` to replot using these new commands. Note
that your commands must appear *before* the `plot`

command.
To get help on any GNUPLOT feature, type, e.g., `g C help set label`.
You may have to type `g C RET` a few times to clear the
"press return for more" or "subtopic of ..." requests.
Note that Calc always sends commands (like ``set nolabel'`) to
reset all plotting parameters to the defaults before each plot, so
to delete a label all you need to do is delete the ``set label'`
line you added (or comment it out with ``#'`) and then replot
with `g p`.

You can use `g q` (`calc-graph-quit`

) to kill the GNUPLOT
process that is running. The next graphing command you give will
start a fresh GNUPLOT process. The word ``Graph'` appears in
the Calc window's mode line whenever a GNUPLOT process is currently
running. The GNUPLOT process is automatically killed when you
exit Emacs if you haven't killed it manually by then.

The `g K` (`calc-graph-kill`

) command is like `g q`
except that it also views the ``*Gnuplot Trail*'` buffer so that
you can see the process being killed. This is better if you are
killing GNUPLOT because you think it has gotten stuck.

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