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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 `[0..360]'
and "y" is the formula `xy(sin(t), cos(t))', the resulting graph
will be a circle.
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 x and y values in these calls, and the "x" and "y" values from the input vectors or intervals are used only to specify the range of inputs to the formula. For example, plotting `[0..360], [0..180], xyz(sin(x)*sin(y), cos(x)*sin(y), cos(y))' will draw a sphere. (Since the default resolution for 3D plots is 5 steps in each of "x" and "y", this will draw a very crude sphere. You could use the g N command, described below, to increase this resolution, or specify the "x" and "y" values as vectors with more than 5 elements.
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 `PlotDatan') 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 g a.
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-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