Basic Graphics
==============

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 Evaluates-To Operator, for a handy way to keep tabs on the
current value of `PlotRejects'.  See 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.