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8.1 Definitions for Plotting |
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Default value: false
When in_netmath
is true
,
plot3d
prints OpenMath output to the console if plot_format
is openmath
;
otherwise in_netmath
(even if true
) has no effect.
in_netmath
has no effect on plot2d
.
Takes a list of curves such as
[[x1, y1, x2, y2, ...], [u1, v1, u2, v2, ...], ..] |
or
[[[x1, y1], [x2, y2], ...], ...] |
and plots them. This is similar to xgraph_curves, but uses the
open plot routines.
Addtional symbol arguments may be given such as
"{xrange -3 4}"
The following plots two curves, using big points, labeling the first one
jim
and the second one jane
.
openplot_curves ([["{plotpoints 1} {pointsize 6} {label jim} {xaxislabel {joe is nice}}"], [1, 2, 3, 4, 5, 6, 7, 8], ["{label jane} {color pink }"], [3, 1, 4, 2, 5, 7]]); |
Some other special keywords are xfun
, color
, plotpoints
, linecolors
,
pointsize
, nolines
, bargraph
, labelposition
, xaxislabel
, and
yaxislabel
.
Displays a plot of one or more expressions as a function of one variable.
In all cases, expr
is an expression to be plotted on the vertical axis as
a function of one variable.
x_range, the range of the horizontal axis,
is a list of the form [variable, min, max]
,
where variable is a variable which appears in expr.
y_range, the range of the vertical axis,
is a list of the form [y, min, max]
.
plot2d (expr, x_range)
plots expr as a function of the variable named in x_range,
over the range specified in x_range.
If the vertical range is not otherwise specified by set_plot_option
,
it is chosen automatically.
All options are assumed to have default values unless otherwise specified by set_plot_option
.
plot2d (expr, x_range, y_range)
plots expr as a function of the variable named in x_range,
over the range specified in x_range.
The vertical range is set to y_range.
All options are assumed to have default values unless otherwise specified by set_plot_option
.
plot2d ([expr_1, ..., expr_n], x_range)
plots expr_1, ..., expr_n as a function of the variable named in x_range,
over the range specified in x_range.
If the vertical range is not otherwise specified by set_plot_option
,
it is chosen automatically.
All options are assumed to have default values unless otherwise specified by set_plot_option
.
plot2d ([expr_1, ..., expr_n], x_range, y_range)
plots expr_1, ..., expr_n as a function of the variable named in x_range,
over the range specified in x_range.
The vertical range is set to y_range.
All options are assumed to have default values unless otherwise specified by set_plot_option
.
When the function to be plotted is a function defined in Maxima by :=
or define
,
or in Lisp by DEFUN or DEFMFUN,
the function can be specified by name.
Functions defined in Lisp by DEFMSPEC, and simplifying functions,
cannot be specified by name;
that includes many built-in functions.
Examples:
Plotting an expression, and setting some commonly-used parameters.
(%i1) plot2d (sin(x), [x, -5, 5])$ (%i2) plot2d (sec(x), [x, -2, 2], [y, -20, 20], [nticks, 200])$ |
Plotting functions by name.
(%i1) F(x) := x^2 $ (%i2) :lisp (defun |$g| (x) (m* x x x)) $g (%i2) H(x) := if x < 0 then x^4 - 1 else 1 - x^5 $ (%i3) plot2d (F, [u, -1, 1])$ (%i4) plot2d ([F, G, H], [u, -1, 1])$ |
Anywhere there may be an ordinary expression, there may be a parametric expression:
parametric_expr is a list of the form
[parametric, x_expr, y_expr, t_range, options]
.
Here x_expr and y_expr are expressions of 1 variable var which is
the first element of the range trange.
The plot is of the path traced out by the pair
[x_expr, y_expr]
as var varies in trange.
In the following example, we plot a circle, then we do the plot with only a few points used, so that we get a star, and finally we plot this together with an ordinary function of X.
Examples:
(%i1) plot2d ([parametric, cos(t), sin(t), [t, -%pi*2, %pi*2], [nticks, 80]])$ |
(%i2) plot2d ([parametric, cos(t), sin(t), [t, -%pi*2, %pi*2], [nticks, 8]])$ |
(%i3) plot2d ([x^3 + 2, [parametric, cos(t), sin(t), [t, -5, 5], [nticks, 80]]], [x, -3, 3])$ |
Discrete expressions may also be used instead or ordinary or
parametric expressions:
discrete_expr is a list of the form
[discrete, x_list, y_list]
or
[discrete, xy_list]
,
where xy_list is a list of [x,y]
pairs.
Examples:
(%i1) xx:makelist(x,x,0,10)$ (%i2) yy:makelist(exp(-x*1.0),x,0,10)$ (%i3) xy:makelist([x,x*x],x,0,5)$ |
(%i4) plot2d([discrete,xx,yy])$ |
(%i5) plot2d([discrete,xy])$ |
(%i6) plot2d([discrete,xx,yy],[gnuplot_curve_styles,["with points"]])$ |
cos(x)
using lines and (xx,yy)
using points.
plot2d([cos(x),[discrete,xx,yy]],[x,0,10],[gnuplot_curve_styles,["with lines","with points pointsize 3"]])$ |
See also plot_options
, which describes plotting options and has more examples.
graphs the list of `point sets' given in list by using xgraph.
A point set may be of the form
[x0, y0, x1, y1, x2, y2, ...] |
or
[[x0, y0], [x1, y1], ...] |
A point set may also contain symbols which give labels or other information.
xgraph_curves ([pt_set1, pt_set2, pt_set3]); |
graph the three point sets as three curves.
pt_set: append (["NoLines: True", "LargePixels: true"], [x0, y0, x1, y1, ...]); |
would make the point set [and subsequent ones], have no lines between points, and to use large pixels. See the man page on xgraph for more options to specify.
pt_set: append ([concat ("\"", "x^2+y")], [x0, y0, x1, y1, ...]); |
would make there be a "label" of "x^2+y" for this particular
point set. The "
at the beginning is what tells
xgraph this is a label.
pt_set: append ([concat ("TitleText: Sample Data")], [x0, ...])$ |
would make the main title of the plot be "Sample Data" instead of "Maxima Plot".
To make a bar graph with bars which are 0.2 units wide, and to plot two possibly different such bar graphs:
xgraph_curves ([append (["BarGraph: true", "NoLines: true", "BarWidth: .2"], create_list ([i - .2, i^2], i, 1, 3)), append (["BarGraph: true", "NoLines: true", "BarWidth: .2"], create_list ([i + .2, .7*i^2], i, 1, 3))]); |
A temporary file `xgraph-out' is used.
Elements of this list state the default options for plotting.
If an option is present in a plot2d
or plot3d
call,
that value takes precedence over the default option.
Otherwise, the value in plot_options
is used.
Default options are assigned by set_plot_option
.
Each element of plot_options
is a list of two or more items.
The first item is the name of an option, and the remainder comprises the value or values
assigned to the option.
In some cases the, the assigned value is a list, which may comprise several items.
The plot options which are recognized by plot2d
and plot3d
are the following:
plot_format
determines which plotting package is used by plot2d
and plot3d
.
gnuplot
Gnuplot is the default, and most advanced, plotting package. It
requires an external gnuplot installation.
mgnuplot
Mgnuplot is a Tk-based wrapper around gnuplot. It is included in the
Maxima distribution. Mgnuplot offers a rudimentary GUI for gnuplot,
but has fewer overall features than the plain gnuplot
interface. Mgnuplot requires an external gnuplot installation and
Tcl/Tk.
openmath
Openmath is a Tcl/Tk GUI plotting program. It is included in the
Maxima distribution.
ps
Generates simple PostScript files directly from
Maxima. Much more sophisticated PostScript output can be generated from gnuplot,
by leaving the option plot_format
unspecified (to accept the default),
and setting the option gnuplot_term
to ps
.
run_viewer
controls whether or not the appropriate viewer for the plot
format should be run.
true
Execute the viewer program.
false
Do not execute the viewer program.
gnuplot_term
Sets the output terminal type for gnuplot.
default
Gnuplot output is displayed in a separate graphical window.
dumb
Gnuplot output is displayed in the Maxima console by an "ASCII art" approximation to graphics.
ps
Gnuplot generates commands in the PostScript page description language.
If the option
gnuplot_out_file
is set to filename, gnuplot writes the PostScript commands to filename.
Otherwise, the commands are printed to the Maxima console.
gnuplot_out_file
Write gnuplot output to a file.
false
No output file specified.
[gnuplot_out_file, "myplot.ps"]
This example sends PostScript output to the file myplot.ps
when
used in conjunction with the PostScript gnuplot terminal.
x
The default horizontal range.
[x, - 3, 3] |
Sets the horizontal range to [-3, 3].
y
The default vertical range.
[y, - 3, 3] |
Sets the vertical range to [-3, 3].
t
The default range for the parameter in parametric plots.
[t, 0, 10] |
Sets the parametric variable range to [0, 10].
nticks
Initial number of points
used by the adaptive plotting routine.
[nticks, 20] |
The default for nticks
is 10.
adapt_depth
The maximum number of splittings used by the adaptive plotting routine.
[adapt_depth, 5] |
The default for adapt_depth
is 10.
grid
Sets the number of grid points to use in the x- and y-directions
for three-dimensional plotting.
[grid, 50, 50] |
sets the grid to 50 by 50 points. The default grid is 30 by 30.
transform_xy
Allows transformations to be applied to three-dimensional plots.
[transform_xy, false] |
The default transform_xy
is false
. If it is not false
, it should be
the output of
make_transform ([x, y, z], f1(x, y, z), f2(x, y, z), f3(x, y, z))$ |
The polar_xy
transformation is built in. It gives the same
transformation as
make_transform ([r, th, z], r*cos(th), r*sin(th), z)$ |
colour_z
is specific to the ps
plot format.
[colour_z, true] |
The default value for colour_z
is false
.
view_direction
Specific to the ps
plot format.
[view_direction, 1, 1, 1] |
The default view_direction
is [1, 1, 1].
There are several plot options specific to gnuplot.
All of these options (except gnuplot_pm3d
) are raw
gnuplot commands, specified as strings. Refer to the gnuplot documentation for more details.
gnuplot_pm3d
Controls the usage PM3D mode, which has advanced 3D
features. PM3D is only available in gnuplot versions after 3.7. The
default value for gnuplot_pm3d
is false
.
Example:
[gnuplot_pm3d, true] |
gnuplot_preamble
Inserts gnuplot commands before the plot is
drawn. Any valid gnuplot commands may be used. Multiple commands
should be separated with a semi-colon. The example shown produces a
log scale plot. The default value for gnuplot_preamble
is the empty string ""
.
Example:
[gnuplot_preamble, "set log y"] |
gnuplot_curve_titles
Controls the titles given in the plot key. The
default value is [default]
, which automatically sets the title of each
curve to the function plotted. If not [default]
, gnuplot_curve_titles
should contain a list of strings,
each of which is "title 'title_string'"
.
(To disable the plot key, add "set nokey"
to gnuplot_preamble
.)
Example:
[gnuplot_curve_titles, ["title 'My first function'", "title 'My second function'"]] |
gnuplot_curve_styles
A list of strings controlling the appearance
of curves, i.e., color, width, dashing, etc., to be sent to the
gnuplot plot command. The default value is
["with lines 3", "with lines 1", "with lines 2", "with lines 5", "with lines 4", "with lines 6", "with lines 7"]
, which cycles through different colors. See the
gnuplot documentation for plot
for more information.
Example:
[gnuplot_curve_styles, ["with lines 7", "with lines 2"]] |
gnuplot_default_term_command
The gnuplot command to set the
terminal type for the default terminal. The default value is the empty string ""
,
i.e., use gnuplot's default.
Example:
[gnuplot_default_term_command, "set term x11"] |
gnuplot_dumb_term_command
The gnuplot command to set the
terminal type for the dumb terminal. The default value is "set term dumb 79 22"
,
which makes the text output 79 characters by 22
characters.
Example:
[gnuplot_dumb_term_command, "set term dumb 132 50"] |
gnuplot_ps_term_command
The gnuplot command to set the terminal
type for the PostScript terminal. The default value is
"set size 1.5, 1.5;set term postscript eps enhanced color solid 24"
,
which sets the
size to 1.5 times gnuplot's default, and the font size to 24, among
other things. See the gnuplot documentation for set term postscript
for more information.
Example:
[gnuplot_ps_term_command, "set term postscript eps enhanced color solid 18"] |
Examples:
sin(x)
to the file sin.eps
.
plot2d (sin(x), [x, 0, 2*%pi], [gnuplot_term, ps], [gnuplot_out_file, "sin.eps"])$ |
plot2d ([gamma(x), 1/gamma(x)], [x, -4.5, 5], [y, -10, 10], [gnuplot_preamble, "set key bottom"])$ |
gnuplot_preamble
to produce fancy x-axis labels.
(Note that the gnuplot_preamble
string must be entered without any line breaks.)
my_preamble: "set xzeroaxis; set xtics ('-2pi' -6.283, '-3pi/2' -4.712, '-pi' -3.1415, '-pi/2' -1.5708, '0' 0,'pi/2' 1.5708, 'pi' 3.1415,'3pi/2' 4.712, '2pi' 6.283)"$ plot2d ([cos(x), sin(x), tan(x), cot(x)], [x, -2*%pi, 2*%pi], [y, -2, 2], [gnuplot_preamble, my_preamble]); |
gnuplot_preamble
to produce fancy x-axis labels,
and produces PostScript
output that takes advantage of the advanced text formatting available
in gnuplot.
(Note that the gnuplot_preamble
string must be entered without any line breaks.)
my_preamble: "set xzeroaxis; set xtics ('-2{/Symbol p}' -6.283, '-3{/Symbol p}/2' -4.712, '-{/Symbol p}' -3.1415, '-{/Symbol p}/2' -1.5708, '0' 0,'{/Symbol p}/2' 1.5708, '{/Symbol p}' 3.1415,'3{/Symbol p}/2' 4.712, '2{/Symbol p}' 6.283)"$ plot2d ([cos(x), sin(x), tan(x)], [x, -2*%pi, 2*%pi], [y, -2, 2], [gnuplot_preamble, my_preamble], [gnuplot_term, ps], [gnuplot_out_file, "trig.eps"]); |
plot3d (atan (-x^2 + y^3/4), [x, -4, 4], [y, -4, 4], [grid, 50, 50], [gnuplot_pm3d, true])$ |
my_preamble: "set pm3d at s;unset surface;set contour;set cntrparam levels 20;unset key"$ plot3d (atan (-x^2 + y^3/4), [x, -4, 4], [y, -4, 4], [grid, 50, 50], [gnuplot_pm3d, true], [gnuplot_preamble, my_preamble])$ |
gnuplot_preamble
string must be entered without any line breaks.)
plot3d (cos (-x^2 + y^3/4), [x, -4, 4], [y, -4, 4], [gnuplot_preamble, "set view map; unset surface"], [gnuplot_pm3d, true], [grid, 150, 150])$ |
Displays a plot of one or three expressions as functions of two variables.
plot3d (2^(-u^2 + v^2), [u, -5, 5], [v, -7, 7]); |
plots z = 2^(-u^2+v^2)
with u
and v
varying in [-5,5] and
[-7,7] respectively, and with u on the x axis, and v
on the y axis.
An example of the third pattern of arguments is
plot3d ([cos(x)*(3 + y*cos(x/2)), sin(x)*(3 + y*cos(x/2)), y*sin(x/2)], [x, -%pi, %pi], [y, -1, 1], ['grid, 50, 15]); |
which plots a Moebius band, parametrized by the three expressions given
as the first argument to plot3d
. An additional optional argument
['grid, 50, 15]
gives the grid number of rectangles in the x direction and
y direction.
When the function to be plotted is a function defined in Maxima by :=
or define
,
or in Lisp by DEFUN or DEFMFUN,
the function can be specified by name.
Functions defined in Lisp by DEFMSPEC, and simplifying functions,
cannot be specified by name;
that includes many built-in functions.
This example shows a plot of the real part of z^1/3
.
plot3d (r^.33*cos(th/3), [r, 0, 1], [th, 0, 6*%pi], ['grid, 12, 80], ['plot_format, ps], ['transform_xy, polar_to_xy], ['view_direction, 1, 1, 1.4], ['colour_z, true]); |
Here the view_direction
option indicates the direction from which we
take a projection. We actually do this from infinitely far away,
but parallel to the line from view_direction
to the origin. This
is currently only used in ps
plot_format, since the other viewers
allow interactive rotating of the object.
Another example is a Klein bottle:
expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y) + 3.0) - 10.0; expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y) + 3.0); expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y)); plot3d ([expr_1, expr_2, expr_3], [x, -%pi, %pi], [y, -%pi, %pi], ['grid, 40, 40]); |
or a torus
expr_1: cos(y)*(10.0+6*cos(x)); expr_2: sin(y)*(10.0+6*cos(x)); expr_3: -6*sin(x); plot3d ([expr_1, expr_2, expr_3], [x, 0, 2*%pi], [y, 0, 2*%pi], ['grid, 40, 40]); |
We can output to gnuplot too:
plot3d (2^(x^2 - y^2), [x, -1, 1], [y, -2, 2], [plot_format, gnuplot]); |
Sometimes you may need to define a function to plot the expression. All the arguments to plot3d are evaluated before being passed to plot3d, and so trying to make an expression which does just what you want may be difficult, and it is just easier to make a function.
M: matrix([1, 2, 3, 4], [1, 2, 3, 2], [1, 2, 3, 4], [1, 2, 3, 3])$ f(x, y) := float (M [?round(x), ?round(y)])$ plot3d (f, [x, 1, 4], [y, 1, 4], ['grid, 4, 4])$ |
See plot_options
for more examples.
Returns a function suitable for the transform function in plot3d. Use
with the plot option transform_xy
.
make_transform ([r, th, z], r*cos(th), r*sin(th), z)$ |
is a transformation to polar coordinates.
Writes to pstream a sequence of PostScript commands which plot expr over range.
expr is an expression.
range is a list of the form [x, min, max]
in which x is a variable which appears in expr.
See also closeps
.
This should usually becalled at the end of a sequence of plotting
commands. It closes the current output stream pstream, and sets
it to nil. It also may be called at the start of a plot, to ensure
pstream is closed if it was open. All commands which write to
pstream, open it if necessary. closeps
is separate from the other
plotting commands, since we may want to plot 2 ranges or superimpose
several plots, and so must keep the stream open.
Assigns one of the global variables for plotting.
option is specified as a list of two or more elements,
in which the first element is one of the keywords
on the plot_options
list.
set_plot_option
evaluates its argument.
set_plot_option
returns plot_options
(after modifying one of its elements).
See also plot_options
, plot2d
, and plot3d
.
Examples:
Modify the grid
and x
values.
When a plot_options
keyword has an assigned value,
quote it to prevent evaluation.
(%i1) set_plot_option ([grid, 30, 40]); (%o1) [[x, - 1.755559702014E+305, 1.755559702014E+305], [y, - 1.755559702014E+305, 1.755559702014E+305], [t, - 3, 3], [grid, 30, 40], [view_direction, 1, 1, 1], [colour_z, false], [transform_xy, false], [run_viewer, true], [plot_format, gnuplot], [gnuplot_term, default], [gnuplot_out_file, false], [nticks, 10], [adapt_depth, 10], [gnuplot_pm3d, false], [gnuplot_preamble, ], [gnuplot_curve_titles, [default]], [gnuplot_curve_styles, [with lines 3, with lines 1, with lines 2, with lines 5, with lines 4, with lines 6, with lines 7]], [gnuplot_default_term_command, ], [gnuplot_dumb_term_command, set term dumb 79 22], [gnuplot_ps_term_command, set size 1.5, 1.5;set term postscript # eps enhanced color solid 24]] (%i2) x: 42; (%o2) 42 (%i3) set_plot_option (['x, -100, 100]); (%o3) [[x, - 100.0, 100.0], [y, - 1.755559702014E+305, 1.755559702014E+305], [t, - 3, 3], [grid, 30, 40], [view_direction, 1, 1, 1], [colour_z, false], [transform_xy, false], [run_viewer, true], [plot_format, gnuplot], [gnuplot_term, default], [gnuplot_out_file, false], [nticks, 10], [adapt_depth, 10], [gnuplot_pm3d, false], [gnuplot_preamble, ], [gnuplot_curve_titles, [default]], [gnuplot_curve_styles, [with lines 3, with lines 1, with lines 2, with lines 5, with lines 4, with lines 6, with lines 7]], [gnuplot_default_term_command, ], [gnuplot_dumb_term_command, set term dumb 79 22], [gnuplot_ps_term_command, set size 1.5, 1.5;set term postscript # eps enhanced color solid 24]] |
Draws a curve connecting the points in ptlist. The latter
may be of the form [x0, y0, x1, y1, ...]
or [[x0, y0], [x1, y1], ...]
The function join
is handy for taking a list of x's and a
list of y's and splicing them together.
psdraw_curve simply invokes the more primitive function pscurve. Here is the definition:
(defun $psdraw_curve (lis) (p "newpath") ($pscurve lis) (p "stroke")) |
cmd is inserted in the PostScript file. Example:
pscom ("4.5 72 mul 5.5 72 mul translate 14 14 scale"); |
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