gnuplotlib 0.10

Gnuplot-based plotting for numpy

* NAME
gnuplotlib: a gnuplot-based plotting backend for numpy

* SYNOPSIS

#+BEGIN_SRC python
import numpy as np
import gnuplotlib as gp

x = np.arange(101) - 50
gp.plot(x**2)
[ basic parabola plot pops up ]


g1 = gp.gnuplotlib(title = 'Parabola with error bars',
_with = 'xyerrorbars')
g1.plot( x**2 * 10, np.abs(x)/10, np.abs(x)*5,
legend = 'Parabola',
tuplesize = 4 )
[ parabola with x,y errobars pops up in a new window ]


x,y = np.ogrid[-10:11,-10:11]
gp.plot( x**2 + y**2,
title = 'Heat map',
unset = 'grid',
cmds = 'set view map',
_with = 'image',
tuplesize = 3)
[ Heat map pops up where first parabola used to be ]


theta = np.linspace(0, 6*np.pi, 200)
z = np.linspace(0, 5, 200)
g2 = gp.gnuplotlib(_3d = True)
g2.plot( np.cos(theta),
np.vstack((np.sin(theta), -np.sin(theta))),
z )
[ Two 3D spirals together in a new window ]
#+END_SRC


* DESCRIPTION

This module allows numpy data to be plotted using Gnuplot as a backend. As much
as was possible, this module acts as a passive pass-through to Gnuplot, thus
making available the full power and flexibility of the Gnuplot backend. Gnuplot
is described in great detail at its upstream website: http://www.gnuplot.info

gnuplotlib has an object-oriented interface (via class gnuplotlib) and a few
helper class-less functions (plot(), plot3d(), plotimage()). Each instance of
class gnuplotlib has a gnuplot process associated with it, which has (usually) a
plot window to go with it. If multiple simultaneous plot windows are desired,
create a separate class gnuplotlib object for each.

The helper functions reuse a single global gnuplotlib instance, so each such
invocation rewrites over the previous gnuplot window.

When making a plot with the object-oriented interface, the gnuplotlib object is
created with a set of plot options, then the plot is made by passing it curves,
possibly with some curve options per curve. Something like this:

#+BEGIN_SRC python
import gnuplotlib as gp
g = gp.gnuplotlib(plot_options)
g.plot( curve, curve, .... )
#+END_SRC

A call to plot(...) is simpler:

#+BEGIN_SRC python
import gnuplotlib as gp
gp.plot( curve, curve, ...., plot_and_default_curve_options )
#+END_SRC

plot3d(...) simply calls plot(...) with an extra plot option _3d=True.
plotimage(...) simply calls plot(...) with extra plot options _with='image',
tuplesize=3.

If just a single curve is plotted, 'curve' can simply be a sequence of numpy
arrays representing coordinates of each point. For instance:

#+BEGIN_SRC python
plot( x, y )
#+END_SRC

If multiple curves are to be drawn on the same plot, then each 'curve' must live
in a separate tuple. The last element of any such tuple can be a dict of curve
options, if desired. For instance:

#+BEGIN_SRC python
plot( (x1,y1),
(x2,y2, {'legend'='Second curve'}) )
#+END_SRC

The plot_and_default_curve_options passed to plot(...) are kwargs. The curve
options present here are used as defaults for each curve; these defaults can be
overriden as desired. For instance:

#+BEGIN_SRC python
plot( (x1,y1),
(x2,y2, {'with':'points'}),
_with='lines')
#+END_SRC

would plot the first curve with lines, but the second with points.

** Options arguments

Plot generation is controlled by two sets of options:

- Plot options: parameters that affect the whole plot, like the title of the
plot, the axis labels, the extents, 2d/3d selection, etc. All the plot options
are described below in "Plot options".

- Curve options: parameters that affect only a single curve. Each is described
below in "Curve options".

** Data arguments

The 'curve' arguments in the plot(...) argument list represent the actual data
being plotted. Each output data point is a tuple (set of values, not a python
"tuple") whose size varies depending on what is being plotted. For example if
we're making a simple 2D x-y plot, each tuple has 2 values; if we're making a 3d
plot with each point having variable size and color, each tuple has 5 values
(x,y,z,size,color). In the plot(...) argument list each tuple element must be
passed separately. If we're making anything fancier than a simple 2D or 3D plot
(2- and 3- tuples respectively) then the 'tuplesize' curve option MUST be passed
in.

Furthermore, broadcasting is fully supported, so multiple curves can be plotted
by stacking data inside the passed-in arrays. Broadcasting works across curve
options also, so things like curve labels and styles can also be stacked inside
arrays. An example:

#+BEGIN_SRC python
th = np.linspace(0, 6*np.pi, 200)
z = np.linspace(0, 5, 200)
size = 0.5 + np.abs(np.cos(th))
color = np.sin(2*th)


# without broadcasting:
plot3d( ( np.cos(th), np.sin(th)
z, size, color,
{ 'legend': 'spiral 1'}),

( -np.cos(th), -np.sin(th)
z, size, color,
{ 'legend': 'spiral 2'})

title = 'double helix', tuplesize = 5,
_with = 'points pointsize variable pointtype 7 palette' )


# identical plot using broadcasting:
plot3d( ( np.cos(th) * np.array([[1,-1]]).T,
np.sin(th) * np.array([[1,-1]]).T,
z, size, color, { 'legend': np.array(('spiral 1', 'spiral 2'))})

title = 'double helix', tuplesize = 5,
_with = 'points pointsize variable pointtype 7 palette' )
#+END_SRC

This is a 3d plot with variable size and color. There are 5 values in the tuple,
which we specify. The first 2 arrays have dimensions (2,N); all the other arrays
have a single dimension. Thus the broadcasting rules generate 2 distinct curves,
with varying values for x,y and identical values for z, size and color. We label
the curves differently by passing an array for the 'legend' curve option. This
array contains strings, and is broadcast like everything else.

*** Implicit domains

When a particular tuplesize is specified, gnuplotlib will attempt to read that
many arrays. If there aren't enough arrays available, gnuplotlib will throw an
error, unless an implicit domain can be used. This happens if we are EXACTLY 1
or 2 arrays short (usually when making 2D and 3D plots respectively).

When making a simple 2D plot, if exactly 1 dimension is missing, gnuplotlib will
use numpy.arange(N) as the domain. This is why code like

#+BEGIN_SRC python
plot(numpy.array([1,5,3,4,4]))
#+END_SRC

works. Only one array is given here, but the default tuplesize is 2, and we are
thus exactly 1 array short. This is thus equivalent to

#+BEGIN_SRC python
plot(numpy.arange(5), numpy.array([1,5,3,4,4]) )
#+END_SRC

If plotting in 3D, an implicit domain will be used if we are exactly 2 arrayss
short. In this case, gnuplotlib will use a 2D grid as a domain. Example:

#+BEGIN_SRC python
xy = numpy.arange(21*21).reshape(21*21)
plot( xy, _with = 'points', _3d=True)
#+END_SRC

Here the only given array has dimensions (21,21). This is a 3D plot, so we are
exactly 2 arrays short. Thus, gnuplotlib generates an implicit domain,
corresponding to a 21-by-21 grid.

Note that while the DEFAULT tuplesize depends on whether we're making a 3d plot,
once we have a tuplesize, the logic doesn't care if a 3d plot is being made. It
can make sense to have a 2D implicit domain when making 2D plots. For example,
one can be plotting a color map:

#+BEGIN_SRC python
x,y = np.ogrid[-10:11,-10:11]
gp.plot( x**2 + y**2,
title = 'Heat map',
set = 'view map',
_with = 'image',
tuplesize = 3)
#+END_SRC

Also note that the 'tuplesize' curve option is independent of implicit domains.
This option specifies not how many data arrays we have, but how many values
represent each data point. For example, if we want a 2D line plot with varying
colors plotted with an implicit domain, set tuplesize=3 as before (x,y,color),
but pass in only 2 arrays (y, color).

** Symbolic equations

Gnuplot can plot both data and equations. This module exists largely for the
data-plotting case, but sometimes it can be useful to plot equations together
with some data. This is supported by the 'equation' plot option. This plot
option is either a string (for a single equation) or a list/tuple containing
multiple strings for multiple equations. Note that plotting only equations
without data is not supported (and generally is better done with gnuplot
directly). An example:

#+BEGIN_SRC python
import numpy as np
import numpy.random as nr
import numpy.linalg
import gnuplotlib as gp

# generate data
x = np.arange(100)
c = np.array([1, 1800, -100, 0.8]) # coefficients
m = x[:, np.newaxis] ** np.arange(4) # 1, x, x**2, ...
noise = 1e4 * nr.random(x.shape)
y = np.dot( m, c) + noise # polynomial corrupted by noise

c_fit = np.dot(numpy.linalg.pinv(m), y) # coefficients obtained by a curve fit

# generate a string that describes the curve-fitted equation
fit_equation = '+'.join( '{} * {}'.format(c,m) for c,m in zip( c_fit.tolist(), ('x**0','x**1','x**2','x**3')))

# plot the data points and the fitted curve
gp.plot(x, y, _with='points', equation = fit_equation)
#+END_SRC

Here I generated some data, performed a curve fit to it, and plotted the data
points together with the best-fitting curve. Here the best-fitting curve was
plotted by gnuplot as an equation, so gnuplot was free to choose the proper
sampling frequency. And as we zoom around the plot, the sampling frequency is
adjusted to keep things looking nice.

Note that the various styles and options set by the other options do NOT apply
to these equation plots. Instead, the string is passed to gnuplot directly, and
any styling can be applied there. For instance, to plot a parabola with thick
lines, you can issue

#+BEGIN_SRC python
gp.plot( ....., equation = 'x**2 with lines linewidth 2')
#+END_SRC

As before, see the gnuplot documentation for details. You can also do fancy
things:

#+BEGIN_SRC python
x = np.arange(100, dtype=float) / 100 * np.pi * 2;
c,s = np.cos(x), np.sin(x)

gp.plot( c,s,
square=1, _with='points',
set = ('parametric', 'trange [0:2*3.14]'),
equation = "sin(t),cos(t)" )
#+END_SRC

Here the data are points evently spaced around a unit circle. Along with these
points we plot a unit circle as a parametric equation.

** Interactivity

The graphical backends of Gnuplot are interactive, allowing the user to pan,
zoom, rotate and measure the data in the plot window. See the Gnuplot
documentation for details about how to do this. Some terminals (such as wxt) are
persistently interactive, and the rest of this section does not apply to them.
Other terminals (such as x11) have the downside described here.

When using an affected terminal, interactivity is only possible if the gnuplot
process is running. As long as the python program calling gnuplotlib is running,
the plots are interactive, but once it exits, the child gnuplot process will
exit also. This will keep the plot windows up, but the interactivity will be
lost. So if the python program makes a plot and exits, the plot will NOT be
interactive.


* OPTIONS

** Plot options

The plot options are a dictionary, passed as the keyword arguments to the global
plot() function or as the only arguments to the gnuplotlib contructor. The
supported keys of this dict are as follows:

- title

Specifies the title of the plot

- 3d

If true, a 3D plot is constructed. This changes the default tuple size from 2 to
3

- _3d

Identical to '3d'. In python, keyword argument keys cannot start with a number,
so '_3d' is accepted for that purpose. Same issue exists with with/_with

- set/unset

These take either a string of a list. If given a string, a set or unset gnuplot
command is executed with that argument. If given a list, elements of that list
are set/unset separately. Example:

#+BEGIN_SRC python
plot(..., set='grid', unset=['xtics', 'ytics])
[ turns on the grid, turns off the x and y axis tics ]
#+END_SRC

- with

If no 'with' curve option is given, use this as a default. See the description
of the 'with' curve option for more detail

- _with

Identical to 'with'. In python 'with' is a reserved word so it is illegal to use
it as a keyword arg key, so '_with' exists as an alias. Same issue exists with
3d/_3d

- square, square_xy

If true, these request a square aspect ratio. For 3D plots, square_xy plots with
a square aspect ratio in x and y, but scales z. Using either of these in 3D
requires Gnuplot >= 4.4

- {x,y,y2,z,cb}{min,max,range,inv}

If given, these set the extents of the plot window for the requested axes.
Either min/max or range can be given but not both. min/max are numerical values.
'*range' is a string 'min:max' with either one allowed to be omitted; it can
also be a [min,max] tuple or list. '*inv' is a boolean that reverses this axis.
If the bounds are known, this can also be accomplished by setting max < min.

The y2 axis is the secondary y-axis that is enabled by the 'y2' curve option.
The 'cb' axis represents the color axis, used when color-coded plots are being
generated

- xlabel, ylabel, zlabel, y2label

These specify axis labels

- equation

This option allows equations represented as formula strings to be plotted along
with data passed in as numpy arrays. This can be a string (for a single
equation) or an array/tuple of strings (for multiple equations). See the
"Symbolic equations" section above.

- hardcopy

Instead of drawing a plot on screen, plot into a file instead. The output
filename is the value associated with this key. The output format is inferred
from the filename. Currently only eps, ps, pdf, png, svg are supported with some
default sets of options. This option is simply a shorthand for the 'terminal'
and 'output' options. If the defaults provided by the 'hardcopy' option are
insufficient, use 'terminal' and 'output' manually. Example:

#+BEGIN_SRC python
plot(..., hardcopy="plot.pdf")
[ Plots into that file ]
#+END_SRC

- terminal

Selects the gnuplot terminal (backend). This determines how Gnuplot generates
its output. Common terminals are 'x11', 'qt', 'pdf', 'dumb' and so on. See the
Gnuplot docs for all the details.

- output

Sets the plot output file. You generally only need to set this if you're
generating a hardcopy, such as a PDF.

There are several gnuplot terminals that are known (at this time) to be
interactive: "x11", "qt" and so on. For these no "output" setting is desired.
For noninteractive terminals ("pdf", "dumb" and so on) the output will go to the
file defined here. If this plot option isn't defined or set to the empty string,
the output will be redirected to the standard output of the python process
calling gnuplotlib.

#+BEGIN_SRC python
gp.plot( np.linspace(-5,5,30)**2,
unset='grid', terminal='dumb 80 40' )
#+END_SRC

#+BEGIN_EXAMPLE
25 A-+---------+-----------+-----------+----------+-----------+---------A-+
* + + + + + * +
|* * |
|* * |
| * * |
| A A |
| * * |
20 +-+ * * +-+
| * * |
| A A |
| * * |
| * * |
| * * |
| A A |
15 +-+ * * +-+
| * * |
| * * |
| A A |
| * * |
| * * |
| A A |
10 +-+ * * +-+
| * * |
| A A |
| * * |
| * * |
| A A |
| * * |
5 +-+ A A +-+
| * ** |
| A** A |
| * |
| A* *A |
| A* *A |
+ + + A** + *A* + + +
0 +-+---------+-----------+------A*A**A*A--------+-----------+---------+-+
0 5 10 15 20 25 30
#+END_EXAMPLE

- cmds

Arbitrary extra commands to pass to gnuplot before the plots are created. These
are passed directly to gnuplot, without any validation. The value is either a
string of a list of strings, one per command

- dump

Used for debugging. If true, writes out the gnuplot commands to STDOUT instead
of writing to a gnuplot process. Useful to see what commands would be sent to
gnuplot. This is a dry run. Note that this dump will contain binary data unless
ascii-only plotting is enabled (see below). This is also useful to generate
gnuplot scripts since the dumped output can be sent to gnuplot later, manually
if desired.

- log

Used for debugging. If true, writes out the gnuplot commands and various
progress logs to STDERR in addition to writing to a gnuplot process. This is NOT
a dry run: data is sent to gnuplot AND to the log. Useful for debugging I/O
issues. Note that this log will contain binary data unless ascii-only plotting
is enabled (see below)

- ascii

If set, ASCII data is passed to gnuplot instead of binary data. Binary is the
default because it is much more efficient (and thus faster). Binary input works
for most plots, but not for all of them. An example where binary plotting
doesn't work is 'with labels', and this option exists to force ASCII
communication


** Curve options

The curve options describe details of specific curves. They are in a dict, whose
keys are as follows:

- legend

Specifies the legend label for this curve

- with

Specifies the style for this curve. The value is passed to gnuplot using its
'with' keyword, so valid values are whatever gnuplot supports. Read the gnuplot
documentation for the 'with' keyword for more information

- _with

Identical to 'with'. In python 'with' is a reserved word so it is illegal to use
it as a keyword arg key, so '_with' exists as an alias

- y2

If true, requests that this curve be plotted on the y2 axis instead of the main y axis

- tuplesize

Specifies how many values represent each data point. For 2D plots this defaults
to 2; for 3D plots this defaults to 3. These defaults are correct for simple
plots


* INTERFACE

** class gnuplotlib

A gnuplotlib object abstracts a gnuplot process and a plot window. Invocation:

#+BEGIN_SRC python
import gnuplotlib as gp
g = gp.gnuplotlib(plot_options)
g.plot( curve, curve, .... )
#+END_SRC

The plot options are passed into the constructor; the curve options and the data
are passed into the plot() method. One advantage of making plots this way is
that there's a gnuplot process associated with each gnuplotlib instance, so as
long as the object exists, the plot will be interactive. Calling 'g.plot()'
multiple times reuses the plot window instead of creating a new one.

** global plot(...)

The convenience plotting routine in gnuplotlib. Invocation:

#+BEGIN_SRC python
import gnuplotlib as gp
gp.plot( curve, curve, ...., plot_and_default_curve_options )
#+END_SRC

Each 'plot()' call reuses the same window.

** global plot3d(...)

Generates 3D plots. Shorthand for 'plot(..., _3d=True)'

** global plotimage(...)

Generates an image plot. Shorthand for 'plot(..., _with='image', tuplesize=3)'


* RECIPES

Some different plots appear here. A longer set of demos is given in demos.py.

** 2D plotting

If we're plotting y-values sequentially (implicit domain), all you need is

#+BEGIN_SRC python
plot(y)
#+END_SRC

If we also have a corresponding x domain, we can plot y vs. x with

#+BEGIN_SRC python
plot(x, y)
#+END_SRC

*** Simple style control

To change line thickness:

#+BEGIN_SRC python
plot(x,y, _with='lines linewidth 3')
#+END_SRC

To change point size and point type:

#+BEGIN_SRC python
gp.plot(x,y, _with='points pointtype 4 pointsize 8')
#+END_SRC

Everything (like _with) feeds directly into Gnuplot, so look at the Gnuplot docs
to know how to change thicknesses, styles and such.

*** Errorbars

To plot errorbars that show y +- 1, plotted with an implicit domain

#+BEGIN_SRC python
plot( y, np.ones(y.shape), _with = 'yerrorbars', tuplesize = 3 )
#+END_SRC

Same with an explicit x domain:

#+BEGIN_SRC python
plot( x, y, np.ones(y.shape), _with = 'yerrorbars', tuplesize = 3 )
#+END_SRC

Symmetric errorbars on both x and y. x +- 1, y +- 2:

#+BEGIN_SRC python
plot( x, y, np.ones(x.shape), 2*np.ones(y.shape), _with = 'xyerrorbars', tuplesize = 4 )
#+END_SRC

To plot asymmetric errorbars that show the range y-1 to y+2 (note that here you
must specify the actual errorbar-end positions, NOT just their deviations from
the center; this is how Gnuplot does it)

#+BEGIN_SRC python
plot( y, y - np.ones(y.shape), y + 2*np.ones(y.shape),
_with = 'yerrorbars', tuplesize = 4 )
#+END_SRC

*** More multi-value styles

Plotting with variable-size circles (size given in plot units, requires Gnuplot >= 4.4)

#+BEGIN_SRC python
plot(x, y, radii,
_with = 'circles', tuplesize = 3)
#+END_SRC

Plotting with an variably-sized arbitrary point type (size given in multiples of
the "default" point size)

#+BEGIN_SRC python
plot(x, y, sizes,
_with = 'points pointtype 7 pointsize variable', tuplesize = 3 )
#+END_SRC

Color-coded points

#+BEGIN_SRC python
plot(x, y, colors,
_with = 'points palette', tuplesize = 3 )
#+END_SRC

Variable-size AND color-coded circles. A Gnuplot (4.4.0) quirk makes it
necessary to specify the color range here

#+BEGIN_SRC python
plot(x, y, radii, colors,
cbmin = mincolor, cbmax = maxcolor,
_with = 'circles palette', tuplesize = 4 )
#+END_SRC


Broadcasting example: the Conchoids of de Sluze. The whole family of curves is
generated all at once, and plotted all at once with broadcasting. Broadcasting
is also used to generate the labels. Generally these would be strings, but here
just printing the numerical value of the parameter is sufficient.

#+BEGIN_SRC python
theta = np.linspace(0, 2*np.pi, 1000) # dim=( 1000,)
a = np.arange(-4,3)[:, np.newaxis] # dim=(7,1)

gp.plot( theta,
1./np.cos(theta) + a*np.cos(theta), # broadcasted. dim=(7,1000)

_with = 'lines',
set = 'polar',
square = True,
yrange = [-5,5],
legend = a.ravel() )
#+END_SRC

** 3D plotting

General style control works identically for 3D plots as in 2D plots.

To plot a set of 3d points, with a square aspect ratio (squareness requires
Gnuplot >= 4.4):

#+BEGIN_SRC python
plot3d(x, y, z, square = 1)
#+END_SRC

If xy is a 2D array, we can plot it as a height map on an implicit domain

#+BEGIN_SRC python
plot3d(xy)
#+END_SRC

Ellipse and sphere plotted together, using broadcasting:

#+BEGIN_SRC python
th = np.linspace(0, np.pi*2, 30)
ph = np.linspace(-np.pi/2, np.pi*2, 30)[:,np.newaxis]

x_3d = (np.cos(ph) * np.cos(th)) .ravel()
y_3d = (np.cos(ph) * np.sin(th)) .ravel()
z_3d = (np.sin(ph) * np.ones( th.shape )) .ravel()

gp.plot3d( (x_3d * np.array([[1,2]]).T,
y_3d * np.array([[1,2]]).T,
z_3d,
{ 'legend': np.array(('sphere', 'ellipse'))}),

title = 'sphere, ellipse',
square = True,
_with = 'points')
#+END_SRC

Image arrays plots can be plotted as a heat map:

#+BEGIN_SRC python
x,y = np.ogrid[-10:11,-10:11]
gp.plot( x**2 + y**2,
title = 'Heat map',
set = 'view map',
_with = 'image',
tuplesize = 3)
#+END_SRC

** Hardcopies

To send any plot to a file, instead of to the screen, one can simply do

#+BEGIN_SRC python
plot(x, y,
hardcopy = 'output.pdf')
#+END_SRC

The 'hardcopy' option is a shorthand for the 'terminal' and 'output'
options. If more control is desired, the latter can be used. For example to
generate a PDF of a particular size with a particular font size for the text,
one can do

#+BEGIN_SRC python
plot(x, y,
terminal = 'pdfcairo solid color font ",10" size 11in,8.5in',
output = 'output.pdf')
#+END_SRC

This command is equivalent to the 'hardcopy' shorthand used previously, but the
fonts and sizes can be changed.


* COMPATIBILITY

Only python 2 is supported. I have no plans to support python 3 (forcing me to
care about unicode is stupid), but patches are welcome.

Everything should work on all platforms that support Gnuplot and Python. That
said, only Debian GNU/Linux has been tested at this point. Comments and/or
patches are welcome.

* REPOSITORY

https://github.com/dkogan/gnuplotlib

* AUTHOR

Dima Kogan <[e-mail]>

* LICENSE AND COPYRIGHT

Copyright 2015 Dima Kogan.

This program is free software; you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (version 3 or higher) as
published by the Free Software Foundation

See https://www.gnu.org/licenses/lgpl.html