'''
.. Automatically generated reST file from Doconce source
   (http://code.google.com/p/doconce/)

.. TITLE: Easyviz Documentation

.. AUTHOR: H. P. Langtangen at Simula Research Laboratory and Univ. of Oslo

.. AUTHOR: J. H. Ring at Simula Research Laboratory and Univ. of Oslo

.. DATE: Jun 12, 2012

Easyviz
=======

Easyviz is a unified interface to various packages for scientific
visualization and plotting.  The Easyviz interface is written in
Python with the purpose of making it very easy to visualize data in
Python scripts. Both curve plots and more advanced 2D/3D visualization
of scalar and vector fields are supported.  The Easyviz interface was
designed with three ideas in mind: 1) a simple, Matlab-like syntax; 2)
a unified interface to lots of visualization engines (called backends
later): Gnuplot, Matplotlib, Grace, Veusz, Pmw.Blt.Graph, PyX,
Matlab, VTK, VisIt, OpenDX; and 3) a minimalistic interface which
offers only basic control of plots: curves, linestyles, legends,
title, axis extent and names.  More fine-tuning of plots can be done
by invoking backend-specific commands.

Easyviz was made so that one can postpone the choice of a particular
visualization package (and its special associated syntax). This is
often useful when you quickly need to visualize curves or 2D/3D fields
in your Python program, but haven't really decided which plotting tool
to go for. As Python is gaining popularity at universities, students
are often forced to continuously switch between Matlab and Python,
which is straightforward for array computing, but (previously)
annoying for plotting. Easyviz was therefore also made to ease the
switch between Python and Matlab.

If you encounter problems with using Easyviz, please visit the
*Troubleshooting* chapter and the *Installation* chapter at the
end of the documentation.

Easyviz Documentation
---------------------

The present documentation is available in a number of formats:

  * `PDF <https://scitools.googlecode.com/hg/doc/easyviz/easyviz.pdf>`_

  * `Plain HTML <https://scitools.googlecode.com/hg/doc/easyviz/easyviz.html>`_

  * `Sphinx HTML <https://scitools.googlecode.com/hg/doc/easyviz/easyviz_sphinx_html/index.html>`_

  * `Plain text <https://scitools.googlecode.com/hg/doc/easyviz/easyviz.txt>`_

  * `Wiki <http://code.google.com/p/scitools/wiki/EasyvizDocumentation>`_

  * `Doconce source <https://scitools.googlecode.com/hg/doc/easyviz/easyviz.do.txt>`_

The documentation is written in the
`Doconce <http://code.google.com/p/doconce>`_
format and can be translated into a
number of different formats (reST, Sphinx, LaTeX, HTML, XML,
OpenOffice, RTF, Word, and plain untagged ASCII).

Guiding Principles
------------------

*First principle.* Array data can be plotted with a minimal
set of keystrokes using a Matlab-like syntax. A simple

.. code-block:: py

        t = linspace(0, 3, 51)    # 51 points between 0 and 3
        y = t**2*exp(-t**2)
        plot(t, y)

plots the data in (the NumPy array) ``t`` versus the data in (the NumPy
array) ``y``. If you need legends, control of the axis, as well as
additional curves, all this is obtained by the standard Matlab-style
commands

.. code-block:: py

        y2 = t**4*exp(-t**2)
        # pick out each 4 points and add random noise:
        t3 = t[::4]
        y3 = y2[::4] + random.normal(loc=0, scale=0.02, size=len(t3))

        plot(t, y1, 'r-')
        hold('on')
        plot(t, y2, 'b-')
        plot(t3, y3, 'bo')
        legend('t^2*exp(-t^2)', 't^4*exp(-t^2)', 'data')
        title('Simple Plot Demo')
        axis([0, 3, -0.05, 0.6])
        xlabel('t')
        ylabel('y')
        show()

        hardcopy('tmp0.eps')  # this one can be included in LaTeX
        hardcopy('tmp0.png')  # this one can be included in HTML

Easyviz also allows these additional function calls to be executed
as a part of the ``plot`` call:

.. code-block:: py

        plot(t, y1, 'r-', t, y2, 'b-', t3, y3, 'bo',
             legend=('t^2*exp(-t^2)', 't^4*exp(-t^2)', 'data'),
             title='Simple Plot Demo',
             axis=(0, 3, -0.05, 0.6),
             xlabel='t', ylabel='y',
             hardcopy='tmp1.eps',
             show=True)

        hardcopy('tmp0.png')

A scalar function :math:`f(x,y)` may be visualized
as an elevated surface with colors using these commands:

.. code-block:: py

        x = linspace(-2, 2, 41)  # 41 point on [-2, 2]
        xv, yv = ndgrid(x, x)    # define a 2D grid with points (xv,yv)
        values = f(xv, yv)       # function values
        surfc(xv, yv, values,
              shading='interp',
              clevels=15,
              clabels='on',
              hidden='on',
              show=True)

*Second princple.* Easyviz is just a unified interface to other
plotting packages that can be called from Python. Such plotting
packages are referred to as backends. Several backends are supported:
Gnuplot, Matplotlib, Grace (Xmgr), Veusz, Pmw.Blt.Graph, PyX, Matlab,
VTK, VisIt, OpenDX. In other words, scripts that use Easyviz commands
only, can work with a variety of backends, depending on what you have
installed on the machine in question and what quality of the plots you
demand. For example, switching from Gnuplot to Matplotlib is trivial.

Scripts with Easyviz commands will most probably run anywhere since at
least the Gnuplot package can always be installed right away on any
platform. In practice this means that when you write a script to
automate investigation of a scientific problem, you can always quickly
plot your data with Easyviz (i.e., Matlab-like) commands and postpone
to marry any specific plotting tool. Most likely, the choice of
plotting backend can remain flexible. This will also allow old scripts
to work with new fancy plotting packages in the future if Easyviz
backends are written for those packages.

*Third principle.* The Easyviz interface is minimalistic, aimed at
rapid prototyping of plots. This makes the Easyviz code easy to read
and extend (e.g., with new backends). If you need more sophisticated
plotting, like controlling tickmarks, inserting annotations, etc., you
must grab the backend object and use the backend-specific syntax to
fine-tune the plot. The idea is that you can get away with Easyviz and
a plotting package-independent script "95 percent" of the time - only
now and then there will be demand for package-dependent code for
fine-tuning and customization of figures.

These three principles and the Easyviz implementation make simple things
simple and unified, and complicated things are not more complicated than
they would otherwise be. You can always start out with the simple
commands - and jump to complicated fine-tuning only when strictly needed.

Tutorial
========

This tutorial starts with plotting a single curve with a simple
``plot(x,y)`` command. Then we add a legend, axis labels, a title, etc.
Thereafter we show how multiple curves are plotted together. We also
explain how line styles and axis range can be controlled. The
next topic deals with animations and making movie files. More advanced
subjects, such as fine tuning of plots (using plotting package-specific
commands) and working with Axis and Figure objects, close the curve
plotting part of the tutorial.

Various methods for visualization of scalar fields in 2D and 3D are
treated next, before we show how 2D and 3D vector fields can be handled.

A Note on Import Statements
---------------------------

The recommended standard import of ``numpy``
and ``matplotlib`` in programs reads:

.. code-block:: python

        import numpy as np
        import matplotlib.pyplot as plt

This import ensures that all functionality from different packages are
prefixed by a short form of the package name. This convention has,
from a computer science perspective, many advantages as one sees
clearly where functionality comes from.  However, convincing
scientists with extensive Matlab, Fortran, or C++ experience to switch
to Python can be hard when mathematical formulas are full of ``np.``
prefixes and all plotting commands are decorated with an "extra"
``plt.`` The developers of Easyviz think it is a major point to have
Python code as close to Matlab and standard mathematical syntax as
possible.  Therefore, examples in this manual employ the "star
import":

.. code-block:: python

        from scitools.std import *

This statement imports the Easyviz plotting commands and also performs
``from numpy import *``. Hence, mathematical functions like ``sin`` and
``log`` are available and work for arrays, as in Matlab, and the plotting
commands are the same as those in Matlab. This type of import statement
is similar to the popular

.. code-block:: python

        from matplotlib.pylab import *

among Matplotlib users (although not promoted by Matplotlib developers).
The primary additional feature of the
``scitools.std`` import is the possibility to choose among many different
backends for plotting, where Matplotlib is one of the options.

Plotting a Single Curve
-----------------------

Let us plot the curve :math:`y = t^2\exp(-t^2)` for
:math:`t` values between 0 and 3.  First we generate equally spaced
coordinates for :math:`t`, say 51 values (50 intervals). Then we compute the
corresponding :math:`y` values at these points, before we call the
``plot(t,y)`` command to make the curve plot.  Here is the complete
program:

.. code-block:: python

        from scitools.std import *

        def f(t):
            return t**2*exp(-t**2)

        t = linspace(0, 3, 51)    # 51 points between 0 and 3
        y = zeros(len(t))         # allocate y with float elements
        for i in xrange(len(t)):
            y[i] = f(t[i])

        plot(t, y)
        show()  # optional

If you have problems running this file, make sure you have installed
SciTools and one or more plotting programs, see the chapter :ref:`ev:tut:install`.

The first line imports all of SciTools and Easyviz that can be handy
to have when doing scientific computations. This includes everything
from ``numpy`` (from ``numpy import *``),
all Easyviz plotting commands, some modules (``sys``, ``math``), and
all of SciPy (``from scipy import *``) if SciPy is installed.
In the program above, we first
pre-allocate the ``y`` array and fill it with values, element by
element, in a Python loop. Alternatively, we may operate
on the whole ``t`` array at once, which yields faster and shorter code:

.. code-block:: python

        from scitools.std import *

        def f(t):
            return t**2*exp(-t**2)

        t = linspace(0, 3, 51)    # 51 points between 0 and 3
        y = f(t)                  # compute all f values at once
        plot(t, y)
        show()                    # optional

The ``f`` function can also be skipped, if desired, so that we can write
directly

.. code-block:: python

        y = t**2*exp(-t**2)

To include the plot in electronic documents, we need a hardcopy of the
figure in PostScript, PNG, or another image format.  The ``hardcopy``
command produces files with images in various formats:

.. code-block:: python

        hardcopy('tmp1.eps') # produce PostScript
        hardcopy('tmp1.png') # produce PNG

An alternative name for ``hardcopy`` is ``savefig``:

.. code-block:: python

        savefig('tmp1.eps') # produce PostScript
        savefig('tmp1.png') # produce PNG

The filename extension determines the format: ``.ps`` or
``.eps`` for PostScript, and ``.png`` for PNG.
Figure :ref:`fig:plot1a` displays the resulting plot. With ``show(False)``
we can suppress the plot from being shown at the screen, which is
useful when create a large number of figure files in programs.

.. _fig:plot1a:

.. figure:: figs/plot1a.png

   *A simple plot in PostScript format*

On some platforms, some backends may result in a plot that is shown in
just a fraction of a second on the screen before the plot window disappears
(using the Gnuplot backend on Windows machines or using the Matplotlib
backend constitute two examples). To make the window stay on the screen,
add

.. code-block:: python

        raw_input('Press the Return key to quit: ')

at the end of the program. The plot window is killed when the program
terminates, and this satement postpones the termination until the user
hits the Return key.

Decorating the Plot
-------------------

The :math:`x` and :math:`y` axes in curve plots should have labels, here :math:`t` and
:math:`y`, respectively. Also, the curve should be identified with a label,
or legend as it is often called.  A title above the plot is also
common.  In addition, we may want to control the extent of the axes (although
most plotting programs will automatically adjust the axes to the range of the
data).
All such things are easily added after the ``plot`` command:

.. code-block:: python

        xlabel('t')
        ylabel('y')
        legend('t^2*exp(-t^2)')
        axis([0, 3, -0.05, 0.6])   # [tmin, tmax, ymin, ymax]
        title('My First Easyviz Demo')

This syntax is inspired by Matlab to make the switch between
Easyviz and Matlab almost trivial.
Easyviz has also introduced a more "Pythonic" ``plot`` command where
all the plot properties can be set at once:

.. code-block:: python

        plot(t, y,
             xlabel='t',
             ylabel='y',
             legend='t^2*exp(-t^2)',
             axis=[0, 3, -0.05, 0.6],
             title='My First Easyviz Demo',
             savefig='tmp1.eps',  # or hardcopy='tmp1.eps'
             show=True)

With ``show=False`` one can avoid the plot window on the screen and
just make the hardcopy. This feature is particularly useful if
one generates a large number of separate figures in the program.
The keyword ``savefig`` can be replaced by ``hardcopy`` if desired.

Note that we in the curve legend write ``t`` square as ``t^2`` (LaTeX style)
rather than ``t**2`` (program style). Whichever form you choose is up to
you, but the LaTeX form sometimes looks better in some plotting
programs (Matplotlib and Gnuplot are two examples).
See Figure :ref:`fig:plot1c` for what the modified
plot looks like and how ``t^2`` is typeset in Gnuplot.

.. _fig:plot1c:

.. figure:: figs/plot1c.png

   *A single curve with*

Plotting Multiple Curves
------------------------

A common plotting task is to compare two or more curves, which
requires multiple curves to be drawn in the same plot.
Suppose we want to plot the two functions :math:`f_1(t)=t^2\exp(-t^2)`
and :math:`f_2(t)=t^4\exp(-t^2)`. If we write two ``plot`` commands after
each other, two separate plots will be made. To make the second
``plot`` command draw the curve in the first plot, we need to
issue a ``hold('on')`` command. Alternatively, we can provide all
data in a single ``plot`` command. A complete program illustrates the
different approaches:

.. code-block:: python

        from scitools.std import *   # for curve plotting

        def f1(t):
            return t**2*exp(-t**2)

        def f2(t):
            return t**2*f1(t)

        t = linspace(0, 3, 51)
        y1 = f1(t)
        y2 = f2(t)

        # Matlab-style syntax
        plot(t, y1)
        hold('on')
        plot(t, y2)

        xlabel('t')
        ylabel('y')
        legend('t^2*exp(-t^2)', 't^4*exp(-t^2)')
        title('Plotting two curves in the same plot')
        savefig('tmp2.eps')  # or hardcopy('tmp2.eps')

        # Alternative "Pythonic" style
        plot(t, y1, t, y2, xlabel='t', ylabel='y',
             legend=('t^2*exp(-t^2)', 't^4*exp(-t^2)'),
             title='Plotting two curves in the same plot',
             savefig='tmp2.eps')

The sequence of the multiple legends is such that the first legend
corresponds to the first curve, the second legend to the second curve,
and so on. The visual result appears in Figure :ref:`fig:plot2a`.

Doing a ``hold('off')`` makes the next ``plot`` command create a new
plot in the same window. This new plot just erases the previous curves.

.. _fig:plot2a:

.. figure:: figs/plot2a.png

   *Two curves in the same plot*

With the keyword argrument ``grid=True`` to ``plot`` we can add a
grid, which is frequently used when plotting curves (see
Figure :ref:`fig:plot2f`).

.. _fig:plot2f:

.. figure:: figs/plot2f.png

   *Curves with a grid*

The default location of the legends is dependent on the backend
(some have a fixed location, like Gnuplot, and some try to find
the most optimal location, like Matplotlib). One can control
the location by the ``loc`` keyword to the ``legend`` function, e.g.,

.. code-block:: py

        legend('t^2*exp(-t^2)', 't^4*exp(-t^2)', loc='upper left')

The most popular values are upper right, upper left, lower left,
and lower right, depending on the shape of the curves and extend
of the axes. The keyword argument ``fancybox`` draws a box around
the legends if ``True``, otherwise no box is drawn. The corresponding
keywords for the ``plot`` function are ``legend_loc`` and ``legend_fancybox``:

.. code-block:: py

        plot(t, y1, t, y2, xlabel='t', ylabel='y',
             legend=('t^2*exp(-t^2)', 't^4*exp(-t^2)'),
             legend_loc=`upper left`, legend_fancybox=True,
             axis=[0, 4, -0.1, 0.8],
             title='Plotting two curves in the same plot',
             savefig='tmp2.eps')

The ``loc`` and ``fancybox`` specifications work (at present)
with Gnuplot and Matplotlib only.

.. figure:: figs/plot2l.png
   :width: 400

   A figure with legends placed to the upper left with a box frame

The ``legend`` function also accepts a list of legends instead of
the legends as separate positional arguments. This allows an overlapping
syntax between Matplotlib and Easyviz so that the same code can apply
either of the packages (however, Matplotlib's keywords to
``plot``, like ``label`` and ``linewidth``, are not recognized so not all
syntax is interchangable).

Making Multiple Figures
-----------------------

The ``hold`` command either adds a new curve or replaces old curve(s) by
new ones. Often one wants to make multiple figures in a program,
realized as multiple windows on the screen. The ``figure()`` command
creates a new figure:

.. code-block:: python

        x = linspace(-2, 2, 81)
        y1 = sin(pi*x)*exp(-0.5*x**2)
        plot(x, y1)

        figure()  # separate plot window
        y2 = sin(pi*x/2)*exp(-0.5*x**2)
        plot(x, y2)

        figure()  # yet another plot window
        y3 = sin(pi*x/4)*exp(-0.5*x**2)
        plot(x, y3)

More information in the ``figure`` command is found later on under the
heading *Working with Axis and Figure Objects*.

Controlling Line Styles
-----------------------

When plotting multiple curves in the same plot, the individual curves
get distinct default line styles, depending on the program that is
used to produce the curve (and the settings for this program). It
might well happen that you get a green and a red curve (which is bad
for a significant portion of the male population).  Therefore,
we often want to control the line style in detail. Say we want the first
curve (``t`` and ``y1``) to be drawn as a red solid line and the second
curve (``t`` and ``y2``) as blue circles at the discrete data points.  The
Matlab-inspired syntax for specifying line types applies a letter for
the color and a symbol from the keyboard for the line type. For
example, ``r-`` represents a red (``r``) line (``-``), while ``bo`` means blue
(``b``) circles (``o``). The line style specification is added as an
argument after the :math:`x` and :math:`y` coordinate arrays of the curve:

.. code-block:: python

        plot(t, y1, 'r-')
        hold('on')
        plot(t, y2, 'bo')

        # or
        plot(t, y1, 'r-', t, y2, 'bo')

The effect of controlling the line styles can be seen in
Figure :ref:`fig:plot2c`.

.. _fig:plot2c:

.. figure:: figs/plot2c.png

   *Two curves in the same plot, with controlled line styles*

Assume now that we want to plot the blue circles at every 4 points only.
We can grab every 4 points out of the ``t`` array by using an appropriate
slice: ``t2 = t[::4]``. Note that the first colon means the range from the
first to the last data point, while the second colon separates this
range from the stride, i.e., how many points we should "jump over"
when we pick out a set of values of the array.

.. code-block:: python

        from scitools.std import *

        def f1(t):
            return t**2*exp(-t**2)

        def f2(t):
            return t**2*f1(t)

        t = linspace(0, 3, 51)
        y1 = f1(t)
        t2 = t[::4]
        y2 = f2(t2)

        plot(t, y1, 'r-6', t2, y2, 'bo3',
             xlabel='t', ylabel='y',
             axis=[0, 4, -0.1, 0.6],
             legend=('t^2*exp(-t^2)', 't^4*exp(-t^2)'),
             title='Plotting two curves in the same plot',
             hardcopy='tmp2.eps')

In this plot we also adjust the size of the line and the circles by
adding an integer: ``r-6`` means a red line with thickness 6 and ``bo5``
means red circles with size 5. The effect of the given line thickness
and symbol size depends on the underlying plotting program. For
the Gnuplot program one can view the effect in Figure :ref:`fig:plot2g`.

.. _fig:plot2g:

.. figure:: figs/plot2g.png

   *Circles at every 4 points and extended line thickness (6) and circle size (3)*

The different available line colors include
  * yellow:   ``'y'``

  * magenta:  ``'m'``

  * cyan:     ``'c'``

  * red:      ``'r'``

  * green:    ``'g'``

  * blue:     ``'b'``

  * white:    ``'w'``

  * black:    ``'k'``

The different available line types are
  * solid line:      ``'-'``

  * dashed line:     ``'--'``

  * dotted line:     ``':'``

  * dash-dot line:   ``'-.'``

During programming, you can find all these details in the
documentation of the ``plot`` function. Just type ``help(plot)``
in an interactive Python shell or invoke ``pydoc`` with
``scitools.easyviz.plot``. This tutorial is available
through ``pydoc scitools.easyviz``.

We remark that in the Gnuplot program all the different line types are
drawn as solid lines on the screen. The hardcopy chooses automatically
different line types (solid, dashed, etc.) and not in accordance with
the line type specification.

Lots of markers at data points are available:
  * plus sign:                     ``'+'``

  * circle:                        ``'o'``

  * asterisk:                      ``'*'``

  * point:                         ``'.'``

  * cross:                         ``'x'``

  * square:                        ``'s'``

  * diamond:                       ``'d'``

  * upward-pointing triangle:      ``'^'``

  * downward-pointing triangle:    ``'v'``

  * right-pointing triangle:       ``'>'``

  * left-pointing triangle:        ``'<'``

  * five-point star (pentagram):   ``'p'``

  * six-point star (hexagram):     ``'h'``

  * no marker (default): ``None``

Symbols and line styles may be combined, for instance as in ``'kx-'``,
which means a black solid line with black crosses at the data points.

*Another Example.* Let us extend the previous example with a third
curve where the data points are slightly randomly distributed around
the :math:`f_2(t)` curve:

.. code-block:: python

        from scitools.std import *

        def f1(t):
            return t**2*exp(-t**2)

        def f2(t):
            return t**2*f1(t)

        t = linspace(0, 3, 51)
        y1 = f1(t)
        y2 = f2(t)

        # Pick out each 4 points and add random noise
        t3 = t[::4]      # slice, stride 4
        random.seed(11)  # fix random sequence
        noise = random.normal(loc=0, scale=0.02, size=len(t3))
        y3 = y2[::4] + noise

        plot(t, y1, 'r-')
        hold('on')
        plot(t, y2, 'ks-')   # black solid line with squares at data points
        plot(t3, y3, 'bo')

        legend('t^2*exp(-t^2)', 't^4*exp(-t^2)', 'data')
        title('Simple Plot Demo')
        axis([0, 3, -0.05, 0.6])
        xlabel('t')
        ylabel('y')
        show()
        savefig('tmp3.eps')   # or hardcopy
        savefig('tmp3.png')   # or hardcopy

The plot is shown in Figure :ref:`fig:plot3`.

.. _fig:plot3:

.. figure:: figs/plot3.png

   *A plot with three curves*

*Minimalistic Typing.* When exploring mathematics in the interactive Python shell, most of us
are interested in the quickest possible commands.
Here is an example of minimalistic syntax for
comparing the two sample functions we have used in the previous examples:

.. code-block:: python

        t = linspace(0, 3, 51)
        plot(t, t**2*exp(-t**2), t, t**4*exp(-t**2))

*Text.* A text can be placed at a point :math:`(x,y)` using the call

.. code-block:: py

        text(x, y, 'Some text')

*More Examples.* The examples in this tutorial, as well as
additional examples, can be found in the ``examples`` directory in the
root directory of the SciTools source code tree.

Math Syntax in Legends and Titles
---------------------------------

Some backends understand some mathematical syntax. Easyviz accepts
LaTeX-style syntax and translates it to something appropriate for the
background in question. As a rule of thumb, write plain LaTeX syntax
if you need mathematical symbols and expressions in legends and
titles. Matplotlib will show the result in an excellent way, Gnuplot
PostScript output will handle super- and subscripts as well as greek
letters. All other backends will strip off backslashes, dollar signs,
curly braces, qand other annoying LaTeX syntax. Normally, power
expressions with double multiplication symbols are replaced by a hat.

Interactive Plotting Sessions
-----------------------------

All the Easyviz commands can of course be issued in an interactive
Python session. The only thing to comment is that the ``plot`` command
returns a result:

.. code-block:: py

        >>> t = linspace(0, 3, 51)
        >>> plot(t, t**2*exp(-t**2))
        [<scitools.easyviz.common.Line object at 0xb5727f6c>]

Most users will just ignore this output line.

All Easyviz commands that produce a plot return an object reflecting the
particular type of plot. The ``plot`` command returns a list of
``Line`` objects, one for each curve in the plot. These ``Line``
objects can be invoked to see, for instance, the value of different
parameters in the plot:

.. code-block:: py

        >>> line, = plot(x, y, 'b')
        >>> getp(line)
        {'description': '',
         'dims': (4, 1, 1),
         'legend': '',
         'linecolor': 'b',
         'pointsize': 1.0,
         ...

Such output is mostly of interest to advanced users.

.. _easyviz:movie:

Making Animations
-----------------

A sequence of plots can be combined into an animation and stored in a
movie file. First we need to generate a series of hardcopies, i.e.,
plots stored in files.  Thereafter we must use a tool to combine the
individual plot files into a movie file.

*Example.* The function
:math:`f(x; m, s) = (2\pi)^{-1/2}s^{-1}\exp{\left[-{1\over2}\left({x-m\over s}\right)^2\right]}`
is known as the Gaussian function or the probability density function
of the normal (or Gaussian) distribution.  This bell-shaped function is
"wide" for large :math:`s` and "peak-formed" for small :math:`s`, see Figure
:ref:`fig:plot4`. The function is symmetric around :math:`x=m` (:math:`m=0` in the
figure).  Our goal is to make an animation where we see how this
function evolves as :math:`s` is decreased. In Python we implement the
formula above as a function ``f(x, m, s)``.

.. _fig:plot4:

.. figure:: figs/plot4.png

   *Different shapes of a Gaussian function*

The animation is created by varying :math:`s` in a loop and for each :math:`s`
issue a ``plot`` command. A moving curve is then visible on the screen.
One can also make a movie file that can be played as any other
computer movie using a standard movie player. To this end, each plot
is saved to a file, and all the files are combined together using some
suitable tool, which is reached through the ``movie`` function in
Easyviz. All necessary steps will be apparent in the complete program
below, but before diving into the code we need to comment upon a
couple of issues with setting up the ``plot`` command for animations.

The underlying plotting program will normally adjust the :math:`y` axis to the
maximum and minimum values of the curve if we do not specify the axis
ranges explicitly. For an animation such automatic axis adjustment is
misleading - the axis ranges must be fixed to avoid a jumping
axis. The relevant values for the axis range is the minimum and
maximum value of :math:`f`. The minimum value is zero, while the maximum
value appears for :math:`x=m` and increases with decreasing :math:`s`. The range
of the :math:`y` axis must therefore be :math:`[0,f(m; m, \min s)]`.

The function :math:`f` is defined for all :math:`-\infty < x < \infty`, but the
function value is very small already :math:`3s` away from :math:`x=m`. We may therefore
limit the :math:`x` coordinates to :math:`[m-3s,m+3s]`.

Now we are ready to take a look at the complete code
for animating how the Gaussian function evolves as the :math:`s` parameter
is decreased from 2 to 0.2:

.. code-block:: python

        from scitools.std import *
        import time

        def f(x, m, s):
            return (1.0/(sqrt(2*pi)*s))*exp(-0.5*((x-m)/s)**2)

        m = 0
        s_start = 2
        s_stop = 0.2
        s_values = linspace(s_start, s_stop, 30)
        x = linspace(m -3*s_start, m + 3*s_start, 1000)
        # f is max for x=m; smaller s gives larger max value
        max_f = f(m, m, s_stop)

        # Show the movie on the screen
        # and make hardcopies of frames simultaneously
        counter = 0
        for s in s_values:
            y = f(x, m, s)
            plot(x, y, axis=[x[0], x[-1], -0.1, max_f],
                 xlabel='x', ylabel='f', legend='s=%4.2f' % s,
                 hardcopy='tmp%04d.png' % counter)
            counter += 1
            #time.sleep(0.2)  # can insert a pause to control movie speed

        # Make movie file the simplest possible way
        movie('tmp*.png')

Note that the :math:`s` values are decreasing (``linspace`` handles this
automatically if the start value is greater than the stop value).
Also note that we, simply because we think it is visually more
attractive, let the :math:`y` axis go from -0.1 although the :math:`f` function is
always greater than zero.

*Remarks on Filenames.* For each frame (plot) in the movie we store the plot in a file.  The
different files need different names and an easy way of referring to
the set of files in right order. We therefore suggest to use filenames
of the form ``tmp0001.png``, ``tmp0002.png``, ``tmp0003.png``, etc.  The
printf format ``04d`` pads the integers with zeros such that ``1`` becomes
``0001``, ``13`` becomes ``0013`` and so on.  The expression ``tmp*.png`` will
now expand (by an alphabetic sort) to a list of all files in proper
order. Without the padding with zeros, i.e., names of the form
``tmp1.png``, ``tmp2.png``, ..., ``tmp12.png``, etc., the alphabetic order
will give a wrong sequence of frames in the movie. For instance,
``tmp12.png`` will appear before ``tmp2.png``.

Note that the names of plot files specified when making hardopies must
be consistent with the specification of names in the call to ``movie``.
Typically, one applies a Unix wildcard notation in the call to
``movie``, say ``plotfile*.png``, where the asterisk will match any set of
characters. When specifying hardcopies, we must then use a filename
that is consistent with ``plotfile*.png``, that is, the filename must
start with ``plotfile`` and end with ``.png``, but in between
these two parts we are free to construct (e.g.) a frame number padded
with zeros.

We recommend to always remove previously generated plot files before
a new set of files is made. Otherwise, the movie may get old and new
files mixed up. The following Python code removes all files
of the form ``tmp*.png``:

.. code-block:: python

        import glob, os
        for filename in glob.glob('tmp*.png'):
            os.remove(filename)

These code lines should be inserted at the beginning of the code example
above. Alternatively, one may store all plotfiles in a subfolder
and later delete the subfolder. Here is a suitable code segment:

.. code-block:: python

        import shutil, os
        subdir = 'temp'            # name of subfolder for plot files
        if os.path.isdir(subdir):  # does the subfolder already exist?
            shutil.rmtree(subdir)  # delete the whole folder
        os.mkdir(subdir)           # make new subfolder
        os.chdir(subdir)           # move to subfolder
        # ...perform all the plotting...
        # ...make movie...
        os.chdir(os.pardir)        # optional: move up to parent folder

*Movie Formats.* Having a set of (e.g.) ``tmp*.png`` files, one can simply generate a movie by
a ``movie('tmp*.png')`` call. The format of the movie is determined by
which video encoders that are installed on the computer. The ``movie``
function runs through a list of encoders (``convert``, ``mencoder``,
``ffmpeg mpeg_encode``, ``ppmtompeg``, ``mpeg2enc``, ``html``) and choses the
first one which is installed. The fall back encoder ``html`` actually
does not create a video file, but makes insetad an HTML file that can
play the series of hardcopies made (``tmp*.png``, for instance).
When no filename is given to the ``movie`` function, the output file
with the movie has filestem ``movie`` and extension depending on the
video format and the encoder used. For example, if ``convert`` was used
to create an animated GIF file, the default output file is ``movie.gif``.
Similarly, ``movie.avi`` is in AVI format, ``movie.mpeg`` is in MPEG format,
and so forth.

You can get complete control of the movie format and the name of the
movie file by supplying the ``encoder`` and ``output_file`` arguments to
the ``movie`` function. This is the recommended use. Here is an
example on generating an animated GIF file ``tmpmovie.gif`` with
the ``convert`` program from the ImageMagick software suite:

.. code-block:: python

        movie('tmp_*.png', encoder='convert', fps=2,
              output_file='tmpmovie.gif')

This call requires ImageMagick to be installed on the machine. The
argument ``fps`` stands for frames per second so here the speed of the
movie is slow in that there is a delay of half a second between each
frame (image file).  To view the animated GIF file, one can use the
``animate`` program (also from ImageMagick) and give the movie file as
command-line argument. One can alternatively put the GIF file in a web
page in an IMG tag such that a browser automatically displays the
movie.

Making an HTML file that can play the movie in a web browser
is carried out by the call

.. code-block:: python

        movie('tmp_*.png', encoder='html', fps=10,
              output_file='tmpmovie.html')

Just load ``tmpmovie.html`` into a browser (e.g., run ``firefox tmpmovie.html``
from the command line).

An AVI movie can be generated by the call

.. code-block:: python

        movie('tmp_*.png', encoder='ffmpeg', fps=4,
              output_file='tmpmovie.avi',

Alternatively, we may generate an MPEG movie using
the ``ppmtompeg`` encoder from the Netpbm suite of
image manipulation tools:

.. code-block:: python

        movie('tmp_*.png', encoder='ppmtompeg', fps=24,
              output_file='tmpmovie.mpeg',

The ``ppmtompeg`` supports only a few (high) frame rates.

The next sample call to ``movie`` uses the Mencoder tool and specifies
some additional arguments (video codec, video bitrate, and the
quantization scale):

.. code-block:: python

        movie('tmp_*.png', encoder='mencoder', fps=24,
              output_file='tmpmovie.mpeg',
              vcodec='mpeg2video', vbitrate=2400, qscale=4)

Here is yet another example:

.. code-block:: py

        movie('tmp_*.png', encoder='ffmpeg',
              output_file='tmpmovie1c.mpeg', vodec='mpeg2video')

The file ``examples/movie_demo1.py`` that comes with the SciTools source
code generates frames in a movie and creates movie files in many formats.

Playing movie files can be done by a lot of programs. Windows Media
Player is a default choice on Windows machines. On Unix, a variety
of tools can be used. For animated GIF files the ``animate`` program
from the ImageMagick suite is suitable, or one can simply
show the file in a web page with the HTML command
``<img src="tmpmovie.gif">``. AVI and MPEG files can be played by,
for example, the
``myplayer``, ``vlc``, or ``totem`` programs.

*Making Movies in Batch.* Sometimes it is desired to carry out
large numbers of computer experiments and create movies in each
individual experiments. Then one probably does not want to have
the screen full of movie windows. To turn off showing the movie
on the screen while creating the individual frames, just
give the ``show=False`` keyword argument to the ``plot`` function.
All hardcopies and the movies are then made in batch, which also
might speed up the program since rendering graphics on the screen
is avoided.

Controlling the Aspect Ratio of Axes
------------------------------------

By default, Gnuplot, Matplotlib and other plotting packages
automatically calculate suitable physical sizes of the axis
in the plotting window. However, sometimes one wants to control
this, i.e., impose a certain ratio of the physical extent of the
axis.

In the ``gnuplot`` and ``matplotlib``
backends, we set ``daspectmode=manual`` and
``daspect=[r,1,1]``, where ``r`` is the ratio of the y-axis length to
the x-axis length
(``r`` equal to ``1`` gives a square plot area). For example,

.. code-block:: python

        plot(x, y, 'r-',
             axis=[0, 1, 0, 1],
             daspect=[1,1,1],
             daspectmode='manual')

Note that one should always use ``axis`` and set axes limits explicitly
when prescribing the aspect ratio.

Suppose the x-axis goes from 0 to 20 and the y-axis from -2 to 2.
Often we want the units on the axes to have the same length, i.e.,
the x-axis should be five times as long as the y-axis in this example.
This is accomplished by ``daspect=[0.2,1,1])``.
Alternatively, one can apply ``daspectmode='equal'`` (which means
equal physical units on the axis).

Here is an example which demonstrates various aspects of setting
the aspect ratio:

.. code-block:: python

        from scitools.std import *
        n = 20  # no of periods of a sine function
        r = 80  # resolution of each period
        x = linspace(0, n, r*n + 1)
        amplitude = 1 + sin(2*pi*0.05*x)
        y = amplitude*sin(2*pi*x)

        # x-axis goes from 0 to 20, y-axis from -2 to 2.

        subplot(2, 1, 1)
        plot(x, y,
             axis=[x[0], x[-1], y.min(), y.max()],
             daspectmode='equal',
             title='daspectmode=equal',
             )
        subplot(2, 1, 2)
        plot(x, y,
             axis=[x[0], x[-1], y.min(), y.max()],
             daspect=[0.5,1,1],
             daspectmode='manual',
             title='daspectmode=manual, daspect=[0.5,1,1]',
             )

        figure()
        plot(x, y,
             axis=[x[0], x[-1], y.min(), y.max()],
             daspect=[1,1,1],
             daspectmode='manual',
             title='daspectmode=manual, daspect=[1,1,1]',
             )

        show()
        raw_input()

Moving Plot Window
------------------

When calculating long time series, it may be desirable to have a
moving plot window that follows the time series. The module
``MovingPlotWindow`` was made for this purpose. There are three
different modes of this tool, where each mode moves the window
in a certain way. With ``mode`` set as ``continuous movement``,
the plot window moves with the curves continuously.
With ``mode`` set as ``continuous drawing``, the curves are drawn
from left to right in the plot window, as an animation (one step
at a time). When the curves reach the right border of the plot window,
the window (or more correctly, the x-axis) is moved in a jump
to the right so that the curves are coming in from the left border
again. With ``mode`` set as ``jumps`` the curves are plotted directly
in the window and shown for a specified period of time (the ``pause``
parameter), then the axis jump one window to the right, and the
curves are displayed in this (time) window. The ``jumps`` mode is
well suited for quickly browsing a time series. The ``continuous
drawing`` mode is aimed at studing the "tip" of the time series
as they are computed, and ``continuous movement`` is a kind of
default choice for most purposes. Running the module file gives
a demo of the three modes.

Below is an example of how to compute a time series by finite
differences and comparing this series with the exact solutions.
For large times, there is a fequency discrepancy that one wants
to investigate.

.. code-block:: python

        def _demo(I, k, dt, T, mode='continuous movement'):
            """
            Solve u' = -k**2*u, u(0)=I, u'(0)=0 by a finite difference
            method with time steps dt, from t=0 to t=T.
            """
            if dt > 2./k:
                print 'Unstable scheme'
            N = int(round(T/float(dt)))
            u = zeros(N+1)
            t = linspace(0, T, N+1)

            umin = -1.2*I
            umax = -umin
            period = 2*pi/k  # period of the oscillations
            plot_manager = MovingPlotWindow(8*period, dt, yaxis=[umin, umax],
                                            mode=mode)
            u[0] = I
            u[1] = u[0] - 0.5*dt**2*k**2*u[0]
            for n in range(1,N):
                u[n+1] = 2*u[n] - u[n-1] - dt**2*k**2*u[n]

                if plot_manager.plot(n):
                    s = plot_manager.first_index_in_plot
                    plot(t[s:n+2], u[s:n+2], 'r-',
                         t[s:n+2], I*cos(k*t)[s:n+2], 'b-',
                         axis=plot_manager.axis(),
                         title="Solution of u'' + k^2 u = 0 for t=%6.3f (mode: %s)" \
                         % (t[n+1], mode))
                plot_manager.update(n)

An appropriate import statement is

.. code-block:: py

        from scitools.MovingPlotWindow import MovingPlotWindow

Advanced Easyviz Topics
-----------------------

The information in the previous sections aims at being sufficient for
the daily work with plotting curves. Sometimes, however, one wants to
fine-control the plot or how Easyviz behaves. First, we explain how to
set the backend. Second, we tell how to speed up the
``from scitools.std import *`` statement.  Third, we show how to operate with
the plotting program directly and using plotting program-specific
advanced features. Fourth, we explain how the user can grab ``Figure``
and ``Axis`` objects that Easyviz produces "behind the curtain".

Controlling the Backend
~~~~~~~~~~~~~~~~~~~~~~~

The Easyviz backend can either be set in a configuration file (see
"Setting Parameters in the Configuration File" below), by
importing a special backend in the program, or by adding a
command-line option

.. code-block:: py

         --SCITOOLS_easyviz_backend name

where ``name`` is the name of the backend: ``gnuplot``, ``vtk``,
``matplotlib``, etc. Which backend you choose depends on what you have
available on your computer system and what kind of plotting
functionality you want.

An alternative method is to import a specific backend in a program. Instead
of the ``from scitools.std import *`` statement one writes

.. code-block:: python

        from numpy import *
        from scitools.easyviz.gnuplot_ import *  # work with Gnuplot
        # or
        from scitools.easyviz.vtk_ import *      # work with VTK

Note the trailing underscore in the module names for the various backends.

The following program prints a list of the names of the
available backends on your computer system:

.. code-block:: python

        from scitools.std import *
        backends = available_backends()
        print 'Available backends:', backends

There will be quite some output explaining the missing backends and
what must be installed to use these backends. Be prepared for exceptions
and error messages too.

.. _easyviz:imports:

Importing Just Easyviz
~~~~~~~~~~~~~~~~~~~~~~

The ``from scitools.std import *`` statement imports many modules and packages:

.. code-block:: python

        from numpy import *
        from scitools.numpyutils import *  # some convenience functions
        from numpy.lib.scimath import *
        from scipy import *                # if scipy is installed
        import sys, operator, math
        from scitools.StringFunction import StringFunction
        from glob import glob

The ``scipy`` import can take some time and lead to slow start-up of plot
scripts. A more minimalistic import for curve plotting is

.. code-block:: python

        from scitools.easyviz import *
        from numpy import *

Alternatively, one can edit the SciTools configuration file as
explained below in the section "Setting Parameters in the
Configuration File".

Many discourage the use of "star import" as shown above. For example,
the standard import of Numerical Python in all of its documentation is

.. code-block:: py

        import numpy as np

A similar import for SciTools and Easyviz is

.. code-block:: py

        import scitools.std as st
        import numpy as np

Although ``np`` functions are important into the namespace of ``st`` in
this case, we recommend to distinguish the packages when using a prefix.
A typical plotting example will then read

.. code-block:: py

        x = np.linspace(0, 3, 51)
        y = x**2*np.exp(-x)
        st.plot(x, y, 'r-', title="Plot")

The corresponding syntax for the
minimalistic import of ``scitools.easyviz`` and ``numpy`` reads

.. code-block:: py

        import scitools.easyviz as ev
        import numpy as np

Setting Parameters in the Configuration File
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Easyviz is a subpackage of SciTools, and the the SciTools
configuration file, called ``scitools.cfg`` has several sections
(``[easyviz]``, ``[gnuplot]``, and ``[matplotlib]``) where parameters
controlling the behavior of plotting can be set. For example, the
backend for Easyviz can be controlled with the ``backend`` parameter:

.. code-block:: py

        [easyviz]
        backend = vtk

Similarly, Matplotlib's use of LaTeX can be controlled by a boolean
parameter:

.. code-block:: py

        [matplotlib]
        text.usetex = <bool> false

The text ``<bool>`` indicates that this is a parameter with a boolean

A configuration file with name ``.scitools.cfg`` file can be placed in
the current working folder, thereby affecting plots made in this
folder, or it can be located in the user's home folder, which will
affect all plotting sessions for the user in question. There is also a
common SciTools config file ``scitools.cfg`` for the whole site, located
in the directory where the ``scitools`` package is installed. It is
recommended to copy the ``scitools.cfg``, either from installation or
the SciTools source folder ``lib/scitools``, to ``.scitools.cfg``
in your home folder. Then you can easily control the Easyviz backend
and other paramteres by editing your local ``.scitools.cfg`` file.

Parameters set in the configuration file can also be set directly
on the command line when running a program. The name of the
command-line option is

.. code-block:: py

        --SCITOOLS_sectionname_parametername

where ``sectionname`` is the name of the section in the file
and ``parametername`` is the name of the
parameter. For example, setting the ``backend`` parameter in the
``[easyviz]`` section by

.. code-block:: py

        --SCITOOLS_easyviz_backend gnuplot

Here is an example where we use Matplotlib as backend, turn on
the use of LaTeX in Matplotlib, and avoid the potentially slow import
of SciPy:

.. code-block:: py

        python myprogram.py --SCITOOLS_easyviz_backend matplotlib \
            --SCITOOLS_matplotlib_text.usetex true --SCITOOLS_scipy_load no

Working with the Plotting Program Directly
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Easyviz supports just the most common plotting commands, typically the
commands you use "95 percent" of the time when exploring curves.
Various plotting packages have lots of additional commands for
diverse advanced features.  When Easyviz does not have a command
that supports a particular feature, one can grab the Python object
that communicates with the underlying plotting program (the
"backend") and work with this object directly, using plotting
program-specific command syntax.  Let us illustrate this principle
with an example where we add a text and an arrow in the plot, see
Figure :ref:`fig:plot2i`.

.. _fig:plot2i:

.. figure:: figs/plot2i.png

   *Illustration of a text and an arrow using Gnuplot-specific commands*

Easyviz does not support arrows at arbitrary places inside the plot,
but Gnuplot does. If we use Gnuplot as backend, we may grab the
``Gnuplot`` object and issue Gnuplot commands to this object
directly. Here is an example of the typical recipe, written after the
core of the plot is made in the ordinary (plotting
program-independent) way:

.. code-block:: python

        if backend == 'gnuplot':
            g = get_backend()
            # g is a Gnuplot object, work with Gnuplot commands directly:
            g('set label "global maximum" at 0.1,0.5 font "Times,18"')
            g('set arrow from 0.5,0.48 to 0.98,0.37 linewidth 2')
            g.refresh()
            g.hardcopy('tmp2.eps')  # make new hardcopy

            g.reset()               # new plot
            data = Gnuplot.Data(t, t**3*exp(-t), with_='points 3 3',
                                title='t**3*exp(-t)')
            func = Gnuplot.Func('t**4*exp(-t)', title='t**4*exp(-t)')
            g('set tics border font "Courier,14"')
            g.plot(func, data)

For the available features and the syntax of commands, we refer to
the Gnuplot manual and the ``demo.py`` program in Python interface to
Gnuplot. Note that one must call ``g.hardcopy`` to save the figure
to file. A call to ``savefig`` or ``hardcopy`` remakes the plot, but
without the special calls ``g('...')`` so the label and arrow are
left out of the hardcopy in the example above.

Here is an example with Matplotlib:

.. code-block:: python

        if backend == 'matplotlib':
            pyplot = get_backend()
            # Work with standard matplotlib.pyplot functions

The files ``grab_backend*.py`` in the ``examples`` folder of the SciTools
source code contain many examples on how to do backend-specific
operations, especially with Matplotlib.  Note that after having issued
calls via the ``pyplot`` object, one must apply ``pyplot.savefig`` to
correctly save the plot (a plain ``savefig`` or ``hardcopy`` remakes the
plot without the features inserted by the ``pyplot`` object).

Here are some useful links to documentation of various plotting packages:

 * `Matplotlib Documentation <http://matplotlib.sourceforge.net/contents.html>`_

 * `Gnuplot Documentation <http://www.gnuplot.info/documentation.html>`_

 * `Gnuplot Tips (Not So Frequently Asked Questions) <http://t16web.lanl.gov/Kawano/gnuplot/index-e.html>`_

 * `Grace User's Guide <http://matplotlib.sourceforge.net/contents.html>`_

 * `PyX Documentation <http://pyx.sourceforge.net/documentation.html>`_

 * `PyX Tutorial for Gnuplot Users <http://alumni.cs.ucr.edu/~titus/pyxTutorial/>`_

The idea advocated by Easyviz goes as follows. You can quickly generate
plots with Easyviz using standard commands that are independent of
the underlying plotting package. However, when you need advanced
features, you must add plotting package-specific code as shown
above. This principle makes Easyviz a light-weight interface, but
without limiting the available functionality of various plotting programs.

Working with Axis and Figure Objects
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Easyviz supports the concept of Axis objects, as in Matlab.
The Axis object represents a set of axes, with curves drawn in the
associated coordinate system. A figure is the complete physical plot.
One may have several axes in one figure, each axis representing a subplot.
One may also have several figures, represented by different
windows on the screen or separate hardcopies.

Users with Matlab experience may prefer to set axis
labels, ranges, and the title using an Axis object instead of
providing the information in separate commands or as part of a ``plot``
command. The ``gca`` (get current axis) command returns an ``Axis``
object, whose ``set`` method can be used to set axis properties:

.. code-block:: python

        plot(t, y1, 'r-', t, y2, 'bo',
             legend=('t^2*exp(-t^2)', 't^4*exp(-t^2)'),
             savefig='tmp2.eps')

        ax = gca()   # get current Axis object
        ax.setp(xlabel='t', ylabel='y',
                axis=[0, 4, -0.1, 0.6],
                title='Plotting two curves in the same plot')
        show()  # show the plot again after ax.setp actions

The ``figure()`` call makes a new figure, i.e., a
new window with curve plots. Figures are numbered as 1, 2, and so on.
The command ``figure(3)`` sets the current figure object to figure number
3.

Suppose we want to plot our ``y1`` and ``y2`` data in two separate windows.
We need in this case to work with two ``Figure`` objects:

.. code-block:: python

        plot(t, y1, 'r-', xlabel='t', ylabel='y',
             axis=[0, 4, -0.1, 0.6])

        figure()  # new figure

        plot(t, y2, 'bo', xlabel='t', ylabel='y')

We may now go back to the first figure (with the ``y1`` data) and
set a title and legends in this plot, show the plot, and make a PostScript
version of the plot:

.. code-block:: python

        figure(1)  # go back to first figure
        title('One curve')
        legend('t^2*exp(-t^2)')
        show()
        savefig('tmp2_1.eps')

We can also adjust figure 2:

.. code-block:: py

        figure(2)  # go to second figure
        title('Another curve')
        savefig('tmp2_2.eps')
        show()

The current ``Figure`` object is reached by ``gcf`` (get current figure),
and the ``dump`` method dumps the internal parameters in the ``Figure``
object:

.. code-block:: python

        fig = gcf(); print fig.dump()

These parameters may be of interest for troubleshooting when Easyviz
does not produce what you expect.

Let us then make a third figure with two plots, or more precisely, two
axes: one with ``y1`` data and one with ``y2`` data.
Easyviz has a command ``subplot(r,c,a)`` for creating ``r``
rows and ``c`` columns and set the current axis to axis number ``a``.
In the present case ``subplot(2,1,1)`` sets the current axis to
the first set of axis in a "table" with two rows and one column.
Here is the code for this third figure:

.. code-block:: python

        figure()  # new, third figure
        # Plot y1 and y2 as two axis in the same figure
        subplot(2, 1, 1)
        plot(t, y1, xlabel='t', ylabel='y')
        subplot(2, 1, 2)
        plot(t, y2, xlabel='t', ylabel='y')
        title('A figure with two plots')
        show()
        savefig('tmp2_3.eps')

Note: The Gnuplot backend will overwrite the tickmarks on the :math:`y` axis
if two or more curves in the same subplot have significantly different
variations in :math:`y` direction. To avoid this cluttering of tickmarks,
set the axes extent explicitly.

If we need to place an axis at an arbitrary position in the figure, we
must use the command

.. code-block:: python

        ax = axes(viewport=[left, bottom, width, height])

The four parameteres ``left``, ``bottom``, ``width``, ``height``
are location values between 0 and 1 ((0,0) is the lower-left corner
and (1,1) is the upper-right corner). However, this might be a bit
different in the different backends (see the documentation for the
backend in question).

Mathematics and LaTeX in Legends, Title, and Axis Labels
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Some plotting packages support nicely formatted mathematics as
axis labels, in legends, and in the figure title. For example,
Matplotlib accepts standard LaTeX syntax, while Gnuplot,
when saving figures to PostScript format, supports
greek letters, sub- and super-scripts, exponentials, etc.
Different plotting engines (backends) will require mathematics in
legends, titles, and labels to be formatted differently.

  * With Matplotlib we recommend to use standard LaTeX.

  * With Gnuplot we recommend plain text when plotting on
    the screen, and greek letters preceded with a backslash
    when saving to file. Gnuplot suports LaTeX syntax for
    sub- and super-scripts (underscore and hat, resp.).
    Other types of mathematics should be expressed in plain text.

The file ``examples/math_text.py`` tests different syntax in legends,
axis labels, and titles. Running this script with
``--SCITOOLS_easyviz_backend X`` for different values of ``X``
(``gnuplot``, ``matplotlib``, ``grace``, ``pyx``, etc.) produces plots
that one can examine to see various formats treat mathematics with and
without LaTeX syntax.

If it is important to have Easyviz code that works with several
backends, one can apply a little if-else test:

.. code-block:: python

        from scitools.std import *
        ...
        if backend == 'gnuplot':
            title_screen = 'mu=0.5, alpha=sum(i=1 to n) tau_i^2'
            title_eps = r'\mu=0.5, \alpha=sum(i=1 to n) \tau_i^2'
        elif backend == 'matplotlib':
            title_screen = title_eps = \
                  r'$mu=0.5$, $\alpha=\sum_{i=1}^n \tau_i^2$'
        else:
            title_screen = title_eps = 'mu=0.5, alpha=sum(i=1 to n) tau_i^2'

        plot(...)
        ...
        title(title_screen)
        show()
        title(title_eps)
        savefig('myplot.eps')

Turning Off All Plotting
~~~~~~~~~~~~~~~~~~~~~~~~

Sometimes, especially during debugging or when trying out a large-scale
experiment, it is nice to turn off all plotting on the screen and
all making of hardcopies. This is easily done by

.. code-block:: python

        turn_off_plotting(globals())

All the plot functions now "do nothing" (actually they are ``DoNothing``
objects from ``scitools.misc``).

Visualization of Scalar Fields
==============================

A scalar field is a function from space or space-time to a real value.
This real value typically reflects a scalar physical parameter at every
point in space (or in space and time). One example is temperature,
which is a scalar quantity defined everywhere in space and time.  In a
visualization context, we work with discrete scalar fields that are
defined on a grid. Each point in the grid is then associated with a
scalar value.

There are several ways to visualize a scalar field in Easyviz. Both
two- and three-dimensional scalar fields are supported. In two
dimensions (2D) we can create elevated surface plots, contour plots,
and pseudocolor plots, while in three dimensions (3D) we can create
isosurface plots, volumetric slice plots, and contour slice plots.

Elevated Surface Plots
----------------------

To create elevated surface plots we can use either the ``surf`` or the
``mesh`` command. Both commands have the same syntax, but the ``mesh``
command creates a wireframe mesh while the ``surf`` command creates a
solid colored surface.

Our examples will make use of the scalar field
:math:`f(x,y) = \sin r`,
where :math:`r` is the distance in the plane from the origin, i.e.,
:math:`r=\sqrt{x^2+y^2}`.
The :math:`x` and :math:`y` values in our 2D domain lie between -5 and 5.

The example first creates the necessary data arrays for 2D scalar
field plotting: the coordinates in each direction, extensions of these
arrays to form a *ndgrid*, and the function values. The latter array
is computed in a vectorized operation which requires the extended
coordinate arrays from the ``ndgrid`` function.  The ``mesh`` command
can then produce the plot with a syntax that mirrors the simplicity of
the ``plot`` command for curves:

.. code-block:: py

        x = y = linspace(-5, 5, 21)
        xv, yv = ndgrid(x, y)
        values = sin(sqrt(xv**2 + yv**2))
        h = mesh(xv, yv, values)

The ``mesh`` command returns a reference to a new ``Surface`` object, here
stored in a variable h. This reference can be used to set or get
properties in the object at a later stage if needed.  The resulting
plot can be seen in Figure :ref:`fig:mesh_ex1`.

We remark that the computations in the previous example are vectorized.
The corresponding scalar computations using a double loop read

.. code-block:: py

        values = zeros(x.size, y.size)
        for i in xrange(x.size):
            for j in xrange(y.size):
                values[i,j] = sin(sqrt(x[i]**2 + y[j]**2))

However, for the ``mesh`` command to work, we need the vectorized
extensions ``xv`` and ``yv`` of ``x`` and ``y``.

.. _fig:mesh_ex1:

.. figure:: figs/mesh_ex1.png

   *Result of the mesh command for plotting a 2D scalar field (Gnuplot backend)*

The ``surf`` command employs the same syntax, but results in a different
plot (see Figure :ref:`fig:surf_ex1`):

.. code-block:: py

        surf(xv, yv, values)

.. _fig:surf_ex1:

.. figure:: figs/surf_ex1.png

   *Result of the surf command (Gnuplot backend)*

The ``surf`` command offers many possibilities to adjust the resulting plot:

.. code-block:: py

        setp(interactive=False)
        surf(xv, yv, values)
        shading('flat')
        colorbar()
        colormap(hot())
        axis([-6,6,-6,6,-1.5,1.5])
        view(35,45)
        show()

Here we have specified a flat shading model, added a color bar, changed
the color map to ``hot``, set some suitable axis values, and changed the
view point (the view takes two arguments: the azimuthal rotation and
the elevation, both given in degrees).
The same plot can also be accomplished with one single, compound
statement (just as Easyviz offers for the ``plot`` command):

.. code-block:: py

        surf(xv, yv, values,
             shading='flat',
             colorbar='on',
             colormap=hot(),
             axis=[-6,6,-6,6,-1.5,1.5],
             view=[35,45])

Figure :ref:`fig:surf_ex2` displays the result.

.. _fig:surf_ex2:

.. figure:: figs/surf_ex2.png

   *Result of an extended surf command (Gnuplot backend)*

Contour Plots
-------------

A contour plot is another useful technique for visualizing scalar
fields. The primary examples on contour plots from everyday life is
the level curves on geographical maps, reflecting the height of the
terrain. Mathematically, a contour line, also called an isoline, is
defined as the implicit curve :math:`f(x,y)=c`. The contour levels :math:`c` are
normally uniformly distributed between the extreme values of the
function :math:`f` (this is the case in a map: the height difference between
two contour lines is constant), but in scientific visualization it is
sometimes useful to use a few carefully selected :math:`c` values to
illustrate particular features of a scalar field.

In Easyviz, there are several commands for creating different kinds of
contour plots:

  * ``contour``: Draw a standard contour plot, i.e., lines in the plane.

  * ``contourf``: Draw a filled 2D contour plot, where the space between
    the contour lines is filled with colors.

  * ``contour3``: Same as ``contour``, but the curves are drawn at their
    corresponding height levels in 3D space.

  * ``meshc``: Works in the same way as ``mesh`` except that a
     contour plot is drawn in the plane beneath the mesh.

  * ``surfc``: Same as ``meshc`` except that a solid surface is
    drawn instead of a wireframe mesh.

We start with illustrating the plain ``contour`` command, assuming that
we already have computed the ``xv``, ``yv``, and ``values``
arrays as shown in our first example on scalar field plotting.
The basic syntax follows that of ``mesh`` and ``surf``:

.. code-block:: py

        contour(xv, yv, values)

By default, five uniformly spaced contour level curves are drawn, see
Figure :ref:`fig:contour_ex1`.

.. _fig:contour_ex1:

.. figure:: figs/contour_ex1.png

   *Result of the simplest possible contour command (Gnuplot backend)*

The number of levels in a contour plot can be specified with an additional
argument:

.. code-block:: py

        n = 15   # number of desired contour levels
        contour(xv, yv, values, n)

The result can be seen in Figure :ref:`fig:contour_ex2`.

.. _fig:contour_ex2:

.. figure:: figs/contour_ex2.png

   *A contour plot with 15 contour levels (Gnuplot backend)*

Sometimes one wants contour levels that are not equidistant or not
distributed throughout the range of the scalar field. Individual
contour levels to be drawn can easily be specified as a list:

.. code-block:: py

        levels = [-0.5, 0.1, 0.3, 0.9]
        contour(xv, yv, values, levels, clabels='on')

Now, the ``levels`` list specify the values of the contour levels, and
the ``clabel`` keyword allows labeling of the level values in the plot.
Figure :ref:`fig:contour_ex3` shows the result. We remark that the
Gnuplot backend colors the contour lines and places the contour values
and corresponding colors beside the plot. Figures that are reproduced
in black and white only can then be hard to analyze. Other backends
may draw the contour lines in black and annotate each line with the
corresponding contour level value.  Such plots are better suited for
being displayed in black and white.

.. _fig:contour_ex3:

.. figure:: figs/contour_ex3.png

   *Four individually specified contour levels (Gnuplot backend)*

The ``contourf`` command,

.. code-block:: py

        contourf(xv, yv, values)

gives a filled contour plot as shown in Figure :ref:`fig:contourf_ex1`.
Only the Matplotlib and VTK backends currently supports filled
contour plots.

.. _fig:contourf_ex1:

.. figure:: figs/contourf_ex1.png

   *Filled contour plot created by the contourf command (VTK backend)*

The contour lines can be "lifted up" in 3D space, as shown in Figure
:ref:`fig:contour3_ex1`, using the ``contour3`` command:

.. code-block:: py

        contour3(xv, yv, values, 15)

.. _fig:contour3_ex1:

.. figure:: figs/contour3_ex1.png

   *Example on the contour3 command for elevated contour levels (Gnuplot backend)*

Finally, we show a simple example illustrating the ``meshc`` and ``surfc``
commands:

.. code-block:: py

        meshc(xv, yv, values,
              clevels=10,
              colormap=hot(),
              grid='off')
        figure()
        surfc(xv, yv, values,
              clevels=15,
              colormap=hsv(),
              grid='off',
              view=(30,40))

The resulting plots are displayed in Figures :ref:`fig:meshc_ex1` and
:ref:`fig:surfc_ex1`.

.. _fig:meshc_ex1:

.. figure:: figs/meshc_ex1.png

   *Wireframe mesh with contours at the bottom (Gnuplot backend)*

.. _fig:surfc_ex1:

.. figure:: figs/surfc_ex1.png

   *Surface plot with contours (Gnuplot backend)*

Pseudocolor Plots
-----------------

Another way of visualizing a 2D scalar field in Easyviz is the
``pcolor`` command. This command creates a pseudocolor plot, which is a
flat surface viewed from above. The simplest form of this command
follows the syntax of the other commands:

.. code-block:: py

        pcolor(xv, yv, values)

We can set the color shading in a pseudocolor plot either by giving
the ``shading`` keyword argument to ``pcolor`` or by calling the ``shading``
command. The color shading is specified by a string that can be either
``'faceted'`` (default), ``'flat'``, or ``'interp'`` (interpolated). The Gnuplot and
Matplotlib backends support ``'faceted'`` and ``'flat'`` only, while the
VTK backend supports all of them.

.. figure:: figs/pcolor_ex1.png

   Pseudocolor plot (Gnuplot backend)

Isosurface Plots
----------------

For 3D scalar fields, isosurfaces or contour surfaces constitute the counterpart to contour
lines or isolines for 2D scalar fields. An isosurface connects points in
a scalar field with (approximately) the same scalar value and is
mathematically defined by the implicit equation :math:`f(x,y,z)=c`. In Easyviz,
isosurfaces are created with the ``isosurface`` command. We will
demonstrate this command using 3D scalar field data from the ``flow``
function. This function, also found in Matlab,
generates fluid flow data. Our first isosurface visualization example
then looks as follows:

.. code-block:: py

        x, y, z, v = flow()  # generate fluid-flow data
        setp(interactive=False)
        h = isosurface(x,y,z,v,-3)
        h.setp(opacity=0.5)
        shading('interp')
        daspect([1,1,1])
        view(3)
        axis('tight')
        show()

After creating some scalar volume data with the ``flow`` function, we
create an isosurface with the isovalue :math:`-3`. The isosurface is then
set a bit transparent (``opacity=0.5``) before we specify the shading
model and the view point. We also set the data aspect ratio to be
equal in all directions with the ``daspect`` command.  The resulting
plot is shown in Figure :ref:`fig:isosurface1`. We remark that the
Gnuplot backend does not support 3D scalar fields and hence not
isosurfaces.

.. _fig:isosurface1:

.. figure:: figs/isosurface1.png

   *Isosurface plot (VTK backend)*

Here is another example that demonstrates the ``isosurface`` command
(again using the ``flow`` function):

.. code-block:: py

        x, y, z, v = flow()
        setp(interactive=False)
        h = isosurface(x,y,z,v,0)
        shading('interp')
        daspect([1,4,4])
        view([-65,20])
        axis('tight')
        show()

Figure :ref:`fig:isosurface2` shows the resulting plot.

.. _fig:isosurface2:

.. figure:: figs/isosurface2.png

   *Another isosurface plot (VTK backend)*

Volumetric Slice Plot
---------------------

Another way of visualizing scalar volume data is by using the ``slice_``
command (since the name ``slice`` is already taken by a built-in
function in Python for array slicing, we have followed the standard
Python convention and added a trailing underscore to the name in
Easyviz - ``slice_`` is thus the counterpart to the Matlab function
``slice``.). This command draws orthogonal slice planes through a
given volumetric data set. Here is an example on how to use the
``slice_`` command:

.. code-block:: py

        x, y, z = ndgrid(seq(-2,2,.2), seq(-2,2,.25), seq(-2,2,.16),
                           sparse=True)
        v = x*exp(-x**2 - y**2 - z**2)
        xslice = [-1.2, .8, 2]
        yslice = 2
        zslice = [-2, 0]
        slice_(x, y, z, v, xslice, yslice, zslice,
               colormap=hsv(), grid='off')

Note that we here use the SciTools function ``seq`` for specifying a
uniform partitioning of an interval - the ``linspace`` function from
``numpy`` could equally well be used.  The first three arguments in the
``slice_`` call are the grid points in the :math:`x`, :math:`y`, and :math:`z`
directions. The fourth argument is the scalar field defined on-top of
the grid. The next three arguments defines either slice planes in the
three space directions or a surface plane (currently not working). In
this example we have created 6 slice planes: Three at the :math:`x` axis (at
:math:`x=-1.2`, :math:`x=0.8`, and :math:`x=2`), one at the :math:`y` axis (at :math:`y=2`), and two
at the :math:`z` axis (at :math:`z=-2` and :math:`z=0.0`). The result is presented in
Figure :ref:`fig:slice1`.

.. _fig:slice1:

.. figure:: figs/slice1.png

   *Slice plot where the :math:`x` axis is sliced at -1.2, 0.8, and 2, the :math:`y` axis is sliced at 2, and the :math:`z` axis is sliced at -2 and 0.0 (VTK backend)*

.. OBS:

.. Slicing with a Surface-object does not work for JHR so far in VTK

*Contours in Slice Planes.* With the ``contourslice`` command we can create contour plots
in planes aligned with the coordinate axes. Here is an example
using 3D scalar field data from the ``flow`` function:

.. code-block:: py

        x, y, z, v = flow()
        setp(interactive=False)
        h = contourslice(x, y, z, v, seq(1,9), [], [0], linspace(-8,2,10))
        axis([0, 10, -3, 3, -3, 3])
        daspect([1, 1, 1])
        ax = gca()
        ax.setp(fgcolor=(1,1,1), bgcolor=(0,0,0))
        box('on')
        view(3)
        show()

The first four arguments given to ``contourslice`` in this example are
the extended coordinates of the grid (``x``, ``y``, ``z``) and the 3D scalar
field values in the volume (``v``). The next three arguments defines the
slice planes in which we want to draw contour lines. In this
particular example we have specified two contour plots in the planes
:math:`x=1,2,\dots,9`, none in :math:`y=\hbox{const}` planes (empty
list) , and one contour plot in the plane :math:`z=0`. The last argument to
``contourslice`` is optional, it can be either an integer specifying the
number of contour lines (the default is five) or, as in the current
example, a list specifying the level curves. Running the set of
commands results in the plot shown in Figure :ref:`fig:contourslice1`.

.. _fig:contourslice1:

.. figure:: figs/contourslice1.png

   *Contours in slice planes (VTK backend)*

Here is another example where we draw contour slices from a
three-dimensional MRI data set:

.. code-block:: py

        import scipy.io
        mri = scipy.io.loadmat('mri_matlab_v6.mat')
        D = mri['D']
        image_num = 8

        # Displaying a 2D Contour Slice
        contourslice(D, [], [], image_num, daspect=[1,1,1], indexing='xy')

The MRI data set is loaded from the file ``mri_matlab_v6.mat`` with the
aid from the ``loadmat`` function available in the ``io`` module in the
SciPy package. We then create a 2D contour slice plot with one slice
in the plane :math:`z=8`. Figure :ref:`fig:contourslice3` displays the result.

.. _fig:contourslice3:

.. figure:: figs/contourslice3.png

   *Contour slice plot of a 3D MRI data set (VTK backend)*

Visualization of Vector Fields
==============================

A vector field is a function from space or space-time to a vector
value, where the number of components in the vector corresponds to
the number of space dimensions. Primary examples on vector fields
are the gradient of a scalar field; or velocity, displacement, or
force in continuum physics.

In Easyviz, a vector field can be visualized either by a quiver
(arrow) plot or by various kinds of stream plots like stream lines,
stream ribbons, and stream tubes. Below we will look closer at each of
these visualization techniques.

Quiver Plots
------------

The ``quiver`` and ``quiver3`` commands draw arrows to illustrate vector
values (length and direction) at discrete points.  As the names
indicate, ``quiver`` is for 2D vector fields in the plane and ``quiver3``
plots vectors in 3D space.  The basic usage of the ``quiver`` command
goes as follows:

.. code-block:: py

        x = y = linspace(-5, 5, 21)
        xv, yv = ndgrid(x, y, sparse=False)
        values = sin(sqrt(xv**2 + yv**2))
        uv, vv = gradient(values)
        quiver(xv, yv, uv, vv)

Our vector field in this example is simply the gradient of the scalar
field used to illustrate the commands for 2D scalar field plotting.
The ``gradient`` function computes the gradient using finite difference
approximations.  The result is a vector field with components ``uv`` and
``vv`` in the :math:`x` and :math:`y` directions, respectively.  The grid points and
the vector components are passed as arguments to ``quiver``, which in
turn produces the plot in Figure :ref:`fig:quiver_ex1`.

.. _fig:quiver_ex1:

.. figure:: figs/quiver_ex1.png

   *Velocity vector plot (Gnuplot backend)*

The arrows in a quiver plot are automatically scaled to fit within the
grid. If we want to control the length of the arrows, we can pass an
additional argument to scale the default lengths:

.. code-block:: py

        scale = 2
        quiver(xv, yv, uv, vv, scale)

This value of ``scale`` will thus stretch the vectors to their double length.
To turn off the automatic scaling, we can set the scale value to zero.

Quiver plots are often used in combination with other plotting
commands such as pseudocolor plots or contour plots, since this may
help to get a better perception of a given set of data. Here is an
example demonstrating this principle for a simple scalar field, where
we plot the field values as colors and add vectors to illustrate the
associated gradient field:

.. code-block:: py

        xv, yv = ndgrid(linspace(-5,5,101), linspace(-5,5,101))
        values = sin(sqrt(xv**2 + yv**2))
        pcolor(xv, yv, values, shading='interp')

        # Create a coarser grid for the gradient field
        xv, yv = ndgrid(linspace(-5,5,21), linspace(-5,5,21))
        values = sin(sqrt(xv**2 + yv**2))
        uv, vv = gradient(values)
        hold('on')
        quiver(xv, yv, uv, vv, 'filled', 'k', axis=[-6,6,-6,6])
        figure(2)
        contour(xv, yv, values, 15)
        hold('on')
        quiver(xv, yv, uv, vv, axis=[-6,6,-6,6])

The resulting plots can be seen in Figure :ref:`fig:quiver_ex2` and
:ref:`fig:quiver_ex3`.

.. _fig:quiver_ex2:

.. figure:: figs/quiver_ex2.png

   *Combined quiver and pseudocolor plot (VTK backend)*

.. _fig:quiver_ex3:

.. figure:: figs/quiver_ex3.png

   *Combined quiver and pseudocolor plot (VTK backend)*

Visualization of 3D vector fields by arrows at grid points can be done
with the ``quiver3`` command. At the time of this writing, only the VTK
backend supports 3D quiver plots. A simple example of plotting the
"radius vector field" :math:`\vec v = (x,y,z)` is given next:

.. code-block:: py

        x = y = z = linspace(-3,3,4)
        xv, yv, zv = ndgrid(x, y, z, sparse=False)
        uv = xv
        vv = yv
        wv = zv
        quiver3(xv, yv, zv, uv, vv, wv, 'filled', 'r', axis=[-7,7,-7,7,-7,7])

The strings ``'filled'`` and ``'r'`` are optional and makes the arrows
become filled
and red, respectively. The resulting plot is presented in Figure
:ref:`fig:quiver3_ex1`.

.. _fig:quiver3_ex1:

.. figure:: figs/quiver3_ex1.png

   *3D quiver plot (VTK backend)*

Stream Plots
------------

Stream plots constitute an alternative to arrow plots for visualizing
vector fields.  The stream plot commands currently available in
Easyviz are ``streamline``, ``streamtube``, and ``streamribbon``.  Stream
lines are lines aligned with the vector field, i.e., the vectors are
tangents to the streamlines. Stream tubes are similar, but now the
surfaces of thin tubes are aligned with the vectors.  Stream ribbons
are also similar: thin sheets are aligned with the vectors. The latter
type of visualization is also known as stream or flow sheets.  In the
near future, Matlab commands such as ``streamslice`` and
``streamparticles`` might also be implemented.

We start with an example on how to use the ``streamline`` command. In
this example (and in the following examples) we will use the ``wind``
data set that is included with Matlab. This data set represents air
currents over a region of North America and is suitable for testing
the different stream plot commands. The following commands will load
the ``wind`` data set and then draw some stream lines from it:

.. code-block:: py

        import scipy.io  # needed to load binary .mat-files

        # Load the wind data set and create variables
        wind = scipy.io.loadmat('wind.mat')
        x = wind['x']
        y = wind['y']
        z = wind['z']
        u = wind['u']
        v = wind['v']
        w = wind['w']

        # Create starting points for the stream lines
        sx, sy, sz = ndgrid([80]*4, seq(20,50,10), seq(0,15,5),
                            sparse=False)

        # Draw stream lines
        streamline(x, y, z, u, v, w, sx, sy, sz,
                   view=3, axis=[60,140,10,60,-5,20])

The ``wind`` data set is stored in a binary `.mat`-file called
``wind.mat``. To load the data in this file into Python, we can use the
``loadmat`` function which is available through the ``io`` module in
SciPy. Using the ``loadmat`` function on the `wind.mat`-file returns a
Python dictionary (called ``wind`` in the current example) containing the NumPy
arrays ``x``, ``y``, ``z``, ``u``, ``v``, and ``w``. The arrays ``u``, ``v``, and ``w``
are the 3D vector data, while the arrays ``x``, ``y``, and ``z`` defines the
(3D extended) coordinates for the associated grid. The data arrays in
the dictionary ``wind`` are then stored in seperate variables for easier
access later.

Before we call the ``streamline`` command we must set up some starting
point coordinates for the stream lines. In this example, we have used
the ``ndgrid`` command to define the starting points with the line:

.. code-block:: py

        sx, sy, sz = ndgrid([80]*4, seq(20,50,10), seq(0,15,5))

This command defines starting points which all lie on :math:`x=80`,
:math:`y=20,30,40,50`, and :math:`z=0,5,10,15`. We now have all the data we need
for calling the ``streamline`` command. The first six arguments to the
``streamline`` command are the grid coordinates ``(x,y,z)`` and the 3D
vector data ``(u,v,w)``, while the next three arguments are the starting
points which we defined with the ``ndgrid`` command above. The
resulting plot is presented in Figure :ref:`fig:streamline_ex1`.

.. _fig:streamline_ex1:

.. figure:: figs/streamline_ex1.png

   *Stream line plot (Vtk backend)*

The next example demonstrates the ``streamtube`` command applied to the
same ``wind`` data set:

.. code-block:: py

        streamtube(x, y, z, u, v, w, sx, sy, sz,
                   daspect=[1,1,1],
        	   view=3,
        	   axis='tight',
        	   shading='interp')

The arrays ``sx``, ``sy``, and ``sz`` are the same as in the previous
example and defines the starting positions for the center lines of the
tubes. The resulting plot is presented in Figure
:ref:`fig:streamtube_ex1`.

.. _fig:streamtube_ex1:

.. figure:: figs/streamtube_ex1.png

   *Stream tubes (Vtk backend)*

Finally, we illustrate the ``streamribbon`` command:

.. code-block:: py

        streamribbon(x, y, z, u, v, w, sx, sy, sz,
                     ribbonwidth=5,
                     daspect=[1,1,1],
                     view=3,
                     axis='tight',
                     shading='interp')

Figure :ref:`fig:streamribbon_ex1` shows the resulting stream ribbons.

.. _fig:streamribbon_ex1:

.. figure:: figs/streamribbon_ex1.png

   *Stream ribbons (VTK backend)*

Bar Charts
----------

Easyviz also supports a unified interface to simple bar charts.
Here is a simple example for displaying tabular values, with one
bar for each data point:

.. code-block:: python

        from scitools.std import *
        languages = ['C', 'Java', 'C++', 'PHP', 'VB', 'C#', 'Python',
                     'Perl', 'JavaScript']
        ratings = [18, 18, 9.7, 9.7, 6.4, 4.4, 4.2, 3.6, 2.5]
        bar(ratings, 'r',
            barticks=languages,
            ylabel='Ratings in percent (TIOBE Index, April 2010)',
            axis=[-1, len(languages), 0, 20],
            hardcopy='tmp.eps')

The bar chart illustrates the data in the ``ratings`` list. These data
correspond to the names in ``languages``.

.. figure:: figs/pyranking.png

   A simple bar chart illustrating the popularity of common programming languages

One may display groups of bars. The data can then be put in a matrix,
where rows (1st index) correspond to the groups the columns to the
data within one group:

.. code-block:: python

        data = [[ 0.15416284  0.7400497   0.26331502]
                [ 0.53373939  0.01457496  0.91874701]
                [ 0.90071485  0.03342143  0.95694934]
                [ 0.13720932  0.28382835  0.60608318]]
        bar(data,
            barticks=['group 1', 'group 2', 'group 3', 'group 4'],
            legend=['bar 1', 'bar 2', 'bar 3'],
            axis=[-1, data.shape[0], 0, 1.3],
            ylabel='Normalized CPU time',
            title='Bars from a matrix, now with more annotations')

When the names of the groups (barticks) are quite long, rotating them
90 degrees is preferable, and this is done by the keyword
argument ``rotated_barticks=True``.

The demo program in ``examples/bar_demo.py`` contains additional examples
and features.

Backends
========

As we have mentioned earlier, Easyviz is just a unified interface to
other plotting packages, which we refer to as backends. We have
currently implemented backends for Gnuplot, Grace, OpenDX, Matlab,
Matplotlib, Pmw.Blt, Veusz, VisIt, and VTK. Some are more early in
developement than others, like the backends for OpenDx and VisIt.

Because of limitations in many of the plotting packages, not all
features in Easyviz are supported by each of the backends.  Gnuplot
has (at the time of this writing) no support for visualization of 3D
vector fields, so this is of course not available in the Gnuplot
backend either.

Some supported visualization programs are commented on below.

*Gnuplot.* Gnuplot is a command-driven interactive or scripted
plotting utility that works on a wide variety of platforms. Gnuplot
supports many types of plots in both 2D and 3D, including curve plots,
contour plots, vector plots, and surface plots.  3D scalar and vector
fields are not supported. To access Gnuplot from Python and send NumPy
arrays to Gnuplot, we use the Python module ``Gnuplot``.

*Matlab.* Many view Matlab as the de facto standard for making curves
and plots of 2D scalar/vector fields.

*Matplotlib.* Matplotlib is now quickly gaining wide popularity in
the scientific Python community and has established itself as the de
facto standard for curve plotting and 2D contour and (recently) surface
plotting. The interface to Matplotlib is Matlab-insipired, and
different backends are used to create the plots: Gtk, Tk, WxWidgets
and many more.  (Since Easyviz and Matplotlib haver very similar
Matlab-style syntax, Easyviz is just a thin layer on top of Matplotlib
to enable Matplotlib to be used with the Easyviz unified syntax.)
Matplotlib is now a comprehensive package with lots of tuning
possibilities that Easyviz does not support - but one can fetch the
underlying Matplotlib from Easyviz and call all the functionality of
Matplotlib directly.

*Grace.* Grace is a highly interactive curve plotting program on the
Unix/X11 platform which has been popular for many years. It does not
support 2D or 3D scalar or vector fields. However, it has a lot of
functionality for computing with curves and adjusting/fine-tuning
plots interactively.

*PyX.* PyX is a Python package for the creation of PostScript and
PDF files. It combines an abstraction of the PostScript drawing model
with a TeX/LaTeX interface. Complex tasks like 2d and 3d plots in
publication-ready quality are built out of these primitives.

*Pmw.Blt.Graph.* Pmw (Python Mega Widgets) extends the Tkinter
package with more sophisticated widgets, included an interactive
widget for curve plotting. This widget is based on the BLT package
(an extension of Tk written in C).
The BLT backend offers currenlty only basic plotting functionality.

*Veusz.* From `Veusz homepage <http://home.gna.org/veusz>`_: Veusz is a
GUI scientific plotting and graphing package. It is designed to
produce publication-ready Postscript or PDF output. SVG, EMF and
bitmap formats export are also supported. Veusz has a comprehensive
GUI and produces really high-quality plots.

*VTK.* VTK (Visualization ToolKit) is a package primarily aimed at
visualizing 2D and 3D scalar and vector fields by a range of techniques.
VTK is used to achieve 2D and 3D visualizations of the same type as
Matlab offers. However, VTK can do much more (although the Easyviz
commands are restricted to what is typically offered by Matlab).

Design
======

Main Objects
------------

All code that is common to all backends is gathered together in a file
called ``common.py``. For each backend there is a separate file where
the backend dependent code is stored. For example, code that are
specific for the Gnuplot backend, are stored in a file called
``gnuplot_.py`` and code specific for the VTK backend are stored in
``vtk_.py`` (note the final underscore in the stem of the filename - all
backend files have this underscore).

Each backend is a subclass of class ``BaseClass``. The ``BaseClass`` code
is found in ``common.py`` and contains all common code for the backends.
Basically, a backend class extends ``BaseClass`` with
rendering capabilities and backend-specific functionality.

The most important method that needs to be implemented in the backend
is the ``_replot`` method, which updates the backend and the plot after a
change in the data. Another important method for the backend class is
the ``hardcopy`` method, which stores an image of the data in the current
figure to a file.

Inspired by Matlab, the Easyviz interface is organized around figures and
axes. A figure contains an arbitrary number of axes, and the axes can
be placed in arbitrary positions in the figure window. Each figure appears
in a separate window on the screen. The current figure is accessed by
the ``gcf()`` call. Similarly, the current axes are accessed by calling
``gca()``.

It is
natural to have one class for figures and one for axes. Class ``Figure``
contains a dictionary with one (default) or more ``Axis`` objects in
addition to several properties such as figure width and height. Class ``Axis``
has another dictionary with the plot data as well as lots of
parameters for colors, text fonts, labels on the axes, hidden surfaces, etc.
For example, when adding an
elevated surface to the current figure, this surface will be
appended to a list in the current ``Axis`` object.
Optionally one can add the surface to another ``Axis``
object by specifying the ``Axis`` instance as an argument.

All the objects that are to be plotted in a figure such as curves,
surfaces, vectors, and so on, are stored in repsectively classes.  An
elevated surface, for instance, is represented as an instance of class
``Surface``.  All such classes are subclasses of
``PlotProperties``. Besides being the base class of all objects that can
be plotted in a figure
(``Line``,
``Surface``,
``Contours``,
``VelocityVectors``,
``Streams``,
``Volume``),
class ``PlotProperties`` also stores various properties that are common
to all objects in a figure. Examples include line properties, material
properties, storage arrays for x and y values for ``Line`` objects,
and x, y, and z values for 3D objects such as ``Volume``.

The classes mentioned above, i.e., ``BaseClass`` with subclasses, class
``PlotProperties`` with subclasses, as well as class ``Figure`` and class
``Axis`` constitute the most important classes in the Easyviz interface.
Other less important classes are ``Camera``, ``Light``, ``Colorbar``, and
``MaterialProperties``.

All the classes in ``common.py`` follows a convention where class parameters
are set by a ``setp`` method and read by a ``getp`` method. For
example, we can set the limits on the :math:`x` axis by using the ``setp``
method in a ``Axis`` instance:

.. code-block:: py

        ax = gca()                  # get current axis
        ax.setp(xmin=-2, xmax=2)

To extract the values of these limits we can write

.. code-block:: py

        xmin = ax.getp('xmin')
        xmax = ax.getp('xmax')

Normal use will seldom involve ``setp`` and ``getp`` functions, since most
users will apply the Matlab-inspired interface and set, e.g., the
limits by

.. code-block:: py

        xlim([-2,2])

.. _ev:tut:install:

Installation
============

Easyviz comes with the SciTools package, so to install Easyviz, you
must install SciTools, which is available from
`Google code <http://code.google.com/p/scitools>`_.

If you run a Linux system that allows installation from Debian
repositories (Ubuntu is such a Linux system), you get SciTools, NumPy, and
Gnuplot with one Unix command:

.. code-block:: console

        Unix> sudo apt-get install python-scitools

because SciTools is in standard Debian. You probably want to be able
to plot with other packages than Gnuplot as well. In addition, it
is convenient to have ImageMagick installed for conversion between
plot file formats and some encoders for videos. Here is a suggested
list for installation on Debian systems:

.. code-block:: console

        Unix> sudo apt-get install python-matplotlib python-tk python-scipy python-scientific imagemagick netpbm ffmpeg python-pyx python-pmw.blt python-vtk dx grace

Otherwise, you download the tarball with the SciTools software, pack it out,
go the ``scitools`` folder, and run the standard command

.. code-block:: py

        Unix/DOS> python setup.py install

Easyviz is reached as the package ``scitools.easyviz`` and can be
imported in several ways (see the paragraph heading
"Importing Just Easyviz" in the Tutorial).

Easyviz will not work unless you have one or more plotting programs
correctly installed. Below, we have collected some brief information
on installing various programs. (Note that if you do an ``apt-get
install python-scitools`` all necessary plotting programs are
automatically installed for you.)

Please check your plotting program independently of Easyviz, as
described in the *Check Your Backends!* section of the *Troubleshooting*
chapter, if you encounter strange errors during Easyviz plotting.

Installing Gnuplot
------------------

Linux/Unix
----------

*Compile from Source.* Gnuplot can be downloaded from gnuplot.sourceforge.net. It builds
easily on most Unix systems. You also need the ``Gnuplot`` Python
module, which can be obtained from ``gnuplot-py.sourceforge.net``.

*Debian/Ubuntu.* Prebuilt versions are available for Debian/Ubuntu:
run

.. code-block:: py

        apt-get install gnuplot gnuplot-x11 python-gnuplot

but running these commands are not necessary since on Debian/Ubuntu you
will install ``python-scitools`` which effectively installs all the
software that SciTools depend on.

Windows
-------

On Windows, one can either use Gnuplot under Cygwin or use a precompiled
binary from sourgeforce.net.

*Using the Gnuplot Cygwin package.* In this case there are two things that needs to be changed in the
``gp_cygwin.py`` file in the top-level directory of the ``Gnuplot.py``
source tree. First you need to change the ``gnuplot_command`` variable
to ``gnuplot`` instead of ``pgnuplot.exe``. Then you should change the
``default_term`` variable to ``x11`` instead of ``windows`` since the
Gnuplot Cygwin package is not compiled with the Windows
terminal. Finally, install ``Gnuplot.py`` (``python setup.py install``)
and launch X11 by running ``startx`` from a Cygwin prompt. Try to run
the ``test.py`` script that comes with ``Gnuplot.py``. If everything
works, Easyviz can use Gnuplot.

*Using Gnuplot Binaries.* First download the Gnuplot 4.2.4 binaries for Windows (or a newer version)
A possible URL is

.. code-block:: py

        http://prdownloads.sourceforge.net/sourceforge/gnuplot/gp424win32.zip

The zip file may have another name for a newer version of Gnuplot on
Windows.

Then unzip the ``gp424win32.zip`` file to the folder

.. code-block:: py

        C:\gnuplot

Add the folder name

.. code-block:: py

        C:\gnuplot\bin

to the ``PATH`` environment variable (this is done in a graphical interface for
setting environment variables).

Check out the latest SVN revision of the Python interface to
Gnuplot, which is the Python module file ``Gnuplot.py``:

.. code-block:: py

        svn co https://gnuplot-py.svn.sourceforge.net/svnroot/gnuplot-py/trunk/gnuplot-py

Install ``Gnuplot.py``:

.. code-block:: py

        cd gnuplot-py
        python setup.py bdist_wininst
        dist\gnuplot-py-1.8+.win32.exe

Check out the latest SVN revision of SciTools:

.. code-block:: py

        svn co http://scitools.googlecode.com/svn/trunk/ scitools

Install SciTools:

.. code-block:: py

        cd scitools
        python setup.py bdist_wininst
        dist\SciTools-0.4.win32.exe

(The SciTools version number differs.)

Installing Matplotlib
---------------------

This is normally just a matter of

.. code-block:: py

        python setup.py install

in the root directory of the Matplotlib code.

*Windows.* You can download prebuilt binaries from the Matplotlib home page.

Troubleshooting
===============

Can I Perform a Diagnostic Test of Easyviz?
-------------------------------------------

Yes. It is wise to perform a diagnostic test before reporting any error
or trouble to the SciTools maintainers. Find the source folder of SciTools
and go to the ``misc`` subfolder. Run

.. code-block:: py

        python diagonstic.py

On the screen, you can see what you have of working software that Easyviz
may use. You do not need to see "ok" after each test, but at least
one plotting program must be properly installed. Include the detailed
diagonstics in the ``scitools_diagnostic.log`` file as attachment in any
mail to the SciTools developers.

The Plot Window Disappears Immediately
--------------------------------------

Depending on the backend used for plotting with Easyviz, the plot
window may be killed when the program terminates. Adding a statement
that makes the program halt provides a remedy:

.. code-block:: python

        raw_input('Press Return key to quit: ')

The plot window will now stay on the screen until hitting the Enter/Return key.

Another remedy can be to add a ``show()`` call at the end of the plotting:

.. code-block:: python

        show()

.. test on Windows!

I Get Thread Errors While Plotting
----------------------------------

With the Gnuplot backend, thread errors from Python may occur if you
plot many curves. The remedy is to do ``import time`` and insert
a ``time.sleep(0.2)`` (pause the program for 0.2 sec) between each call
to the ``plot`` command.

Remark: Scitools v0.8 automatically inserts a 0.2 sec pause when
plotting many curves with the Gnuplot backend.

I Get Strange Errors Saying Something About LaTeX
-------------------------------------------------

You probably run Easyviz with Matplotlib as backend, and you do not
have a working LaTeX installation. Matplotlib applies LaTeX for
improved rendering of legends, titles, and numbers.  The fix is to
turn off the use of LaTeX, which is done by the ``text.usetex``
parameter in the ``matplotlib`` section of the configuration file.  Set
this parameter to ``false``. See the subsection "Setting Parameters in
the Configuration File" in the section "Advanced Easyviz Topics" in
the Easyviz tutorial. The tutorial can be reached from the code.google.com
site or by running pydoc scitools.easyviz. If you use Matplotlib as
default plotting engine, we recommend to have a ``.scitools.cfg``
configuration file in your home folder and that use control the use
of Matplotlib parameters in this file.

Another fix of LaTeX-related problems is to switch to another backend
than Matplotlib.

Old Programs with 2D Scalar/Vector Field Plotting Do Not Work
-------------------------------------------------------------

SciTools version 0.7 changed the default backend for plotting to
Matplotlib instead of Gnuplot (provided you have Matplotlib and you
run ``setup.py`` to install SciTools - binaries for Debian still has
Gnuplot as the plotting engine). Some functionality in Gnuplot, especially
regarding 2D vector/scalar fields, is not yet present in Matplotlib
and/or supported by the Easyviz interface to Matplotlib.
You then need to explicitly run the script with Gnuplot as plottin
engine:

.. code-block:: py

        python myprogram.py --SCITOOLS_easyviz_backend gnuplot

or you must import gnuplot explicitly in the program:

.. code-block:: py

        from scitools.std import *
        from scitools.easyviz.gnuplot_ import *

or you can edit the installed ``scitools.cfg`` file ("backend" keyword
in the "easyviz" section), or your local version ``.scitools.cfg`` in
your home folder, or maybe the simplest solution is to reinstall
SciTools with Gnuplot as plotting engine:

.. code-block:: py

        python setup.py install --easyviz_backend gnuplot

Check Your Backends!
--------------------

When you encounter a problem with Easyviz plotting, make sure that the
backend works correctly on its own (there may, e.g., be installation
problems with the backend - Easyviz just calls the backend to do the
plotting).

Gnuplot
~~~~~~~

For the Gnuplot backend you can try the following commands in a
terminal window:

.. code-block:: py

        Unix/DOS> gnuplot
        gnuplot> plot sin(x)

This should result in a plot of the sine function on the screen.
If this command does not work, Easyviz will not work with the Gnuplot
backend. A common problem is that Gnuplot is installed, but the path
to the Gnuplot executable is not registered in the ``PATH`` environment
variable. See the section *Installing Gnuplot* if you need help with
installing the Gnuplot program and its Python interface.

Matplotlib
~~~~~~~~~~

The following code tests if you have installed Matplotlib correctly:

.. code-block:: py

        import matplotlib.pyplot as plt
        import numpy as np
        x = np.linspace(0, 2*np.pi, 101)
        y = np.sin(x)
        plt.plot(x, y)
        plt.show()

In case of problems, go to the Matplotlib source directory, remove the
``build`` subdirectory, and try a new install with ``python setup.py install``.

Can I Easily Turn Off All Plotting?
-----------------------------------

Yes, this is very convenient when debugging other (non-plotting) parts
of a program. Just write

.. code-block:: py

        from scitools.std import *
        turn_off_plotting(globals())

How Can I Change the Type of Gnuplot Window?
--------------------------------------------

The configuration file (``.scitools.cfg`` in your home directory or a
local directory, copied from ``scitools.cfg`` in the SciTools source
code distribution) has an item for controlling the type of *terminal*
used by Gnuplot:

.. code-block:: py

        [gnuplot]
        ...
        default_term               = <str> wxt

Here, the ``wxt`` terminal, based on wxWidgets, is chosen. Other
choices are ``x11`` on systems supporting X11 graphics, or ``aqua`` on
Mac. The ``wxt`` value is an allround choice since wxWidgets work, in theory,
on all platforms.

How Can The Aspect Ratio of The Axes Be Controlled?
---------------------------------------------------

See the section "Controlling the Aspect Ratio of Axes" in the
tutorial.

Trouble with Gnuplot and Threads
--------------------------------

When using the Gnuplot backend, the following error may be encountered:

.. code-block:: py

        thread.error: can't start new thread

A remedy is to create fewer plots, and for animations, update the plot
window less frequently. For example,

.. code-block:: python

        for i in range(number_of_frames_in_animation):
            <prepare data>
            if i % == 100:     # plot every 100 frames
                <make plot>

Trouble with Movie Making
-------------------------

The call to ``movie`` demands that you have video encoders installed.
The legal encoders are ``mencoder``, ``ffmpeg``, ``mpeg_encode``, ``ppmtompeg``,
``mpeg2enc``, and ``convert``. Some of these also require additional
software to be installed.

To install (e.g.) ``convert``, you need to install the ImageMagick
software suite, since ``convert`` is a part of that package. ImageMagick
is easy to install on most platforms. The ``ppmtompeg`` encoder is a part
of the Netpbm software, while ``mpeg2enc`` is a part of ``mjpegtools``.

On Linux Ubuntu you can issue the following installation command to install most of the available encoders for the ``movie`` function:

.. code-block:: py

        Unix> sudo apt-get install mencoder ffmpeg libavcodec-unstripped-51 netpbm mjpegtools imagemagick

When something goes wrong with the movie making, check the output in
the terminal window. By default, Easyviz prints the command that makes
the movie. You can manually copy this command and run it again to start
finding out what can be wrong. Just switching to a different encoder can be
a quick remedy. The switch is done with the ``encoder`` keyword argument
to ``movie``, e.g.,

.. code-block:: py

        # Make animated GIF movie in the file tmpmovie.gif
        movie('tmp_*.png', encoder='convert', fps=2,
              output_file='tmpmovie.gif')

I Get Thread Errors with Gnuplot
--------------------------------

When plotting inside a loop, e.g.,

.. code-block:: py

        for i in some_values:
            ...
            plot(t, X0, 'r-6', axis=(0, 1, -2, 2),
                 xlabel='t', ylabel='Xt', title='My Title')

Gnuplot may lead to thread errors. A remedy is to do some plotting
outside the loop and then only update the data inside the loop:

.. code-block:: py

        plot(t, X0, 'r-6', axis=(0, 1, -2, 2),
             xlabel='t', ylabel='Xt', title='My Title')
        for i in some_values:
            ...
            plot(t, X0)

Where Can I Find Easyviz Documentation?
---------------------------------------

There is a verbose Easyviz documentation that mainly focuses on an
introduction to Easyviz (what you read now is a part of that
documentation).

Another useful source of information is the many examples that come
with the SciTools/Easyviz source code. The examples are located in
the ``examples`` subfolder of the source.

Grace Gives Error Messages When Calling Savefig/Hardcopy
--------------------------------------------------------

Some versions of grace do not like commands for printing the plot
to file. Try the interactive GUI: set options in Print setup... and
then click on Print.

I Cannot Find Out How My Plot Can Be Created
--------------------------------------------

Note that Easyviz only support the most basic types of plots:

  * y=f(x) curves

  * bar plots

  * contour plots of 2D scalar fields

  * elevated 3D surfaces of 2D scalar fields

  * 3D isosurfaces of 3D scalar fields

  * arrows reflecting 2D/3D vector fields

  * streamlines, streamtubes, and streamribbon for 3D vector fields.

For such standard plots you can use Easyviz, otherwise you have to
use a plotting package like Matplotlib, Gnuplot, or VTK directly
from your Python program.

The following Matlab-like commands (functions) are available (but not
supported by all backends):

  * autumn,

  * axes,

  * axis,

  * bone,

  * box,

  * brighten,

  * camdolly,

  * camlight,

  * camlookat,

  * campos,

  * camproj,

  * camroll,

  * camtarget,

  * camup,

  * camva,

  * camzoom,

  * caxis,

  * cla,

  * clabel,

  * clf,

  * close,

  * closefig,

  * closefigs,

  * colorbar,

  * colorcube,

  * colormap,

  * coneplot,

  * contour,

  * contour3,

  * contourf,

  * contourslice,

  * cool,

  * copper,

  * daspect,

  * figure,

  * fill,

  * fill3,

  * flag,

  * gca,

  * gcf,

  * get,

  * gray,

  * grid,

  * hardcopy,

  * hidden,

  * hold,

  * hot,

  * hsv,

  * ishold,

  * isocaps,

  * isosurface,

  * jet,

  * legend,

  * light,

  * lines,

  * loglog,

  * material,

  * mesh,

  * meshc,

  * openfig,

  * pcolor,

  * pink,

  * plot,

  * plot3,

  * prism,

  * quiver,

  * quiver3,

  * reducevolum,

  * savefig,

  * semilogx,

  * semilogy,

  * set,

  * shading,

  * show,

  * slice_,

  * spring,

  * streamline,

  * streamribbon,

  * streamslice,

  * streamtube,

  * subplot,

  * subvolume,

  * summer,

  * surf,

  * surfc,

  * surfl,

  * title,

  * vga,

  * view,

  * white,

  * winter,

  * xlabel,

  * ylabel,

  * zlabel'''

__author__ = "Johannes H. Ring, Hans Petter Langtangen, Rolv Erlend Bredesen"

_import_list = []  # used as in basics.py to keep track of what we import
import time as _time; _t0 = _time.clock();
_import_times = 'easyviz import times: '

from scitools.globaldata import backend, VERBOSE   # read-only import
_import_list.append("from scitools.globaldata import backend, VERBOSE")

_t1 = _time.clock(); _import_times += 'config: %s ' % (_t1 - _t0)

# Note: this import is always performed, also before any
# specialized import a la from scitools.easyviz.matplotlib_ import *
# For quicker import of special backends, use command-line or config
# file specification of the backend
cmd = 'from %s_ import *' % backend
exec(cmd)
_t2 = _time.clock(); _import_times += '%s: %s ' % (backend, _t2 - _t1)
_import_list.append(cmd)

from utils import *
from movie import movie
_import_list.append('from utils import *\nfrom movie import movie')

_t3 = _time.clock(); _import_times += 'utils: %s ' % (_t3 - _t2)

if VERBOSE >= 2:
    for i in _import_list:
        print i
if VERBOSE >= 3:
    print _import_times
if VERBOSE >= 1:
    print "scitools.easyviz backend is %s" % backend

__doc__ += '\nImport statements in this module:\n' + '\n'.join(_import_list)

# add plot doc string to package doc string:
#__doc__ += plot.__doc__

import numpy,from numpy,import scipy,from scipy