using bytes in image type conversions

[PyX.git] / manual / graph.rst

.. module:: graph

******
Graphs
******


Introduction
============

PyX can be used for data and function plotting. At present x-y-graphs and
x-y-z-graphs are supported only. However, the component architecture of the
graph system described in section :ref:`graph_components` allows for additional
graph geometries while reusing most of the existing components.

Creating a graph splits into two basic steps. First you have to create a graph
instance. The most simple form would look like::

   from pyx import *
   g = graph.graphxy(width=8)

The graph instance ``g`` created in this example can then be used to actually
plot something into the graph. Suppose you have some data in a file
:file:`graph.dat` you want to plot. The content of the file could look like:


.. include:: graph.dat
   :literal:

To plot these data into the graph ``g`` you must perform::

   g.plot(graph.data.file("graph.dat", x=1, y=2))

The method :meth:`plot` takes the data to be plotted and optionally a list of
graph styles to be used to plot the data. When no styles are provided, a default
style defined by the data instance is used. For data read from a file by an
instance of :class:`graph.data.file`, the default are symbols. When
instantiating :class:`graph.data.file`, you not only specify the file name, but
also a mapping from columns to axis names and other information the styles might
make use of (*e.g.* data for error bars to be used by the errorbar style).

While the graph is already created by that, we still need to perform a write of
the result into a file. Since the graph instance is a canvas, we can just call
its :meth:`writeEPSfile` method.  ::

   g.writeEPSfile("graph")

The result :file:`graph.eps` is shown in figure :ref:`fig_graph`.

.. _fig_graph:
.. figure:: graph.*
   :align:  center

   A minimalistic plot for the data from file :file:`graph.dat`.

Instead of plotting data from a file, other data source are available as well.
For example function data is created and placed into :meth:`plot` by the
following line::

   g.plot(graph.data.function("y(x)=x**2"))

You can plot different data in a single graph by calling :meth:`plot` several
times before :meth:`writeEPSfile` or :meth:`writePDFfile`. Note that a calling
:meth:`plot` will fail once a graph was forced to "finish" itself. This happens
automatically, when the graph is written to a file. Thus it is not an option to
call :meth:`plot` after :meth:`writeEPSfile` or :meth:`writePDFfile`. The topic
of the finalization of a graph is addressed in more detail in section
:mod:`graph.graph`. As you can see in figure :ref:`fig_graph2`, a function is
plotted as a line by default.

.. _fig_graph2:
.. figure:: graph2.*
   :align:  center

   Plotting data from a file together with a function.

While the axes ranges got adjusted automatically in the previous example, they
might be fixed by keyword options in axes constructors. Plotting only a function
will need such a setting at least in the variable coordinate. The following code
also shows how to set a logathmic axis in y-direction:


.. include:: graph3.py
   :literal:

The result is shown in figure :ref:`fig_graph3`.

.. _fig_graph3:
.. figure:: graph3.*
   :align:  center

   Plotting a function for a given axis range and use a logarithmic y-axis.


.. _graph_components:

Component architecture
======================

Creating a graph involves a variety of tasks, which thus can be separated into
components without significant additional costs. This structure manifests itself
also in the PyX source, where there are different modules for the different
tasks. They interact by some well-defined interfaces. They certainly have to be
completed and stabilized in their details, but the basic structure came up in
the continuous development quite clearly. The basic parts of a graph are:

graph
   Defines the geometry of the graph by means of graph coordinates with range
   [0:1]. Keeps lists of plotted data, axes *etc.*

data
   Produces or prepares data to be plotted in graphs.

style
   Performs the plotting of the data into the graph. It gets data, converts them
   via the axes into graph coordinates and uses the graph to finally plot the data
   with respect to the graph geometry methods.

key
   Responsible for the graph keys.

axis
   Creates axes for the graph, which take care of the mapping from data values to
   graph coordinates. Because axes are also responsible for creating ticks and
   labels, showing up in the graph themselves and other things, this task is
   splitted into several independent subtasks. Axes are discussed separately in
   chapter :mod:`axis`.

.. module:: graph.graph

Module :mod:`graph.graph`: Graph geometry
=========================================


The classes :class:`graphxy` and :class:`graphxyz` are part of the module
:mod:`graph.graph`. However, there are shortcuts to access the classes via
``graph.graphxy`` and ``graph.graphxyz``, respectively.


.. class:: graphxy(xpos=0, ypos=0, width=None, height=None, ratio=goldenmean, key=None, backgroundattrs=None, axesdist=0.8*unit.v_cm, xaxisat=None, yaxisat=None, **axes)

   This class provides an x-y-graph. A graph instance is also a fully functional
   canvas.

   The position of the graph on its own canvas is specified by *xpos* and *ypos*.
   The size of the graph is specified by *width*, *height*, and *ratio*. These
   parameters define the size of the graph area not taking into account the
   additional space needed for the axes. Note that you have to specify at least
   *width* or *height*. *ratio* will be used as the ratio between *width* and
   *height* when only one of these is provided.

   *key* can be set to a :class:`graph.key.key` instance to create an automatic
   graph key. ``None`` omits the graph key.

   *backgroundattrs* is a list of attributes for drawing the background of the
   graph. Allowed are decorators, strokestyles, and fillstyles. ``None`` disables
   background drawing.

   *axisdist* is the distance between axes drawn at the same side of a graph.

   *xaxisat* and *yaxisat* specify a value at the y and x axis, where the
   corresponding axis should be moved to. It's a shortcut for corresonding calls of
   :meth:`axisatv` described below. Moving an axis by *xaxisat* or *yaxisat*
   disables the automatic creation of a linked axis at the opposite side of the
   graph.

   *\*\*axes* receives axes instances. Allowed keywords (axes names) are ``x``,
   ``x2``, ``x3``, *etc.* and ``y``, ``y2``, ``y3``, *etc.* When not providing an
   ``x`` or ``y`` axis, linear axes instances will be used automatically. When not
   providing a ``x2`` or ``y2`` axis, linked axes to the ``x`` and ``y`` axes are
   created automatically and *vice versa*. As an exception, a linked axis is not
   created automatically when the axis is placed at a specific position by
   *xaxisat* or *yaxisat*. You can disable the automatic creation of axes by
   setting the linked axes to ``None``. The even numbered axes are plotted at the
   top (``x`` axes) and right (``y`` axes) while the others are plotted at the
   bottom (``x`` axes) and left (``y`` axes) in ascending order each.

Some instance attributes might be useful for outside read-access. Those are:


.. attribute:: graphxy.axes

   A dictionary mapping axes names to the :class:`anchoredaxis` instances.

To actually plot something into the graph, the following instance method
:meth:`plot` is provided:


.. method:: graphxy.plot(data, styles=None)

   Adds *data* to the list of data to be plotted. Sets *styles* to be used for
   plotting the data. When *styles* is ``None``, the default styles for the data as
   provided by *data* is used.

   *data* should be an instance of any of the data described in section
   :mod:`graph.data`.

   When the same combination of styles (*i.e.* the same references) are used
   several times within the same graph instance, the styles are kindly asked by the
   graph to iterate their appearance. Its up to the styles how this is performed.

   Instead of calling the plot method several times with different *data* but the
   same style, you can use a list (or something iterateable) for *data*.

While a graph instance only collects data initially, at a certain point it must
create the whole plot. Once this is done, further calls of :meth:`plot` will
fail. Usually you do not need to take care about the finalization of the graph,
because it happens automatically once you write the plot into a file. However,
sometimes position methods (described below) are nice to be accessible. For
that, at least the layout of the graph must have been finished. However, the
drawing order is based on canvas layers and thus the order in which the
:meth:`do`\ -methods are called will not alter the output. Multiple calls to
any of the :meth:`do`\ -methods have no effect (only the first call counts).
The orginal order in which the :meth:`do`\ -methods are called is:


.. method:: graphxy.dolayout()

   Fixes the layout of the graph. As part of this work, the ranges of the axes are
   fitted to the data when the axes ranges are allowed to adjust themselves to the
   data ranges. The other :meth:`do`\ -methods ensure, that this method is always
   called first.


.. method:: graphxy.dobackground()

   Draws the background.


.. method:: graphxy.doaxes()

   Inserts the axes.


.. method:: graphxy.doplotitem(plotitem)

   Plots the plotitem as returned by the graphs plot method.


.. method:: graphxy.doplot()

   Plots all (remaining) plotitems.


.. method:: graphxy.dokeyitem()

   Inserts a plotitem in the graph key as returned by the graphs plot method.


.. method:: graphxy.dokey()

   Inserts the graph key.


.. method:: graphxy.finish()

   Finishes the graph by calling all pending :meth:`do`\ -methods. This is done
   automatically, when the output is created.

The graph provides some methods to access its geometry:


.. method:: graphxy.pos(x, y, xaxis=None, yaxis=None)

   Returns the given point at *x* and *y* as a tuple ``(xpos, ypos)`` at the graph
   canvas. *x* and *y* are anchoredaxis instances for the two axes *xaxis* and
   *yaxis*. When *xaxis* or *yaxis* are ``None``, the axes with names ``x`` and
   ``y`` are used. This method fails if called before :meth:`dolayout`.


.. method:: graphxy.vpos(vx, vy)

   Returns the given point at *vx* and *vy* as a tuple ``(xpos, ypos)`` at the
   graph canvas. *vx* and *vy* are graph coordinates with range [0:1].


.. method:: graphxy.vgeodesic(vx1, vy1, vx2, vy2)

   Returns the geodesic between points *vx1*, *vy1* and *vx2*, *vy2* as a path. All
   parameters are in graph coordinates with range [0:1]. For :class:`graphxy` this
   is a straight line.


.. method:: graphxy.vgeodesic_el(vx1, vy1, vx2, vy2)

   Like :meth:`vgeodesic` but this method returns the path element to connect the
   two points.

.. index::
   single: xbasepath()@xbasepath() (graphxy method)
   single: xvbasepath()@xvbasepath() (graphxy method)
   single: xgridpath()@xgridpath() (graphxy method)
   single: xvgridpath()@xvgridpath() (graphxy method)
   single: xtickpoint()@xtickpoint() (graphxy method)
   single: xvtickpoint()@xvtickpoint() (graphxy method)
   single: xtickdirection()@xtickdirection() (graphxy method)
   single: xvtickdirection()@xvtickdirection() (graphxy method)
   single: ybasepath()@ybasepath() (graphxy method)
   single: yvbasepath()@yvbasepath() (graphxy method)
   single: ygridpath()@ygridpath() (graphxy method)
   single: yvgridpath()@yvgridpath() (graphxy method)
   single: ytickpoint()@ytickpoint() (graphxy method)
   single: yvtickpoint()@yvtickpoint() (graphxy method)
   single: ytickdirection()@ytickdirection() (graphxy method)
   single: yvtickdirection()@yvtickdirection() (graphxy method)

Further geometry information is available by the :attr:`axes` instance variable,
with is a dictionary mapping axis names to :class:`anchoredaxis` instances.
Shortcuts to the anchoredaxis positioner methods for the ``x``\ - and ``y``\
-axis become available after :meth:`dolayout` as :class:`graphxy` methods
``Xbasepath``, ``Xvbasepath``, ``Xgridpath``, ``Xvgridpath``, ``Xtickpoint``,
``Xvtickpoint``, ``Xtickdirection``, and ``Xvtickdirection`` where the prefix
``X`` stands for ``x`` and ``y``.


.. method:: graphxy.axistrafo(axis, t)

   This method can be used to apply a transformation *t* to an
   :class:`anchoredaxis` instance *axis* to modify the axis position and the like.
   This method fails when called on a not yet finished axis, i.e. it should be used
   after :meth:`dolayout`.


.. method:: graphxy.axisatv(axis, v)

   This method calls :meth:`axistrafo` with a transformation to move the axis
   *axis* to a graph position *v* (in graph coordinates).

The class :class:`graphxyz` is very similar to the :class:`graphxy` class,
except for its additional dimension. In the following documentation only the
differences to the :class:`graphxy` class are described.


.. class:: graphxyz(xpos=0, ypos=0, size=None, xscale=1, yscale=1, zscale=1/goldenmean, projector=central(10, -30, 30), key=None, **axes)

   This class provides an x-y-z-graph.

   The position of the graph on its own canvas is specified by *xpos* and *ypos*.
   The size of the graph is specified by *size* and the length factors *xscale*,
   *yscale*, and *zscale*. The final size of the graph depends on the projector
   *projector*, which is called with ``x``, ``y``, and ``z`` values up to *xscale*,
   *yscale*, and  *zscale* respectively and scaling the result by *size*. For a
   parallel projector changing *size* is thus identical to changing *xscale*,
   *yscale*, and *zscale* by the same factor. For the central projector the
   projectors internal distance would also need to be changed by this factor. Thus
   *size* changes the size of the whole graph without changing the projection.

   *projector* defines the conversion of 3d coordinates to 2d coordinates. It can
   be an instance of :class:`central` or :class:`parallel` described below.

   *\*\*axes* receives axes instances as for :class:`graphxy`. The graphxyz allows
   for 4 axes per graph dimension ``x``, ``x2``, ``x3``, ``x4``, ``y``, ``y2``,
   ``y3``, ``y4``, ``z``, ``z2``, ``z3``, and ``z4``. The x-y-plane is the
   horizontal plane at the bottom and the ``x``, ``x2``, ``y``, and ``y2`` axes are
   placed at the boundary of this plane with ``x`` and ``y`` always being in front.
   ``x3``, ``x4``, ``y3``, and ``y4`` are handled similar, but for the top plane of
   the graph. The ``z`` axis is placed at the origin of the ``x`` and ``y``
   dimension, whereas ``z2`` is placed at the final point of the ``x`` dimension,
   ``z3`` at the final point of the ``y`` dimension and ``z4`` at the final point
   of the ``x`` and ``y`` dimension together.


.. attribute:: graphxyz.central

   The central attribute of the graphxyz is the :class:`central` class. See the
   class description below.


.. attribute:: graphxyz.parallel

   The parallel attribute of the graphxyz is the :class:`parallel` class. See the
   class description below.

Regarding the 3d to 2d transformation the methods :meth:`pos`, :meth:`vpos`,
:meth:`vgeodesic`, and :meth:`vgeodesic_el` are available as for class
:class:`graphxy` and just take an additional argument for the dimension. Note
that a similar transformation method (3d to 2d) is available as part of the
projector as well already, but only the graph acknowledges its size, the scaling
and the internal tranformation of the graph coordinates to the scaled
coordinates. As the projector also implements a :meth:`zindex` and a
:meth:`angle` method, those are also available at the graph level in the graph
coordinate variant (i.e. having an additional v in its name and using values
from 0 to 1 per dimension).


.. method:: graphxyz.vzindex(vx, vy, vz)

   The depths of the point defined by *vx*, *vy*, and *vz* scaled to a range [-1:1]
   where 1 is closest to the viewer. All arguments passed to the method are in graph
   coordinates with range [0:1].


.. method:: graphxyz.vangle(vx1, vy1, vz1, vx2, vy2, vz2, vx3, vy3, vz3)

   The cosine of the angle of the view ray thru point ``(vx1, vy1, vz1)`` and the
   plane defined by the points ``(vx1, vy1, vz1)``, ``(vx2, vy2, vz2)``, and
   ``(vx3, vy3, vz3)``. All arguments passed to the method are in graph coordinates
   with range [0:1].

There are two projector classes :class:`central` and :class:`parallel`:


.. class:: central(distance, phi, theta, anglefactor=math.pi/180)

   Instances of this class implement a central projection for the given parameters.

   *distance* is the distance of the viewer from the origin. Note that the
   :class:`graphxyz` class uses the range ``-xscale`` to ``xscale``, ``-yscale`` to
   ``yscale``, and ``-zscale`` to ``zscale`` for the coordinates ``x``, ``y``, and
   ``z``. As those scales are of the order of one (by default), the distance should
   be of the order of 10 to give nice results. Smaller distances increase the
   central projection character while for huge distances the central projection
   becomes identical to the parallel projection.

   ``phi`` is the angle of the viewer in the x-y-plane and ``theta`` is the angle
   of the viewer to the x-y-plane. The standard notation for spheric coordinates
   are used. The angles are multiplied by *anglefactor* which is initialized to do
   a degree in radiant transformation such that you can specify ``phi`` and
   ``theta`` in degree while the internal computation is always done in radiants.


.. class:: parallel(phi, theta, anglefactor=math.pi/180)

   Instances of this class implement a parallel projection for the given
   parameters. There is no distance for that transformation (compared to the
   central projection). All other parameters are identical to the :class:`central`
   class.


.. module:: graph.data

Module :mod:`graph.data`: Graph data
====================================


The following classes provide data for the :meth:`plot` method of a graph. The
classes are implemented in :mod:`graph.data`.


.. class:: file(filename, commentpattern=defaultcommentpattern, columnpattern=defaultcolumnpattern, stringpattern=defaultstringpattern, skiphead=0, skiptail=0, every=1, title=notitle, context={}, copy=1, replacedollar=1, columncallback="__column__", **columns)

   This class reads data from a file and makes them available to the graph system.
   *filename* is the name of the file to be read. The data should be organized in
   columns.

   The arguments *commentpattern*, *columnpattern*, and *stringpattern* are
   responsible for identifying the data in each line of the file. Lines matching
   *commentpattern* are ignored except for the column name search of the last non-
   empty comment line before the data. By default a line starting with one of the
   characters ``'#'``, ``'%'``, or ``'!'`` as well as an empty line is treated as a
   comment.

   A non-comment line is analysed by repeatedly matching *stringpattern* and,
   whenever the stringpattern does not match, by *columnpattern*. When the
   *stringpattern* matches, the result is taken as the value for the next column
   without further transformations. When *columnpattern* matches, it is tried to
   convert the result to a float. When this fails the result is taken as a string
   as well. By default, you can write strings with spaces surrounded by ``'"'``
   immediately surrounded by spaces or begin/end of line in the data file.
   Otherwise ``'"'`` is not taken to be special.

   *skiphead* and *skiptail* are numbers of data lines to be ignored at the
   beginning and end of the file while *every* selects only every *every* line from
   the data.

   *title* is the title of the data to be used in the graph key. A default title is
   constructed out of *filename* and *\*\*columns*. You may set *title* to ``None``
   to disable the title.

   Finally, *columns* define columns out of the existing columns from the file by a
   column number or a mathematical expression (see below). When *copy* is set the
   names of the columns in the file (file column names) and the freshly created
   columns having the names of the dictionary key (data column names) are passed as
   data to the graph styles. The data columns may hide file columns when names are
   equal. For unset *copy* the file columns are not available to the graph styles.

   File column names occur when the data file contains a comment line immediately
   in front of the data (except for empty or empty comment lines). This line will
   be parsed skipping the matched comment identifier as if the line would be
   regular data, but it will not be converted to floats even if it would be
   possible to convert the items. The result is taken as file column names, *i.e.*
   a string representation for the columns in the file.

   The values of *\*\*columns* can refer to column numbers in the file starting at
   ``1``. The column ``0`` is also available and contains the line number starting
   from ``1`` not counting comment lines, but lines skipped by *skiphead*,
   *skiptail*, and *every*. Furthermore values of *\*\*columns* can be strings:
   file column names or complex mathematical expressions. To refer to columns
   within mathematical expressions you can also use file column names when they are
   valid variable identifiers. Equal named items in context will then be hidden.
   Alternatively columns can be access by the syntax ``$<number>`` when
   *replacedollar* is set. They will be translated into function calls to
   *columncallback*, which is a function to access column data by index or name.

   *context* allows for accessing external variables and functions when evaluating
   mathematical expressions for columns. Additionally to the identifiers in
   *context*, the file column names, the *columncallback* function and the
   functions shown in the table "builtins in math expressions" at the end of the
   section are available.

   Example::

      graph.data.file("test.dat", a=1, b="B", c="2*B+$3")

   with :file:`test.dat` looking like::

      # A   B C
      1.234 1 2
      5.678 3 4

   The columns with name ``"a"``, ``"b"``, ``"c"`` will become ``"[1.234,
   5.678]"``, ``"[1.0, 3.0]"``, and ``"[4.0, 10.0]"``, respectively. The columns
   ``"A"``, ``"B"``, ``"C"`` will be available as well, since *copy* is enabled by
   default.

   When creating several data instances accessing the same file, the file is read
   only once. There is an inherent caching of the file contents.

For the sake of completeness we list the default patterns:


.. attribute:: file.defaultcommentpattern

   ``re.compile(r"(#+|!+|%+)\s*")``


.. attribute:: file.defaultcolumnpattern

   ``re.compile(r"\"(.*?)\"(\s+|$)")``


.. attribute:: file.defaultstringpattern

   ``re.compile(r"(.*?)(\s+|$)")``


.. class:: function(expression, title=notitle, min=None, max=None, points=100, context={})

   This class creates graph data from a function. *expression* is the mathematical
   expression of the function. It must also contain the result variable name
   including the variable the function depends on by assignment. A typical example
   looks like ``"y(x)=sin(x)"``.

   *title* is the title of the data to be used in the graph key. By default
   *expression* is used. You may set *title* to ``None`` to disable the title.

   *min* and *max* give the range of the variable. If not set, the range spans the
   whole axis range. The axis range might be set explicitly or implicitly by ranges
   of other data. *points* is the number of points for which the function is
   calculated. The points are choosen linearly in terms of graph coordinates.

   *context* allows for accessing external variables and functions. Additionally to
   the identifiers in *context*, the variable name and the functions shown in the
   table "builtins in math expressions" at the end of the section are available.


.. class:: paramfunction(varname, min, max, expression, title=notitle, points=100, context={})

   This class creates graph data from a parametric function. *varname* is the
   parameter of the function. *min* and *max* give the range for that variable.
   *points* is the number of points for which the function is calculated. The
   points are choosen lineary in terms of the parameter.

   *expression* is the mathematical expression for the parametric function. It
   contains an assignment of a tuple of functions to a tuple of variables. A
   typical example looks like ``"x, y = cos(k), sin(k)"``.

   *title* is the title of the data to be used in the graph key. By default
   *expression* is used. You may set *title* to ``None`` to disable the title.

   *context* allows for accessing external variables and functions. Additionally to
   the identifiers in *context*, *varname* and the functions shown in the table
   "builtins in math expressions" at the end of the section are available.


.. class:: values(title="user provided values", **columns)

   This class creates graph data from externally provided data. Each column is a
   list of values to be used for that column.

   *title* is the title of the data to be used in the graph key.


.. class:: points(data, title="user provided points", addlinenumbers=1, **columns)

   This class creates graph data from externally provided data. *data* is a list of
   lines, where each line is a list of data values for the columns.

   *title* is the title of the data to be used in the graph key.

   The keywords of *\*\*columns* become the data column names. The values are the
   column numbers starting from one, when *addlinenumbers* is turned on (the zeroth
   column is added to contain a line number in that case), while the column numbers
   starts from zero, when *addlinenumbers* is switched off.


.. class:: data(data, title=notitle, context=, copy=1, replacedollar=1, columncallback="__column__", **columns)

   This class provides graph data out of other graph data. *data* is the source of
   the data. All other parameters work like the equally called parameters in
   :class:`graph.data.file`. Indeed, the latter is built on top of this class by
   reading the file and caching its contents in a :class:`graph.data.list`
   instance.


.. class:: conffile(filename, title=notitle, context=, copy=1, replacedollar=1, columncallback="__column__", **columns)

   This class reads data from a config file with the file name *filename*. The
   format of a config file is described within the documentation of the
   :mod:`ConfigParser` module of the Python Standard Library.

   Each section of the config file becomes a data line. The options in a section
   are the columns. The name of the options will be used as file column names. All
   other parameters work as in *graph.data.file* and *graph.data.data* since they
   all use the same code.


.. class:: cbdfile(filename, minrank=None, maxrank=None, title=notitle, context=, copy=1, replacedollar=1, columncallback="__column__", **columns)

   This is an experimental class to read map data from cbd-files. See
   `<http://sepwww.stanford.edu/ftp/World_Map/>`_ for some world-map data.

The builtins in math expressions are listed in the following table:

+------------------+--------------------------------------------+
| name             | value                                      |
+==================+============================================+
| ``neg``          | ``lambda x: -x``                           |
+------------------+--------------------------------------------+
| ``abs``          | ``lambda x: x < 0 and -x or x``            |
+------------------+--------------------------------------------+
| ``sgn``          | ``lambda x: x < 0 and -1 or 1``            |
+------------------+--------------------------------------------+
| ``sqrt``         | ``math.sqrt``                              |
+------------------+--------------------------------------------+
| ``exp``          | ``math.exp``                               |
+------------------+--------------------------------------------+
| ``log``          | ``math.log``                               |
+------------------+--------------------------------------------+
| ``sin``          | ``math.sin``                               |
+------------------+--------------------------------------------+
| ``cos``          | ``math.cos``                               |
+------------------+--------------------------------------------+
| ``tan``          | ``math.tan``                               |
+------------------+--------------------------------------------+
| ``asin``         | ``math.asin``                              |
+------------------+--------------------------------------------+
| ``acos``         | ``math.acos``                              |
+------------------+--------------------------------------------+
| ``atan``         | ``math.atan``                              |
+------------------+--------------------------------------------+
| ``sind``         | ``lambda x: math.sin(math.pi/180*x)``      |
+------------------+--------------------------------------------+
| ``cosd``         | ``lambda x: math.cos(math.pi/180*x)``      |
+------------------+--------------------------------------------+
| ``tand``         | ``lambda x: math.tan(math.pi/180*x)``      |
+------------------+--------------------------------------------+
| ``asind``        | ``lambda x: 180/math.pi*math.asin(x)``     |
+------------------+--------------------------------------------+
| ``acosd``        | ``lambda x: 180/math.pi*math.acos(x)``     |
+------------------+--------------------------------------------+
| ``atand``        | ``lambda x: 180/math.pi*math.atan(x)``     |
+------------------+--------------------------------------------+
| ``norm``         | ``lambda x, y: math.hypot(x, y)``          |
+------------------+--------------------------------------------+
| ``splitatvalue`` | see the ``splitatvalue`` description below |
+------------------+--------------------------------------------+
| ``pi``           | ``math.pi``                                |
+------------------+--------------------------------------------+
| ``e``            | ``math.e``                                 |
+------------------+--------------------------------------------+

``math`` refers to Pythons :mod:`math` module. The ``splitatvalue`` function is
defined as:


.. function:: splitatvalue(value, *splitpoints)

   This method returns a tuple ``(section, value)``. The section is calculated by
   comparing *value* with the values of splitpoints. If *splitpoints* contains only
   a single item, ``section`` is ``0`` when value is lower or equal this item and
   ``1`` else. For multiple splitpoints, ``section`` is ``0`` when its lower or
   equal the first item, ``None`` when its bigger than the first item but lower or
   equal the second item, ``1`` when its even bigger the second item, but lower or
   equal the third item. It continues to alter between ``None`` and ``2``, ``3``,
   etc.


.. module:: graph.style

Module :mod:`graph.style`: Graph styles
=======================================

Please note that we are talking about graph styles here. Those are responsible
for plotting symbols, lines, bars and whatever else into a graph. Do not mix it
up with path styles like the line width, the line style (solid, dashed, dotted
*etc.*) and others.

The following classes provide styles to be used at the :meth:`plot` method of a
graph. The plot method accepts a list of styles. By that you can combine several
styles at the very same time.

Some of the styles below are hidden styles. Those do not create any output, but
they perform internal data handling and thus help on modularization of the
styles. Usually, a visible style will depend on data provided by one or more
hidden styles but most of the time it is not necessary to specify the hidden
styles manually. The hidden styles register themself to be the default for
providing certain internal data.


.. class:: pos(usenames={}, epsilon=1e-10)

   This class is a hidden style providing a position in the graph. It needs a data
   column for each graph dimension. For that the column names need to be equal to
   an axis name, or a name translation from axis names to column names need to be
   given by *usenames*. Data points are considered to be out of graph when their
   position in graph coordinates exceeds the range [0:1] by more than *epsilon*.


.. class:: range(usenames={}, epsilon=1e-10)

   This class is a hidden style providing an errorbar range. It needs data column
   names constructed out of a axis name ``X`` for each dimension errorbar data
   should be provided as follows:

   +-----------+---------------------------+
   | data name | description               |
   +===========+===========================+
   | ``Xmin``  | minimal value             |
   +-----------+---------------------------+
   | ``Xmax``  | maximal value             |
   +-----------+---------------------------+
   | ``dX``    | minimal and maximal delta |
   +-----------+---------------------------+
   | ``dXmin`` | minimal delta             |
   +-----------+---------------------------+
   | ``dXmax`` | maximal delta             |
   +-----------+---------------------------+

   When delta data are provided the style will also read column data for the axis
   name ``X`` itself. *usenames* allows to insert a translation dictionary from
   axis names to the identifiers ``X``.

   *epsilon* is a comparison precision when checking for invalid errorbar ranges.


.. class:: symbol(symbol=changecross, size=0.2*unit.v_cm, symbolattrs=[])

   This class is a style for plotting symbols in a graph. *symbol* refers to a
   (changeable) symbol function with the prototype ``symbol(c, x_pt, y_pt, size_pt,
   attrs)`` and draws the symbol into the canvas ``c`` at the position ``(x_pt,
   y_pt)`` with size ``size_pt`` and attributes ``attrs``. Some predefined symbols
   are available in member variables listed below. The symbol is drawn at size
   *size* using *symbolattrs*. *symbolattrs* is merged with ``defaultsymbolattrs``
   which is a list containing the decorator :class:`deco.stroked`. An instance of
   :class:`symbol` is the default style for all graph data classes described in
   section :mod:`graph.data` except for :class:`function` and
   :class:`paramfunction`.

The class :class:`symbol` provides some symbol functions as member variables,
namely:


.. attribute:: symbol.cross

   A cross. Should be used for stroking only.


.. attribute:: symbol.plus

   A plus. Should be used for stroking only.


.. attribute:: symbol.square

   A square. Might be stroked or filled or both.


.. attribute:: symbol.triangle

   A triangle. Might be stroked or filled or both.


.. attribute:: symbol.circle

   A circle. Might be stroked or filled or both.


.. attribute:: symbol.diamond

   A diamond. Might be stroked or filled or both.

:class:`symbol` provides some changeable symbol functions as member variables,
namely:


.. attribute:: symbol.changecross

   attr.changelist([cross, plus, square, triangle, circle, diamond])


.. attribute:: symbol.changeplus

   attr.changelist([plus, square, triangle, circle, diamond, cross])


.. attribute:: symbol.changesquare

   attr.changelist([square, triangle, circle, diamond, cross, plus])


.. attribute:: symbol.changetriangle

   attr.changelist([triangle, circle, diamond, cross, plus, square])


.. attribute:: symbol.changecircle

   attr.changelist([circle, diamond, cross, plus, square, triangle])


.. attribute:: symbol.changediamond

   attr.changelist([diamond, cross, plus, square, triangle, circle])


.. attribute:: symbol.changesquaretwice

   attr.changelist([square, square, triangle, triangle, circle, circle, diamond,
   diamond])


.. attribute:: symbol.changetriangletwice

   attr.changelist([triangle, triangle, circle, circle, diamond, diamond, square,
   square])


.. attribute:: symbol.changecircletwice

   attr.changelist([circle, circle, diamond, diamond, square, square, triangle,
   triangle])


.. attribute:: symbol.changediamondtwice

   attr.changelist([diamond, diamond, square, square, triangle, triangle, circle,
   circle])

The class :class:`symbol` provides two changeable decorators for alternated
filling and stroking. Those are especially useful in combination with the
:meth:`change`\ -\ :meth:`twice`\ -symbol methods above. They are:


.. attribute:: symbol.changestrokedfilled

   attr.changelist([deco.stroked, deco.filled])


.. attribute:: symbol.changefilledstroked

   attr.changelist([deco.filled, deco.stroked])


.. class:: line(lineattrs=[], epsilon=1e-10)

   This class is a style to stroke lines in a graph. *lineattrs* is merged with
   ``defaultlineattrs`` which is a list containing the member variable
   ``changelinestyle`` as described below. An instance of :class:`line` is the
   default style of the graph data classes :class:`function` and
   :class:`paramfunction` described in section :mod:`graph.data`. *epsilon* is
   a precision in graph coordinates for line clipping.

The class :class:`line` provides a changeable line style. Its definition is:


.. attribute:: line.changelinestyle

   attr.changelist([style.linestyle.solid, style.linestyle.dashed,
   style.linestyle.dotted, style.linestyle.dashdotted])


.. class:: impulses(lineattrs=[], fromvalue=0, frompathattrs=[], valueaxisindex=1)

   This class is a style to plot impulses. *lineattrs* is merged with
   ``defaultlineattrs`` which is a list containing the member variable
   ``changelinestyle`` of the :class:`line` class. *fromvalue* is the baseline
   value of the impulses. When set to ``None``, the impulses will start at the
   baseline. When fromvalue is set, *frompathattrs* are the stroke attributes used
   to show the impulses baseline path.


.. class:: errorbar(size=0.1*unit.v_cm, errorbarattrs=[], epsilon=1e-10)

   This class is a style to stroke errorbars in a graph. *size* is the size of the
   caps of the errorbars and *errorbarattrs* are the stroke attributes. Errorbars
   and error caps are considered to be out of the graph when their position in
   graph coordinates exceeds the range [0:1] by more that *epsilon*. Out of graph
   caps are omitted and the errorbars are cut to the valid graph range.


.. class:: text(textname="text", dxname=None, dyname=None, dxunit=0.3*unit.v_cm, dyunit=0.3*unit.v_cm, textdx=0*unit.v_cm, textdy=0.3*unit.v_cm, textattrs=[])

   This class is a style to stroke text in a graph. The text to be written has to
   be provided in the data column named ``textname``. *textdx* and *textdy* are the
   position of the text with respect to the position in the graph. Alternatively
   you can specify a ``dxname`` and a ``dyname`` and provide appropriate data in
   those columns to be taken in units of *dxunit* and *dyunit* to specify the
   position of the text for each point separately. *textattrs* are text attributes
   for the output of the text. Those attributes are merged with the default
   attributes ``textmodule.halign.center`` and ``textmodule.vshift.mathaxis``.


.. class:: arrow(linelength=0.25*unit.v_cm, arrowsize=0.15*unit.v_cm, lineattrs=[], arrowattrs=[], arrowpos=0.5, epsilon=1e-10, decorator=deco.earrow)

   This class is a style to plot short lines with arrows into a two-dimensional
   graph to a given graph position. The arrow parameters are defined by two
   additional data columns named ``size`` and ``angle`` define the size and angle
   for each arrow. ``size`` is taken as a factor to *arrowsize* and *linelength*,
   the size of the arrow and the length of the line the arrow is plotted at.
   ``angle`` is the angle the arrow points to with respect to a horizontal line.
   The ``angle`` is taken in degrees and used in mathematically positive sense.
   *lineattrs* and *arrowattrs* are styles for the arrow line and arrow head,
   respectively. *arrowpos* defines the position of the arrow line with respect to
   the position at the graph. The default ``0.5`` means centered at the graph
   position, whereas ``0`` and ``1`` creates the arrows to start or end at the
   graph position, respectively. *epsilon* is used as a cutoff for short arrows in
   order to prevent numerical instabilities. *decorator* defines the decorator to
   be added to the line.


.. class:: rect(colorname="color", gradient=color.gradient.Grey, coloraxis=None, keygraph=_autokeygraph)

   This class is a style to plot colored rectangles into a two-dimensional graph.
   The size of the rectangles is taken from the data provided by the :class:`range`
   style. The additional data column named *colorname* specifies the color of the
   rectangle defined by *gradient*. The translation of the data values to the
   gradient is done by the *coloraxis*, which is set to be a linear axis if not
   provided by *coloraxis*. A key graph, a graphx instance, is generated
   automatically to indicate the color scale if not provided by *keygraph*.
   If a *keygraph* is given, its ``x`` axis defines the color conversion and
   *coloraxis* is ignored.


.. class:: histogram(lineattrs=[], steps=0, fromvalue=0, frompathattrs=[], fillable=0, rectkey=0, autohistogramaxisindex=0, autohistogrampointpos=0.5, epsilon=1e-10)

   This class is a style to plot histograms. *lineattrs* is merged with
   ``defaultlineattrs`` which is ``[deco.stroked]``. When *steps* is set, the
   histrogram is plotted as steps instead of the default being a boxed histogram.
   *fromvalue* is the baseline value of the histogram. When set to ``None``, the
   histogram will start at the baseline. When fromvalue is set, *frompathattrs* are
   the stroke attributes used to show the histogram baseline path.

   The *fillable* flag changes the stoke line of the histogram to make it fillable
   properly. This is important on non-steped histograms or on histograms, which hit
   the graph boundary. *rectkey* can be set to generate a rectanglar area instead
   of a line in the graph key.

   In the most general case, a histogram is defined by a range specification (like
   for an errorbar) in one graph dimension (say, along the x-axis) and a value for
   the other graph dimension. This allows for the widths of the histogram boxes
   being variable. Often, however, all histogram bin ranges are equally sized, and
   instead of passing the range, the position of the bin along the x-axis fully
   specifies the histogram - assuming that there are at least two bins. This common
   case is supported via two parameters: *autohistogramaxisindex*, which defines
   the index of the independent histogram axis (in the case just described this
   would be ``0`` designating the x axis). *autohistogrampointpos*, defines the
   relative position of the center of the histogram bin: ``0.5`` means that the bin
   is centered at the values passed to the style, ``0`` (``1``) means that the bin
   is aligned at the right-(left-)hand side.

   XXX describe, how to specify general histograms with varying bin widths

   Positions of the histograms are considered to be out of graph when they exceed
   the graph coordinate range [0:1] by more than *epsilon*.


.. class:: barpos(fromvalue=None, frompathattrs=[], epsilon=1e-10)

   This class is a hidden style providing position information in a bar graph.
   Those graphs need to contain a specialized axis, namely a bar axis. The data
   column for this bar axis is named ``Xname`` where ``X`` is an axis name. In the
   other graph dimension the data column name must be equal to an axis name. To
   plot several bars in a single graph side by side, you need to have a nested bar
   axis and provide a tuple as data for nested bar axis.

   The bars start at *fromvalue* when provided. The *fromvalue* is marked by a
   gridline stroked using *frompathattrs*. Thus this hidden style might actually
   create some output. The value of a bar axis is considered to be out of graph
   when its position in graph coordinates exceeds the range [0:1] by more than
   *epsilon*.


.. class:: stackedbarpos(stackname, addontop=0, epsilon=1e-10)

   This class is a hidden style providing position information in a bar graph by
   stacking a new bar on top of another bar. The value of the new bar is taken from
   the data column named *stackname*. When *addontop* is set, the values is taken
   relative to the previous top of the bar.


.. class:: bar(barattrs=[], epsilon=1e-10, gradient=color.gradient.RedBlack)

   This class draws bars in a bar graph. The bars are filled using *barattrs*.
   *barattrs* is merged with ``defaultbarattrs`` which is a list containing
   ``[color.gradient.Rainbow, deco.stroked([color.grey.black])]``.

   The bar style has limited support for 3d graphs: Occlusion does not work
   properly on stacked bars or multiple dataset. *epsilon* is used in 3d to prevent
   numerical instabilities on bars without hight. When *gradient* is not ``None``
   it is used to calculate a lighting coloring taking into account the angle
   between the view ray and the bar and the distance between viewer and bar. The
   precise conversion is defined in the :meth:`lighting` method.


.. class:: changebar(barattrs=[])

   This style works like the :class:`bar` style, but instead of the *barattrs* to
   be changed on subsequent data instances the *barattrs* are changed for each
   value within a single data instance. In the result the style can't be applied to
   several data instances and does not support 3d. The style raises an error
   instead.


.. class:: gridpos(index1=0, index2=1, gridlines1=1, gridlines2=1, gridattrs=[], epsilon=1e-10)

   This class is a hidden style providing rectangular grid information out of graph
   positions for graph dimensions *index1* and *index2*. Data points are considered
   to be out of graph when their position in graph coordinates exceeds the range
   [0:1] by more than *epsilon*. Data points are merged to a single graph
   coordinate value when their difference in graph coordinates is below *epsilon*.


.. class:: grid(gridlines1=1, gridlines2=1, gridattrs=[], epsilon=1e-10)

   Strokes a rectangular grid in the first grid direction, when *gridlines1* is set
   and in the second grid direction, when *gridlines2* is set. *gridattrs* is
   merged with ``defaultgridattrs`` which is a list containing the member variable
   ``changelinestyle`` of the :class:`line` class. *epsilon* is a precision in graph
   coordinates for line clipping.


.. class:: surface(gridlines1=0.05, gridlines2=0.05, gridcolor=None, backcolor=color.gray.black, **kwargs)

   Draws a surface of a rectangular grid. Each rectangle is divided into 4
   triangles.

   If a *gridcolor* is set, the rectangular grid is marked by small stripes of the
   relative (compared to each rectangle) size of *gridlines1* and *gridlines2* for
   the first and second grid direction, respectively.

   *backcolor* is used to fill triangles shown from the back. If *backcolor* is set
   to ``None``, back sides are not drawn differently from the front sides.

   The surface is encoded using a single mesh. While this is quite space efficient,
   it has the following implications:

* All colors must use the same color space.

* HSB colors are not allowed, whereas Gray, RGB, and CMYK are allowed. You can
     convert HSB colors into a different color space by means of
     :class:`rgbgradient` and class:`cmykgradient` before passing it to the
     surface style.

* The grid itself is also constructed out of triangles. The grid is transformed
     along with the triangles thus looking quite different from a stroked grid (as
     done by the grid style).

* Occlusion is handled by proper painting order.

* Color changes are continuous (in the selected color space) for each triangle.

   Further arguments are identical to the :class:`graph.style.rect` style. However,
   if no *colorname* column exists, the surface style falls back to a lighting
   coloring taking into account the angle between the view ray and the triangle and
   the distance between viewer and triangle. The precise conversion is defined in
   the :meth:`lighting` method.


.. class:: density(epsilon=1e-10, **kwargs):

   Density plots can be created by the density style. It is similar to a surface
   plot in 2d, but it does not use a mesh, but a bitmap representation instead.
   Due to that difference, the file size is smaller and no color interpolation
   takes place. Furthermore the style can be used with equidistantly spaced data
   only (after conversion by the axis, so logarithmic raw data and such are
   possible using proper axes). Further arguments are identical to the
   :class:`graph.style.rect` style.


.. module:: graph.key

Module :mod:`graph.key`: Graph keys
===================================

The following class provides a key, whose instances can be passed to the
constructor keyword argument ``key`` of a graph. The class is implemented in
:mod:`graph.key`.


.. class:: key(dist=0.2*unit.v_cm, pos="tr", hpos=None, vpos=None, hinside=1, vinside=1, hdist=0.6*unit.v_cm, vdist=0.4*unit.v_cm, symbolwidth=0.5*unit.v_cm, symbolheight=0.25*unit.v_cm, symbolspace=0.2*unit.v_cm, textattrs=[], columns=1, columndist=0.5*unit.v_cm, border=0.3*unit.v_cm, keyattrs=None)

   This class writes the title of the data in a plot together with a small
   illustration of the style. The style is responsible for its illustration.

   *dist* is a visual length and a distance between the key entries. *pos* is the
   position of the key with respect to the graph. Allowed values are combinations
   of ``"t"`` (top), ``"m"`` (middle) and ``"b"`` (bottom) with ``"l"`` (left),
   ``"c"`` (center) and ``"r"`` (right). Alternatively, you may use *hpos* and
   *vpos* to specify the relative position using the range [0:1]. *hdist* and
   *vdist* are the distances from the specified corner of the graph. *hinside* and
   *vinside* are numbers to be set to 0 or 1 to define whether the key should be
   placed horizontally and vertically inside of the graph or not.

   *symbolwidth* and *symbolheight* are passed to the style to control the size of
   the style illustration. *symbolspace* is the space between the illustration and
   the text. *textattrs* are attributes for the text creation. They are merged with
   ``[text.vshift.mathaxis]``.

   *columns* is a number of columns of the graph key and *columndist* is the
   distance between those columns.

   When *keyattrs* is set to contain some draw attributes, the graph key is
   enlarged by *border* and the key area is drawn using *keyattrs*.