2 - Differences between 2D backends
-----------------------------------

In this tutorial we are going to compare the same plot produced with 3 different backends. In particular, we will focus on usability and
interactivity.

First, let's initialize the tutorial by running:

.. code-block:: python

   %matplotlib widget
   from sympy import *
   from spb import *
   x = symbols("x")

In the above code cell we first imported every plot function
from this plotting module. Remember: while some plot functions are identical
to the ones from ``sympy.plotting``, they are not compatible when using a
different backend!

We also imported the following backends:

+---------------------+-------+
| Backend             | Alias |
+=====================+=======+
|   BokehBackend      |   BB  |
+---------------------+-------+
|   MatplotlibBackend |   MB  |
+---------------------+-------+
|   PlotlyBackend     |   PB  |
+---------------------+-------+
|   K3DBackend        |   KB  |
+---------------------+-------+

Only ``MatplotlibBackend``, ``BokehBackend`` and ``PlotlyBackend`` support
2D plots. We will use their aliases in order to type less.

Now, let's visualize a plot created with Matplotlib:

.. plot::
   :context: reset
   :format: doctest
   :include-source: True

   >>> from sympy import *
   >>> from spb import *
   >>> x = symbols("x")
   >>> p = plot(sin(x), cos(x), log(x), backend=MB)


In the previous command we specified the optional keyword argument
``backend=``. If not provided, the default backend will be used. Refer to
:doc:`Tutorial 3 </tutorials/tut-3>` to learn how to customize the
module and set a different default backend.

We can see a `RuntimeWarning` in the output cell: it was generated by the
evaluation algorithm while processing `log(x)`, which is only defined for
`x > 0`, whereas we asked the plot function to evaluate it over the interval
`-10 < x < 10`.

Once we plot multiple expression simultaneously, the legend will automatically
show up. We can disable it by setting ``legend=False``.

Note that:

* In order to interact with the plot we have to use the buttons on the toolbar.
* If we move the cursor over the figure, we can see its coordinates.
  By moving it over a line we only get approximate coordinates.

With the previous command, we plotted 3 different expressions. Therefore, the
plot object ``p`` contains 3 data series. We can easily access the data
series by using the index notation: this is useful in order to extract
numerical data as we will see in :doc:`Tutorial 4 </tutorials/tut-4>`.

.. plot::
   :context: close-figs
   :format: doctest
   :include-source: True

   >>> print(p)
   Plot object containing:
   [0]: cartesian line: sin(x) for x over (-10, 10)
   [1]: cartesian line: cos(x) for x over (-10, 10)
   [2]: cartesian line: log(x) for x over (-10, 10)
   >>> print(p[0])
   cartesian line: sin(x) for x over (-10, 10)

Let's now do the same with Plotly:

.. plotly::

   from sympy import *
   from spb import *
   var("x")
   plot(sin(x), cos(x), log(x), backend=PB)


The top toolbar can be used to interact with the plot. However, there are
more natural ways:

* Click and drag to zoom into a rectangular selection.
* Move the cursor in the middle of the horizontal axis, click and drag to
  pan horizontally.
* Move the cursor in the middle of the vertical axis, click and drag to
  pan vertically.
* Move the cursor near the ends of the horizontal/vertical axis: click and
  drag to resize.
* Move the cursor over a line: a tooltip will show the coordinate of that
  point in the data series. Note that there is no interpolation between two
  consecutive points.
* Click over a label in the legend to hide/show that data series.

Finally, let's use Bokeh:

.. code-block:: python

   plot(sin(x), cos(x), log(x), backend=BB)

.. raw:: html

   <iframe src="../_static/tut-1/bokeh-1.html" height="450px" width="100%"></iframe>

Here, we can:

* Click and drag to pan the plot around.
* Click and drag the axis to pan the plot only on one direction.
* Click the legend entries to hide/show the data series.
* Move the cursor over a line: a tooltip will show the coordinate of that
  point in the data series.
* Use the toolbar to change the tool, for example we can select the
  *Box Zoom* to zoom into a rectangular region.