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1 - Combining plots

Let's understand what happens when a plot command is executed:

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

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

The plot function is going to loop over the provided arguments: it will create and store one data series for each expression. So, in the previous example p contains 3 data series. Once the data series are created, they will be used by the backend (the wrapper to the plotting library) to generate numerical data.

Effectively, p is a container of data series. We can quickly visualize them by printing the plot object:

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

   >>> print(p)
   Plot object containing:
   [0]: cartesian line: sin(x) for x over (-10.0, 10.0)
   [1]: cartesian line: cos(x) for x over (-10.0, 10.0)
   [2]: cartesian line: log(x) for x over (-10.0, 10.0)

We can retrieve a list containing all data series from a plot object by calling the series attribute:

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

   p.series

Alternatively, we can retrieve a single data series by indexing the plot object:

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

   >>> print(p[0])
   cartesian line: sin(x) for x over (-10.0, 10.0)

We can combine multiple plots together in three ways:

  1. summing them up: this will create a new plot containing all data series from all initial plots. For example:

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

   c = S(2) / 10
   p1 = plot(cos(x) * exp(-c * x), (x, 0, 10), "f(x)", title="plot 1")
   p2 = plot(
       (exp(-c * x), "upper limit"),
       (-exp(-c * x), "lower limit"), (x, 0, 10), {"linestyle": "--"},
       title="plot 2", xlabel="xx", ylabel="yy")

    And then:

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

  p3 = p1 + p2
  p3.show()
  # or more quickly: (p1 + p2).show()

    Note that the final plot uses the keyword arguments of the left-most plot in the summation. In the previous example, the resulting plot has the title of p1. Now, let's sum them up in a different order:

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

  (p2 + p1).show()

    Here, the resulting plot is using the title and axis labels of p2.

  2. We can use the extend method to achieve the same goal as before:

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

  p1.extend(p2)
  p1.show()

  3. using the append method to append one specific data series from one plot object to another. For example:

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

   >>> p1 = plot(cos(x) * exp(-c * x), (x, 0, 10), "f(x)",
   ...     title="plot 1", show=False)
   >>> p2 = plot(
   ...     (exp(-c * x), "upper limit"),
   ...     (-exp(-c * x), "lower limit"), (x, 0, 10), {"linestyle": "--"},
   ...     title="plot 2", xlabel="xx", ylabel="yy", show=False)
   >>> p1.append(p2[0])
   >>> print(p1)
   Plot object containing:
   [0]: cartesian line: exp(-x/5)*cos(x) for x over (0.0, 10.0)
   [1]: cartesian line: exp(-x/5) for x over (0.0, 10.0)
   >>> p1.show()