vice.migration.migration_matrix
===============================

A square matrix designed to detail the manner in which gas migrates
between zones in multizone models. This is a 2-dimensional array-like
object denoted by :math:`G_{ij}`, defined as the mass fraction of the
interstellar gas in zone :math:`i` that migrates to zone :math:`j` in a
10 Myr time interval.

**Signature**: vice.migration.migration_matrix(size)

.. versionadded:: 1.2.0

Parameters
----------
size : ``int``
	The number of rows and columns. This is also the number of zones in
	the multizone model.

Attributes
----------
size : ``int``
	See parameter "size".

Allowed Data Types
------------------
* real number
	:math:`G_{ij}` does not vary with time, and is given by this value.
* <function>
	:math:`G_{ij}` varies with time, and is described by this function.
	Time in Gyr is the only parameter the function takes.

Indexing
--------
- ``int``, ``int`` : the row and column numbers
	The value of :math:`G_{ij}` can be accessed by indexing this object
	with :math:`i` as the first index and :math:`j` as the second. For
	instance, ``example[1][0]`` and ``example[1, 0]`` both look up
	:math:`G_{1,0}`.

Functions
---------
- tolist
- tonumpyarray

Example Code
------------
>>> import math
>>> import vice
>>> example = vice.migration.migration_matrix(3)
>>> example
	MigrationMatrix{
		0 ---------> {0.0, 0.0, 0.0}
		1 ---------> {0.0, 0.0, 0.0}
		2 ---------> {0.0, 0.0, 0.0}
	}
>>> example[1][0] = 0.1
>>> def f(t):
	return 0.1 * math.exp(-t / 5)
>>> example[0, 1] = f
>>> example
	MigrationMatrix{
		0 ---------> {0.0, <function f at 0x120588560>, 0.0}
		1 ---------> {0.1, 0.0, 0.0}
		2 ---------> {0.0, 0.0, 0.0}
	}
>>> example.tonumpyarray()
	array([[0.0, <function f at 0x120588560>, 0.0],
		[0.0, 0.0, 0.0],
		[0.0, 0.0, 0.0]])




.. toctree::
	:titlesonly:
	:maxdepth: 5

	vice.migration.migration_matrix.size
	vice.migration.migration_matrix.tolist
	vice.migration.migration_matrix.tonumpyarray