vice.imf.kroupa
===============

The (unnormalized) Kroupa (2001) [1]_ stellar initial mass function (IMF).

**Signature**: vice.imf.kroupa(mass)

.. versionadded:: 1.1.0

Parameters
----------
mass : real number
	The stellar mass in solar masses.

Returns
-------
dndm : real number
	The unnormalized value of the Kroupa IMF at that stellar mass,
	defined by:

	.. math:: \frac{dN}{dm} \propto m^{-\alpha}

	where :math:`\alpha` = 2.3, 1.3, and 0.3 for :math:`m` > 0.5,
	0.08 :math:`\leq m \leq` 0.5, and :math:`m` < 0.08, respectively.

Raises
------
* TypeError
	- mass is not a real number
* ValueError
	- mass is non-positive

Example Code
------------
>>> vice.imf.kroupa(1)
	0.04
>>> vice.imf.kroupa(0.5)
	0.1969831061351866
>>> vice.imf.kroupa(2)
	0.008122523963562356

.. [1] Kroupa (2001), MNRAS, 322, 231