# irfpy.util.isotropy¶

Functions for isotropic distribution

 getRandom([size]) Return the randomly generated distribution getRandom_tp([size]) Return the randomly generated distribution in $$\theta$$ and $$\phi$$
irfpy.util.isotropy.getRandom_tp(size=None)[source]

Return the randomly generated distribution in $$\theta$$ and $$\phi$$

Parameters

size – The size of the array.

Returns

Randomly generated isotropic distribution. (theta, phi) = retval in radians

Return type

(2, size[0], size[1], …)-shaped numpy array.

>>> rnd = getRandom_tp()
>>> rnd.shape
(2,)
>>> rnd = getRandom_tp(size=(2, 4))   # (3, 2, 4) array will be returned.
>>> rnd.shape
(2, 2, 4)

Way of generation

The polar angle, $$\theta$$, should distribute considering the area at spherical surface, namely depending on $$\sin\theta$$. To realize this, one can start from uniform random, convert it according to

$\theta = \cos^{-1} (1-2P)$

where P is the (array of) value generated from random distribution.

The azimuth angle, $$\phi$$, is random in the range of (0, 2 $$\pi$$).

irfpy.util.isotropy.getRandom(size=None)[source]

Return the randomly generated distribution

Parameters

size – The size of the array.

Returns

Randomly generated isotropic distribution. Unit vector.

Return type

(3, size[0], size[1], …)-shaped numpy array.

>>> np.random.seed(0)   # Set the random seed.
>>> rnd = getRandom()
>>> rnd.shape
(3,)
>>> print('{:.3f}'.format((rnd ** 2).sum()))
1.000
>>> rnd = getRandom(size=(2, 4))   # (3, 2, 4) array will be returned.
>>> rnd.shape
(3, 2, 4)

Way of generation

The polar angle, $$\theta$$, should distribute considering the area at spherical surface, namely depending on $$\sin\theta$$. To realize this, one can start from uniform random, convert it according to

$\theta = \cos^{-1} (1-2P)$

where P is the (array of) value generated from random distribution.

The azimuth angle, $$\phi$$, is random in the range of (0, 2 $$\pi$$).