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 $\varphi$

irfpy.util.isotropy.getRandom_tp(size=None)

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

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, $\varphi$, is random in the range of (0, 2 $\pi$).

irfpy.util.isotropy.getRandom(size=None)

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, $\varphi$, is random in the range of (0, 2 $\pi$).