comnum.GammaGamma

class comnum.GammaGamma(alpha, beta)

The gamma–gamma distribution of the intensity, of unit mean (Al-Habash, Andrews & Phillips 2001).

Parameters:

• alpha (float) – the effective number of large-scale cells.

• beta (float) – the effective number of small-scale cells.

Raises:

ValueError – for an invalid parameter (the message names it).

Examples

>>> import comnum
>>> g = comnum.GammaGamma.from_rytov(25.0, "plane")
>>> round(g.alpha, 2), round(g.beta, 2), round(g.scintillation_index(), 3)
(8.05, 1.03, 1.214)

static from_rytov(rytov, wave='plane')

The parameters predicted by the Rytov variance for a negligible inner scale.

Parameters:

• rytov (float) – σ₁².

• wave (str) – "plane" or "spherical".

Returns:

the distribution.

Return type:

GammaGamma

Raises:

ValueError – for an invalid parameter (the message names it).

draw(n, rng)

Independent draws of the intensity (a product of two gamma variables).

Parameters:

• rng (Rng) – the generator.

• n (int) – the number of draws.

Returns:

(n,) (float64).

Return type:

numpy.ndarray

Raises:

ValueError – for a negative count.

pdf(i)

The density of the intensity.

Parameters:

i (float | array_like) – the intensities (of unit mean).

Returns:

the density, of the shape of i.

Return type:

float | numpy.ndarray

Raises:

ValueError – for values that are not real numbers.

scintillation_index()

The scintillation index 1/α + 1/β + 1/(αβ).

Returns:

the scintillation index.

Return type:

float

alpha

α.

Type:

float

beta

β.

Type:

float