nitorch_fastmath.special

mvdigamma

mvdigamma(input, order=1)

Derivative of the log of the Gamma function, eventually multivariate

Parameters:

Name	Type	Description	Default
`input`	`tensor`	Input tensor	required
`order`	`int`	Multivariate order	`1`

Returns:

Name	Type	Description
`output`	`tensor`	Output tensor

besseli(nu, z, mode=None)

Modified Bessel function of the first kind

Parameters:

Name	Type	Default
`nu`	`float`	required
`z`		required
`mode`		`0 or None`

Returns:

Name	Type	Description
`b`	`tensor`	besseli(nu,z) if mode is None besseli(ni,z)/exp(z) if mode == 'norm' log(besseli(nu,z)) if mode == 'log'

Garber, D.P., 1993. On the use of the noncentral chi-square density function for the distribution of helicopter spectral estimates. (No. NAS 1.26: 191546).

besseli_ratio(nu, X, N=4, K=10)

Approximates ratio of the modified Bessel functions of the first kind: besseli(nu+1,x)/besseli(nu,x)

Parameters:

Name	Type	Description	Default
`nu`	`float`		required
`X`	`tensor`		required
`N`	`int`	Terms in summation, higher number, better approximation.	`4`
`K`	`int`	Terms in summation, higher number, better approximation.	`4`

Returns:

Name	Type	Description
`I`	`tensor`	Ratio of the modified Bessel functions of the first kind.

Amos, D.E., 1974. Computation of modified Bessel functions and their ratios. Mathematics of computation, 28(125), pp.239-251.