naginterfaces.library.specfun.beta_​log_​real_​vector

naginterfaces.library.specfun.beta_log_real_vector(a, b)[source]

beta_log_real_vector returns an array of values of the logarithm of the beta function, .

For full information please refer to the NAG Library document for s14cp

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s14cpf.html

Parameters
afloat, array-like, shape

The argument of the function, for .

bfloat, array-like, shape

The argument of the function, for .

Returns
ffloat, ndarray, shape

, the function values.

ivalidint, ndarray, shape

contains the error code for and , for .

No error.

.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of or was invalid.

Check for more information.

Notes

beta_log_real_vector calculates values for , for arrays of arguments and , for , where is the beta function given by

or equivalently

and is the gamma function. Note that the beta function is symmetric, so that .

In order to efficiently obtain accurate results several methods are used depending on the parameters and .

Let and . Then:

for ,

where

,

and

;

for ,

for ,

for ,

for , is reduced to the interval by ;

for ,

for ,

for , is reduced to the interval ;

for ,

beta_log_real_vector is derived from BETALN in DiDonato and Morris (1992).

References

DiDonato, A R and Morris, A H, 1992, Algorithm 708: Significant digit computation of the incomplete beta function ratios, ACM Trans. Math. Software (18), 360–373