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://support.nag.com/numeric/nl/nagdoc_30.2/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 byor 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