for $b_{0} \geq 8$ ,

$\ln B = \ln Γ (a_{0}) + \ln \frac{Γ (b_{0})}{Γ (a_{0} + b_{0})};$
for $b_{0} < 8$ ,

$\ln B = \ln Γ (a_{0}) + \ln Γ (b_{0}) - \ln Γ (a_{0} + b_{0});$

for

2 < a_{0} < 8

a_{0}

is reduced to the interval

[1, 2]

B (a, b) = \frac{a_{0} - 1}{a_{0} + b_{0} - 1} B (a_{0} - 1, b_{0})

;

for

1 \leq a_{0} \leq 2

for $b_{0} \geq 8$ ,

$\ln B = \ln Γ (a_{0}) + \ln \frac{Γ (b_{0})}{Γ (a_{0} + b_{0})};$
for $2 < b_{0} < 8$ , $b_{0}$ is reduced to the interval $[1, 2]$ ;
for $b_{0} \leq 2$ ,

$\ln B = \ln Γ (a_{0}) + \ln Γ (b_{0}) - \ln Γ (a_{0} + b_{0}) .$

s14cpc is derived from BETALN in DiDonato and Morris (1992).

4 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

5 Arguments

1: $n$ – Integer Input

On entry:

n

, the number of points.

Constraint:

n \geq 0

2: $a [n]$ – const double Input

On entry: the argument

a_{i}

of the function, for

i = 1, 2, \dots, n

Constraint:

a [i - 1] > 0

, for

i = 1, 2, \dots, n

3: $b [n]$ – const double Input

On entry: the argument

b_{i}

of the function, for

i = 1, 2, \dots, n

Constraint:

b [i - 1] > 0

, for

i = 1, 2, \dots, n

4: $f [n]$ – double Output

On exit:

\ln B (a_{i}, b_{i})

, the function values.

5: $ivalid [n]$ – Integer Output

On exit:

ivalid [i - 1]

contains the error code for

a_{i}

and

b_{i}

, for

i = 1, 2, \dots, n

$ivalid [i - 1] = 0$: No error.
$ivalid [i - 1] = 1$: $a_{i} or b_{i} \leq 0$ .

6: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
NE_INT: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 0$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NW_IVALID: On entry, at least one value of a or b was invalid.
Check ivalid for more information.

7 Accuracy

s14cpc should produce full relative accuracy for all input arguments.

8 Parallelism and Performance

s14cpc is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example reads values of a and b from a file, evaluates the function at each value of

a_{i}

and

b_{i}

and prints the results.

s14cp: FL CL CPP AD

NAG CL Interfaces14cpc (beta_​log_​real_​vector)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
s14cpc (beta_log_real_vector)