NAG CL Interface
s14cbc (beta_​log_​real)

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1 Purpose

s14cbc returns the value of the logarithm of the beta function, lnB(a,b).

2 Specification

#include <nag.h>
double  s14cbc (double a, double b, NagError *fail)
The function may be called by the names: s14cbc, nag_specfun_beta_log_real or nag_log_beta.

3 Description

s14cbc calculates values for lnB(a,b) where B is the beta function given by
B(a,b) = 0 1 ta-1 (1-t) b-1 dt  
or equivalently
B(a,b) = Γ(a) Γ(b) Γ(a+b)  
and Γ(x) is the gamma function. Note that the beta function is symmetric, so that B(a,b)=B(b,a).
In order to efficiently obtain accurate results several methods are used depending on the parameters a and b.
Let a0=min(a,b) and b0=max(a,b). Then:
for a08,
lnB = 0.5 ln (2π) -0.5 ln(b0) + Δ(a0) + Δ (b0) - Δ (a0+b0) - u - v ;  
where for a0<1, for 2<a0<8, a0 is reduced to the interval [1,2] by B(a,b)=a0-1a0+b0-1 B(a0-1,b0);
for 1a02,
s14cbc 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: a double Input
On entry: the argument a of the function.
Constraint: a>0.0.
2: b double Input
On entry: the argument b of the function.
Constraint: b>0.0.
3: 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

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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.
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.
On entry, a=value.
Constraint: a>0.0.
On entry, b=value.
Constraint: b>0.0.

7 Accuracy

s14cbc should produce full relative accuracy for all input arguments.

8 Parallelism and Performance

s14cbc is not threaded in any implementation.

9 Further Comments


10 Example

This example reads values of the arguments a and b from a file, evaluates the function and prints the results.

10.1 Program Text

Program Text (s14cbce.c)

10.2 Program Data

Program Data (s14cbce.d)

10.3 Program Results

Program Results (s14cbce.r)