Temme N M (1987) On the computation of the incomplete gamma functions for large values of the parameters Algorithms for Approximation (eds J C Mason and M G Cox) Oxford University Press

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: $x [n]$ – const double Input

On entry: the argument

x_{i}

of the function, for

i = 1, 2, \dots, n

Constraint:

x [i - 1] \geq 0

, for

i = 1, 2, \dots, n

4: $tol$ – double Input

On entry: the relative accuracy required by you in the results. If s14bnc is entered with tol greater than

1.0

or less than machine precision, then the value of machine precision is used instead.

5: $p [n]$ – double Output

On exit:

P (a_{i}, x_{i})

, the function values.

6: $q [n]$ – double Output

On exit:

Q (a_{i}, x_{i})

, the function values.

7: $ivalid [n]$ – Integer Output

On exit:

ivalid [i - 1]

contains the error code for

a_{i}

and

x_{i}

, for

i = 1, 2, \dots, n

$ivalid [i - 1] = 0$: No error.
$ivalid [i - 1] = 1$: $a_{i} \leq 0$ .
$ivalid [i - 1] = 2$: $x_{i} < 0$ .
$ivalid [i - 1] = 3$: Algorithm fails to terminate.

8: $fail$ – 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 x was invalid.
Check ivalid for more information.

7 Accuracy

There are rare occasions when the relative accuracy attained is somewhat less than that specified by argument tol. However, the error should never exceed more than one or two decimal places. Note also that there is a limit of

18

decimal places on the achievable accuracy, because constants in the function are given to this precision.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

s14bnc is not threaded in any implementation.

9 Further Comments

The time taken for a call of s14bnc depends on the precision requested through tol, and n.

10 Example

This example reads values of a and x from a file, evaluates the functions at each value of

a_{i}

and

x_{i}

and prints the results.

s14bn: FL CL CPP AD PY MB

NAG CL Interfaces14bnc (gamma_​incomplete_​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
s14bnc (gamma_incomplete_vector)