which grows less rapidly than the number of operations required by d01gyc. The associated error is likely to be larger although it may be the only practical alternative for high values of

p

4 References

Korobov N M (1963) Number Theoretic Methods in Approximate Analysis Fizmatgiz, Moscow

5 Arguments

1: $ndim$ – Integer Input: On entry: $n$ , the number of dimensions of the integral.

Constraint: $ndim \geq 1$ .
2: $np1$ – Integer Input: On entry: the larger prime factor $p_{1}$ of the number of points in the integration rule.

Constraint: $np1$ must be a prime number $\geq 5$ .
3: $np2$ – Integer Input: On entry: the smaller prime factor $p_{2}$ of the number of points in the integration rule. For maximum efficiency, $p_{2}^{2}$ should be close to $p_{1}$ .

Constraint: $np2$ must be a prime number such that $np1 > np2 \geq 2$ .
4: $vk [ndim]$ – double Output: On exit: the $n$ optimal coefficients.
5: $fail$ – 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_ACCURACY: The machine precision is insufficient to perform the computation exactly. Try reducing np1 or np2: $np1 = ⟨ value ⟩$ and $np2 = ⟨ value ⟩$ .
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, $ndim = ⟨ value ⟩$ .
Constraint: $ndim \geq 1$ .

On entry, $np1 = ⟨ value ⟩$ .
Constraint: np1 must be a prime number.

On entry, $np1 = ⟨ value ⟩$ .
Constraint: $np1 \geq 5$ .

On entry, $np2 = ⟨ value ⟩$ .
Constraint: np2 must be a prime number.

On entry, $np2 = ⟨ value ⟩$ .
Constraint: $np2 \geq 2$ .
NE_INT_2: On entry, $np1 \times np2$ exceeds largest machine integer. $np1 = ⟨ value ⟩$ and $np2 = ⟨ value ⟩$ .

On entry, $np1 = ⟨ value ⟩$ and $np2 = ⟨ value ⟩$ .
Constraint: $np1 > np2$ .
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.

7 Accuracy

The optimal coefficients are returned as exact integers (though stored in a double array).

8 Parallelism and Performance

d01gzc is not threaded in any implementation.

9 Further Comments

The time taken by d01gzc grows at least as fast as

{(p_{1} p_{2})}^{4 / 3}

. (See Section 3.)

10 Example

This example calculates the Korobov optimal coefficients where the number of dimensons is

4

and the number of points is the product of the two prime numbers,

89

and

11

d01gz: FL CL CPP AD

NAG CL Interfaced01gzc (md_​numth_​coeff_​2prime)

▸▿ 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
d01gzc (md_numth_coeff_2prime)