which grows less rapidly than the number of operations required by d01gyf. 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: $vk (ndim)$ – Real (Kind=nag_wp) array Output: On exit: the $n$ optimal coefficients.
5: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $−1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $ndim = ⟨ value ⟩$ .
Constraint: $ndim \geq 1$ .

$ifail = 2$: On entry, $np1 = ⟨ value ⟩$ .
Constraint: $np1 \geq 5$ .

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

On entry, $np2 = ⟨ value ⟩$ .
Constraint: $np2 \geq 2$ .

$ifail = 3$: On entry, $np1 \times np2$ exceeds largest machine integer. $np1 = ⟨ value ⟩$ and $np2 = ⟨ value ⟩$ .

$ifail = 4$: On entry, $np1 = ⟨ value ⟩$ .
Constraint: np1 must be a prime number.

$ifail = 5$: On entry, $np2 = ⟨ value ⟩$ .
Constraint: np2 must be a prime number.

$ifail = 6$: The machine precision is insufficient to perform the computation exactly. Try reducing np1 or np2: $np1 = ⟨ value ⟩$ and $np2 = ⟨ value ⟩$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.