) and there is a practical upper limit to the number of points that can be used. Routine d01gzf is computationally more economical in this respect but the associated error is likely to be larger.

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: $npts$ – Integer Input: On entry: $p$ , the number of points to be used.

Constraint: $npts$ must be a prime number $\geq 5$ .
3: $vk (ndim)$ – Real (Kind=nag_wp) array Output: On exit: the $n$ optimal coefficients.
4: $ifail$ – 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, $npts = ⟨ value ⟩$ .
Constraint: $npts \geq 5$ .

$ifail = 3$: On entry, $npts = ⟨ value ⟩$ .
Constraint: npts must be a prime number.

$ifail = 4$: The machine precision is insufficient to perform the computation exactly. Try reducing npts: $npts = ⟨ value ⟩$ .

$ifail = - 99$: 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.