NAG FL Interface
d01gzf (md_​numth_​coeff_​2prime)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{ndim}$ – Integer Input

On entry: $n$, the number of dimensions of the integral.

Constraint: $\mathbf{ndim}\ge 1$.

2: $\mathbf{np1}$ – Integer Input

On entry: the larger prime factor $p_1$ of the number of points in the integration rule.

Constraint: $\mathbf{np1}$ must be a prime number $\ge 5$.

3: $\mathbf{np2}$ – 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: $\mathbf{np2}$ must be a prime number such that $\mathbf{np1}>\mathbf{np2}\ge 2$.

4: $\mathbf{vk}\left(\mathbf{ndim}\right)$ – Real (Kind=nag_wp) array Output

On exit: the $n$ optimal coefficients.

5: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

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

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{ndim}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ndim}\ge 1$.

$\mathbf{ifail}=2$

On entry, $\mathbf{np1}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{np1}\ge 5$.

On entry, $\mathbf{np1}=〈\mathit{\text{value}}〉$ and $\mathbf{np2}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{np1}>\mathbf{np2}$.

On entry, $\mathbf{np2}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{np2}\ge 2$.

$\mathbf{ifail}=3$

On entry, $\mathbf{np1}\times \mathbf{np2}$ exceeds largest machine integer. $\mathbf{np1}=〈\mathit{\text{value}}〉$ and $\mathbf{np2}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=4$

On entry, $\mathbf{np1}=〈\mathit{\text{value}}〉$.
Constraint: np1 must be a prime number.

$\mathbf{ifail}=5$

On entry, $\mathbf{np2}=〈\mathit{\text{value}}〉$.
Constraint: np2 must be a prime number.

$\mathbf{ifail}=6$

The machine precision is insufficient to perform the computation exactly. Try reducing np1 or np2: $\mathbf{np1}=〈\mathit{\text{value}}〉$ and $\mathbf{np2}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=-99$

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.

$\mathbf{ifail}=-399$

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.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results