NAG Library Function Document

nag_quad_md_numth_coeff_2prime (d01gzc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{ndim}$ – IntegerInput

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

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

2:    $\mathbf{np1}$ – IntegerInput

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:    $\mathbf{np2}$ – IntegerInput

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:    $\mathbf{vk}\left[\mathbf{ndim}\right]$ – doubleOutput

On exit: the $n$ optimal coefficients.

5:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ACCURACY

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

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

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

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

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

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

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

NE_INT_2

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

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

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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d01gzce.c)

10.2

Program Data

10.3

Program Results

Program Results (d01gzce.r)