NAG FL Interface
e01bhf (dim1_​monotonic_​intg)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

2: $\mathbf{x}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) array Input

3: $\mathbf{f}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) array Input

4: $\mathbf{d}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) array Input

On entry: n, x, f and d must be unchanged from the previous call of e01bef.

5: $\mathbf{a}$ – Real (Kind=nag_wp) Input

6: $\mathbf{b}$ – Real (Kind=nag_wp) Input

On entry: the interval $\left[a,b\right]$ over which integration is to be performed.

7: $\mathbf{pint}$ – Real (Kind=nag_wp) Output

On exit: the value of the definite integral of the interpolant over the interval $\left[a,b\right]$.

8: $\mathbf{ifail}$ – 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, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 2$.

$\mathbf{ifail}=2$

On entry, $r=〈\mathit{\text{value}}〉$, $\mathbf{x}\left(r-1\right)=〈\mathit{\text{value}}〉$ and $\mathbf{x}\left(r\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}\left(r-1\right)<\mathbf{x}\left(r\right)$ for all $r$.

$\mathbf{ifail}=3$

Warning – either a or b is outside the range $\mathbf{x}\left(1\right)\cdots \mathbf{x}\left(\mathbf{n}\right)$. The result has been computed by extrapolation and is unreliable. $\mathbf{a}=〈\mathit{\text{value}}〉$ $\mathbf{b}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=-99$

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