NAG Library Routine Document

e01bhf (dim1_monotonic_intg)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

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

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

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

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:     $\mathbf{ifail}$ – IntegerInput/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 3.4 in How to Use the NAG Library and its Documentation 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 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 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 (e01bhfe.f90)

10.2

Program Data

Program Data (e01bhfe.d)

10.3

Program Results

Program Results (e01bhfe.r)