NAG Library Routine Document

E01BHF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

2:     X(N) – REAL (KIND=nag_wp) arrayInput

3:     F(N) – REAL (KIND=nag_wp) arrayInput

4:     D(N) – REAL (KIND=nag_wp) arrayInput

On entry: N, X, F and D must be unchanged from the previous call of E01BEF.

5:     A – REAL (KIND=nag_wp)Input

6:     B – REAL (KIND=nag_wp)Input

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

7:     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:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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,

$\mathbf{N}<2$.

$\mathbf{IFAIL}=2$

The values of $\mathbf{X}\left(\mathit{r}\right)$, for $\mathit{r}=1,2,\dots ,\mathbf{N}$, are not in strictly increasing order.

$\mathbf{IFAIL}=3$

On entry, at least one of A or B lies outside the interval [$\mathbf{X}\left(1\right),\mathbf{X}\left(\mathbf{N}\right)$], and extrapolation was performed to compute the integral. The value returned is therefore unreliable.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (e01bhfe.f90)

9.2  Program Data

Program Data (e01bhfe.d)

9.3  Program Results

Program Results (e01bhfe.r)