NAG FL Interface
d01ubf (dim1_​inf_​exp_​wt)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{f}$ – Subroutine, supplied by the user. External Procedure

f must return the integrand function values $f\left(x_i\right)$ for the given $x_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

The specification of f is:

Fortran Interface

Subroutine f ( x, fv, n, iuser, ruser, istop) Integer, Intent (In) :: n Integer, Intent (Inout) :: iuser(*), istop Real (Kind=nag_wp), Intent (In) :: x(n) Real (Kind=nag_wp), Intent (Inout) :: ruser(*) Real (Kind=nag_wp), Intent (Out) :: fv(n)

C Header Interface

void  f_ (const double x[], double fv[], const Integer *n, Integer iuser[], double ruser[], Integer *istop)

C++ Header Interface

#include <nag.h> extern "C" { void  f_ (const double x[], double fv[], const Integer &n, Integer iuser[], double ruser[], Integer &istop) }

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

On entry: the points at which the integrand function $f$ must be evaluated.

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

On exit: $\mathbf{fv}\left(\mathit{i}\right)$ must contain the value of the integrand $f\left(x_i\right)$ evaluated at the point $\mathbf{x}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

3: $\mathbf{n}$ – Integer Input

On entry: n specifies the number of weights and abscissae to be used.

4: $\mathbf{iuser}\left(*\right)$ – Integer array User Workspace

5: $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) array User Workspace

f is called with the arguments iuser and ruser as supplied to d01ubf. You should use the arrays iuser and ruser to supply information to f.

6: $\mathbf{istop}$ – Integer Input/Output

On entry: $\mathbf{istop}=0$.

On exit: you may set istop to a negative number if at any time it is impossible to evaluate the function $f\left(x\right)$. In this case d01ubf halts with ifail set to the value of istop and the value returned in ans will be that of a non-signalling NaN.

f must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which d01ubf is called. Arguments denoted as Input must not be changed by this procedure.

2: $\mathbf{n}$ – Integer Input

On entry: n specifies the number of weights and abscissae to be used.

Constraint: $\mathbf{n}=1$, $2$, $3$, $4$, $5$, $10$, $15$, $20$ or $25$.

3: $\mathbf{ans}$ – Real (Kind=nag_wp) Output

On exit: if $\mathbf{ifail}=\mathbf{0}$, ans contains an approximation to the integral. Otherwise, ans will be a non-signalling NaN.

4: $\mathbf{iuser}\left(*\right)$ – Integer array User Workspace

5: $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) array User Workspace

iuser and ruser are not used by d01ubf, but are passed directly to f and may be used to pass information to this routine.

6: $\mathbf{ifail}$ – 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

$\mathbf{ifail}<0$

The user has halted the calculation.

$\mathbf{ifail}=1$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{n}\le 25$.

$\mathbf{ifail}=2$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
n is not one of the allowed values.

$\mathbf{ifail}=-99$

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