NAG Library Routine Document

d01ubf (dim1_inf_exp_wt)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

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

fun must return the integrands $f\left(x_i\right)$ in $\mathbf{f}\left(\mathit{i}\right)$ for each $x_i$ in $\mathbf{x}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$ at a given point.

The specification of fun is:

Fortran Interface

Subroutine fun ( x, f, 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) :: f(n)

C Header Interface

#include <nagmk26.h> void  fun (const double x[], double f[], const Integer *n, Integer iuser[], double ruser[], Integer *istop)

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

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

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

On exit: $\mathbf{f}\left(\mathit{i}\right)$ 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:     $\mathbf{n}$ – IntegerInput

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

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

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

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

6:     $\mathbf{istop}$ – IntegerInput/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.

fun 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:     $\mathbf{n}$ – IntegerInput

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

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

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

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

6:     $\mathbf{ifail}$ – 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

$\mathbf{ifail}<0$

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 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 (d01ubfe.f90)

10.2

Program Data

10.3

Program Results

Program Results (d01ubfe.r)