NAG FL Interface
d01rgf (dim1_​fin_​gonnet_​vec)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

On entry: $a$, the lower limit of integration.

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

On entry: $b$, the upper limit of integration. It is not necessary that $a<b$.

Note: if $\mathbf{a}=\mathbf{b}$, the routine will immediately return with $\mathbf{dinest}=0.0$, $\mathbf{errest}=0.0$ and $\mathbf{nevals}=0$.

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

f must return the value of the integrand $f$ at a set of points.

The specification of f is:

Fortran Interface copy

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

C Header Interface copy

void  f (const double x[], const Integer *nx, double fv[], Integer *iflag, Integer iuser[], double ruser[])

C++ Header Interface copy

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

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

On entry: the abscissae, $x_i$, for $\mathit{i}=1,2,\dots ,\mathbf{nx}$, at which function values are required.

2: $\mathbf{nx}$ – Integer Input

On entry: the number of abscissae at which a function value is required. nx will be of size equal to the number of Kronrod points in the quadrature rule used.

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

On exit: fv must contain the values of the integrand $f$. $\mathbf{fv}\left(i\right)=f\left(x_i\right)$ for all $i=1,2,\dots ,\mathbf{nx}$.

4: $\mathbf{iflag}$ – Integer Input/Output

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

On exit: set $\mathbf{iflag}<0$ to force an immediate exit with $\mathbf{ifail}=-\mathbf{1}$.

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

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

f is called with the arguments iuser and ruser as supplied to d01rgf. You should use the arrays iuser and ruser to supply information to f.

f must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which d01rgf is called. Arguments denoted as Input must not be changed by this procedure.

4: $\mathbf{epsabs}$ – Real (Kind=nag_wp) Input

On entry: the absolute accuracy required.

If epsabs is negative, $\left|\mathbf{epsabs}\right|$ is used. See Section 7.

If $\mathbf{epsabs}=0.0$, only the relative error will be used.

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

On entry: the relative accuracy required.

If epsrel is negative, $\left|\mathbf{epsrel}\right|$ is used. See Section 7.

If $\mathbf{epsrel}=0.0$, only the absolute error will be used otherwise the actual value of epsrel used by d01rgf is $\max (\mathit{machine precision},\left|\mathbf{epsrel}\right|)$.

Constraint: at least one of epsabs and epsrel must be nonzero.

6: $\mathbf{dinest}$ – Real (Kind=nag_wp) Output

On exit: the estimate of the definite integral f.

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

On exit: the error estimate of the definite integral f.

8: $\mathbf{nevals}$ – Integer Output

On exit: the total number of points at which the integrand, $f$, has been evaluated.

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

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

iuser and ruser are not used by d01rgf, but are passed directly to f and may be used to pass information to this routine.

11: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $\mathrm{-1}$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $\mathrm{-1}$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $\mathrm{-1}$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $\mathrm{-1}$ is recommended since useful values can be provided in some output arguments even when $\mathbf{ifail}\ne \mathbf{0}$ on exit. When the value $-\mathbf{1}$ 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

$\mathbf{ifail}=1$

The requested accuracy was not achieved. Consider using larger values of epsabs and epsrel.

$\mathbf{ifail}=2$

The integral is probably divergent or slowly convergent.

$\mathbf{ifail}=14$

Both $\mathbf{epsabs}=0.0$ and $\mathbf{epsrel}=0.0$.

$\mathbf{ifail}=-1$

Exit requested from f with $\mathbf{iflag}=⟨\mathit{\text{value}}⟩$.

$\mathbf{ifail}=-99$

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