d01rg_ad_f : NAG AD Library Routine Document, Mark 26

Fortran Interface

Subroutine d01rg_a1w_f (

ad_handle, a, b, f, epsabs, epsrel, dinest, errest, nevals, iuser, ruser, ifail)

Integer, Intent (Inout)	::	iuser(*), ifail
Integer, Intent (Out)	::	nevals
Type (nagad_a1w_w_rtype), Intent (In)	::	a, b, epsabs, epsrel
Type (nagad_a1w_w_rtype), Intent (Inout)	::	ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out)	::	dinest, errest
Type (c_ptr), Intent (In)	::	ad_handle
External	::	f

Subroutine f (

ad_handle, x, nx, fv, iflag, iuser, ruser)

Integer, Intent (In)	::	nx
Integer, Intent (Inout)	::	iflag, iuser(*)
Type (nagad_a1w_w_rtype), Intent (Inout)	::	x(nx), ruser(*), fv(nx)
Type (c_ptr), Intent (In)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void d01rg_a1w_f_ (

void *&ad_handle, const nagad_a1w_w_rtype &a, const nagad_a1w_w_rtype &b,
void (NAG_CALL f)(void *&ad_handle, nagad_a1w_w_rtype x[], const Integer &nx, nagad_a1w_w_rtype fv[], Integer &iflag, Integer iuser[], nagad_a1w_w_rtype ruser[]),
const nagad_a1w_w_rtype &epsabs, const nagad_a1w_w_rtype &epsrel, nagad_a1w_w_rtype &dinest, nagad_a1w_w_rtype &errest, Integer &nevals, Integer iuser[], nagad_a1w_w_rtype ruser[], Integer &ifail)

Description

d01rgf is a general purpose integrator which calculates an approximation to the integral of a function

f (x)

over a finite interval

[a, b]

I = \int_{a}^{b} f (x) d x .

The routine is suitable as a general purpose integrator, and can be used when the integrand has singularities and infinities. In particular, the routine can continue if the subroutine f explicitly returns a quiet or signalling NaN or a signed infinity. For further information see Section 3 in the documentation for d01rgf .

References

Arguments

d01rg_a1w_f provides access to all the arguments available in the primal routine. There are also additional arguments specific to AD. A tooltip popup for each argument can be found by hovering over the argument name in Section 2 and a summary of the arguments are provided below:

ad_handle – a handle to the AD configuration data object, as created by x10aa_a1w_f.
a – $a$ , the lower limit of integration.
b – $b$ , the upper limit of integration.
f – f must return the value of the integrand $f$ at a set of points.
epsabs – the absolute accuracy required.
epsrel – the relative accuracy required.
dinest – on exit: the estimate of the definite integral f.
errest – on exit: the error estimate of the definite integral f.
nevals – on exit: the total number of points at which the integrand, $f$ , has been evaluated.
iuser – may be used to pass information to user-supplied argument(s).
ruser – may be used to pass information to user-supplied argument(s).
ifail – on entry: ifail must be set to $0$ , $- 1 or 1$ . on exit: ifail = 0 unless the routine detects an error or a warning has been flagged (see Section 6).

Error Indicators and Warnings

d01rg_a1w_f preserves all error codes from d01rgf and in addition can return:

$ifail = - 89$: An unexpected AD error has been triggered by this routine. Please contact NAG.
See Section 5.2 in the NAG AD Library Introduction for further information.

$ifail = - 899$: Dynamic memory allocation failed for AD.
See Section 5.1 in the NAG AD Library Introduction for further information.

Language	Source File	Data	Results
Fortan	d01rg_a1w_fe.f90	d01rg_a1w_fe.d	d01rg_a1w_fe.r
C++	d01rg_a1w_hcppe.cpp	d01rg_a1w_hcppe.d	d01rg_a1w_hcppe.r

NAG AD Library Routine Document

d01rg_a1w_f (dim1_fin_gonnet_vec_a1w)

▸▿ Contents

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

6

Error Indicators and Warnings

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

NAG AD Library Routine Document

d01rg_a1w_f (dim1_fin_gonnet_vec_a1w)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example