Note: a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document. Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.

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1Purpose

d01rg_a1w_f is the adjoint version of the primal routine d01rgf.

2Specification

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 (Inout) :: ad_handle External :: f
The routine may be called by the names d01rg_a1w_f or nagf_quad_dim1_fin_gonnet_vec_a1w. The corresponding t1w and p0w variants of this routine are also available.

3Description

d01rg_a1w_f is the adjoint version of the primal routine d01rgf.
d01rgf is a general purpose integrator which calculates an approximation to the integral of a function $f\left(x\right)$ over a finite interval $\left[a,b\right]$:
 $I= ∫ab f(x) dx .$
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.

4References

Gonnet P (2010) Increasing the reliability of adaptive quadrature using explicit interpolants ACM Trans. Math. software 37 26
Piessens R, de Doncker–Kapenga E, Überhuber C and Kahaner D (1983) QUADPACK, A Subroutine Package for Automatic Integration Springer–Verlag

5Arguments

In addition to the arguments present in the interface of the primal routine, d01rg_a1w_f includes some arguments specific to AD.
A brief summary of the AD specific arguments is given below. For the remainder, links are provided to the corresponding argument from the primal routine. A tooltip popup for all arguments can be found by hovering over the argument name in Section 2 and in this section.
1: ad_handle – Type (c_ptr) Input/Output
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: Input
3: Input
4: f – Subroutine External Procedure
The specification of f is:
Fortran Interface
 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 (In) :: x(nx) Type (nagad_a1w_w_rtype), Intent (Inout) :: ruser(*) Type (nagad_a1w_w_rtype), Intent (Out) :: fv(nx) Type (c_ptr), Intent (Inout) :: ad_handle
1: ad_handle – Type (c_ptr) Input/Output
On entry: a handle to the AD configuration data object.
2: Input
3: nx – Integer Input
4: Output
5: iflag – Integer Input/Output
6: iuser – Integer array User Workspace
7: User Workspace
5: Input
6: Input
7: Output
8: Output
9: nevals – Integer Output
10: iuser($*$) – Integer array User Workspace
11: ruser($*$) – Type (nagad_a1w_w_rtype) array User Workspace
12: ifail – Integer Input/Output

6Error Indicators and Warnings

d01rg_a1w_f preserves all error codes from d01rgf and in addition can return:
${\mathbf{ifail}}=-89$
See Section 4.8.2 in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-899$
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.

Not applicable.

8Parallelism and Performance

d01rg_a1w_f is not threaded in any implementation.

None.

10Example

The following examples are variants of the example for d01rgf, modified to demonstrate calling the NAG AD Library.