# NAG AD Library Routine Document

## d01rg_a1w_f (dim1_fin_gonnet_vec_a1w)

Note: _a1w_ denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Further implementations, for example for higher order differentiation or using the tangent linear approach, may become available at later marks of the NAG AD Library. The method of codifying AD implementations in routine name and corresponding argument types is described in the NAG AD Library Introduction.

## 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 (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

## 3Description

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

None.

## 5Arguments

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.
• ff 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 $\mathrm{0}$, $-\mathrm{1}\text{ or }\mathrm{1}$. on exit: ifail = 0 unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error Indicators and Warnings

d01rg_a1w_f preserves all error codes from d01rgf and in addition can return:
$\mathbf{ifail}=-89$
See Section 5.2 in the NAG AD Library Introduction for further information.
$\mathbf{ifail}=-899$
Dynamic memory allocation failed for AD.
See Section 5.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

d01rg_a1w_f is not threaded in any implementation.