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

d01ga_a1w_f is the adjoint version of the primal routine d01gaf.

## 2Specification

Fortran Interface
 Subroutine d01ga_a1w_f ( ad_handle, x, y, n, ans, er, ifail)
 Integer, Intent (In) :: n Integer, Intent (Inout) :: ifail Type (nagad_a1w_w_rtype), Intent (In) :: x(n), y(n) Type (nagad_a1w_w_rtype), Intent (Out) :: ans, er Type (c_ptr), Intent (Inout) :: ad_handle
The routine may be called by the names d01ga_a1w_f or nagf_quad_dim1_data_a1w. The corresponding t1w and p0w variants of this routine are also available.

## 3Description

d01ga_a1w_f is the adjoint version of the primal routine d01gaf.
d01gaf integrates a function which is specified numerically at four or more points, over the whole of its specified range, using third-order finite difference formulae with error estimates, according to a method due to Gill and Miller (1972). For further information see Section 3 in the documentation for d01gaf.

## 4References

Gill P E and Miller G F (1972) An algorithm for the integration of unequally spaced data Comput. J. 15 80–83

## 5Arguments

In addition to the arguments present in the interface of the primal routine, d01ga_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: x(n) – Type (nagad_a1w_w_rtype) array Input
3: y(n) – Type (nagad_a1w_w_rtype) array Input
4: n – Integer Input
5: Output
6: Output
7: ifail – Integer Input/Output

## 6Error Indicators and Warnings

d01ga_a1w_f preserves all error codes from d01gaf 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

d01ga_a1w_f is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for d01gaf, modified to demonstrate calling the NAG AD Library.