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

c05rd_a1w_f is the adjoint version of the primal routine c05rdf.

## 2Specification

Fortran Interface
 Subroutine c05rd_a1w_f ( ad_handle, irevcm, n, x, fvec, fjac, xtol, mode, diag, factor, r, qtf, iwsav, rwsav, ifail)
 Integer, Intent (In) :: n, mode Integer, Intent (Inout) :: irevcm, iwsav(17), ifail Type (nagad_a1w_w_rtype), Intent (In) :: xtol, factor Type (nagad_a1w_w_rtype), Intent (Inout) :: x(n), fvec(n), fjac(n,n), diag(n), r(n*(n+1)/2), qtf(n), rwsav(4*n+10) Type (c_ptr), Intent (Inout) :: ad_handle
The routine may be called by the names c05rd_a1w_f or nagf_roots_sys_deriv_rcomm_a1w. The corresponding t1w and p0w variants of this routine are also available.

## 3Description

c05rd_a1w_f is the adjoint version of the primal routine c05rdf.
c05rdf is a comprehensive reverse communication routine that finds a solution of a system of nonlinear equations by a modification of the Powell hybrid method. You must provide the Jacobian. For further information see Section 3 in the documentation for c05rdf.

## 4References

Moré J J, Garbow B S and Hillstrom K E (1980) User guide for MINPACK-1 Technical Report ANL-80-74 Argonne National Laboratory
Powell M J D (1970) A hybrid method for nonlinear algebraic equations Numerical Methods for Nonlinear Algebraic Equations (ed P Rabinowitz) Gordon and Breach

## 5Arguments

In addition to the arguments present in the interface of the primal routine, c05rd_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: irevcm – Integer Input/Output
3: n – Integer Input
4: x(n) – Type (nagad_a1w_w_rtype) array Input/Output
5: fvec(n) – Type (nagad_a1w_w_rtype) array Input/Output
6: fjac(n, n) – Type (nagad_a1w_w_rtype) array Input/Output
7: Input
8: mode – Integer Input
9: diag(n) – Type (nagad_a1w_w_rtype) array Input/Output
10: Input
11: r(${\mathbf{n}}×\left({\mathbf{n}}+1\right)/2$) – Type (nagad_a1w_w_rtype) array Input/Output
12: qtf(n) – Type (nagad_a1w_w_rtype) array Input/Output
13: iwsav($17$) – Integer array Communication Array
14: rwsav($4×{\mathbf{n}}+10$) – Type (nagad_a1w_w_rtype) array Communication Array
15: ifail – Integer Input/Output

## 6Error Indicators and Warnings

c05rd_a1w_f preserves all error codes from c05rdf 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

c05rd_a1w_f is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for c05rdf, modified to demonstrate calling the NAG AD Library.