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

f03bn_a1w_f is the adjoint version of the primal routine f03bnf.

## 2Specification

Fortran Interface
 Subroutine f03bn_a1w_f ( ad_handle, n, a, lda, ipiv, d, id, ifail)
 Integer, Intent (In) :: n, lda, ipiv(n) Integer, Intent (Inout) :: ifail Integer, Intent (Out) :: id(2) Type (nagad_a1w_w_ctype), Intent (In) :: a(lda,*) Type (nagad_a1w_w_ctype), Intent (Out) :: d Type (c_ptr), Intent (Inout) :: ad_handle
 void f03bn_a1w_f_ ( void *&ad_handle, const Integer &n, const nagad_w_rcype a[], const Integer &lda, const Integer ipiv[], nagad_w_rcype &d, Integer id[], Integer &ifail)
The routine may be called by the names f03bn_a1w_f or nagf_det_complex_gen_a1w. The corresponding t1w and p0w variants of this routine are also available.

## 3Description

f03bn_a1w_f is the adjoint version of the primal routine f03bnf.
f03bnf computes the determinant of a complex $n×n$ matrix $A$. f07arf must be called first to supply the matrix $A$ in factorized form. For further information see Section 3 in the documentation for f03bnf.

## 4References

Wilkinson J H and Reinsch C (1971) Handbook for Automatic Computation II, Linear Algebra Springer–Verlag

## 5Arguments

In addition to the arguments present in the interface of the primal routine, f03bn_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: n – Integer Input
3: a(lda, $*$) – Type (nagad_a1w_w_ctype) array Input
4: lda – Integer Input
5: ipiv(n) – Integer array Input
6: d – Type (nagad_a1w_w_ctype) Output
7: id($2$) – Integer array Output
8: ifail – Integer Input/Output

## 6Error Indicators and Warnings

f03bn_a1w_f preserves all error codes from f03bnf 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

f03bn_a1w_f is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for f03bnf, modified to demonstrate calling the NAG AD Library.