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 the routine name and corresponding argument types is described in the NAG AD Library Introduction.

## 1Purpose

f07fe_a1w_f is the adjoint version of the primal routine f07fef (dpotrs).

## 2Specification

Fortran Interface
 Subroutine f07fe_a1w_f ( ad_handle, uplo, n, nrhs, a, lda, b, ldb, ifail)
 Integer, Intent (In) :: n, nrhs, lda, ldb Integer, Intent (Inout) :: ifail Type (nagad_a1w_w_rtype), Intent (In) :: a(lda,*) Type (nagad_a1w_w_rtype), Intent (Inout) :: b(ldb,*) Character (1), Intent (In) :: uplo Type (c_ptr), Intent (In) :: ad_handle
 void f07fe_a1w_f_ ( void *&ad_handle, const char *uplo, const Integer &n, const Integer &nrhs, nagad_a1w_w_rtype a[], const Integer &lda, nagad_a1w_w_rtype b[], const Integer &ldb, Integer &ifail, const Charlen length_uplo)
The routine may be called by the names f07fe_a1w_f or nagf_lapacklin_dpotrs_a1w.

## 3Description

f07fe_a1w_f is the adjoint version of the primal routine f07fef (dpotrs).
f07fef (dpotrs) solves a real symmetric positive definite system of linear equations with multiple right-hand sides,
 $AX=B ,$
where $A$ has been factorized by f07fdf. For further information see Section 3 in the documentation for f07fef (dpotrs).

None.

## 5Arguments

In addition to the arguments present in the interface of the primal routine, f07fe_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
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: uplo – character Input
3: n – Integer Input
4: nrhs – Integer Input
5: a(lda, $*$) – Type (nagad_a1w_w_rtype) array Input
6: lda – Integer Input
7: b(ldb, $*$) – Type (nagad_a1w_w_rtype) array Input/Output
8: ldb – Integer Input
9: ifail – Integer Input/Output
On entry: must be set to $0$, .
On exit: any errors are indicated as described in Section 6.

## 6Error Indicators and Warnings

f07fe_a1w_f uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f07fef may be indicated with the same value returned by ifail. In addition, this routine may return:
$\mathbf{ifail}=-89$
See Section 4.5.2 in the NAG AD Library Introduction for further information.
$\mathbf{ifail}=-899$
Dynamic memory allocation failed for AD.
See Section 4.5.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

f07fe_a1w_f is not threaded in any implementation.