# NAG AD Library Routine Document

## f07fd_a1w_f (dpotrf_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

f07fd_a1w_f is the adjoint version of the primal routine f07fdf (dpotrf).

## 2Specification

Fortran Interface
 Subroutine f07fd_a1w_f ( ad_handle, uplo, n, a, lda, ifail)
 Integer, Intent (In) :: n, lda Integer, Intent (Out) :: info Type (nagad_a1w_w_rtype), Intent (Inout) :: a(lda,*) Character (1), Intent (In) :: uplo Type (c_ptr), Intent (In) :: ad_handle
 void f07fd_a1w_f_ ( void *&ad_handle, const char *uplo, const Integer &n, nagad_a1w_w_rtype a[], const Integer &lda, Integer &ifail, const Charlen length_uplo)

## 3Description

f07fdf (dpotrf) computes the Cholesky factorization of a real symmetric positive definite matrix. For further information see Section 3 in the documentation for f07fdf (dpotrf).

None.

## 5Arguments

f07fd_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.
• uplo – specifies whether the upper or lower triangular part of $A$ is stored and how $A$ is to be factorized.
• n$n$, the order of the matrix $A$.
• a – on entry: the $n$ by $n$ symmetric positive definite matrix $A$. on exit: the upper or lower triangle of $A$ is overwritten by the Cholesky factor $U$ or $L$ as specified by uplo.
• lda – the first dimension of the array a.
• ifail – on exit: $\mathbf{ifail}=\mathrm{0}$ unless the routine detects an error (see Section 6).

## 6Error Indicators and Warnings

f07fd_a1w_f uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f07fdf may be indicated with the same value returned by ifail. In addition, this routine may 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

f07fd_a1w_f is not threaded in any implementation.