Settings help

## 1Purpose

f07fd is the AD Library version of the primal routine f07fdf (dpotrf). Based (in the C++ interface) on overload resolution, f07fd can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

## 2Specification

Fortran Interface
 Subroutine f07fd_AD_f ( uplo, n, a, lda, ifail)
 Integer, Intent (In) :: n, lda Integer, Intent (Inout) :: ifail ADTYPE, Intent (Inout) :: a(lda,*) Character (1), Intent (In) :: uplo Type (c_ptr), Intent (Inout) :: ad_handle
Corresponding to the overloaded C++ function, the Fortran interface provides five routines with names reflecting the type used for active real arguments. The actual subroutine and type names are formed by replacing AD and ADTYPE in the above as follows:
C++ Interface
#include <dco.hpp>
namespace nag {
 void f07fd ( handle_t &ad_handle, const char *uplo, const Integer &n, ADTYPE a[], const Integer &lda, Integer &ifail)
}
}
The function is overloaded on ADTYPE which represents the type of active arguments. ADTYPE may be any of the following types:
double,
dco::ga1s<double>::type,
dco::gt1s<double>::type

## 3Description

f07fd is the AD Library version of the primal routine f07fdf (dpotrf).
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).

## 4References

Demmel J W (1989) On floating-point errors in Cholesky LAPACK Working Note No. 14 University of Tennessee, Knoxville https://www.netlib.org/lapack/lawnspdf/lawn14.pdf
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore

## 5Arguments

In addition to the arguments present in the interface of the primal routine, f07fd 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.
On entry: a configuration object that holds information on the differentiation strategy. Details on setting the AD strategy are described in AD handle object in the NAG AD Library Introduction.
2: uplo – character Input
3: n – Integer Input
4: a(lda, $*$) – ADTYPE array Input/Output
5: lda – Integer Input
6: 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

f07fd 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 Error Handling in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
The routine was called using a strategy that has not yet been implemented.
See AD Strategies in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-444$
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
${\mathbf{ifail}}=-899$
Dynamic memory allocation failed for AD.
See Error Handling in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

f07fd is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for f07fdf (dpotrf), modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example computes the Cholesky factorization of the matrix $A$, where
 $A= ( 4.16 -3.12 0.56 -0.10 -3.12 5.03 -0.83 1.18 0.56 -0.83 0.76 0.34 -0.10 1.18 0.34 1.18 ) .$

Language Source File Data Results
Fortran f07fd_a1w_fe.f90 f07fd_a1w_fe.d f07fd_a1w_fe.r
C++ f07fd_a1w_hcppe.cpp f07fd_a1w_hcppe.d f07fd_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran f07fd_t1w_fe.f90 f07fd_t1w_fe.d f07fd_t1w_fe.r
C++ f07fd_t1w_hcppe.cpp f07fd_t1w_hcppe.d f07fd_t1w_hcppe.r

### 10.3Passive mode

Language Source File Data Results
Fortran f07fd_p0w_fe.f90 f07fd_p0w_fe.d f07fd_p0w_fe.r
C++ f07fd_p0w_hcppe.cpp f07fd_p0w_hcppe.d f07fd_p0w_hcppe.r