Settings help

## 1Purpose

f07aj is the AD Library version of the primal routine f07ajf (dgetri). Based (in the C++ interface) on overload resolution, f07aj can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

## 2Specification

Fortran Interface
 Integer, Intent (In) :: n, lda, ipiv(*), lwork Integer, Intent (Inout) :: ifail ADTYPE, Intent (Inout) :: a(lda,*) ADTYPE, Intent (Out) :: work(max(1,lwork)) 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:
#include <dco.hpp>
namespace nag {
 void f07aj ( void *&ad_handle, const Integer &n, ADTYPE a[], const Integer &lda, const Integer ipiv[], ADTYPE work[], const Integer &lwork, 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

f07aj is the AD Library version of the primal routine f07ajf (dgetri).
f07ajf (dgetri) computes the inverse of a real matrix $A$, where $A$ has been factorized by f07adf. For further information see Section 3 in the documentation for f07ajf (dgetri).

## 4References

Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion IMA J. Numer. Anal. 12 1–19

## 5Arguments

In addition to the arguments present in the interface of the primal routine, f07aj 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 handle to the AD configuration data object, as created by x10aa.
2: n – Integer Input
3: a(lda, $*$) – ADTYPE array Input/Output
4: lda – Integer Input
5: ipiv($*$) – Integer array Input
6: work($\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{lwork}}\right)$) – ADTYPE array Workspace
7: lwork – Integer Input
8: 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

f07aj uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f07ajf may be indicated with the same value returned by ifail. In addition, this routine may return:
${\mathbf{ifail}}=-89$
See Section 4.8.2 in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
The routine was called using a mode that has not yet been implemented.
${\mathbf{ifail}}=-443$
This check is only made if the overloaded C++ interface is used with arguments not of type double.
${\mathbf{ifail}}=-444$
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 Section 4.8.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

f07aj is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for f07ajf (dgetri), modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example computes the inverse of the matrix $A$, where
 $A= ( 1.80 2.88 2.05 -0.89 5.25 -2.95 -0.95 -3.80 1.58 -2.69 -2.90 -1.04 -1.11 -0.66 -0.59 0.80 ) .$
Here $A$ is nonsymmetric and must first be factorized by f07ad.

Language Source File Data Results
Fortran f07aj_a1w_fe.f90 f07aj_a1w_fe.d f07aj_a1w_fe.r
C++ f07aj_a1w_hcppe.cpp f07aj_a1w_hcppe.d f07aj_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran f07aj_t1w_fe.f90 f07aj_t1w_fe.d f07aj_t1w_fe.r
C++ f07aj_t1w_hcppe.cpp f07aj_t1w_hcppe.d f07aj_t1w_hcppe.r

### 10.3Passive mode

Language Source File Data Results
Fortran f07aj_p0w_fe.f90 f07aj_p0w_fe.d f07aj_p0w_fe.r
C++ f07aj_p0w_hcppe.cpp f07aj_p0w_hcppe.d f07aj_p0w_hcppe.r