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## 1Purpose

f03ba is the AD Library version of the primal routine f03baf. Based (in the C++ interface) on overload resolution, f03ba can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

## 2Specification

Fortran Interface
 Subroutine f03ba_AD_f ( n, a, lda, ipiv, d, id, ifail)
 Integer, Intent (In) :: n, lda, ipiv(n) Integer, Intent (Inout) :: ifail Integer, Intent (Out) :: id ADTYPE, Intent (In) :: a(lda,*) ADTYPE, Intent (Out) :: d 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 f03ba ( handle_t &ad_handle, const Integer &n, const ADTYPE a[], const Integer &lda, const Integer ipiv[], ADTYPE &d, Integer &id, 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

f03ba is the AD Library version of the primal routine f03baf.
f03baf computes the determinant of a real $n×n$ matrix $A$. f07adf must be called first to supply the matrix $A$ in factorized form. For further information see Section 3 in the documentation for f03baf.

## 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, f03ba 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: n – Integer Input
3: a(lda, $*$) – ADTYPE array Input
4: lda – Integer Input
5: ipiv(n) – Integer array Input
6: Output
7: id – Integer Output
8: ifail – Integer Input/Output

## 6Error Indicators and Warnings

f03ba preserves all error codes from f03baf and in addition can 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

f03ba is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for f03baf, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example computes the $LU$ factorization with partial pivoting, and calculates the determinant, of the real matrix
 $( 33 16 72 −24 −10 −57 −8 −4 −17 ) .$

Language Source File Data Results
Fortran f03ba_a1w_fe.f90 f03ba_a1w_fe.d f03ba_a1w_fe.r
C++ f03ba_a1w_hcppe.cpp f03ba_a1w_hcppe.d f03ba_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran f03ba_t1w_fe.f90 f03ba_t1w_fe.d f03ba_t1w_fe.r
C++ f03ba_t1w_hcppe.cpp f03ba_t1w_hcppe.d f03ba_t1w_hcppe.r

### 10.3Passive mode

Language Source File Data Results
Fortran f03ba_p0w_fe.f90 f03ba_p0w_fe.d f03ba_p0w_fe.r
C++ f03ba_p0w_hcppe.cpp f03ba_p0w_hcppe.d f03ba_p0w_hcppe.r