f01ej is the AD Library version of the primal routine f01ejf. Based (in the C++ interface) on overload resolution, f01ej can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine f01ej_AD_f (

n, a, lda, imnorm, ifail)

Integer, Intent (In)	::	n, lda
Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (Inout)	::	a(lda,*)
ADTYPE, Intent (Out)	::	imnorm
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:

when ADTYPE is	Real(kind=nag_wp)	then AD is p0w
when ADTYPE is	Type(nagad_a1w_w_rtype)	then AD is a1w
when ADTYPE is	Type(nagad_t1w_w_rtype)	then AD is t1w

C++ Interface

#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {

void f01ej (

handle_t &ad_handle, const Integer &n, ADTYPE a[], const Integer &lda, ADTYPE &imnorm, 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

Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

f01ej is the AD Library version of the primal routine f01ejf.

f01ejf computes the principal matrix logarithm,

\log (A)

, of a real

n \times n

matrix

A

, with no eigenvalues on the closed negative real line. For further information see Section 3 in the documentation for f01ejf.

4 References

Al–Mohy A H and Higham N J (2011) Improved inverse scaling and squaring algorithms for the matrix logarithm SIAM J. Sci. Comput. 34(4) C152–C169

Al–Mohy A H, Higham N J and Relton S D (2012) Computing the Fréchet derivative of the matrix logarithm and estimating the condition number SIAM J. Sci. Comput. 35(4) C394–C410

Higham N J (2008) Functions of Matrices: Theory and Computation SIAM, Philadelphia, PA, USA

5 Arguments

In addition to the arguments present in the interface of the primal routine, f01ej 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 – nag::ad::handle_t Input/Output: 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/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
4: lda – Integer Input
5: imnorm – ADTYPE Output
6: ifail – Integer Input/Output

6 Error Indicators and Warnings

f01ej preserves all error codes from f01ejf and in addition can return:

$ifail = - 89$: An unexpected AD error has been triggered by this routine. Please contact NAG.
See Error Handling in the NAG AD Library Introduction for further information.

$ifail = - 199$: 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.

$ifail = - 444$: A C++ exception was thrown.
The error message will show the details of the C++ exception text.

$ifail = - 899$: Dynamic memory allocation failed for AD.
See Error Handling in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

f01ej is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f01ejf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example finds the principal matrix logarithm of the matrix

A = (\begin{array}{r} 3 & −3 & 1 & 1 \\ 2 & 1 & −2 & 1 \\ 1 & 1 & 3 & −1 \\ 2 & 0 & 2 & 0 \end{array}) .

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	f01ej_a1w_fe.f90	f01ej_a1w_fe.d	f01ej_a1w_fe.r
C++	f01ej_a1w_hcppe.cpp	f01ej_a1w_hcppe.d	f01ej_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	f01ej_t1w_fe.f90	f01ej_t1w_fe.d	f01ej_t1w_fe.r
C++	f01ej_t1w_hcppe.cpp	f01ej_t1w_hcppe.d	f01ej_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	f01ej_p0w_fe.f90	f01ej_p0w_fe.d	f01ej_p0w_fe.r
C++	f01ej_p0w_hcppe.cpp	f01ej_p0w_hcppe.d	f01ej_p0w_hcppe.r

NAG Library Manual, Mark 28.6

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F01 (Matop) Chapter Contents

F01 (Matop) Chapter Introduction (FL)

f01ej: FL CL CPP AD

NAG AD Libraryf01ej (real_gen_matrix_log)

▸▿ Contents

1 Purpose