NAG AD Library
f01ej (real_gen_matrix_log)

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1 Purpose

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:
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×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_handlenag::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: imnormADTYPE Output
6: ifail – Integer Input/Output

6 Error Indicators and Warnings

f01ej preserves all error codes from f01ejf and in addition can return:
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.
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.
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
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


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 = ( 3 −3 1 1 2 1 −2 1 1 1 3 −1 2 0 2 0 ) .  

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