NAG AD Library
f01fj (complex_gen_matrix_log)

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1 Purpose

f01fj is the AD Library version of the primal routine f01fjf. Based (in the C++ interface) on overload resolution, f01fj can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface
Subroutine f01fj_AD_f ( ad_handle, n, a, lda, ifail)
Integer, Intent (In) :: n, lda
Integer, Intent (Inout) :: ifail
ADCTYPE, Intent (Inout) :: a(lda,*)
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++ Header Interface
#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {
void f01fj ( void *&ad_handle, const Integer &n, ADCTYPE 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
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

f01fj is the AD Library version of the primal routine f01fjf.
f01fjf computes the principal matrix logarithm, log(A), of a complex n×n matrix A, with no eigenvalues on the closed negative real line. For further information see Section 3 in the documentation for f01fjf.

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
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, f01fj 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 – Pointer to AD Data Input/Output
On entry: a handle to the AD configuration data object, as created by x10aa.
2: n – Integer Input
3: a(lda, *) – ADCTYPE array Input/Output
4: lda – Integer Input
5: ifail – Integer Input/Output

6 Error Indicators and Warnings

f01fj preserves all error codes from f01fjf and in addition can return:
ifail=-89
An unexpected AD error has been triggered by this routine. Please contact NAG.
See Section 4.8.2 in the NAG AD Library Introduction for further information.
ifail=-199
The routine was called using a mode that has not yet been implemented.
ifail=-443
On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.
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 Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

f01fj is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f01fjf, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example finds the principal matrix logarithm of the matrix
A = ( 1.0+2.0i 0.0+1.0i 1.0+0.0i 3.0+2.0i 0.0+3.0i -2.0+0.0i 0.0+0.0i 1.0+0.0i 1.0+0.0i -2.0+0.0i 3.0+2.0i 0.0+3.0i 2.0+0.0i 0.0+1.0i 0.0+1.0i 2.0+3.0i ) .  

10.1 Adjoint modes

Language Source File Data Results
Fortran f01fj_a1w_fe.f90 f01fj_a1w_fe.d f01fj_a1w_fe.r
C++ f01fj_a1w_hcppe.cpp f01fj_a1w_hcppe.d f01fj_a1w_hcppe.r

10.2 Tangent modes

Language Source File Data Results
Fortran f01fj_t1w_fe.f90 f01fj_t1w_fe.d f01fj_t1w_fe.r
C++ f01fj_t1w_hcppe.cpp f01fj_t1w_hcppe.d f01fj_t1w_hcppe.r

10.3 Passive mode

Language Source File Data Results
Fortran f01fj_p0w_fe.f90 f01fj_p0w_fe.d f01fj_p0w_fe.r
C++ f01fj_p0w_hcppe.cpp f01fj_p0w_hcppe.d f01fj_p0w_hcppe.r