f01fc is the AD Library version of the primal routine f01fcf. Based (in the C++ interface) on overload resolution, f01fc can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine f01fc_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++ Interface

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

void f01fc (

handle_t &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

f01fc is the AD Library version of the primal routine f01fcf.

f01fcf computes the matrix exponential,

e^{A}

, of a complex

n \times n

matrix

A

. For further information see Section 3 in the documentation for f01fcf.

4 References

Al–Mohy A H and Higham N J (2009) A new scaling and squaring algorithm for the matrix exponential SIAM J. Matrix Anal. 31(3) 970–989

Higham N J (2005) The scaling and squaring method for the matrix exponential revisited SIAM J. Matrix Anal. Appl. 26(4) 1179–1193

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

Moler C B and Van Loan C F (2003) Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later SIAM Rev. 45 3–49

5 Arguments

In addition to the arguments present in the interface of the primal routine, f01fc 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, $*$ ) – ADCTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
4: lda – Integer Input
5: ifail – Integer Input/Output

6 Error Indicators and Warnings

f01fc preserves all error codes from f01fcf 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

f01fc is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f01fcf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example finds the matrix exponential of the matrix

A = (\begin{matrix} 1 + i & 2 + i & 2 + i & 2 + i \\ 3 + 2 i & 1 & 1 & 2 + i \\ 3 + 2 i & 2 + i & 1 & 2 + i \\ 3 + 2 i & 3 + 2 i & 3 + 2 i & 1 + i \end{matrix}) .

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	f01fc_a1w_fe.f90	f01fc_a1w_fe.d	f01fc_a1w_fe.r
C++	f01fc_a1w_hcppe.cpp	f01fc_a1w_hcppe.d	f01fc_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	f01fc_t1w_fe.f90	f01fc_t1w_fe.d	f01fc_t1w_fe.r
C++	f01fc_t1w_hcppe.cpp	f01fc_t1w_hcppe.d	f01fc_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	f01fc_p0w_fe.f90	f01fc_p0w_fe.d	f01fc_p0w_fe.r
C++	f01fc_p0w_hcppe.cpp	f01fc_p0w_hcppe.d	f01fc_p0w_hcppe.r

NAG Library Manual, Mark 30.1

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F01 (Matop) Chapter Contents

F01 (Matop) Chapter Introduction (FL)

f01fc: FL CL CPP AD

NAG AD Libraryf01fc (complex_gen_matrix_exp)

▸▿ Contents

1 Purpose