f01ec: FL CL CPP AD

NAG AD Library
f01ec_a1w_f (real_gen_matrix_exp_a1w)

Note: a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document. Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.

Keyword Search:

NAG Library Manual, Mark 27.1

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F01 (Matop) Chapter Contents

F01 (Matop) Chapter Introduction (FL)

f01ec: FL CL CPP AD

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Adjoint mode (a1w)

10.2 Tangent mode (t1w)

10.3 Passive mode (p0w)

1 Purpose

f01ec_a1w_f is the adjoint version of the primal routine f01ecf.

2 Specification

Fortran Interface

Subroutine f01ec_a1w_f (

ad_handle, n, a, lda, ifail)

Integer, Intent (In)	::	n, lda
Integer, Intent (Inout)	::	ifail
Type (nagad_a1w_w_rtype), Intent (Inout)	::	a(lda,*)
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void f01ec_a1w_f_ (

void *&ad_handle, const Integer &n, nagad_a1w_w_rtype a[], const Integer &lda, Integer &ifail)

The routine may be called by the names f01ec_a1w_f or nagf_matop_real_gen_matrix_exp_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

f01ec_a1w_f is the adjoint version of the primal routine f01ecf.

f01ecf computes the matrix exponential,

e^{A}

, of a real

n \times n

matrix

A

. For further information see Section 3 in the documentation for f01ecf.

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, f01ec_a1w_f 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 – Type (c_ptr) Input/Output: On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: n – Integer Input
3: a(lda, $*$ ) – Type (nagad_a1w_w_rtype) array Input/Output
4: lda – Integer Input
5: ifail – Integer Input/Output

6 Error Indicators and Warnings

f01ec_a1w_f preserves all error codes from f01ecf 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.

$ifail = - 899$: 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

f01ec_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f01ecf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

Language	Source File	Data	Results
Fortran	f01ec_a1w_fe.f90	f01ec_a1w_fe.d	f01ec_a1w_fe.r
C++	f01ec_a1w_hcppe.cpp	f01ec_a1w_hcppe.d	f01ec_a1w_hcppe.r

10.2 Tangent mode (t1w)

Language	Source File	Data	Results
Fortran	f01ec_t1w_fe.f90	f01ec_t1w_fe.d	f01ec_t1w_fe.r
C++	f01ec_t1w_hcppe.cpp	f01ec_t1w_hcppe.d	f01ec_t1w_hcppe.r

10.3 Passive mode (p0w)

Language	Source File	Data	Results
Fortran	f01ec_p0w_fe.f90	f01ec_p0w_fe.d	f01ec_p0w_fe.r
C++	f01ec_p0w_hcppe.cpp	f01ec_p0w_hcppe.d	f01ec_p0w_hcppe.r