f03bf: FL CL CPP AD

NAG AD Library
f03bf_a1w_f (real_sym_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

F03 (Det) Chapter Contents

F03 (Det) Chapter Introduction (FL)

f03bf: 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

f03bf_a1w_f is the adjoint version of the primal routine f03bff.

2 Specification

Fortran Interface

Subroutine f03bf_a1w_f (

ad_handle, n, a, lda, d, id, ifail)

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

C++ Header Interface

#include <nagad.h>

void f03bf_a1w_f_ (

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

The routine may be called by the names f03bf_a1w_f or nagf_det_real_sym_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

f03bf_a1w_f is the adjoint version of the primal routine f03bff.

f03bff computes the determinant of a real

n \times n

symmetric positive definite matrix

A

. f07fdf must be called first to supply the symmetric matrix

A

in Cholesky factorized form. The storage (upper or lower triangular) used by f07fdf is not relevant to f03bff since only the diagonal elements of the factorized

A

are referenced. For further information see Section 3 in the documentation for f03bff.

4 References

Wilkinson J H and Reinsch C (1971) Handbook for Automatic Computation II, Linear Algebra Springer–Verlag

5 Arguments

In addition to the arguments present in the interface of the primal routine, f03bf_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
4: lda – Integer Input
5: d – Type (nagad_a1w_w_rtype) Output
6: id – Integer Output
7: ifail – Integer Input/Output

6 Error Indicators and Warnings

f03bf_a1w_f preserves all error codes from f03bff 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

f03bf_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f03bff, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

Language	Source File	Data	Results
Fortran	f03bf_a1w_fe.f90	f03bf_a1w_fe.d	f03bf_a1w_fe.r
C++	f03bf_a1w_hcppe.cpp	f03bf_a1w_hcppe.d	f03bf_a1w_hcppe.r

10.2 Tangent mode (t1w)

Language	Source File	Data	Results
Fortran	f03bf_t1w_fe.f90	f03bf_t1w_fe.d	f03bf_t1w_fe.r
C++	f03bf_t1w_hcppe.cpp	f03bf_t1w_hcppe.d	f03bf_t1w_hcppe.r

10.3 Passive mode (p0w)

Language	Source File	Data	Results
Fortran	f03bf_p0w_fe.f90	f03bf_p0w_fe.d	f03bf_p0w_fe.r
C++	f03bf_p0w_hcppe.cpp	f03bf_p0w_hcppe.d	f03bf_p0w_hcppe.r