f07fe is the AD Library version of the primal routine f07fef (dpotrs). Based (in the C++ interface) on overload resolution, f07fe can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine f07fe_AD_f (

uplo, n, nrhs, a, lda, b, ldb, ifail)

Integer, Intent (In)	::	n, nrhs, lda, ldb
Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	a(lda,*)
ADTYPE, Intent (Inout)	::	b(ldb,*)
Character (1), Intent (In)	::	uplo
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 f07fe (

handle_t &ad_handle, const char *uplo, const Integer &n, const Integer &nrhs, const ADTYPE a[], const Integer &lda, ADTYPE b[], const Integer &ldb, 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

f07fe is the AD Library version of the primal routine f07fef (dpotrs).

f07fef (dpotrs) solves a real symmetric positive definite system of linear equations with multiple right-hand sides,

A X = B,

where

A

has been factorized by f07fdf. For further information see Section 3 in the documentation for f07fef (dpotrs).

4 References

Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore

5 Arguments

In addition to the arguments present in the interface of the primal routine, f07fe 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: uplo – character Input
3: n – Integer Input
4: nrhs – Integer Input
5: a(lda, $*$ ) – ADTYPE array Input
6: lda – Integer Input
7: b(ldb, $*$ ) – ADTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
8: ldb – Integer Input
9: ifail – Integer Input/Output: On entry: must be set to $0$ , $- 1 or 1$ .
On exit: any errors are indicated as described in Section 6.

6 Error Indicators and Warnings

f07fe uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f07fef may be indicated with the same value returned by ifail. In addition, this routine may 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

f07fe is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f07fef (dpotrs), modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example solves the system of equations

A X = B

, where

A = (\begin{matrix} 4.16 & - 3.12 & 0.56 & - 0.10 \\ - 3.12 & 5.03 & - 0.83 & 1.18 \\ 0.56 & - 0.83 & 0.76 & 0.34 \\ - 0.10 & 1.18 & 0.34 & 1.18 \end{matrix}) and B = (\begin{matrix} 8.70 & 8.30 \\ - 13.35 & 2.13 \\ 1.89 & 1.61 \\ - 4.14 & 5.00 \end{matrix}) .

Here

A

is symmetric positive definite and must first be factorized by f07fd.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	f07fe_a1w_fe.f90	f07fe_a1w_fe.d	f07fe_a1w_fe.r
C++	f07fe_a1w_hcppe.cpp	f07fe_a1w_hcppe.d	f07fe_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	f07fe_t1w_fe.f90	f07fe_t1w_fe.d	f07fe_t1w_fe.r
C++	f07fe_t1w_hcppe.cpp	f07fe_t1w_hcppe.d	f07fe_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	f07fe_p0w_fe.f90	f07fe_p0w_fe.d	f07fe_p0w_fe.r
C++	f07fe_p0w_hcppe.cpp	f07fe_p0w_hcppe.d	f07fe_p0w_hcppe.r

NAG Library Manual, Mark 28.5

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F07 (Lapacklin) Chapter Contents

F07 (Lapacklin) Chapter Introduction (FL)

f07fe: FL CL CPP AD

NAG AD Libraryf07fe (dpotrs)

▸▿ Contents

1 Purpose