NAG AD Library Routine Document

f07fe_a1w_f (dpotrs_a1w)

Note: _a1w_ denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Further implementations, for example for higher order differentiation or using the tangent linear approach, may become available at later marks of the NAG AD Library. The method of codifying AD implementations in routine name and corresponding argument types is described in the NAG AD Library Introduction.

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NAG AD Library Manual, Mark 26

NAG Library Manual, Mark 26

NAG C Library Manual, Mark 26

NAG AD Library Introduction

Primal Routine f07fef

Primal NAG Library F07 Contents

Primal NAG Library F07 Chapter Introduction

▸▿ 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

1

Purpose

f07fe_a1w_f is the adjoint version of the primal routine f07fef (dpotrs).

2

Specification

Fortran Interface

Subroutine f07fe_a1w_f (

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

Integer, Intent (In)	::	n, nrhs, lda, ldb
Integer, Intent (Out)	::	info
Type (nagad_a1w_w_rtype), Intent (In)	::	a(lda,*)
Type (nagad_a1w_w_rtype), Intent (Inout)	::	b(ldb,*)
Character (1), Intent (In)	::	uplo
Type (c_ptr), Intent (In)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void f07fe_a1w_f_ (

void *&ad_handle, const char *uplo, const Integer &n, const Integer &nrhs, nagad_a1w_w_rtype a[], const Integer &lda, nagad_a1w_w_rtype b[], const Integer &ldb, Integer &ifail, const Charlen length_uplo)

3

Description

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 (dpotrf). For further information see Section 3 in the documentation for f07fef (dpotrs).

4

References

None.

5

Arguments

f07fe_a1w_f provides access to all the arguments available in the primal routine. There are also additional arguments specific to AD. A tooltip popup for each argument can be found by hovering over the argument name in Section 2 and a summary of the arguments are provided below:

ad_handle – a handle to the AD configuration data object, as created by x10aa_a1w_f.
uplo – specifies how $A$ has been factorized.
n – $n$ , the order of the matrix $A$ .
nrhs – $r$ , the number of right-hand sides.
a – the Cholesky factor of $A$ , as returned by routine.
lda – the first dimension of the array a.
b – on entry: the $n$ by $r$ right-hand side matrix $B$ . on exit: the $n$ by $r$ solution matrix $X$ .
ldb – the first dimension of the array b.
ifail – on exit: $ifail = 0$ unless the routine detects an error (see Section 6).

6

Error Indicators and Warnings

f07fe_a1w_f 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 Section 5.2 in the NAG AD Library Introduction for further information.

$ifail = - 899$: Dynamic memory allocation failed for AD.
See Section 5.1 in the NAG AD Library Introduction for further information.

7

Accuracy

Not applicable.

8

Parallelism and Performance

f07fe_a1w_f 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.

Language	Source File	Data	Results
Fortan	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