f07cd is the AD Library version of the primal routine f07cdf (dgttrf). Based (in the C++ interface) on overload resolution, f07cd can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine f07cd_AD_f (

ad_handle, n, dl, d, du, du2, ipiv, ifail)

Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	ipiv(n)
ADTYPE, Intent (Inout)	::	dl(), d(), du(*)
ADTYPE, Intent (Out)	::	du2(n-2)
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 f07cd (

handle_t &ad_handle, const Integer &n, ADTYPE dl[], ADTYPE d[], ADTYPE du[], ADTYPE du2[], Integer ipiv[], 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

f07cd is the AD Library version of the primal routine f07cdf (dgttrf).

f07cdf (dgttrf) computes the

L U

factorization of a real

n \times n

tridiagonal matrix

A

. For further information see Section 3 in the documentation for f07cdf (dgttrf).

4 References

Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999) LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia https://www.netlib.org/lapack/lug

5 Arguments

In addition to the arguments present in the interface of the primal routine, f07cd 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: dl( $*$ ) – ADTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
4: d( $*$ ) – ADTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
5: du( $*$ ) – ADTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
6: du2( $n - 2$ ) – ADTYPE array Output
7: ipiv(n) – Integer array Output
8: 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

f07cd uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f07cdf 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

f07cd is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f07cdf (dgttrf), modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example factorizes the tridiagonal matrix

A

given by

A = (\begin{array}{r} 3.0 & 2.1 & 0 & 0 & 0 \\ 3.4 & 2.3 & - 1.0 & 0 & 0 \\ 0 & 3.6 & - 5.0 & 1.9 & 0 \\ 0 & 0 & 7.0 & - 0.9 & 8.0 \\ 0 & 0 & 0 & - 6.0 & 7.1 \end{array}) .

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	f07cd_a1w_fe.f90	f07cd_a1w_fe.d	f07cd_a1w_fe.r
C++	f07cd_a1w_hcppe.cpp	f07cd_a1w_hcppe.d	f07cd_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	f07cd_t1w_fe.f90	f07cd_t1w_fe.d	f07cd_t1w_fe.r
C++	f07cd_t1w_hcppe.cpp	f07cd_t1w_hcppe.d	f07cd_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	f07cd_p0w_fe.f90	f07cd_p0w_fe.d	f07cd_p0w_fe.r
C++	f07cd_p0w_hcppe.cpp	f07cd_p0w_hcppe.d	f07cd_p0w_hcppe.r

NAG Library Manual, Mark 30.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F07 (Lapacklin) Chapter Contents

F07 (Lapacklin) Chapter Introduction (FL)

f07cd: FL CL CPP AD

NAG AD Libraryf07cd (dgttrf)

▸▿ Contents

1 Purpose