f07ce is the AD Library version of the primal routine f07cef (dgttrs). Based (in the C++ interface) on overload resolution, f07ce can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine f07ce_AD_f (

ad_handle, trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, ifail)

Integer, Intent (In)	::	n, nrhs, ipiv(*), ldb
Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	dl(), d(), du(), du2()
ADTYPE, Intent (Inout)	::	b(ldb,*)
Character (1), Intent (In)	::	trans
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++ Header Interface

#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {

void f07ce (

void *&ad_handle, const char *trans, const Integer &n, const Integer &nrhs, const ADTYPE dl[], const ADTYPE d[], const ADTYPE du[], const ADTYPE du2[], const Integer ipiv[], 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

f07ce is the AD Library version of the primal routine f07cef (dgttrs).

f07cef (dgttrs) computes the solution to a real system of linear equations

A X = B

A^{T} X = B

, where

A

is an

n \times n

tridiagonal matrix and

X

and

B

are

n \times r

matrices, using the

L U

factorization returned by f07cdf. For further information see Section 3 in the documentation for f07cef (dgttrs).

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, f07ce 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 – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object, as created by x10aa.
2: trans – character Input
3: n – Integer Input
4: nrhs – Integer Input
5: dl( $*$ ) – ADTYPE array Input
6: d( $*$ ) – ADTYPE array Input
7: du( $*$ ) – ADTYPE array Input
8: du2( $*$ ) – ADTYPE array Input
9: ipiv( $*$ ) – Integer array Input
10: b(ldb, $*$ ) – ADTYPE array Input/Output
11: ldb – Integer Input
12: 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

f07ce uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f07cef 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 4.8.2 in the NAG AD Library Introduction for further information.

$ifail = - 199$: The routine was called using a mode that has not yet been implemented.

$ifail = - 443$: On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.

$ifail = - 444$: 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 Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

f07ce is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f07cef (dgttrs), modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example solves the equations

A X = B,

where

A

is the tridiagonal matrix

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}) and B = (\begin{matrix} 2.7 & 6.6 \\ - 0.5 & 10.8 \\ 2.6 & - 3.2 \\ 0.6 & - 11.2 \\ 2.7 & 19.1 \end{matrix}) .

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	f07ce_a1w_fe.f90	f07ce_a1w_fe.d	f07ce_a1w_fe.r
C++	f07ce_a1w_hcppe.cpp	f07ce_a1w_hcppe.d	f07ce_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	f07ce_t1w_fe.f90	f07ce_t1w_fe.d	f07ce_t1w_fe.r
C++	f07ce_t1w_hcppe.cpp	f07ce_t1w_hcppe.d	f07ce_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	f07ce_p0w_fe.f90	f07ce_p0w_fe.d	f07ce_p0w_fe.r
C++	f07ce_p0w_hcppe.cpp	f07ce_p0w_hcppe.d	f07ce_p0w_hcppe.r

NAG Library Manual, Mark 27.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F07 (Lapacklin) Chapter Contents

F07 (Lapacklin) Chapter Introduction (FL)

f07ce: FL CL CPP AD

NAG AD Libraryf07ce (dgttrs)

▸▿ Contents

1 Purpose