NAG AD Library
f07ce (dgttrs)

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1 Purpose

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++ Interface
#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {
void f07ce ( handle_t &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:
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 AX=B or ATX=B , where A is an n × n tridiagonal matrix and X and B are n × r matrices, using the LU 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

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_handlenag::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: 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
Please consult Overwriting of Inputs in the NAG AD Library Introduction.
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:
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.
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.
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
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

f07ce is not threaded in any implementation.

9 Further Comments


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
AX=B ,  
where A is the tridiagonal matrix
A = ( 3.0 2.1 0.0 0.0 0.0 3.4 2.3 -1.0 0.0 0.0 0.0 3.6 -5.0 1.9 0.0 0.0 0.0 7.0 -0.9 8.0 0.0 0.0 0.0 -6.0 7.1 )   and   B = ( 2.7 6.6 -0.5 10.8 2.6 -3.2 0.6 -11.2 2.7 19.1 ) .  

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