f11jb is the AD Library version of the primal routine f11jbf. Based (in the C++ interface) on overload resolution, f11jb can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine f11jb_AD_f (

n, a, la, irow, icol, ipiv, istr, check, y, x, ifail)

Integer, Intent (In)	::	n, la, irow(la), icol(la), istr(n+1)
Integer, Intent (Inout)	::	ipiv(n), ifail
ADTYPE, Intent (In)	::	a(la), y(n)
ADTYPE, Intent (Out)	::	x(n)
Character (1), Intent (In)	::	check
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 f11jb (

handle_t &ad_handle, const Integer &n, const ADTYPE a[], const Integer &la, const Integer irow[], const Integer icol[], Integer ipiv[], const Integer istr[], const char *check, const ADTYPE y[], ADTYPE x[], 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

f11jb is the AD Library version of the primal routine f11jbf.

f11jbf solves a system of linear equations involving the incomplete Cholesky preconditioning matrix generated by f11jaf. For further information see Section 3 in the documentation for f11jbf.

4 References

5 Arguments

In addition to the arguments present in the interface of the primal routine, f11jb 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: a(la) – ADTYPE array Input
4: la – Integer Input
5: irow(la) – Integer array Input
6: icol(la) – Integer array Input
7: ipiv(n) – Integer array Input
8: istr( $n + 1$ ) – Integer array Input
9: check – character Input
10: y(n) – ADTYPE array Input
11: x(n) – ADTYPE array Output
12: ifail – Integer Input/Output

6 Error Indicators and Warnings

f11jb preserves all error codes from f11jbf and in addition can 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

f11jb is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f11jbf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example reads in a symmetric positive definite sparse matrix

A

and a vector

y

. It then calls f11ja, with

lfill = −1

and

dtol = 0.0

, to compute the complete Cholesky decomposition of

A

A = P L D L^{T} P^{T} .

Then it calls f11jb to solve the system

P L D L^{T} P^{T} x = y .

It then repeats the exercise for the same matrix permuted with the bandwidth-reducing Reverse Cuthill–McKee permutation, calculated with f11ye.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	f11jb_a1w_fe.f90	f11jb_a1w_fe.d	f11jb_a1w_fe.r
C++	f11jb_a1w_hcppe.cpp	f11jb_a1w_hcppe.d	f11jb_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	f11jb_t1w_fe.f90	f11jb_t1w_fe.d	f11jb_t1w_fe.r
C++	f11jb_t1w_hcppe.cpp	f11jb_t1w_hcppe.d	f11jb_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	f11jb_p0w_fe.f90	f11jb_p0w_fe.d	f11jb_p0w_fe.r
C++	f11jb_p0w_hcppe.cpp	f11jb_p0w_hcppe.d	f11jb_p0w_hcppe.r

NAG Library Manual, Mark 28.6

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F11 (Sparse) Chapter Contents

F11 (Sparse) Chapter Introduction (FL)

f11jb: FL CL CPP AD

NAG AD Libraryf11jb (real_symm_precon_ichol_solve)

▸▿ Contents

1 Purpose