NAG AD Library
f11jb (real_symm_precon_ichol_solve)

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1 Purpose

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 ( ad_handle, 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++ Header Interface
#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {
void f11jb ( void *&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:
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 – Pointer to AD Data Input/Output
On entry: a handle to the AD configuration data object, as created by x10aa.
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:
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.
The routine was called using a mode that has not yet been implemented.
On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
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

f11jb is not threaded in any implementation.

9 Further Comments


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:
Then it calls f11jb to solve the system
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