NAG AD Library
f11jc_a1w_f (real_symm_solve_ichol_a1w)

Note: a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document. Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.
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1 Purpose

f11jc_a1w_f is the adjoint version of the primal routine f11jcf.

2 Specification

Fortran Interface
Subroutine f11jc_a1w_f ( ad_handle, method, n, nnz, a, la, irow, icol, ipiv, istr, b, tol, maxitn, x, rnorm, itn, work, lwork, ifail)
Integer, Intent (In) :: n, nnz, la, irow(la), icol(la), istr(n+1), maxitn, lwork
Integer, Intent (Inout) :: ipiv(n), ifail
Integer, Intent (Out) :: itn
Type (nagad_a1w_w_rtype), Intent (In) :: a(la), b(n), tol
Type (nagad_a1w_w_rtype), Intent (Inout) :: x(n)
Type (nagad_a1w_w_rtype), Intent (Out) :: rnorm, work(lwork)
Character (*), Intent (In) :: method
Type (c_ptr), Intent (Inout) :: ad_handle
C++ Header Interface
#include <nagad.h>
void f11jc_a1w_f_ ( void *&ad_handle, const char *method, const Integer &n, const Integer &nnz, const nagad_a1w_w_rtype a[], const Integer &la, const Integer irow[], const Integer icol[], Integer ipiv[], const Integer istr[], const nagad_a1w_w_rtype b[], const nagad_a1w_w_rtype &tol, const Integer &maxitn, nagad_a1w_w_rtype x[], nagad_a1w_w_rtype &rnorm, Integer &itn, nagad_a1w_w_rtype work[], const Integer &lwork, Integer &ifail, const Charlen length_method)
The routine may be called by the names f11jc_a1w_f or nagf_sparse_real_symm_solve_ichol_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

f11jc_a1w_f is the adjoint version of the primal routine f11jcf.
f11jcf solves a real sparse symmetric system of linear equations, represented in symmetric coordinate storage format, using a conjugate gradient or Lanczos method, with incomplete Cholesky preconditioning. For further information see Section 3 in the documentation for f11jcf.

4 References

Barrett R, Berry M, Chan T F, Demmel J, Donato J, Dongarra J, Eijkhout V, Pozo R, Romine C and Van der Vorst H (1994) Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods SIAM, Philadelphia
Meijerink J and Van der Vorst H (1977) An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix Math. Comput. 31 148–162
Paige C C and Saunders M A (1975) Solution of sparse indefinite systems of linear equations SIAM J. Numer. Anal. 12 617–629
Salvini S A and Shaw G J (1995) An evaluation of new NAG Library solvers for large sparse symmetric linear systems NAG Technical Report TR1/95

5 Arguments

In addition to the arguments present in the interface of the primal routine, f11jc_a1w_f 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 – Type (c_ptr) Input/Output
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: method – character Input
3: n – Integer Input
4: nnz – Integer Input
5: a(la) – Type (nagad_a1w_w_rtype) array Input
6: la – Integer Input
7: irow(la) – Integer array Input
8: icol(la) – Integer array Input
9: ipiv(n) – Integer array Input
10: istr(n+1) – Integer array Input
11: b(n) – Type (nagad_a1w_w_rtype) array Input
12: tolType (nagad_a1w_w_rtype) Input
13: maxitn – Integer Input
14: x(n) – Type (nagad_a1w_w_rtype) array Input/Output
15: rnormType (nagad_a1w_w_rtype) Output
16: itn – Integer Output
17: work(lwork) – Type (nagad_a1w_w_rtype) array Workspace
18: lwork – Integer Input
19: ifail – Integer Input/Output

6 Error Indicators and Warnings

f11jc_a1w_f preserves all error codes from f11jcf 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.
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

f11jc_a1w_f is not threaded in any implementation.

9 Further Comments


10 Example

The following examples are variants of the example for f11jcf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

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10.2 Tangent mode (t1w)

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10.3 Passive mode (p0w)

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