NAG CL Interface
f11gfc (real_​symm_​basic_​diag)

1 Purpose

f11gfc is the third in a suite of three functions for the iterative solution of a symmetric system of simultaneous linear equations (see Golub and Van Loan (1996)). f11gfc returns information about the computations during an iteration and/or after this has been completed. The first function of the suite, f11gdc, is a setup function, the second function, f11gec is the proper iterative solver.
These three functions are suitable for the solution of large sparse symmetric systems of equations.

2 Specification

#include <nag.h>
void  f11gfc (Integer *itn, double *stplhs, double *stprhs, double *anorm, double *sigmax, Integer *its, double *sigerr, const double work[], Integer lwork, NagError *fail)
The function may be called by the names: f11gfc, nag_sparse_real_symm_basic_diag or nag_sparse_sym_basic_diagnostic.

3 Description

f11gfc returns information about the solution process. It can be called both during a monitoring step of the solver f11gec, or after this solver has completed its tasks. Calling f11gfc at any other time will result in an error condition being raised.
For further information you should read the documentation for f11gdc and f11gec.

4 References

Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore

5 Arguments

1: itn Integer * Output
On exit: the number of iterations carried out by f11gec.
2: stplhs double * Output
On exit: the current value of the left-hand side of the termination criterion used by f11gec.
3: stprhs double * Output
On exit: the current value of the right-hand side of the termination criterion used by f11gec.
4: anorm double * Output
On exit: for CG and SYMMLQ methods, the norm A1=A when either it has been supplied to f11gdc or it has been estimated by f11gec (see also Sections 3 and 5 in f11gdc). Otherwise, anorm=0.0 is returned.
For MINRES method, an estimate of the infinity norm of the preconditioned matrix operator.
5: sigmax double * Output
On exit: for CG and SYMMLQ methods, the current estimate of the largest singular value σ1A¯ of the preconditioned iteration matrix A¯=E-1AE-T, when either it has been supplied to f11gdc or it has been estimated by f11gec (see also Sections 3 and 5 in f11gdc). Note that if its<itn then sigmax contains the final estimate. If, on final exit from f11gec, its=itn, the estimation of σ1A¯ may have not converged; in this case you should look at the value returned in sigerr. Otherwise, sigmax=0.0 is returned.
For MINRES method, an estimate of the final transformed residual.
6: its Integer * Output
On exit: for CG and SYMMLQ methods, the number of iterations employed so far in the computation of the estimate of σ1A¯, the largest singular value of the preconditioned matrix A¯=E-1AE-T, when σ1A¯ has been estimated by f11gec using the bisection method (see also Sections 3, 5 and 9 in f11gdc). Otherwise, its=0 is returned.
7: sigerr double * Output
On exit: for CG and SYMMLQ methods, if σ1A¯ has been estimated by f11gec using bisection,
sigerr=maxσ1k-σ1k-1σ1k,σ1k-σ1k-2σ1k ,  
where k=its denotes the iteration number. The estimation has converged if sigerrsigtol where sigtol is an input argument to f11gdc. Otherwise, sigerr=0.0 is returned.
For MINRES method, an estimate of the condition number of the preconditioned matrix.
8: work[lwork] const double Communication Array
On entry: the array work as returned by f11gec (see also Section 3 in f11gec).
9: lwork Integer Input
On entry: the dimension of the array work (see also Section 5 in f11gdc).
Constraint: lwork120.
Note:  although the minimum value of lwork ensures the correct functioning of f11gfc, a larger value is required by the iterative solver f11gec (see also Section 5 in f11gdc).
10: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, lwork=value.
Constraint: lwork120.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_OUT_OF_SEQUENCE
f11gfc has been called out of sequence.

7 Accuracy

Not applicable.

8 Parallelism and Performance

f11gfc is not threaded in any implementation.

9 Further Comments

None.

10 Example

See Section 10 in f11gdc.