f11gff is the third in a suite of three routines for the iterative solution of a symmetric system of simultaneous linear equations (see Golub and Van Loan (1996)). f11gff returns information about the computations during an iteration and/or after this has been completed. The first routine of the suite, f11gdf, is a setup routine, the second routine, f11gef is the proper iterative solver.

These three routines are suitable for the solution of large sparse symmetric systems of equations.

2 Specification

Fortran Interface

Subroutine f11gff (

itn, stplhs, stprhs, anorm, sigmax, its, sigerr, work, lwork, ifail)

Integer, Intent (In)	::	lwork
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	itn, its
Real (Kind=nag_wp), Intent (In)	::	work(lwork)
Real (Kind=nag_wp), Intent (Out)	::	stplhs, stprhs, anorm, sigmax, sigerr

C Header Interface

#include <nag.h>

void	f11gff_ (Integer itn, double stplhs, double stprhs, double anorm, double sigmax, Integer its, double sigerr, const double work[], const Integer lwork, Integer *ifail)

The routine may be called by the names f11gff or nagf_sparse_real_symm_basic_diag.

3 Description

f11gff returns information about the solution process. It can be called both during a monitoring step of the solver f11gef, or after this solver has completed its tasks. Calling f11gff at any other time will result in an error condition being raised.

For further information you should read the documentation for f11gdf and f11gef.

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 f11gef.

2: $stplhs$ – Real (Kind=nag_wp) Output

On exit: the current value of the left-hand side of the termination criterion used by f11gef.

3: $stprhs$ – Real (Kind=nag_wp) Output

On exit: the current value of the right-hand side of the termination criterion used by f11gef.

4: $anorm$ – Real (Kind=nag_wp) Output

On exit: for CG and SYMMLQ methods, the norm

{‖ A ‖}_{1} = {‖ A ‖}_{\infty}

when either it has been supplied to f11gdf or it has been estimated by f11gef (see also Sections 3 and 5 in f11gdf). Otherwise,

anorm = 0.0

is returned.

For MINRES method, an estimate of the infinity norm of the preconditioned matrix operator.

5: $sigmax$ – Real (Kind=nag_wp) Output

On exit: for CG and SYMMLQ methods, the current estimate of the largest singular value

σ_{1} (\bar{A})

of the preconditioned iteration matrix

\bar{A} = E^{- 1} A E^{- T}

, when either it has been supplied to f11gdf or it has been estimated by f11gef (see also Sections 3 and 5 in f11gdf). Note that if

its < itn

then sigmax contains the final estimate. If, on final exit from f11gef,

its = itn

, the estimation of

σ_{1} (\bar{A})

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

σ_{1} (\bar{A})

, the largest singular value of the preconditioned matrix

\bar{A} = E^{- 1} A E^{- T}

, when

σ_{1} (\bar{A})

has been estimated by f11gef using the bisection method (see also Sections 3, 5 and 9 in f11gdf). Otherwise,

its = 0

is returned.

7: $sigerr$ – Real (Kind=nag_wp) Output

On exit: for CG and SYMMLQ methods, if

σ_{1} (\bar{A})

has been estimated by f11gef using bisection,

sigerr = \max (\frac{| σ_{1}^{(k)} - σ_{1}^{(k - 1)} |}{σ_{1}^{(k)}}, \frac{| σ_{1}^{(k)} - σ_{1}^{(k - 2)} |}{σ_{1}^{(k)}}),

where

k = its

denotes the iteration number. The estimation has converged if

sigerr \leq sigtol

where sigtol is an input argument to f11gdf. Otherwise,

sigerr = 0.0

is returned.

For MINRES method, an estimate of the condition number of the preconditioned matrix.

8: $work (lwork)$ – Real (Kind=nag_wp) array Communication Array

On entry: the array work as returned by f11gef (see also Section 3 in f11gef).

9: $lwork$ – Integer Input

On entry: the dimension of the array work as declared in the (sub)program from which f11gff is called (see also Section 5 in f11gdf).

Constraint:

lwork \geq 120

Note: although the minimum value of lwork ensures the correct functioning of f11gff, a larger value is required by the iterative solver f11gef (see also Section 5 in f11gdf).

10: $ifail$ – Integer Input/Output

On entry: ifail must be set to

0

- 1

1

to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of

0

causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of

- 1

means that an error message is printed while a value of

1

means that it is not.

If halting is not appropriate, the value

- 1

1

is recommended. If message printing is undesirable, then the value

1

is recommended. Otherwise, the value

0

is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: f11gff has been called out of sequence.

$ifail = - 9$: On entry, $lwork = ⟨ value ⟩$ .
Constraint: $lwork \geq 120$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.