F11 Chapter Contents
F11 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF11GFF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

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

 SUBROUTINE F11GFF ( ITN, STPLHS, STPRHS, ANORM, SIGMAX, ITS, SIGERR, WORK, LWORK, IFAIL)
 INTEGER ITN, ITS, LWORK, IFAIL REAL (KIND=nag_wp) STPLHS, STPRHS, ANORM, SIGMAX, SIGERR, WORK(LWORK)

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

## 5  Parameters

1:     ITN – INTEGEROutput
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 SYMMQ 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, ${\mathbf{ANORM}}=0.0$ 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 SYMMQ methods, the current estimate of the largest singular value ${\sigma }_{1}\left(\stackrel{-}{A}\right)$ of the preconditioned iteration matrix $\stackrel{-}{A}={E}^{-1}A{E}^{-\mathrm{T}}$, 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 ${\mathbf{ITS}}<{\mathbf{ITN}}$ then SIGMAX contains the final estimate. If, on final exit from F11GEF, ${\mathbf{ITS}}={\mathbf{ITN}}$, then the estimation of ${\sigma }_{1}\left(\stackrel{-}{A}\right)$ may have not converged; in this case you should look at the value returned in SIGERR. Otherwise, ${\mathbf{SIGMAX}}=0.0$ is returned.
For MINRES method, an estimate of the final transformed residual.
6:     ITS – INTEGEROutput
On exit: for CG and SYMMQ methods, the number of iterations employed so far in the computation of the estimate of ${\sigma }_{1}\left(\stackrel{-}{A}\right)$, the largest singular value of the preconditioned matrix $\stackrel{-}{A}={E}^{-1}A{E}^{-\mathrm{T}}$, when ${\sigma }_{1}\left(\stackrel{-}{A}\right)$ has been estimated by F11GEF using the bisection method (see also Sections 3, 5 and 8 in F11GDF). Otherwise, ${\mathbf{ITS}}=0$ is returned.
7:     SIGERR – REAL (KIND=nag_wp)Output
On exit: for CG and SYMMQ methods, if ${\sigma }_{1}\left(\stackrel{-}{A}\right)$ has been estimated by F11GEF using bisection,
 $SIGERR=maxσ1k-σ1k-1σ1k,σ1k-σ1k-2σ1k ,$
where $k={\mathbf{ITS}}$ denotes the iteration number. The estimation has converged if ${\mathbf{SIGERR}}\le {\mathbf{SIGTOL}}$ where SIGTOL is an input parameter to F11GDF. Otherwise, ${\mathbf{SIGERR}}=0.0$ is returned.
For MINRES method, an estimate of the condition number of the preconditioned matrix.
8:     WORK(LWORK) – REAL (KIND=nag_wp) arrayCommunication Array
On entry: the array WORK as returned by F11GEF (see also Section 3 in F11GEF).
9:     LWORK – INTEGERInput
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: ${\mathbf{LWORK}}\ge 120$.
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 – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{​ or ​}1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{​ or ​}1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{​ or ​}\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.
On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6  Error Indicators and Warnings

If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
${\mathbf{IFAIL}}=-i$
On entry, the $i$th argument had an illegal value.
${\mathbf{IFAIL}}=1$
F11GFF has been called out of sequence. For example, the last call to F11GEF did not return ${\mathbf{IREVCM}}=3$ or $4$.

Not applicable.