F11 Chapter Contents
F11 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF11GTF

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

F11GTF is the third in a suite of three routines for the iterative solution of a complex Hermitian system of simultaneous linear equations (see Golub and Van Loan (1996)). F11GTF returns information about the computations during an iteration and/or after this has been completed. The first routine of the suite, F11GRF, is a setup routine, the second routine, F11GSF is the proper iterative solver.
These three routines are suitable for the solution of large sparse complex Hermitian systems of equations.

## 2  Specification

 SUBROUTINE F11GTF ( ITN, STPLHS, STPRHS, ANORM, SIGMAX, ITS, SIGERR, WORK, LWORK, IFAIL)
 INTEGER ITN, ITS, LWORK, IFAIL REAL (KIND=nag_wp) STPLHS, STPRHS, ANORM, SIGMAX, SIGERR COMPLEX (KIND=nag_wp) WORK(LWORK)

## 3  Description

F11GTF returns information about the solution process. It can be called both during a monitoring step of the solver F11GSF or after this solver has completed its tasks. Calling F11GTF at any other time will result in an error condition being raised.
For further information you should read the documentation for F11GRF and F11GSF.
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 F11GSF.
2:     STPLHS – REAL (KIND=nag_wp)Output
On exit: the current value of the left-hand side of the termination criterion used by F11GSF.
3:     STPRHS – REAL (KIND=nag_wp)Output
On exit: the current value of the right-hand side of the termination criterion used by F11GSF.
4:     ANORM – REAL (KIND=nag_wp)Output
On exit: the norm ${‖A‖}_{1}={‖A‖}_{\infty }$ when either it has been supplied to F11GRF or it has been estimated by F11GSF (see also Sections 3 and 5 in F11GRF). Otherwise, ${\mathbf{ANORM}}=0.0$ is returned.
5:     SIGMAX – REAL (KIND=nag_wp)Output
On exit: the current estimate of the largest singular value ${\sigma }_{1}\left(\stackrel{-}{A}\right)$ of the preconditioned iteration matrix $\stackrel{-}{A}={E}^{-1}A{E}^{-\mathrm{H}}$, when either it has been supplied to F11GRF or it has been estimated by F11GSF (see also Sections 3 and 5 in F11GRF). Note that if ${\mathbf{ITS}}<{\mathbf{ITN}}$ then SIGMAX contains the final estimate. If, on final exit from F11GSF, ${\mathbf{ITS}}={\mathbf{ITN}}$, 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.
6:     ITS – INTEGEROutput
On exit: 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 $\stackrel{-}{A}={E}^{-1}A{E}^{-\mathrm{H}}$, when ${\sigma }_{1}\left(\stackrel{-}{A}\right)$ has been estimated by F11GSF using the bisection method (see also Sections 3, 5 and 8 in F11GRF). Otherwise, ${\mathbf{ITS}}=0$ is returned.
7:     SIGERR – REAL (KIND=nag_wp)Output
On exit: if ${\sigma }_{1}\left(\stackrel{-}{A}\right)$ has been estimated by F11GSF 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 F11GRF. Otherwise, ${\mathbf{SIGERR}}=0.0$ is returned.
8:     WORK(LWORK) – COMPLEX (KIND=nag_wp) arrayCommunication Array
On entry: the array WORK as returned by F11GSF (see also Section 3 in F11GSF).
9:     LWORK – INTEGERInput
On entry: the dimension of the array WORK as declared in the (sub)program from which F11GTF is called (see also Section 5 in F11GRF).
Constraint: ${\mathbf{LWORK}}\ge 120$.
Note:  although the minimum value of LWORK ensures the correct functioning of F11GTF, a larger value is required by the iterative solver F11GSF (see also Section 5 in F11GRF).
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.
${\mathbf{IFAIL}}=1$
F11GTF has been called out of sequence. For example, the last call to F11GSF did not return ${\mathbf{IREVCM}}=3$ or $4$.

Not applicable.