# NAG Library Routine Document

## 1Purpose

f11btf is the third in a suite of three routines for the iterative solution of a complex general (non-Hermitian) system of simultaneous linear equations (see Golub and Van Loan (1996)). f11btf returns information about the computations during an iteration and/or after this has been completed. The first routine of the suite, f11brf, is a setup routine; the second routine, f11bsf, is the iterative solver itself.
These three routines are suitable for the solution of large sparse general (non-Hermitian) systems of equations.

## 2Specification

Fortran Interface
 Subroutine f11btf ( itn, work,
 Integer, Intent (In) :: lwork Integer, Intent (Inout) :: ifail Integer, Intent (Out) :: itn Real (Kind=nag_wp), Intent (Out) :: stplhs, stprhs, anorm, sigmax Complex (Kind=nag_wp), Intent (Inout) :: work(lwork)
#include nagmk26.h
 void f11btf_ (Integer *itn, double *stplhs, double *stprhs, double *anorm, double *sigmax, Complex work[], const Integer *lwork, Integer *ifail)

## 3Description

f11btf returns information about the solution process. It can be called either during a monitoring step of f11bsf or after f11bsf has completed its tasks. Calling f11btf at any other time will result in an error condition being raised.
For further information you should read the documentation for f11brf and f11bsf.

## 4References

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

## 5Arguments

1:     $\mathbf{itn}$ – IntegerOutput
On exit: the number of iterations carried out by f11bsf.
2:     $\mathbf{stplhs}$ – Real (Kind=nag_wp)Output
On exit: the current value of the left-hand side of the termination criterion used by f11bsf.
3:     $\mathbf{stprhs}$ – Real (Kind=nag_wp)Output
On exit: the current value of the right-hand side of the termination criterion used by f11bsf.
4:     $\mathbf{anorm}$ – Real (Kind=nag_wp)Output
On exit: if ${\mathbf{iterm}}=1$ in the previous call to f11brf, then anorm contains ${‖A‖}_{p}$, where $p=1$, $2$ or $\infty$, either supplied or, in the case of $1$ or $\infty$, estimated by f11bsf; otherwise ${\mathbf{anorm}}=0.0$.
5:     $\mathbf{sigmax}$ – Real (Kind=nag_wp)Output
On exit: if ${\mathbf{iterm}}=2$ in the previous call to f11brf, the current estimate of the largest singular value ${\sigma }_{1}\left(\stackrel{-}{A}\right)$ of the preconditioned iteration matrix when it is used by the termination criterion in f11bsf, either when it has been supplied to f11brf or it has been estimated by f11bsf (see also Sections 3 and 5 in f11brf); otherwise, ${\mathbf{sigmax}}=0.0$ is returned.
6:     $\mathbf{work}\left({\mathbf{lwork}}\right)$ – Complex (Kind=nag_wp) arrayCommunication Array
On entry: the array work as returned by f11bsf (see also Sections 3 and 5 in f11bsf).
7:     $\mathbf{lwork}$ – IntegerInput
On entry: the dimension of the array work as declared in the (sub)program from which f11btf is called (see also f11brf).
Constraint: ${\mathbf{lwork}}\ge 120$.
Note:  although the minimum value of lwork ensures the correct functioning of f11btf, a larger value is required by the iterative solver f11bsf (see also f11brf).
8:     $\mathbf{ifail}$ – IntegerInput/Output
On entry: ifail must be set to $0$, $-1\text{​ or ​}1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation 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 argument, 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).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, 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.
${\mathbf{ifail}}=1$
f11btf has been called out of sequence. For example, the last call to f11bsf did not return ${\mathbf{irevcm}}=3$ or $4$.
${\mathbf{ifail}}=-99$
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

Not applicable.

## 8Parallelism and Performance

f11btf is not threaded in any implementation.