# NAG FL Interfacef11gtf (complex_​herm_​basic_​diag)

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## 1Purpose

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.

## 2Specification

Fortran Interface
 Subroutine f11gtf ( itn, its, work,
 Integer, Intent (In) :: lwork Integer, Intent (Inout) :: ifail Integer, Intent (Out) :: itn, its Real (Kind=nag_wp), Intent (Out) :: stplhs, stprhs, anorm, sigmax, sigerr Complex (Kind=nag_wp), Intent (In) :: work(lwork)
#include <nag.h>
 void f11gtf_ (Integer *itn, double *stplhs, double *stprhs, double *anorm, double *sigmax, Integer *its, double *sigerr, const Complex work[], const Integer *lwork, Integer *ifail)
The routine may be called by the names f11gtf or nagf_sparse_complex_herm_basic_diag.

## 3Description

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.

## 4References

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

## 5Arguments

1: $\mathbf{itn}$Integer Output
On exit: the number of iterations carried out by f11gsf.
2: $\mathbf{stplhs}$Real (Kind=nag_wp) Output
On exit: the current value of the left-hand side of the termination criterion used by f11gsf.
3: $\mathbf{stprhs}$Real (Kind=nag_wp) Output
On exit: the current value of the right-hand side of the termination criterion used by f11gsf.
4: $\mathbf{anorm}$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: $\mathbf{sigmax}$Real (Kind=nag_wp) Output
On exit: the current estimate of the largest singular value ${\sigma }_{1}\left(\overline{A}\right)$ of the preconditioned iteration matrix $\overline{A}={E}^{-1}A{E}^{-\mathrm{H}}$, 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, ${\mathbf{its}}={\mathbf{itn}}$, the estimation of ${\sigma }_{1}\left(\overline{A}\right)$ may have not converged: in this case you should look at the value returned in sigerr. Otherwise, ${\mathbf{sigmax}}=0.0$ is returned.
6: $\mathbf{its}$Integer Output
On exit: the number of iterations employed so far in the computation of the estimate of ${\sigma }_{1}\left(\overline{A}\right)$, the largest singular value of the preconditioned matrix $\overline{A}={E}^{-1}A{E}^{-\mathrm{H}}$, when ${\sigma }_{1}\left(\overline{A}\right)$ has been estimated by f11gsf using the bisection method (see also Sections 3, 5 and 9 in f11grf). Otherwise, ${\mathbf{its}}=0$ is returned.
7: $\mathbf{sigerr}$Real (Kind=nag_wp) Output
On exit: if ${\sigma }_{1}\left(\overline{A}\right)$ has been estimated by f11gsf using bisection,
 $sigerr=max(|σ1(k)-σ1(k-1)|σ1(k),|σ1(k)-σ1(k-2)|σ1(k)) ,$
where $k={\mathbf{its}}$ denotes the iteration number. The estimation has converged if ${\mathbf{sigerr}}\le {\mathbf{sigtol}}$ where sigtol is an input argument to f11grf.
Otherwise, ${\mathbf{sigerr}}=0.0$ is returned.
8: $\mathbf{work}\left({\mathbf{lwork}}\right)$Complex (Kind=nag_wp) array Communication Array
On entry: the array work as returned by f11gsf (see also Section 3 in f11gsf).
9: $\mathbf{lwork}$Integer Input
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: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ 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 $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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:
${\mathbf{ifail}}=1$
f11gtf has been called out of sequence.
${\mathbf{ifail}}=-9$
On entry, ${\mathbf{lwork}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{lwork}}\ge 120$.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
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.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

Not applicable.

## 8Parallelism and Performance

f11gtf is not threaded in any implementation.