NAG Library Routine Document

f11gff (real_symm_basic_diag)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{itn}$ – IntegerOutput

On exit: the number of iterations carried out by f11gef.

2:     $\mathbf{stplhs}$ – Real (Kind=nag_wp)Output

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

3:     $\mathbf{stprhs}$ – Real (Kind=nag_wp)Output

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

4:     $\mathbf{anorm}$ – 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, $\mathbf{anorm}=0.0$ is returned.

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

5:     $\mathbf{sigmax}$ – Real (Kind=nag_wp)Output

On exit: for CG and SYMMLQ 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, $\mathbf{its}=\mathbf{itn}$, 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:     $\mathbf{its}$ – IntegerOutput

On exit: for CG and SYMMLQ 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 9 in f11gdf). Otherwise, $\mathbf{its}=0$ is returned.

7:     $\mathbf{sigerr}$ – Real (Kind=nag_wp)Output

On exit: for CG and SYMMLQ methods, if ${\sigma }_1\left(\stackrel{-}{A}\right)$ has been estimated by f11gef using bisection,

$$\mathbf{sigerr}=\max \left(\frac{\left|{\sigma }_1^{\left(k\right)}-{\sigma }_1^{\left(k-1\right)}\right|}{{\sigma }_1^{\left(k\right)}},\frac{\left|{\sigma }_1^{\left(k\right)}-{\sigma }_1^{\left(k-2\right)}\right|}{{\sigma }_1^{\left(k\right)}}\right)\text{,}$$

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 f11gdf. Otherwise, $\mathbf{sigerr}=0.0$ is returned.

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

8:     $\mathbf{work}\left(\mathbf{lwork}\right)$ – Real (Kind=nag_wp) arrayCommunication Array

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

9:     $\mathbf{lwork}$ – 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:   $\mathbf{ifail}$ – 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).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

f11gff has been called out of sequence.

$\mathbf{ifail}=-9$

On entry, $\mathbf{lwork}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lwork}\ge 120$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

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.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example