NAG CL Interface
f11gfc (real_​symm_​basic_​diag)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{itn}$ – Integer * Output

On exit: the number of iterations carried out by f11gec.

2: $\mathbf{stplhs}$ – double * Output

On exit: the current value of the left-hand side of the termination criterion used by f11gec.

3: $\mathbf{stprhs}$ – double * Output

On exit: the current value of the right-hand side of the termination criterion used by f11gec.

4: $\mathbf{anorm}$ – double * Output

On exit: for CG and SYMMLQ methods, the norm ${‖A‖}_1={‖A‖}_{\infty }$ when either it has been supplied to f11gdc or it has been estimated by f11gec (see also Sections 3 and 5 in f11gdc). Otherwise, $\mathbf{anorm}=0.0$ is returned.

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

5: $\mathbf{sigmax}$ – double * Output

On exit: for CG and SYMMLQ methods, the current estimate of the largest singular value ${\sigma }_1\left(\overline{A}\right)$ of the preconditioned iteration matrix $\overline{A}=E^{-1}A{E}^{-\mathrm{T}}$, when either it has been supplied to f11gdc or it has been estimated by f11gec (see also Sections 3 and 5 in f11gdc). Note that if $\mathbf{its}<\mathbf{itn}$ then sigmax contains the final estimate. If, on final exit from f11gec, $\mathbf{its}=\mathbf{itn}$, 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.

For MINRES method, an estimate of the final transformed residual.

6: $\mathbf{its}$ – Integer * Output

On exit: for CG and SYMMLQ methods, 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 $\overline{A}=E^{-1}A{E}^{-\mathrm{T}}$, when ${\sigma }_1\left(\overline{A}\right)$ has been estimated by f11gec using the bisection method (see also Sections 3, 5 and 9 in f11gdc). Otherwise, $\mathbf{its}=0$ is returned.

7: $\mathbf{sigerr}$ – double * Output

On exit: for CG and SYMMLQ methods, if ${\sigma }_1\left(\overline{A}\right)$ has been estimated by f11gec 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 f11gdc. Otherwise, $\mathbf{sigerr}=0.0$ is returned.

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

8: $\mathbf{work}\left[\mathbf{lwork}\right]$ – const double Communication Array

On entry: the array work as returned by f11gec (see also Section 3 in f11gec).

9: $\mathbf{lwork}$ – Integer Input

On entry: the dimension of the array work (see also Section 5 in f11gdc).

Constraint: $\mathbf{lwork}\ge 120$.

Note:  although the minimum value of lwork ensures the correct functioning of f11gfc, a larger value is required by the iterative solver f11gec (see also Section 5 in f11gdc).

10: $\mathbf{fail}$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

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

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

NE_OUT_OF_SEQUENCE

f11gfc has been called out of sequence.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example