NAG CL Interface
f11gtc (complex_​herm_​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 f11gsc.

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

On exit: the current value of the left-hand side of the termination criterion used by f11gsc.

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

On exit: the current value of the right-hand side of the termination criterion used by f11gsc.

4: $\mathbf{anorm}$ – double * Output

On exit: the norm ${\Vert A\Vert }_1={\Vert A\Vert }_{\infty }$ when either it has been supplied to f11grc or it has been estimated by f11gsc (see also Sections 3 and 5 in f11grc).
Otherwise, $\mathbf{anorm}=0.0$ is returned.

5: $\mathbf{sigmax}$ – double * 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 f11grc or it has been estimated by f11gsc (see also Sections 3 and 5 in f11grc). Note that if $\mathbf{its}<\mathbf{itn}$ then sigmax contains the final estimate. If, on final exit from f11gsc, $\mathbf{its}=\mathbf{itn}$, 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 f11gsc using the bisection method (see also Sections 3, 5 and 9 in f11grc). Otherwise, $\mathbf{its}=0$ is returned.

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

On exit: if ${\sigma }_1\left(\overline{A}\right)$ has been estimated by f11gsc using bisection,

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

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 f11grc.
Otherwise, $\mathbf{sigerr}=0.0$ is returned.

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

On entry: the array work as returned by f11gsc (see also Section 3 in f11gsc).

9: $\mathbf{lwork}$ – Integer Input

On entry: the dimension of the array work (see also Section 5 in f11grc).

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

Note:  although the minimum value of lwork ensures the correct functioning of f11gtc, a larger value is required by the iterative solver f11gsc (see also Section 5 in f11grc).

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

f11gtc has been called out of sequence.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example