NAG Library Function Document

nag_sparse_sym_basic_diagnostic (f11gfc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{itn}$ – Integer *Output

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

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

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

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

On exit: the current value of the right-hand side of the termination criterion used by nag_sparse_sym_basic_solver (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 nag_sparse_sym_basic_setup (f11gdc) or it has been estimated by nag_sparse_sym_basic_solver (f11gec) (see also Sections 3 and 5 in nag_sparse_sym_basic_setup (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 ${\sigma }_1\left(\stackrel{-}{A}\right)$ of the preconditioned iteration matrix $\stackrel{-}{A}=E^{-1}A{E}^{-\mathrm{T}}$, when either it has been supplied to nag_sparse_sym_basic_setup (f11gdc) or it has been estimated by nag_sparse_sym_basic_solver (f11gec) (see also Sections 3 and 5 in nag_sparse_sym_basic_setup (f11gdc)). Note that if $\mathbf{its}<\mathbf{itn}$ then sigmax contains the final estimate. If, on final exit from nag_sparse_sym_basic_solver (f11gec), $\mathbf{its}=\mathbf{itn}$, then 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:    $\mathbf{its}$ – Integer *Output

On exit: for CG and SYMMLQ methods, the number of iterations employed so far in the computation of the estimate of ${\sigma }_1\left(\stackrel{-}{A}\right)$, 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 nag_sparse_sym_basic_solver (f11gec) using the bisection method (see also Sections 3, 5 and 9 in nag_sparse_sym_basic_setup (f11gdc)). Otherwise, $\mathbf{its}=0$ is returned.

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

On exit: for CG and SYMMLQ methods, if ${\sigma }_1\left(\stackrel{-}{A}\right)$ has been estimated by nag_sparse_sym_basic_solver (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 nag_sparse_sym_basic_setup (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 doubleCommunication Array

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

9:    $\mathbf{lwork}$ – IntegerInput

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

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

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

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

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction 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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.

NE_OUT_OF_SEQUENCE

nag_sparse_sym_basic_diagnostic (f11gfc) has been called out of sequence.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example