NAG FL Interface
f11drf (complex_​gen_​precon_​ssor_​solve)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{trans}$ – Character(1) Input

On entry: specifies whether or not the matrix $M$ is transposed.

$\mathbf{trans}=\text{'N'}$

$Mx=y$ is solved.

$\mathbf{trans}=\text{'T'}$

$M^{\mathrm{H}}x=y$ is solved.

Constraint: $\mathbf{trans}=\text{'N'}$ or $\text{'T'}$.

2: $\mathbf{n}$ – Integer Input

On entry: $n$, the order of the matrix $A$.

Constraint: $\mathbf{n}\ge 1$.

3: $\mathbf{nnz}$ – Integer Input

On entry: the number of nonzero elements in the matrix $A$.

Constraint: $1\le \mathbf{nnz}\le {\mathbf{n}}^2$.

4: $\mathbf{a}\left(\mathbf{nnz}\right)$ – Complex (Kind=nag_wp) array Input

On entry: the nonzero elements in the matrix $A$, ordered by increasing row index, and by increasing column index within each row. Multiple entries for the same row and column indices are not permitted. The routine f11znf may be used to order the elements in this way.

5: $\mathbf{irow}\left(\mathbf{nnz}\right)$ – Integer array Input

6: $\mathbf{icol}\left(\mathbf{nnz}\right)$ – Integer array Input

On entry: the row and column indices of the nonzero elements supplied in a.

Constraints:

irow and icol must satisfy the following constraints (which may be imposed by a call to f11znf):

• $1\le \mathbf{irow}\left(\mathit{i}\right)\le \mathbf{n}$ and $1\le \mathbf{icol}\left(\mathit{i}\right)\le \mathbf{n}$, for $\mathit{i}=1,2,\dots ,\mathbf{nnz}$;
• either $\mathbf{irow}\left(\mathit{i}-1\right)<\mathbf{irow}\left(\mathit{i}\right)$ or both $\mathbf{irow}\left(\mathit{i}-1\right)=\mathbf{irow}\left(\mathit{i}\right)$ and $\mathbf{icol}\left(\mathit{i}-1\right)<\mathbf{icol}\left(\mathit{i}\right)$, for $\mathit{i}=2,3,\dots ,\mathbf{nnz}$.

7: $\mathbf{rdiag}\left(\mathbf{n}\right)$ – Complex (Kind=nag_wp) array Input

On entry: the elements of the diagonal matrix $D^{-1}$, where $D$ is the diagonal part of $A$.

8: $\mathbf{omega}$ – Real (Kind=nag_wp) Input

On entry: the relaxation parameter $\omega$.

Constraint: $0.0<\mathbf{omega}<2.0$.

9: $\mathbf{check}$ – Character(1) Input

On entry: specifies whether or not the CS representation of the matrix $M$ should be checked.

$\mathbf{check}=\text{'C'}$

Checks are carried on the values of n, nnz, irow, icol and omega.

$\mathbf{check}=\text{'N'}$

None of these checks are carried out.

See also Section 9.2.

Constraint: $\mathbf{check}=\text{'C'}$ or $\text{'N'}$.

10: $\mathbf{y}\left(\mathbf{n}\right)$ – Complex (Kind=nag_wp) array Input

On entry: the right-hand side vector $y$.

11: $\mathbf{x}\left(\mathbf{n}\right)$ – Complex (Kind=nag_wp) array Output

On exit: the solution vector $x$.

12: $\mathbf{iwork}\left(2\times \mathbf{n}+1\right)$ – Integer array Workspace

13: $\mathbf{ifail}$ – Integer Input/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 4 in the Introduction to the NAG Library FL Interface 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

$\mathbf{ifail}=1$

On entry, $\mathbf{check}\ne \text{'C'}$ or $\text{'N'}$: $\mathbf{check}=〈\mathit{\text{value}}〉$.

On entry, $\mathbf{trans}\ne \text{'N'}$ or $\text{'T'}$: $\mathbf{trans}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=2$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

On entry, $\mathbf{nnz}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nnz}\ge 1$.

On entry, $\mathbf{nnz}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nnz}\le {\mathbf{n}}^2$.

On entry, $\mathbf{omega}=〈\mathit{\text{value}}〉$.
Constraint: $0.0<\mathbf{omega}<2.0$

$\mathbf{ifail}=3$

On entry, $\mathbf{a}\left(i\right)$ is out of order: $i=〈\mathit{\text{value}}〉$.

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{icol}\left(i\right)=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{icol}\left(i\right)\ge 1$ and $\mathbf{icol}\left(i\right)\le \mathbf{n}$.

On entry, $i=〈\mathit{\text{value}}〉$, $\mathbf{irow}\left(i\right)=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{irow}\left(i\right)\ge 1$ and $\mathbf{irow}\left(i\right)\le \mathbf{n}$.

On entry, the location ($\mathbf{irow}\left(\mathit{I}\right),\mathbf{icol}\left(\mathit{I}\right)$) is a duplicate: $\mathit{I}=〈\mathit{\text{value}}〉$.

A nonzero element has been supplied which does not lie in the matrix $A$, is out of order, or has duplicate row and column indices. Consider calling f11znf to reorder and sum or remove duplicates.

$\mathbf{ifail}=4$

The matrix $A$ has no diagonal entry in row $〈\mathit{\text{value}}〉$.

The SSOR preconditioner is not appropriate for this problem.

$\mathbf{ifail}=-99$

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

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.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

9.1 Timing

9.2 Use of check

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results