NAG FL Interface
f11jrf (complex_​herm_​precon_​ssor_​solve)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

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

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

2: $\mathbf{nnz}$ – Integer Input

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

Constraint: $1\le \mathbf{nnz}\le \mathbf{n}\times \left(\mathbf{n}+1\right)/2$.

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

On entry: the nonzero elements in the lower triangular part of 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 f11zpf may be used to order the elements in this way.

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

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

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

Constraints:

irow and icol must satisfy the following constraints (which may be imposed by a call to f11zpf):

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

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

On entry: the elements of the diagonal matrix $D^{-1}$, where $D$ is the diagonal part of $A$. Note that since $A$ is Hermitian the elements of $D^{-1}$ are necessarily real.

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

On entry: the relaxation parameter $\omega$.

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

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

On entry: specifies whether or not the input data should be checked.

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

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

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

None of these checks are carried out.

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

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

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

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

On exit: the solution vector $x$.

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

12: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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, $\mathbf{check}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{check}=\text{'C'}$ or $\text{'N'}$.

$\mathbf{ifail}=2$

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: $\mathbf{nnz}\le \mathbf{n}\times \left(\mathbf{n}+1\right)/2$.

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, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathbf{icol}\left(\mathit{I}\right)=〈\mathit{\text{value}}〉$, $\mathbf{irow}\left(\mathit{I}\right)=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{icol}\left(i\right)\le \mathbf{irow}\left(i\right)$.

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

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 lower triangular part of $A$, is out of order, or has duplicate row and column indices. Consider calling f11zpf to reorder and sum or remove duplicates.

$\mathbf{ifail}=4$

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

$\mathbf{ifail}=-99$

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

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results