NAG CL Interface
f11jrc (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: $\mathbf{a}\left[\mathbf{nnz}\right]$ – const Complex 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 function f11zpc may be used to order the elements in this way.

4: $\mathbf{irow}\left[\mathbf{nnz}\right]$ – const Integer Input

5: $\mathbf{icol}\left[\mathbf{nnz}\right]$ – const Integer 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 f11zpc):

• $1\le \mathbf{irow}\left[\mathit{i}\right]\le \mathbf{n}$ and $1\le \mathbf{icol}\left[\mathit{i}\right]\le \mathbf{irow}\left[\mathit{i}\right]$, for $\mathit{i}=0,1,\dots ,\mathbf{nnz}-1$;
• $\mathbf{irow}\left[\mathit{i}-1\right]<\mathbf{irow}\left[\mathit{i}\right]$ 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 $\mathit{i}=1,2,\dots ,\mathbf{nnz}-1$.

6: $\mathbf{rdiag}\left[\mathbf{n}\right]$ – const double 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: $\mathbf{omega}$ – double Input

On entry: the relaxation parameter $\omega$.

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

8: $\mathbf{check}$ – Nag_SparseSym_CheckData Input

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

$\mathbf{check}=\mathrm{Nag\_SparseSym\_Check}$

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

$\mathbf{check}=\mathrm{Nag\_SparseSym\_NoCheck}$

None of these checks are carried out.

Constraint: $\mathbf{check}=\mathrm{Nag\_SparseSym\_Check}$ or $\mathrm{Nag\_SparseSym\_NoCheck}$.

9: $\mathbf{y}\left[\mathbf{n}\right]$ – const Complex Input

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

10: $\mathbf{x}\left[\mathbf{n}\right]$ – Complex Output

On exit: the solution vector $x$.

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

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

6 Error Indicators and Warnings

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 f11zpc to reorder and sum or remove duplicates.

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

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

NE_INT_2

On entry, $\mathbf{nnz}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nnz}\le \mathbf{n}\times \left(\mathbf{n}+1\right)/2$.

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_INVALID_SCS

On entry, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathbf{icol}\left[\mathit{I}-1\right]=〈\mathit{\text{value}}〉$, $\mathbf{irow}\left[\mathit{I}-1\right]=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{icol}\left[i-1\right]\le \mathbf{irow}\left[i-1\right]$.

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

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_NOT_STRICTLY_INCREASING

On entry, $\mathbf{a}\left[i-1\right]$ is out of order: $i=〈\mathit{\text{value}}〉$.

On entry, the location ($\mathbf{irow}\left[\mathit{I}-1\right],\mathbf{icol}\left[\mathit{I}-1\right]$) is a duplicate: $\mathit{I}=〈\mathit{\text{value}}〉$.

NE_REAL

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

NE_ZERO_DIAG_ELEM

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

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