NAG Library Function Document

nag_sparse_herm_precon_ssor_solve (f11jrc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{n}$ – IntegerInput

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

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

2:    $\mathbf{nnz}$ – IntegerInput

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 ComplexInput

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 nag_sparse_herm_sort (f11zpc) may be used to order the elements in this way.

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

5:    $\mathbf{icol}\left[\mathbf{nnz}\right]$ – const IntegerInput

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 nag_sparse_herm_sort (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 doubleInput

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:    $\mathbf{omega}$ – doubleInput

On entry: the relaxation parameter $\omega$.

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

8:    $\mathbf{check}$ – Nag_SparseSym_CheckDataInput

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 ComplexInput

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

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

On exit: the solution vector $x$.

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

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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 2.7.6 in How to Use the NAG Library and its Documentation 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 2.7.5 in How to Use the NAG Library and its Documentation 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: $\mathit{I}=〈\mathit{\text{value}}〉$. Consider calling nag_sparse_herm_sort (f11zpc) to reorder and sum or remove duplicates.

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

Program Text (f11jrce.c)

10.2

Program Data

Program Data (f11jrce.d)

10.3

Program Results

Program Results (f11jrce.r)