NAG Library Function Document

nag_sparse_herm_precon_ssor_solve (f11jrc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     n – IntegerInput

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

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

2:     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:     a[nnz] – 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:     irow[nnz] – const IntegerInput

5:     icol[nnz] – 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:     rdiag[n] – 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:     omega – doubleInput

On entry: the relaxation argument $\omega$.

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

8:     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:     y[n] – const ComplexInput

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

10:   x[n] – ComplexOutput

On exit: the solution vector $x$.

11:   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.

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.

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_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)