NAG Library Routine Document

F11JRF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

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) – COMPLEX (KIND=nag_wp) arrayInput

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:     IROW(NNZ) – INTEGER arrayInput

5:     ICOL(NNZ) – INTEGER arrayInput

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:     RDIAG(N) – REAL (KIND=nag_wp) arrayInput

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 – REAL (KIND=nag_wp)Input

On entry: the relaxation parameter $\omega$.

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

8:     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:     Y(N) – COMPLEX (KIND=nag_wp) arrayInput

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

10:   X(N) – COMPLEX (KIND=nag_wp) arrayOutput

On exit: the solution vector $x$.

11:   IWORK($\mathbf{N}+1$) – INTEGER arrayWorkspace

12:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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 $\text{'N'}$.

$\mathbf{IFAIL}=2$

On entry,	$\mathbf{N}<1$,
or	$\mathbf{NNZ}<1$,
or	$\mathbf{NNZ}>\mathbf{N}\times \left(\mathbf{N}+1\right)/2$,
or	OMEGA lies outside the interval $\left(0.0,2.0\right)$.

$\mathbf{IFAIL}=3$

On entry, the arrays IROW and ICOL fail to satisfy the following constraints:

• $1\le \mathbf{IROW}\left(i\right)\le \mathbf{N}$ and $1\le \mathbf{ICOL}\left(i\right)\le \mathbf{IROW}\left(i\right)$, for $i=1,2,\dots ,\mathbf{NNZ}$;
• $\mathbf{IROW}\left(i-1\right)<\mathbf{IROW}\left(i\right)$ or $\mathbf{IROW}\left(i-1\right)=\mathbf{IROW}\left(i\right)$ and $\mathbf{ICOL}\left(i-1\right)<\mathbf{ICOL}\left(i\right)$, for $i=2,3,\dots ,\mathbf{NNZ}$.

Therefore 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. Call F11ZPF to reorder and sum or remove duplicates.

$\mathbf{IFAIL}=4$

On entry,

a row of $A$ has no diagonal entry.

7  Accuracy

8  Further Comments

8.1  Timing

9  Example

9.1  Program Text

Program Text (f11jrfe.f90)

9.2  Program Data

Program Data (f11jrfe.d)

9.3  Program Results

Program Results (f11jrfe.r)