NAG Library Routine Document

f11yef  (sym_rcm)

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 matrix $A$.

Constraint: $\mathbf{nnz}\ge 0$.

3:     $\mathbf{icolzp}\left(\mathbf{n}+1\right)$ – Integer arrayInput

On entry: icolzp records the index into irowix which starts each new column.

Constraints:

• $1\le \mathbf{icolzp}\left(\mathit{i}\right)\le \mathbf{nnz}+1$, for $\mathit{i}=2,3,\dots ,\mathbf{n}$;
• $\mathbf{icolzp}\left(1\right)=1$;
• $\mathbf{icolzp}\left(\mathbf{n}+1\right)=\mathbf{nnz}+1$, where $\mathbf{icolzp}\left(i\right)$ holds the position integer for the starts of the columns in irowix.

4:     $\mathbf{irowix}\left(\mathbf{nnz}\right)$ – Integer arrayInput

On entry: the row indices corresponding to the nonzero elements in the matrix $A$.

Constraint: $1\le \mathbf{irowix}\left(\mathit{i}\right)\le \mathbf{n}$, for $\mathit{i}=1,2,\dots ,\mathbf{nnz}$.

5:     $\mathbf{lopts}\left(5\right)$ – Logical arrayInput

On entry: the options to be used by f11yef.

$\mathbf{lopts}\left(1\right)=\mathrm{.TRUE.}$

Row/column $i$ of the matrix $A$ will only be referenced if $\mathbf{mask}\left(i\right)\ne 0$, otherwise $\mathbf{mask}$ will be ignored.

$\mathbf{lopts}\left(2\right)=\mathrm{.TRUE.}$

The final permutation will not be reversed, that is, the Cuthill–McKee ordering will be returned. The bandwidth of the non-reversed matrix will be the same but the profile will be the same or larger (see Wai-Hung and Sherman (1976)).

$\mathbf{lopts}\left(3\right)=\mathrm{.TRUE.}$

The matrix $A$ will be checked for symmetrical sparsity pattern, otherwise not.

$\mathbf{lopts}\left(4\right)=\mathrm{.TRUE.}$

The bandwidth and profile of the unpermuted matrix will be calculated, otherwise not.

$\mathbf{lopts}\left(5\right)=\mathrm{.TRUE.}$

The bandwidth and profile of the permuted matrix will be calculated, otherwise not.

6:     $\mathbf{mask}\left(*\right)$ – Integer arrayInput

Note: the dimension of the array mask must be at least $\mathbf{n}$ if $\mathbf{lopts}\left(1\right)=\mathrm{.TRUE.}$, and at least $0$ otherwise.

On entry: mask is only referenced if $\mathbf{lopts}\left(1\right)$ is .TRUE.. A value of $\mathbf{mask}\left(i\right)=0$ indicates that the node corresponding to row or column $i$ is not to be referenced. A value of $\mathbf{mask}\left(i\right)\ne 0$ indicates that the node corresponding to row or column $i$ is to be referenced. In particular, rows and columns not referenced will not be permuted.

7:     $\mathbf{perm}\left(\mathbf{n}\right)$ – Integer arrayOutput

On exit: this will contain the permutation vector that describes the permutation matrix $P$ for the reordering of the matrix $A$. The elements of the permutation matrix $P$ are zero except for the unit elements in row $i$ and column $\mathbf{perm}\left(i\right)$, $i=1,2,\dots n$.

8:     $\mathbf{info}\left(4\right)$ – Integer arrayOutput

On exit: statistics about the matrix $A$ and the permuted matrix. The quantities below are calculated using any masking in effect otherwise the value zero is returned.

$\mathbf{info}\left(1\right)$

The bandwidth of the matrix $A$, if $\mathbf{lopts}\left(4\right)=\mathrm{.TRUE.}$.

$\mathbf{info}\left(2\right)$

The profile of the matrix $A$, if $\mathbf{lopts}\left(4\right)=\mathrm{.TRUE.}$.

$\mathbf{info}\left(3\right)$

The bandwidth of the permuted matrix $PA{P}^{\mathrm{T}}$, if $\mathbf{lopts}\left(5\right)=\mathrm{.TRUE.}$.

$\mathbf{info}\left(4\right)$

The profile of the permuted matrix $PA{P}^{\mathrm{T}}$, if $\mathbf{lopts}\left(5\right)=\mathrm{.TRUE.}$.

9:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation 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 argument, 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, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

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

$\mathbf{ifail}=4$

On entry, $\mathbf{icolzp}\left(〈\mathit{\text{value}}〉\right)=〈\mathit{\text{value}}〉$ and $\mathbf{nnz}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{icolzp}\left(i\right)\le \mathbf{nnz}$ for all $i$.

$\mathbf{ifail}=5$

On entry, $\mathbf{icolzp}\left(1\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{icolzp}\left(1\right)=1$.

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

$\mathbf{ifail}=6$

On entry, the matrix $A$ is not symmetric.
Element $\left(〈\mathit{\text{value}}〉,〈\mathit{\text{value}}〉\right)$ has no symmetric element.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f11yefe.f90)

10.2

Program Data

Program Data (f11yefe.d)

10.3

Program Results

Program Results (f11yefe.r)