NAG Library Function Document

nag_sparse_sym_rcm (f11yec)

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:    $\mathbf{icolzp}\left[\mathbf{n}+1\right]$ – const IntegerInput

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

Constraints:

• $1\le \mathbf{icolzp}\left[\mathit{i}-1\right]\le \mathbf{nnz}+1$, for $\mathit{i}=2,3,\dots ,\mathbf{n}$;
• $\mathbf{icolzp}\left[0\right]=1$;
• $\mathbf{icolzp}\left[\mathbf{n}\right]=\mathbf{nnz}+1$, where $\mathbf{icolzp}\left[i-1\right]$ holds the position integer for the starts of the columns in irowix.

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

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

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

5:    $\mathbf{lopts}\left[5\right]$ – const Nag_BooleanInput

On entry: the options to be used by nag_sparse_sym_rcm (f11yec).

$\mathbf{lopts}\left[0\right]=\mathrm{Nag\_TRUE}$

Row/column $i$ of the matrix $A$ will only be referenced if $\mathbf{mask}\left[i-1\right]\ne 0$, otherwise $\mathbf{mask}$ will be ignored.

$\mathbf{lopts}\left[1\right]=\mathrm{Nag\_TRUE}$

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)).

$\mathbf{lopts}\left[2\right]=\mathrm{Nag\_TRUE}$

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

$\mathbf{lopts}\left[3\right]=\mathrm{Nag\_TRUE}$

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

$\mathbf{lopts}\left[4\right]=\mathrm{Nag\_TRUE}$

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

6:    $\mathbf{mask}\left[\mathit{dim}\right]$ – const IntegerInput

Note: the dimension, dim, of the array mask must be at least

• $\mathbf{n}$ when $\mathbf{lopts}\left[0\right]=\mathrm{Nag\_TRUE}$;
• otherwise mask may be NULL.

On entry: mask is only referenced if $\mathbf{lopts}\left[0\right]$ is Nag_TRUE otherwise mask may be set to NULL. A value of $\mathbf{mask}\left[i-1\right]=0$ indicates that the node corresponding to row or column $i$ is not to be referenced. A value of $\mathbf{mask}\left[i-1\right]\ne 0$ 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:    $\mathbf{perm}\left[\mathbf{n}\right]$ – IntegerOutput

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 $\mathbf{perm}\left[i-1\right]$, $i=1,2,\dots n$.

8:    $\mathbf{info}\left[4\right]$ – IntegerOutput

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.

$\mathbf{info}\left[0\right]$

The bandwidth of the matrix $A$, if $\mathbf{lopts}\left[3\right]=\mathrm{Nag\_TRUE}$.

$\mathbf{info}\left[1\right]$

The profile of the matrix $A$, if $\mathbf{lopts}\left[3\right]=\mathrm{Nag\_TRUE}$.

$\mathbf{info}\left[2\right]$

The bandwidth of the permuted matrix $PA{P}^{\mathrm{T}}$, if $\mathbf{lopts}\left[4\right]=\mathrm{Nag\_TRUE}$.

$\mathbf{info}\left[3\right]$

The profile of the permuted matrix $PA{P}^{\mathrm{T}}$, if $\mathbf{lopts}\left[4\right]=\mathrm{Nag\_TRUE}$.

9:    $\mathbf{fail}$ – 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_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_CS

On entry, $\mathbf{icolzp}\left[0\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{icolzp}\left[0\right]=1$.

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

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_NONSYMM_MATRIX

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

NE_SPARSE_COL

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

NE_SPARSE_ROW

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

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f11yece.c)

10.2

Program Data

Program Data (f11yece.d)

10.3

Program Results

Program Results (f11yece.r)