NAG Library Function Document

nag_sparse_herm_sort (f11zpc)

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:    $\mathbf{nnz}$ – Integer *Input/Output

On entry: the number of nonzero elements in the lower triangular part of the matrix $A$.

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

On exit: the number of lower triangular nonzero elements with unique row and column indices.

3:    $\mathbf{a}\left[\mathit{dim}\right]$ – ComplexInput/Output

Note: the dimension, dim, of the array a must be at least $\max \left(1,\mathbf{nnz}\right)$.

On entry: the nonzero elements of the lower triangular part of the complex matrix $A$. These may be in any order and there may be multiple nonzero elements with the same row and column indices.

On exit: the lower triangular nonzero elements ordered by increasing row index, and by increasing column index within each row. Each nonzero element has a unique row and column index.

4:    $\mathbf{irow}\left[\mathit{dim}\right]$ – IntegerInput/Output

Note: the dimension, dim, of the array irow must be at least $\max \left(1,\mathbf{nnz}\right)$.

On entry: the row indices corresponding to the nonzero elements supplied in the array a.

Constraint: $1\le \mathbf{irow}\left[\mathit{i}\right]\le \mathbf{n}$, for $\mathit{i}=0,1,\dots ,\mathbf{nnz}-1$.

On exit: the first nnz elements contain the row indices corresponding to the nonzero elements returned in the array a.

5:    $\mathbf{icol}\left[\mathit{dim}\right]$ – IntegerInput/Output

Note: the dimension, dim, of the array icol must be at least $\max \left(1,\mathbf{nnz}\right)$.

On entry: the column indices corresponding to the nonzero elements supplied in the array a.

Constraint: $1\le \mathbf{icol}\left[\mathit{i}\right]\le \mathbf{irow}\left[\mathit{i}\right]$, for $\mathit{i}=0,1,\dots ,\mathbf{nnz}-1$.

On exit: the first nnz elements contain the column indices corresponding to the nonzero elements returned in the array a.

6:    $\mathbf{dup}$ – Nag_SparseSym_DupsInput

On entry: indicates how any nonzero elements with duplicate row and column indices are to be treated.

$\mathbf{dup}=\mathrm{Nag\_SparseSym\_RemoveDups}$

The entries are removed.

$\mathbf{dup}=\mathrm{Nag\_SparseSym\_SumDups}$

The relevant values in a are summed.

$\mathbf{dup}=\mathrm{Nag\_SparseSym\_FailDups}$

The function fails with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NON_ZERO_DUP on detecting a duplicate.

Constraint: $\mathbf{dup}=\mathrm{Nag\_SparseSym\_RemoveDups}$, $\mathrm{Nag\_SparseSym\_SumDups}$ or $\mathrm{Nag\_SparseSym\_FailDups}$.

7:    $\mathbf{zero}$ – Nag_SparseSym_ZerosInput

On entry: indicates how any elements with zero values in array a are to be treated.

$\mathbf{zero}=\mathrm{Nag\_SparseSym\_RemoveZeros}$

The entries are removed.

$\mathbf{zero}=\mathrm{Nag\_SparseSym\_KeepZeros}$

The entries are kept.

$\mathbf{zero}=\mathrm{Nag\_SparseSym\_FailZeros}$

The function fails with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_ZERO_COEFF on detecting a zero.

Constraint: $\mathbf{zero}=\mathrm{Nag\_SparseSym\_RemoveZeros}$, $\mathrm{Nag\_SparseSym\_KeepZeros}$ or $\mathrm{Nag\_SparseSym\_FailZeros}$.

8:    $\mathbf{istr}\left[\mathbf{n}+1\right]$ – IntegerOutput

On exit: $\mathbf{istr}\left[\mathit{i}-1\right]-1$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$, is the starting address in the arrays a, irow and icol of row $i$ of the matrix $A$. $\mathbf{istr}\left[\mathbf{n}\right]-1$ is the address of the last nonzero element in $A$ plus one.

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

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, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathbf{icol}\left[\mathit{I}-1\right]=〈\mathit{\text{value}}〉$ and $\mathbf{irow}\left[\mathit{I}-1\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{icol}\left[\mathit{I}-1\right]\ge 1$ and $\mathbf{icol}\left[\mathit{I}-1\right]\le \mathbf{irow}\left[\mathit{I}-1\right]$.

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

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_NON_ZERO_DUP

On entry, a duplicate entry has been found in row $\mathit{I}$ and column $\mathit{J}$: $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$.

NE_ZERO_COEFF

On entry, a zero entry has been found in row $\mathit{I}$ and column $\mathit{J}$: $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f11zpce.c)

10.2

Program Data

Program Data (f11zpce.d)

10.3

Program Results

Program Results (f11zpce.r)