nag_sparse_herm_sort (f11zpc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_sparse_herm_sort (f11zpc)

## 1  Purpose

nag_sparse_herm_sort (f11zpc) sorts the nonzero elements of a sparse complex Hermitian matrix, represented in symmetric coordinate storage format.

## 2  Specification

 #include #include
 void nag_sparse_herm_sort (Integer n, Integer *nnz, Complex a[], Integer irow[], Integer icol[], Nag_SparseSym_Dups dup, Nag_SparseSym_Zeros zero, Integer istr[], NagError *fail)

## 3  Description

nag_sparse_herm_sort (f11zpc) takes a symmetric coordinate storage (SCS) representation (see Section 2.1.2 in the f11 Chapter Introduction) of a sparse $n$ by $n$ complex Hermitian matrix $A$, and reorders the nonzero elements by increasing row index and increasing column index within each row. Entries with duplicate row and column indices may be removed, or the values may be summed. Any entries with zero values may optionally be removed.
The function also returns a pointer array istr to the starting address of each row in $A$.

None.

## 5  Arguments

1:     nIntegerInput
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 1$.
2:     nnzInteger *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:     a[$\mathit{dim}$]ComplexInput/Output
Note: the dimension, dim, of the array a must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nnz}}\right)$.
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:     irow[$\mathit{dim}$]IntegerInput/Output
Note: the dimension, dim, of the array irow must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nnz}}\right)$.
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:     icol[$\mathit{dim}$]IntegerInput/Output
Note: the dimension, dim, of the array icol must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nnz}}\right)$.
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:     dupNag_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 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:     zeroNag_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 NE_ZERO_COEFF on detecting a zero.
Constraint: ${\mathbf{zero}}=\mathrm{Nag_SparseSym_RemoveZeros}$, $\mathrm{Nag_SparseSym_KeepZeros}$ or $\mathrm{Nag_SparseSym_FailZeros}$.
8:     istr[${\mathbf{n}}+1$]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:     failNagError *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: ${\mathbf{nnz}}\ge 0$.
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.
NE_INVALID_SCS
On entry, $i=〈\mathit{\text{value}}〉$, ${\mathbf{icol}}\left[i-1\right]=〈\mathit{\text{value}}〉$, ${\mathbf{irow}}\left[i-1\right]=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{icol}}\left[i-1\right]\ge 1$ and ${\mathbf{icol}}\left[i-1\right]\le {\mathbf{irow}}\left[i-1\right]$.
On entry, $i=〈\mathit{\text{value}}〉$, ${\mathbf{irow}}\left[i-1\right]=〈\mathit{\text{value}}〉$, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{irow}}\left[i-1\right]\ge 1$ and ${\mathbf{irow}}\left[i-1\right]\le {\mathbf{n}}$.
NE_NON_ZERO_DUP
On entry, a duplicate entry has been found in row $i$ and column $j$: $i=〈\mathit{\text{value}}〉$, $j=〈\mathit{\text{value}}〉$.
NE_ZERO_COEFF
On entry, a zero entry has been found in row $i$ and column $j$: $i=〈\mathit{\text{value}}〉$, $j=〈\mathit{\text{value}}〉$.

Not applicable.

## 8  Further Comments

The time taken for a call to nag_sparse_herm_sort (f11zpc) is proportional to nnz.
Note that the resulting matrix may have either rows or columns with no entries. If row $i$ has no entries then ${\mathbf{istr}}\left[i\right]={\mathbf{istr}}\left[i+1\right]$.

## 9  Example

This example reads the SCS representation of a complex sparse Hermitian matrix $A$, calls nag_sparse_herm_sort (f11zpc) to reorder the nonzero elements, and outputs the original and the reordered representations.

### 9.1  Program Text

Program Text (f11zpce.c)

### 9.2  Program Data

Program Data (f11zpce.d)

### 9.3  Program Results

Program Results (f11zpce.r)

nag_sparse_herm_sort (f11zpc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual