# NAG C Library Function Document

## 1Purpose

nag_sparse_sym_sort (f11zbc) sorts the nonzero elements of a real sparse symmetric matrix, represented in symmetric coordinate storage format.

## 2Specification

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

## 3Description

nag_sparse_sym_sort (f11zbc) takes a symmetric coordinate storage (SCS) representation (see the f11 Chapter Introduction) of a real $n$ by $n$ sparse symmetric 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.
nag_sparse_sym_sort (f11zbc) also returns istr which contains the starting indices of each row in $A$.

None.

## 5Arguments

1:    $\mathbf{n}$IntegerInput
On entry: 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:    $\mathbf{a}\left[\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nnz}}\right)\right]$doubleInput/Output
On entry: the nonzero elements of the lower triangular part of the 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:    $\mathbf{irow}\left[\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nnz}}\right)\right]$IntegerInput/Output
On entry: the row indices of the elements supplied in 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 elements returned in array a.
5:    $\mathbf{icol}\left[\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nnz}}\right)\right]$IntegerInput/Output
On entry: the column indices of the elements supplied in 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 elements returned in 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:
• if ${\mathbf{dup}}=\mathrm{Nag_SparseSym_RemoveDups}$ then duplicate elements are removed;
• if ${\mathbf{dup}}=\mathrm{Nag_SparseSym_SumDups}$ then duplicate elements are summed.
Constraint: ${\mathbf{dup}}=\mathrm{Nag_SparseSym_RemoveDups}$ or $\mathrm{Nag_SparseSym_SumDups}$.
7:    $\mathbf{zero}$Nag_SparseSym_ZerosInput
On entry: indicates how any elements with zero values in a are to be treated:
• if ${\mathbf{zero}}=\mathrm{Nag_SparseSym_RemoveZeros}$ then elements with zero value are removed;
• if ${\mathbf{zero}}=\mathrm{Nag_SparseSym_KeepZeros}$ then elements with zero value are kept.
Constraint: ${\mathbf{zero}}=\mathrm{Nag_SparseSym_RemoveZeros}$ or $\mathrm{Nag_SparseSym_KeepZeros}$.
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 index in the arrays a, irow and icol of each row $i$ of the matrix $A$. ${\mathbf{istr}}\left[n\right]-1$ is the index 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).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
On entry, argument dup had an illegal value.
On entry, argument zero had an illegal value.
NE_INT_ARG_LT
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_SYMM_MATRIX
A nonzero element has been supplied which does not lie in the lower triangular part of the matrix $A$, i.e., one or more of the following constraints has been violated: $1\le {\mathbf{irow}}\left[\mathit{i}\right]\le {\mathbf{n}}$, $1\le {\mathbf{icol}}\left[\mathit{i}\right]\le {\mathbf{irow}}\left[\mathit{i}\right]$, for $\mathit{i}=0,1,\dots ,{\mathbf{nnz}}-1$.

Not applicable.

## 8Parallelism and Performance

nag_sparse_sym_sort (f11zbc) is not threaded in any implementation.

The time taken for a call to nag_sparse_sym_sort (f11zbc) 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 ${\mathbf{istr}}\left[i-1\right]={\mathbf{istr}}\left[i\right]$.

## 10Example

This example program reads the SCS representation of a real sparse symmetric matrix $A$, reorders the nonzero elements, and outputs the original and the reordered representations.

### 10.1Program Text

Program Text (f11zbce.c)

### 10.2Program Data

Program Data (f11zbce.d)

### 10.3Program Results

Program Results (f11zbce.r)