# NAG C Library Function Document

## 1Purpose

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

## 2Specification

 #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)

## 3Description

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. Alternatively, duplicate entries may be summed, which facilitates spare matrix addition (see Section 9). Any entries with zero values may optionally be removed.
nag_sparse_herm_sort (f11zpc) also returns a pointer array istr to the starting address of each row in $A$.

None.

## 5Arguments

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 elements supplied in the array a.
Constraint: ${\mathbf{nnz}}\ge 0$.
On exit: the number of 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 $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nnz}}\right)$.
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:    $\mathbf{irow}\left[\mathit{dim}\right]$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 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 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 $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nnz}}\right)$.
On entry: the column indices corresponding to the 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 elements returned in the array a.
6:    $\mathbf{dup}$Nag_SparseSym_DupsInput
On entry: indicates how elements in a with duplicate row and column indices are to be treated.
${\mathbf{dup}}=\mathrm{Nag_SparseSym_RemoveDups}$
Duplicate entries are removed, only the first entry is kept.
${\mathbf{dup}}=\mathrm{Nag_SparseSym_SumDups}$
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 elements in a with zero values 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 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.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
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 $\mathit{J}$: $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$.

Not applicable.

## 8Parallelism and Performance

nag_sparse_herm_sort (f11zpc) is not threaded in any implementation.

The time taken for a call to nag_sparse_herm_sort (f11zpc) is the sum of two contributions, where one is proportional to nnz and the other is proportional to n.
Note that the resulting matrix may have either rows or columns with no entries. If row $i$ has no entries then ${\mathbf{istr}}\left[i\right]={\mathbf{istr}}\left[i+1\right]$.
Two sparse matrices can be added by concatenating the three pairs of SCS format arrays, representing the two matrices, and passing these new arrays to nag_sparse_herm_sort (f11zpc), specifying that duplicates should be summed. This functionality is illustrated in Section 10 in nag_sparse_nsym_sort (f11zac).

## 10Example

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.

### 10.1Program Text

Program Text (f11zpce.c)

### 10.2Program Data

Program Data (f11zpce.d)

### 10.3Program Results

Program Results (f11zpce.r)