# NAG Library Routine Document

## 1Purpose

f11znf sorts the nonzero elements of a complex sparse non-Hermitian matrix, represented in coordinate storage format.

## 2Specification

Fortran Interface
 Subroutine f11znf ( n, nnz, a, irow, icol, dup, zer, istr,
 Integer, Intent (In) :: n Integer, Intent (Inout) :: nnz, irow(*), icol(*), ifail Integer, Intent (Out) :: istr(n+1), iwork(n) Complex (Kind=nag_wp), Intent (Inout) :: a(*) Character (1), Intent (In) :: dup, zer
#include <nagmk26.h>
 void f11znf_ (const Integer *n, Integer *nnz, Complex a[], Integer irow[], Integer icol[], const char *dup, const char *zer, Integer istr[], Integer iwork[], Integer *ifail, const Charlen length_dup, const Charlen length_zer)

## 3Description

f11znf takes a coordinate storage (CS) representation (see Section 2.1.1 in the F11 Chapter Introduction) of a sparse $n$ by $n$ complex non-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.
f11znf also returns a pointer array istr to the starting address of each row in $A$. This can be used to construct a compressed column storage (CCS) representation of the matrix (see Section 9).

None.

## 5Arguments

1:     $\mathbf{n}$ – IntegerInput
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 1$.
2:     $\mathbf{nnz}$ – IntegerInput/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:     $\mathbf{a}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput/Output
Note: the dimension 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 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 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:     $\mathbf{irow}\left(*\right)$ – Integer arrayInput/Output
Note: the dimension 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 $\mathit{i}=1,2,\dots ,{\mathbf{nnz}}$.
On exit: the first nnz elements contain the row indices corresponding to the elements returned in the array a.
5:     $\mathbf{icol}\left(*\right)$ – Integer arrayInput/Output
Note: the dimension 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: $1\le {\mathbf{icol}}\left(\mathit{i}\right)\le {\mathbf{n}}$, for $\mathit{i}=1,2,\dots ,{\mathbf{nnz}}$.
On exit: the first nnz elements contain the column indices corresponding to the elements returned in the array a.
6:     $\mathbf{dup}$ – Character(1)Input
On entry: indicates how elements in a with duplicate row and column indices are to be treated.
${\mathbf{dup}}=\text{'R'}$
Duplicate entries are removed, only the first entry is kept.
${\mathbf{dup}}=\text{'S'}$
The relevant values in a are summed.
${\mathbf{dup}}=\text{'F'}$
The routine fails with ${\mathbf{ifail}}={\mathbf{3}}$ on detecting a duplicate.
Constraint: ${\mathbf{dup}}=\text{'R'}$, $\text{'S'}$ or $\text{'F'}$.
7:     $\mathbf{zer}$ – Character(1)Input
On entry: indicates how elements in a with zero values are to be treated.
${\mathbf{zer}}=\text{'R'}$
The entries are removed.
${\mathbf{zer}}=\text{'K'}$
The entries are kept.
${\mathbf{zer}}=\text{'F'}$
The routine fails with ${\mathbf{ifail}}={\mathbf{4}}$ on detecting a zero.
Constraint: ${\mathbf{zer}}=\text{'R'}$, $\text{'K'}$ or $\text{'F'}$.
8:     $\mathbf{istr}\left({\mathbf{n}}+1\right)$ – Integer arrayOutput
On exit: ${\mathbf{istr}}\left(\mathit{i}\right)$, 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 $A$. ${\mathbf{istr}}\left({\mathbf{n}}+1\right)$ is the address of the last element in a plus one.
9:     $\mathbf{iwork}\left({\mathbf{n}}\right)$ – Integer arrayWorkspace
10:   $\mathbf{ifail}$ – IntegerInput/Output
On entry: ifail must be set to $0$, . If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value  is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value  is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{dup}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{dup}}=\text{'R'}$, $\text{'S'}$ or $\text{'F'}$.
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 1$.
On entry, ${\mathbf{nnz}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{nnz}}\ge 0$.
On entry, ${\mathbf{zer}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{zer}}=\text{'R'}$, $\text{'K'}$ or $\text{'F'}$.
${\mathbf{ifail}}=2$
On entry, $i=〈\mathit{\text{value}}〉$, ${\mathbf{icol}}\left(i\right)=〈\mathit{\text{value}}〉$ and ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{icol}}\left(i\right)\ge 1$ and ${\mathbf{icol}}\left(i\right)\le {\mathbf{n}}$.
On entry, $i=〈\mathit{\text{value}}〉$, ${\mathbf{irow}}\left(i\right)=〈\mathit{\text{value}}〉$ and ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{irow}}\left(i\right)\ge 1$ and ${\mathbf{irow}}\left(i\right)\le {\mathbf{n}}$.
${\mathbf{ifail}}=3$
On entry, a duplicate entry has been found in row $\mathit{I}$ and column $\mathit{J}$: $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$.
${\mathbf{ifail}}=4$
On entry, a zero entry has been found in row $\mathit{I}$ and column $\mathit{J}$: $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$.
${\mathbf{ifail}}=-99$
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

Not applicable.

## 8Parallelism and Performance

f11znf is not threaded in any implementation.

The time taken for a call to f11znf 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 ${\mathbf{istr}}\left(i\right)={\mathbf{istr}}\left(i+1\right)$.
To transpose a matrix in CS format simply interchange irow and icol. If you need the elements to be sorted, then pass these interchanged arrays to f11znf.
Two sparse matrices can be added by concatenating the three pairs of CS format arrays, representing the two matrices, and passing these new arrays to f11znf, specifying that duplicates should be summed. This functionality is illustrated in Section 10 in f11zaf.
It is also possible to use this routine to convert between coordinate storage (CS) and compressed column storage (CCS) formats. To achieve this the CS format array holding the row indices must be passed as icol and the array holding the column indices must be passed as irow in a call to f11znf. On exit from f11znf, the CCS representation of the matrix is given by the output arrays a, icol, and istr, where icol holds irowix and istr holds icolzp as described in Section 2.1.3 in the F11 Chapter Introduction. This is illustrated in Section 10 in f11zaf.

## 10Example

This example reads the CS representation of a complex sparse matrix $A$, calls f11znf to reorder the nonzero elements, and outputs the original and the reordered representations.

### 10.1Program Text

Program Text (f11znfe.f90)

### 10.2Program Data

Program Data (f11znfe.d)

### 10.3Program Results

Program Results (f11znfe.r)