# NAG Library Routine Document

## 1Purpose

f11zbf sorts the nonzero elements of a real sparse symmetric matrix, represented in symmetric coordinate storage format.

## 2Specification

Fortran Interface
 Subroutine f11zbf ( 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) Real (Kind=nag_wp), Intent (Inout) :: a(*) Character (1), Intent (In) :: dup, zer
#include nagmk26.h
 void f11zbf_ (const Integer *n, Integer *nnz, double 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

f11zbf takes a symmetric coordinate storage (SCS) representation (see Section 2.1.2 in 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.
f11zbf also returns a pointer 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:     $\mathbf{nnz}$ – IntegerInput/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:     $\mathbf{a}\left(*\right)$ – Real (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 lower triangular part of the real 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:     $\mathbf{irow}\left(*\right)$ – 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 nonzero 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 nonzero 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 nonzero elements supplied in the array a.
Constraint: $1\le {\mathbf{icol}}\left(\mathit{i}\right)\le {\mathbf{irow}}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{nnz}}$.
On exit: the first nnz elements contain the column indices corresponding to the nonzero elements returned in the array a.
6:     $\mathbf{dup}$ – Character(1)Input
On entry: indicates how any nonzero elements with duplicate row and column indices are to be treated.
${\mathbf{dup}}=\text{'R'}$
The entries are removed.
${\mathbf{dup}}=\text{'S'}$
The relevant values in a are summed.
Constraint: ${\mathbf{dup}}=\text{'R'}$ or $\text{'S'}$.
7:     $\mathbf{zer}$ – Character(1)Input
On entry: indicates how any elements with zero values in a are to be treated.
${\mathbf{zer}}=\text{'R'}$
The entries are removed.
${\mathbf{zer}}=\text{'K'}$
The entries are kept.
Constraint: ${\mathbf{zer}}=\text{'R'}$ or $\text{'K'}$.
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 nonzero 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 $0$, $-1\text{​ or ​}1$. 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 $-1\text{​ or ​}1$ 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 $-\mathbf{1}\text{​ or ​}\mathbf{1}$ 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, ${\mathbf{n}}<1$, or ${\mathbf{nnz}}<0$, or ${\mathbf{dup}}\ne \text{'R'}$ or $\text{'S'}$. or ${\mathbf{zer}}\ne \text{'R'}$ or $\text{'K'}$.
${\mathbf{ifail}}=2$
On entry, a nonzero element has been supplied which does not lie in the lower triangular part of $A$, i.e., one or more of the following constraints has been violated:
• $1\le {\mathbf{irow}}\left(i\right)\le {\mathbf{n}}$,
• $1\le {\mathbf{icol}}\left(i\right)\le {\mathbf{irow}}\left(i\right)$,
for $i=1,2,\dots ,{\mathbf{nnz}}$.
${\mathbf{ifail}}=-99$
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

f11zbf is not threaded in any implementation.

The time taken for a call to f11zbf 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 ${\mathbf{istr}}\left(i\right)={\mathbf{istr}}\left(i+1\right)$.

## 10Example

This example reads the SCS representation of a real sparse symmetric matrix $A$, calls f11zbf to reorder the nonzero elements, and outputs the original and the reordered representations.

### 10.1Program Text

Program Text (f11zbfe.f90)

### 10.2Program Data

Program Data (f11zbfe.d)

### 10.3Program Results

Program Results (f11zbfe.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017