F11 Chapter Contents
F11 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF11ZPF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F11ZPF sorts the nonzero elements of a sparse complex Hermitian matrix, represented in symmetric coordinate storage format.

## 2  Specification

 SUBROUTINE F11ZPF ( N, NNZ, A, IROW, ICOL, DUP, ZER, ISTR, IWORK, IFAIL)
 INTEGER N, NNZ, IROW(*), ICOL(*), ISTR(N+1), IWORK(N), IFAIL COMPLEX (KIND=nag_wp) A(*) CHARACTER(1) DUP, ZER

## 3  Description

F11ZPF 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 routine also returns a pointer array ISTR to the starting address of each row in $A$.

None.

## 5  Parameters

1:     N – INTEGERInput
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{N}}\ge 1$.
2:     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:     A($*$) – 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 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($*$) – 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:     ICOL($*$) – 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:     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.
${\mathbf{DUP}}=\text{'F'}$
The routine fails with ${\mathbf{IFAIL}}={\mathbf{3}}$ on detecting a duplicate.
Constraint: ${\mathbf{DUP}}=\text{'R'}$, $\text{'S'}$ or $\text{'F'}$.
7:     ZER – CHARACTER(1)Input
On entry: indicates how any elements with zero values in array A 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:     ISTR(${\mathbf{N}}+1$) – 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:     IWORK(N) – INTEGER arrayWorkspace
10:   IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{​ or ​}1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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).

## 6  Error Indicators and Warnings

If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, 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 ${\mathbf{DUP}}\ne \text{'R'}$, $\text{'S'}$ or $\text{'F'}$, or ${\mathbf{ZER}}\ne \text{'R'}$, $\text{'K'}$ or $\text{'F'}$.
${\mathbf{IFAIL}}=2$
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 have 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 $i=1,2,\dots ,{\mathbf{NNZ}}$.
${\mathbf{IFAIL}}=3$
On entry, ${\mathbf{DUP}}=\text{'F'}$ and nonzero elements have been supplied which have duplicate row and column indices.
${\mathbf{IFAIL}}=4$
On entry, ${\mathbf{ZER}}=\text{'F'}$ and at least one matrix element has been supplied with a zero coefficient value.

## 7  Accuracy

Not applicable.

The time taken for a call to F11ZPF 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 F11ZPF to reorder the nonzero elements, and outputs the original and the reordered representations.

### 9.1  Program Text

Program Text (f11zpfe.f90)

### 9.2  Program Data

Program Data (f11zpfe.d)

### 9.3  Program Results

Program Results (f11zpfe.r)