# NAG FL Interfacef11zpf (complex_​herm_​sort)

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## 1Purpose

f11zpf sorts the nonzero elements of a sparse complex Hermitian matrix, represented in symmetric coordinate storage format.

## 2Specification

Fortran Interface
 Subroutine f11zpf ( 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 <nag.h>
 void f11zpf_ (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)
The routine may be called by the names f11zpf or nagf_sparse_complex_herm_sort.

## 3Description

f11zpf takes a symmetric coordinate storage (SCS) representation (see Section 2.1.2 in the F11 Chapter Introduction) of a sparse $n×n$ 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.
f11zpf also returns a pointer array istr to the starting address of each row in $A$.

None.

## 5Arguments

1: $\mathbf{n}$Integer Input
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: $\mathbf{a}\left(*\right)$Complex (Kind=nag_wp) array Input/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: $\mathbf{irow}\left(*\right)$Integer array Input/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 array Input/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: $1\le {\mathbf{icol}}\left(\mathit{i}\right)\le {\mathbf{irow}}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,{\mathbf{nnz}}$.
On exit: the first nnz elements contain the column indices corresponding to the 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 array Output
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 array Workspace
10: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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, ${\mathbf{dup}}=⟨\mathit{\text{value}}⟩$.
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, $\mathit{I}=⟨\mathit{\text{value}}⟩$, ${\mathbf{icol}}\left(\mathit{I}\right)=⟨\mathit{\text{value}}⟩$ and ${\mathbf{irow}}\left(\mathit{I}\right)=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{icol}}\left(\mathit{I}\right)\ge 1$ and ${\mathbf{icol}}\left(\mathit{I}\right)\le {\mathbf{irow}}\left(\mathit{I}\right)$.
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 $\mathit{J}$: $\mathit{I}=⟨\mathit{\text{value}}⟩$, $\mathit{J}=⟨\mathit{\text{value}}⟩$.
${\mathbf{ifail}}=-99$
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

Not applicable.

## 8Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f11zpf is not threaded in any implementation.

The time taken for a call to f11zpf 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 f11zpf, specifying that duplicates should be summed.

## 10Example

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.

### 10.1Program Text

Program Text (f11zpfe.f90)

### 10.2Program Data

Program Data (f11zpfe.d)

### 10.3Program Results

Program Results (f11zpfe.r)