\par
\subsection{Sorting routines}
\label{subsection:Utilities:proto:sort}
\par
\subsubsection{Validation routines}
\label{subsubsection:Utilities:proto:sort:validate}
\par
%=======================================================================
\begin{enumerate}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int IVisascending ( int n, int ivec[] ) ;
int IVisdescending ( int n, int ivec[] ) ;
\end{verbatim}
\index{IVisascending@{\tt IVisascending()}}
\index{IVisdescending@{\tt IVisdescending()}}
These methods returns {\tt 1} if the array {\tt ivec[]} is in ascending
or descending order and returns {\tt 0} otherwise.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int DVisascending ( int n, double dvec[] ) ;
int DVisdescending ( int n, double dvec[] ) ;
\end{verbatim}
\index{DVisascending@{\tt DVisascending()}}
\index{DVisdescending@{\tt DVisdescending()}}
These methods returns {\tt 1} if the array {\tt dvec[]} is in ascending
or descending order and returns {\tt 0} otherwise.
%-----------------------------------------------------------------------
\end{enumerate}
\par
\subsubsection{Insert sort routines}
\label{subsubsection:Utilities:proto:sort:insert}
\par
%=======================================================================
\begin{enumerate}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IVisortUp ( int n, int ivec[] ) ;
void IVisortDown ( int n, int ivec[] ) ;
\end{verbatim}
\index{IVisortUp@{\tt IVisortUp()}}
\index{IVisortDown@{\tt IVisortDown()}}
These methods sort an {\tt int} array into ascending or descending
order using an insertion sort.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IV2isortUp ( int n, int ivec1[], int ivec2[] ) ;
void IV2isortDown ( int n, int ivec1[], int ivec2[] ) ;
\end{verbatim}
\index{IV2isortUp@{\tt IV2isortUp()}}
\index{IV2isortDown@{\tt IV2isortDown()}}
These methods sort the array {\tt ivec1[]} into ascending or
descending order using an insertion sort and permutes 
the {\tt int} companion array {\tt ivec2[]} in the same fashion.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IVDVisortUp ( int n, int ivec[], double dvec[] ) ;
void IVDVisortDown ( int n, int ivec[], double dvec[] ) ;
\end{verbatim}
\index{IVDVisortUp@{\tt IVDVisortUp()}}
\index{IVDVisortDown@{\tt IVDVisortDown()}}
This sorts the array {\tt ivec[]} into ascending or descending order 
using an insertion sort and permutes the companion array {\tt dvec[]}
in the same fashion.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IV2DVisortUp ( int n, int ivec1[], int ivec2[], double dvec[] ) ;
void IV2DVisortDown ( int n, int ivec1[], int ivec2[], double dvec[] ) ;
\end{verbatim}
\index{IV2DVisortUp@{\tt IV2DVisortUp()}}
\index{IV2DVisortDown@{\tt IV2DVisortDown()}}
These methods sort the array {\tt ivec1[]} into ascending or
descending order using an insertion sort and permutes 
the {\tt int} and {\tt double} companion array
{\tt ivec2[]} and {\tt dvec[]} in the same fashion.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IVZVisortUp ( int n, int ivec[], double dvec[] ) ;
void IVZVisortDown ( int n, int ivec[], double dvec[] ) ;
\end{verbatim}
\index{IVZVisortUp@{\tt IVZVisortUp()}}
\index{IVZVisortDown@{\tt IVZVisortDown()}}
This sorts the array {\tt ivec[]} into ascending or descending order 
using an insertion sort and permutes the double precision complex
companion array {\tt dvec[]} in the same fashion.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IV2ZVisortUp ( int n, int ivec1[], int ivec2[], double dvec[] ) ;
void IV2ZVisortDown ( int n, int ivec1[], int ivec2[], double dvec[] ) ;
\end{verbatim}
\index{IV2ZVisortUp@{\tt IV2ZVisortUp()}}
\index{IV2ZVisortDown@{\tt IV2ZVisortDown()}}
These methods sort the array {\tt ivec1[]} into ascending 
or descending order 
using an insertion sort and permutes the companion arrays
{\tt ivec2[]} and {\tt dvec[]} in the same fashion.
The {\tt dvec[]} array is double precision complex.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void DVisortUp ( int n, double dvec[] ) ;
void DVisortDown ( int n, double dvec[] ) ;
\end{verbatim}
\index{DVisortUp@{\tt DVisortUp()}}
\index{DVisortDown@{\tt DVisortDown()}}
These methods sort a {\tt double} array into ascending 
or descending order using an insertion sort.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void DV2isortUp ( int n, double dvec1[], double dvec2[] ) ;
void DV2isortDown ( int n, double dvec1[], double dvec2[] ) ;
\end{verbatim}
\index{DV2isortUp@{\tt DV2isortUp()}}
\index{DV2isortDown@{\tt DV2isortDown()}}
These methods sort the array {\tt dvec1[]} into ascending or
descending order 
using an insertion sort and permutes the companion array {\tt dvec2[]}
in the same fashion.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void DVIVisortUp ( int n, double dvec[], int ivec[] ) ;
void DVIVisortDown ( int n, double dvec[], int ivec[] ) ;
\end{verbatim}
\index{DVIVisortUp@{\tt DVIVisortUp()}}
\index{DVIVisortDown@{\tt DVIVisortDown()}}
These methods sort the array {\tt dvec[]} into ascending or
descending order using an insertion sort and permutes 
the companion array {\tt ivec[]} in the same fashion.
%-----------------------------------------------------------------------
\end{enumerate}
\par
\subsubsection{Quicksort routines}
\label{subsubsection:Utilities:proto:sort:quicksort}
\par
%=======================================================================
\begin{enumerate}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IVqsortUp ( int n, int ivec[] ) ;
void IVqsortDown ( int n, int ivec[] ) ;
\end{verbatim}
\index{IVqsortUp@{\tt IVqsortUp()}}
\index{IVqsortDown@{\tt IVqsortDown()}}
These methods sort an {\tt int} array into ascending or descending
order using a quick sort.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IV2qsortUp ( int n, int ivec1[], int ivec2[] ) ;
void IV2qsortDown ( int n, int ivec1[], int ivec2[] ) ;
\end{verbatim}
\index{IV2qsortUp@{\tt IV2qsortUp()}}
\index{IV2qsortDown@{\tt IV2qsortDown()}}
These methods sort the array {\tt ivec1[]} into ascending or
descending order using a quick sort and permutes 
the companion array {\tt ivec2[]} in the same fashion.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IVDVqsortUp ( int n, int ivec[], double dvec[] ) ;
void IVDVqsortDown ( int n, int ivec[], double dvec[] ) ;
\end{verbatim}
\index{IVDVqsortUp@{\tt IVDVqsortUp()}}
\index{IVDVqsortDown@{\tt IVDVqsortDown()}}
These methods sort the array {\tt ivec[]} into ascending or
descending order using a quick sort and permutes 
the companion array {\tt dvec[]} in the same fashion.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IV2DVqsortUp ( int n, int ivec1[], int ivec2[], double dvec[] ) ;
void IV2DVqsortDown ( int n, int ivec1[], int ivec2[], double dvec[] ) ;
\end{verbatim}
\index{IV2DVqsortUp@{\tt IV2DVqsortUp()}}
\index{IV2DVqsortDown@{\tt IV2DVqsortDown()}}
These methods sort the array {\tt ivec1[]} into ascending 
or descending order using a quick sort and permutes the companion arrays
{\tt ivec2[]} and {\tt dvec[]} in the same fashion.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IVZVqsortUp ( int n, int ivec[], double dvec[] ) ;
void IVZVqsortDown ( int n, int ivec[], double dvec[] ) ;
\end{verbatim}
\index{IVZVqsortUp@{\tt IVZVqsortUp()}}
\index{IVZVqsortDown@{\tt IVZVqsortDown()}}
These methods sort the array {\tt ivec[]} into ascending or
descending order using a quick sort and permutes 
the double precision complex companion array 
{\tt dvec[]} in the same fashion.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void IV2ZVqsortUp ( int n, int ivec1[], int ivec2[], double dvec[] ) ;
void IV2ZVqsortDown ( int n, int ivec1[], int ivec2[], double dvec[] ) ;
\end{verbatim}
\index{IV2ZVqsortUp@{\tt IV2ZVqsortUp()}}
\index{IV2ZVqsortDown@{\tt IV2ZVqsortDown()}}
These methods sort the array {\tt ivec1[]} into ascending 
or descending order using a quick sort and permutes the companion arrays
{\tt ivec2[]} and {\tt dvec[]} in the same fashion.
The {\tt dvec[]} array is double precision complex.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void DVqsortUp ( int n, double dvec[] ) ;
void DVqsortDown ( int n, double dvec[] ) ;
\end{verbatim}
\index{DVqsortUp@{\tt DVqsortUp()}}
\index{DVqsortDown@{\tt DVqsortDown()}}
Thes methods sort a {\tt double} array into ascending or
descending order using a quick sort.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void DV2qsortUp ( int n, double dvec1[], double dvec2[] ) ;
void DV2qsortDown ( int n, double dvec1[], double dvec2[] ) ;
\end{verbatim}
\index{DV2qsortUp@{\tt DV2qsortUp()}}
\index{DV2qsortDown@{\tt DV2qsortDown()}}
These methods sort the array {\tt dvec1[]} into ascending or
descending order using a quick sort and permutes 
the companion array {\tt dvec2[]} in the same fashion.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
void DVIVqsortUp ( int n, double dvec[], int ivec[] ) ;
void DVIVqsortDown ( int n, double dvec[], int ivec[] ) ;
\end{verbatim}
\index{DVIVqsortUp@{\tt DVIVqsortUp()}}
\index{DVIVqsortDown@{\tt DVIVqsortDown()}}
These methods sort the array {\tt dvec[]} into ascending or
descending order using a quick sort and permutes 
the companion array {\tt ivec[]} in the same fashion.
%-----------------------------------------------------------------------
\end{enumerate}
\par
\subsection{Sort and compress routines}
\label{subsection:Utilities:proto:sortAndCompress}
\par
%=======================================================================
\begin{enumerate}
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int IVsortUpAndCompress ( int n, int ivec[] ) ;
\end{verbatim}
\index{IVsortUpAndCompress@{\tt IVsortUpAndCompress()}}
This method sorts {\tt ivec[]} into ascending order,
and removes (compresses) any duplicate entries.
The return value is the number of unique entries
stored in the leading locations of the vector {\tt ivec[]}.
\par \noindent {\it Error checking:}
If {\tt n < 0} or {\tt ivec} is {\tt NULL},
an error message is printed and the program exits.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int IVDVsortUpAndCompress ( int n, int ivec[], double dvec[] ) ;
\end{verbatim}
\index{IVDVsortUpAndCompress@{\tt IVDVsortUpAndCompress()}}
This method sorts {\tt ivec[]} into ascending order with {\tt dvec[]} 
as a companion vector.
It then compresses the pairs, adding the {\tt dvec[]} entries
together when their {\tt ivec[]} values are identical.
The return value is the number of unique entries stored in the 
leading locations of the vectors {\tt ivec[]} and {\tt dvec[]}.
\par \noindent {\it Error checking:}
If {\tt n < 0},
or if {\tt ivec} or {\tt dvec} is {\tt NULL},
an error message is printed and the program exits.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int IVZVsortUpAndCompress ( int n, int ivec[], double dvec[] ) ;
\end{verbatim}
\index{IVZVsortUpAndCompress@{\tt IVZVsortUpAndCompress()}}
This method sorts {\tt ivec[]} into ascending order with the
double precision complex {\tt dvec[]} companion vector.
It then compresses the pairs, adding the complex {\tt dvec[]} entries
together when their {\tt ivec[]} values are identical.
The return value is the number of unique entries stored in the 
leading locations of the vectors {\tt ivec[]} and {\tt dvec[]}.
\par \noindent {\it Error checking:}
If {\tt n < 0},
or if {\tt ivec} or {\tt dvec} is {\tt NULL},
an error message is printed and the program exits.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int IV2sortUpAndCompress ( int n, int ivec1[], int ivec2[] ) ;
\end{verbatim}
\index{IV2sortUpAndCompress@{\tt IV2sortUpAndCompress()}}
This method sorts {\tt ivec1[]} into ascending order 
with {\tt ivec2[]} as a companion vector.
It then compresses the pairs, dropping all but one of identical pairs.
The return value is the number of unique entries stored in the 
leading locations of the vectors {\tt ivec1[]} and {\tt ivec2[]}.
\par \noindent {\it Error checking:}
If {\tt n < 0},
or if {\tt ivec1} or {\tt ivec2} is {\tt NULL},
an error message is printed and the program exits.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int IV2DVsortUpAndCompress ( int n, int ivec1[], int ivec2[], double dvec[] ) ;
\end{verbatim}
\index{IV2DVsortUpAndCompress@{\tt IV2DVsortUpAndCompress()}}
This method sorts {\tt ivec1[]} into ascending order 
with {\tt ivec2[]} and {\tt dvec[]} as companion vectors.
It then compresses the pairs, summing the {\tt dvec[]} entries for
identical {\tt (ivec1[], ivec2[])} pairs.
The return value is the number of unique entries stored in the 
leading locations of the vectors {\tt ivec1[]}, {\tt ivec2[]}
and {\tt dvec[]}.
\par \noindent {\it Error checking:}
If {\tt n < 0},
or if {\tt ivec1}, {\tt ivec2} or {\tt dvec} is {\tt NULL},
an error message is printed and the program exits.
%-----------------------------------------------------------------------
\item
\begin{verbatim}
int IV2ZVsortUpAndCompress ( int n, int ivec1[], int ivec2[], double dvec[] ) ;
\end{verbatim}
\index{IV2ZVsortUpAndCompress@{\tt IV2ZVsortUpAndCompress()}}
This method sorts {\tt ivec1[]} into ascending order 
with {\tt ivec2[]} and the double precision {\tt dvec[]} 
as companion vectors.
It then compresses the pairs, summing the complex {\tt dvec[]} entries 
for identical {\tt (ivec1[], ivec2[])} pairs.
The return value is the number of unique entries stored in the 
leading locations of the vectors {\tt ivec1[]}, {\tt ivec2[]}
and {\tt dvec[]}.
\par \noindent {\it Error checking:}
If {\tt n < 0},
or if {\tt ivec1}, {\tt ivec2} or {\tt dvec} is {\tt NULL},
an error message is printed and the program exits.
%-----------------------------------------------------------------------
\end{enumerate}