# NAG Library Routine Document

## 1Purpose

m01eaf rearranges a vector of real numbers into the order specified by a vector of ranks.

## 2Specification

Fortran Interface
 Subroutine m01eaf ( rv, m1, m2,
 Integer, Intent (In) :: m1, m2 Integer, Intent (Inout) :: irank(m2), ifail Real (Kind=nag_wp), Intent (Inout) :: rv(m2)
#include nagmk26.h
 void m01eaf_ (double rv[], const Integer *m1, const Integer *m2, Integer irank[], Integer *ifail)

## 3Description

m01eaf is designed to be used typically in conjunction with the M01D ranking routines. After one of the M01D routines has been called to determine a vector of ranks, m01eaf can be called to rearrange a vector of real numbers into the rank order. If the vector of ranks has been generated in some other way, then m01zbf should be called to check its validity before m01eaf is called.

None.

## 5Arguments

1:     $\mathbf{rv}\left({\mathbf{m2}}\right)$ – Real (Kind=nag_wp) arrayInput/Output
On entry: elements m1 to m2 of rv must contain real values to be rearranged.
On exit: these values are rearranged into rank order. For example, if ${\mathbf{irank}}\left(i\right)={\mathbf{m1}}$, then the initial value of ${\mathbf{rv}}\left(i\right)$ is moved to ${\mathbf{rv}}\left({\mathbf{m1}}\right)$.
2:     $\mathbf{m1}$ – IntegerInput
3:     $\mathbf{m2}$ – IntegerInput
On entry: m1 and m2 must specify the range of the ranks supplied in irank and the elements of rv to be rearranged.
Constraint: $0<{\mathbf{m1}}\le {\mathbf{m2}}$.
4:     $\mathbf{irank}\left({\mathbf{m2}}\right)$ – Integer arrayInput/Output
On entry: elements m1 to m2 of irank must contain a permutation of the integers m1 to m2, which are interpreted as a vector of ranks.
On exit: used as internal workspace prior to being restored and hence is unchanged.
5:     $\mathbf{ifail}$ – 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, ${\mathbf{m2}}<1$, or ${\mathbf{m1}}<1$, or ${\mathbf{m1}}>{\mathbf{m2}}$.
${\mathbf{ifail}}=2$
Elements m1 to m2 of irank contain a value outside the range m1 to m2.
${\mathbf{ifail}}=3$
Elements m1 to m2 of irank contain a repeated 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.
If ${\mathbf{ifail}}={\mathbf{2}}$ or ${\mathbf{3}}$, elements m1 to m2 of irank do not contain a permutation of the integers m1 to m2. On exit, the contents of rv may be corrupted. To check the validity of irank without the risk of corrupting rv, use m01zbf.

Not applicable.

## 8Parallelism and Performance

m01eaf is not threaded in any implementation.

The average time taken by the routine is approximately proportional to $n$, where $n={\mathbf{m2}}-{\mathbf{m1}}+1$.

## 10Example

This example reads a matrix of real numbers and rearranges its rows so that the elements of the $k$th column are in ascending order. To do this, the program first calls m01daf to rank the elements of the $k$th column, and then calls m01eaf to rearrange each column into the order specified by the ranks. The value of $k$ is read from the datafile.

### 10.1Program Text

Program Text (m01eafe.f90)

### 10.2Program Data

Program Data (m01eafe.d)

### 10.3Program Results

Program Results (m01eafe.r)

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