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M01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentM01EDF

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

M01EDF rearranges a vector of complex numbers into the order specified by a vector of ranks.

## 2  Specification

 SUBROUTINE M01EDF ( CV, M1, M2, IRANK, IFAIL)
 INTEGER M1, M2, IRANK(M2), IFAIL COMPLEX (KIND=nag_wp) CV(M2)

## 3  Description

M01EDF 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, M01EDF can be called to rearrange a vector of complex 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 M01EDF is called.

None.

## 5  Parameters

1:     CV(M2) – COMPLEX (KIND=nag_wp) arrayInput/Output
On entry: elements M1 to M2 of CV must contain complex 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 ${\mathbf{CV}}\left(i\right)$ is moved to ${\mathbf{CV}}\left({\mathbf{M1}}\right)$.
2:     M1 – INTEGERInput
3:     M2 – INTEGERInput
On entry: M1 and M2 must specify the range of the ranks supplied in IRANK and the elements of CV to be rearranged.
Constraint: $0<{\mathbf{M1}}\le {\mathbf{M2}}$.
4:     IRANK(M2) – 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:     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, ${\mathbf{M2}}<1$, 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.
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 CV may be corrupted. To check the validity of IRANK without the risk of corrupting CV, use M01ZBF.

## 7  Accuracy

Not applicable.

The average time taken by the routine is approximately proportional to $n$, where $n={\mathbf{M2}}-{\mathbf{M1}}+1$.

## 9  Example

This example reads a matrix of complex numbers and rearranges its rows so that the elements in the $k$th column are in ascending order of modulus. To do this, the program first calls M01DAF to rank the moduli of the elements in the $k$th column, and then calls M01EDF to rearrange each column into the order specified by the ranks. The value of $k$ is read from the datafile.

### 9.1  Program Text

Program Text (m01edfe.f90)

### 9.2  Program Data

Program Data (m01edfe.d)

### 9.3  Program Results

Program Results (m01edfe.r)