M01 Chapter Contents
M01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentM01DEF

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

M01DEF ranks the rows of a matrix of real numbers in ascending or descending order.

## 2  Specification

 SUBROUTINE M01DEF ( RM, LDM, M1, M2, N1, N2, ORDER, IRANK, IFAIL)
 INTEGER LDM, M1, M2, N1, N2, IRANK(M2), IFAIL REAL (KIND=nag_wp) RM(LDM,N2) CHARACTER(1) ORDER

## 3  Description

M01DEF ranks rows M1 to M2 of a matrix, using the data in columns N1 to N2 of those rows. The ordering is determined by first ranking the data in column N1, then ranking any tied rows according to the data in column ${\mathbf{N1}}+1$, and so on up to column N2.
M01DEF uses a variant of list-merging, as described on pages 165–166 in Knuth (1973). The routine takes advantage of natural ordering in the data, and uses a simple list insertion in a preparatory pass to generate ordered lists of length at least $10$. The ranking is stable: equal rows preserve their ordering in the input data.

## 4  References

Knuth D E (1973) The Art of Computer Programming (Volume 3) (2nd Edition) Addison–Wesley

## 5  Parameters

1:     RM(LDM,N2) – REAL (KIND=nag_wp) arrayInput
On entry: columns N1 to N2 of rows M1 to M2 of RM must contain real data to be ranked.
2:     LDM – INTEGERInput
On entry: the first dimension of the array RM as declared in the (sub)program from which M01DEF is called.
Constraint: ${\mathbf{LDM}}\ge {\mathbf{M2}}$.
3:     M1 – INTEGERInput
On entry: the index of the first row of RM to be ranked.
Constraint: ${\mathbf{M1}}>0$.
4:     M2 – INTEGERInput
On entry: the index of the last row of RM to be ranked.
Constraint: ${\mathbf{M2}}\ge {\mathbf{M1}}$.
5:     N1 – INTEGERInput
On entry: the index of the first column of RM to be used.
Constraint: ${\mathbf{N1}}>0$.
6:     N2 – INTEGERInput
On entry: the index of the last column of RM to be used.
Constraint: ${\mathbf{N2}}\ge {\mathbf{N1}}$.
7:     ORDER – CHARACTER(1)Input
On entry: if ${\mathbf{ORDER}}=\text{'A'}$, the rows will be ranked in ascending (i.e., nondecreasing) order.
If ${\mathbf{ORDER}}=\text{'D'}$, into descending order.
Constraint: ${\mathbf{ORDER}}=\text{'A'}$ or $\text{'D'}$.
8:     IRANK(M2) – INTEGER arrayOutput
On exit: elements M1 to M2 of IRANK contain the ranks of the corresponding rows of RM. Note that the ranks are in the range M1 to M2: thus, if the $i$th row of RM is the first in the rank order, ${\mathbf{IRANK}}\left(i\right)$ is set to M1.
9:     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 ${\mathbf{N2}}<1$, or ${\mathbf{M1}}<1$, or ${\mathbf{M1}}>{\mathbf{M2}}$, or ${\mathbf{N1}}<1$, or ${\mathbf{N1}}>{\mathbf{N2}}$, or ${\mathbf{LDM}}<{\mathbf{M2}}$.
${\mathbf{IFAIL}}=2$
 On entry, ORDER is not 'A' or 'D'.

## 7  Accuracy

Not applicable.

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

## 9  Example

This example reads a matrix of real numbers and ranks the rows in ascending order.

### 9.1  Program Text

Program Text (m01defe.f90)

### 9.2  Program Data

Program Data (m01defe.d)

### 9.3  Program Results

Program Results (m01defe.r)