# NAG Library Routine Document

## 1Purpose

m01dzf ranks arbitrary data according to a user-supplied comparison routine.

## 2Specification

Fortran Interface
 Subroutine m01dzf ( m1, m2,
 Integer, Intent (In) :: m1, m2 Integer, Intent (Inout) :: ifail Integer, Intent (Out) :: irank(m2) Logical, External :: compar
#include nagmk26.h
 void m01dzf_ (logical (NAG_CALL *compar)(const Integer *i, const Integer *j),const Integer *m1, const Integer *m2, Integer irank[], Integer *ifail)

## 3Description

m01dzf is a general purpose routine for ranking arbitrary data. m01dzf does not access the data directly; instead it calls compar to determine the relative ordering of any two data items. The data items are identified simply by an integer in the range m1 to m2.
m01dzf 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 $10$.

## 4References

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

## 5Arguments

1:     $\mathbf{compar}$ – Logical Function, supplied by the user.External Procedure
compar must specify the relative ordering of any two data items; it must return .TRUE. if item i must come strictly after item j in the rank ordering.
The specification of compar is:
Fortran Interface
 Function compar ( i, j)
 Logical :: compar Integer, Intent (In) :: i, j
#include nagmk26.h
 Nag_Boolean compar (const Integer *i, const Integer *j)
1:     $\mathbf{i}$ – IntegerInput
2:     $\mathbf{j}$ – IntegerInput
On entry: i and j identify the data items to be compared.
compar must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which m01dzf is called. Arguments denoted as Input must not be changed by this procedure.
2:     $\mathbf{m1}$ – IntegerInput
3:     $\mathbf{m2}$ – IntegerInput
On entry: m1 and m2 must specify the range of data items to be ranked, and the range of ranks to be assigned. Specifically, m01dzf ranks the data items identified by integers in the range m1 to m2, and assigns ranks in the range m1 to m2 which are stored in elements m1 to m2 of irank.
Constraint: $0<{\mathbf{m1}}\le {\mathbf{m2}}$.
4:     $\mathbf{irank}\left({\mathbf{m2}}\right)$ – Integer arrayOutput
On exit: elements m1 to m2 of irank contain the ranks of the data items m1 to m2. Note that the ranks are in the range m1 to m2: thus, if item $i$ is first in the rank ordering, ${\mathbf{irank}}\left(i\right)$ contains m1.
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 ${\mathbf{m1}}>{\mathbf{m2}}$.
${\mathbf{ifail}}=-99$
An unexpected error has been triggered by this routine. Please contact NAG.
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.

Not applicable.

## 8Parallelism and Performance

m01dzf is not threaded in any implementation.

The average time taken by the routine is approximately proportional to $n×\mathrm{log}\left(n\right)$, where $n={\mathbf{m2}}-{\mathbf{m1}}+1$; it will usually be dominated by the time taken in compar.

## 10Example

This example reads records, each of which contains an integer key and a real number. The program ranks the records first of all in ascending order of the integer key; records with equal keys are ranked in descending order of the real number if the key is negative, in ascending order of the real number if the key is positive, and in their original order if the key is zero. After calling m01dzf, the program calls m01zaf to convert the ranks to indices, and prints the records in rank order. Note the use of global variables to communicate the data between the main program and compar.

### 10.1Program Text

Program Text (m01dzfe.f90)

### 10.2Program Data

Program Data (m01dzfe.d)

### 10.3Program Results

Program Results (m01dzfe.r)

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