NAG Library Routine Document

M01ZAF

The M01D routines generate ranks, and the M01E routines require ranks to be supplied to specify the reordering. However if it is desired simply to refer to the data in sorted order without actually reordering them, indices are more convenient than ranks (see the example in Section 9).

M01ZAF can be used to convert ranks to indices, or indices to ranks, as the two permutations are inverses of each another.

4 References

None.

5 Parameters

1: IPERM(M2) – INTEGER arrayInput/Output: On entry: elements M1 to M2 of IPERM must contain a permutation of the integers M1 to M2.

On exit: these elements contain the inverse permutation of the integers M1 to M2.
2: M1 – INTEGERInput
3: M2 – INTEGERInput: On entry: M1 and M2 must specify the range of elements used in the array IPERM and the range of values in the permutation, as specified under IPERM.
Constraint: $0 < M1 \leq M2$ .
4: IFAIL – INTEGERInput/Output: On entry: IFAIL must be set to $0$ , $- 1 or 1$ . 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 $- 1 or 1$ 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 $- 1 or 1$ is used it is essential to test the value of IFAIL on exit.

On exit: $IFAIL = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

IFAIL = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by X04AAF).

Errors or warnings detected by the routine:

$IFAIL = 1$

On entry,	$M2 < 1$ ,
or	$M1 < 1$ ,
or	$M1 > M2$ .

$IFAIL = 2$: Elements M1 to M2 of IPERM contain a value outside the range M1 to M2.

$IFAIL = 3$: Elements M1 to M2 of IPERM contain a repeated value.

IFAIL = 2

3

, elements M1 to M2 of IPERM do not contain a permutation of the integers M1 to M2; on exit these elements are usually corrupted. To check the validity of a permutation without the risk of corrupting it, use M01ZBF.

7 Accuracy

Not applicable.

8 Further Comments

None.

9 Example

This example reads a matrix of real numbers and prints its rows in ascending order as ranked by M01DEF. The program first calls M01DEF to rank the rows, and then calls M01ZAF to convert the rank vector to an index vector, which is used to refer to the rows in sorted order.

NAG Library Routine DocumentM01ZAF

+− Contents

1 Purpose

2 Specification

3 Description