M01ZCF decomposes a permutation into cycles, as an aid to reordering ranked data.
M01ZCF is provided as an aid to reordering arbitrary data structures without using additional storage. However, you should consider carefully whether it is necessary to rearrange yourr data, or whether it would be simpler and more efficient to refer to the data in sorted order using an index vector, or to create a copy of the data in sorted order.
To rearrange data into a different order without using additional storage, the simplest method is to decompose the permutation which specifies the new order into cycles and then to do a cyclic permutation of the data items in each cycle. (This is the method used by the M01E reordering routines.) Given a vector IRANK which specifies the ranks of the data (as generated by the M01D routines), M01ZCF generates a new vector
ICYCL, in which the permutation is represented in its component cycles, with the first element of each cycle negated. For example, the permutation
is composed of the cycles
and the vector
ICYCL generated by M01ZCF contains
In order to rearrange the data according to the specified ranks:
- item $6$ must be left in place;
- items $1$ and $5$ must be interchanged;
- items $4$, $2$, $7$ and $3$ must be moved right one place round the cycle.
The complete rearrangement can be achieved by the following code:
DO 10 K = M1, M2
I = ICYCL(K)
IF (I.LT.0) THEN
J = -I
ELSE
[swap items I and J]
ENDIF
10 CONTINUE
None.
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).
If
${\mathbf{IFAIL}}={\mathbf{2}}$ or
${\mathbf{3}}$, elements
M1 to
M2 of
IPERM do not contain a permutation of the integers
M1 to
M2.
Not applicable.
Not applicable.
None.
This example reads a matrix of real numbers and rearranges its columns so that the elements of the
$l$th row are in ascending order. To do this, the program first calls
M01DJF to rank the elements of the
$l$th row, and then calls M01ZCF to decompose the rank vector into cycles. It then rearranges the columns using the framework of code suggested in
Section 3. The value of
$l$ is read from the data file.