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 reordering routines
m01eaf,
m01ebf,
m01ecf and
m01edf.) Given a vector IRANK which specifies the ranks of the data (as generated by the routines
m01daf,
m01dbf,
m01dcf,
m01def,
m01dff,
m01djf,
m01dkf and
m01dzf),
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 must be left in place;
- items and must be interchanged;
- items , , and must be moved right one place round the cycle.
The complete rearrangement can be achieved by the following
code:
do k = m1, m2
i = icycl(k)
if (i < 0) then
j = -i
else
[swap items i and j]
end if
end do
None.
If on entry
or
, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
Not applicable.
Background information to multithreading can be found in the
Multithreading documentation.
None.
This example reads a matrix of real numbers and rearranges its columns so that the elements of the
th row are in ascending order. To do this, the program first calls
m01djf to rank the elements of the
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
is read from the data file.