NAG Library Routine Document
M01CAF rearranges a vector of real numbers into ascending or descending order.
||M1, M2, IFAIL
M01CAF is based on Singleton's implementation of the ‘median-of-three’ Quicksort algorithm (see Singleton (1969)
), but with two additional modifications. First, small subfiles are sorted by an insertion sort on a separate final pass (see Sedgewick (1978)
). Second, if a subfile is partitioned into two very unbalanced subfiles, the larger of them is flagged for special treatment: before it is partitioned, its end points are swapped with two random points within it; this makes the worst case behaviour extremely unlikely.
Sedgewick R (1978) Implementing Quicksort programs Comm. ACM 21 847–857
Singleton R C (1969) An efficient algorithm for sorting with minimal storage: Algorithm 347 Comm. ACM 12 185–187
- 1: RV(M2) – REAL (KIND=nag_wp) arrayInput/Output
: elements M1
must contain real values to be sorted.
On exit: these values are rearranged into sorted order.
- 2: M1 – INTEGERInput
: the index of the first element of RV
to be sorted.
- 3: M2 – INTEGERInput
: the index of the last element of RV
to be sorted.
- 4: ORDER – CHARACTER(1)Input
, the values will be sorted into ascending (i.e., nondecreasing) order.
If , into descending order.
- 5: IFAIL – INTEGERInput/Output
must be set to
. 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
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
|On entry,||ORDER is not 'A' or 'D'.|
The average time taken by M01CAF is approximately proportional to , where . The worst case time is proportional to but this is extremely unlikely to occur.
This example reads a list of real numbers and sorts them into ascending order.
9.1 Program Text
Program Text (m01cafe.f90)
9.2 Program Data
Program Data (m01cafe.d)
9.3 Program Results
Program Results (m01cafe.r)