NAG Library Routine Document
M01DKF ranks the columns of a matrix of integer numbers in ascending or descending order.
||IM(LDM,N2), LDM, M1, M2, N1, N2, IRANK(N2), IFAIL
M01DKF ranks columns N1
of a matrix, using the data in rows M1
of those columns. The ordering is determined by first ranking the data in row M1
, then ranking any tied columns according to the data in row
, and so on up to row M2
M01DKF 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
. The ranking is stable: equal columns preserve their ordering in the input data.
Knuth D E (1973) The Art of Computer Programming (Volume 3) (2nd Edition) Addison–Wesley
- 1: IM(LDM,N2) – INTEGER arrayInput
: rows M1
of columns N1
must contain integer data to be ranked.
- 2: LDM – INTEGERInput
: the first dimension of the array IM
as declared in the (sub)program from which M01DKF is called.
- 3: M1 – INTEGERInput
: the index of the first row of IM
to be used.
- 4: M2 – INTEGERInput
: the index of the last row of IM
to be used.
- 5: N1 – INTEGERInput
: the index of the first column of IM
to be ranked.
- 6: N2 – INTEGERInput
: the index of the last column of IM
to be ranked.
- 7: ORDER – CHARACTER(1)Input
, the columns will be ranked in ascending (i.e., nondecreasing) order.
If , into descending order.
- 8: IRANK(N2) – INTEGER arrayOutput
: elements N1
contain the ranks of the corresponding columns of IM
. Note that the ranks are in the range N1
: thus, if the
th column of IM
is the first in the rank order,
is set to N1
- 9: 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 the routine is approximately proportional to , where .
This example reads a matrix of integers and ranks the columns in descending order.
9.1 Program Text
Program Text (m01dkfe.f90)
9.2 Program Data
Program Data (m01dkfe.d)
9.3 Program Results
Program Results (m01dkfe.r)