NAG Library Routine Document
M01DEF ranks the rows of a matrix of real numbers in ascending or descending order.
||LDM, M1, M2, N1, N2, IRANK(M2), IFAIL
M01DEF ranks rows M1
of a matrix, using the data in columns N1
of those rows. The ordering is determined by first ranking the data in column N1
, then ranking any tied rows according to the data in column
, and so on up to column N2
M01DEF 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 rows preserve their ordering in the input data.
Knuth D E (1973) The Art of Computer Programming (Volume 3) (2nd Edition) Addison–Wesley
- 1: RM(LDM,N2) – REAL (KIND=nag_wp) arrayInput
: columns N1
of rows M1
must contain real data to be ranked.
- 2: LDM – INTEGERInput
: the first dimension of the array RM
as declared in the (sub)program from which M01DEF is called.
- 3: M1 – INTEGERInput
: the index of the first row of RM
to be ranked.
- 4: M2 – INTEGERInput
: the index of the last row of RM
to be ranked.
- 5: N1 – INTEGERInput
: the index of the first column of RM
to be used.
- 6: N2 – INTEGERInput
: the index of the last column of RM
to be used.
- 7: ORDER – CHARACTER(1)Input
, the rows will be ranked in ascending (i.e., nondecreasing) order.
If , into descending order.
- 8: IRANK(M2) – INTEGER arrayOutput
: elements M1
contain the ranks of the corresponding rows of RM
. Note that the ranks are in the range M1
: thus, if the
th row of RM
is the first in the rank order,
is set to M1
- 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 real numbers and ranks the rows in ascending order.
9.1 Program Text
Program Text (m01defe.f90)
9.2 Program Data
Program Data (m01defe.d)
9.3 Program Results
Program Results (m01defe.r)