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NAG Toolbox: nag_sort_realvec_rank (m01da)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_sort_realvec_rank (m01da) ranks a vector of double numbers in ascending or descending order.


[irank, ifail] = m01da(rv, m1, order, 'm2', m2)
[irank, ifail] = nag_sort_realvec_rank(rv, m1, order, 'm2', m2)


nag_sort_realvec_rank (m01da) uses a variant of list-merging, as described on pages 165–166 in Knuth (1973). The function 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 10. The ranking is stable: equal elements preserve their ordering in the input data.


Knuth D E (1973) The Art of Computer Programming (Volume 3) (2nd Edition) Addison–Wesley


Compulsory Input Parameters

1:     rvm2 – double array
Elements m1 to m2 of rv must contain double values to be ranked.
2:     m1 int64int32nag_int scalar
The index of the first element of rv to be ranked.
Constraint: m1>0.
3:     order – string (length ≥ 1)
If order='A', the values will be ranked in ascending (i.e., nondecreasing) order.
If order='D', into descending order.
Constraint: order='A' or 'D'.

Optional Input Parameters

1:     m2 int64int32nag_int scalar
Default: the dimension of the array rv.
The index of the last element of rv to be ranked.
Constraint: m2m1.

Output Parameters

1:     irankm2 int64int32nag_int array
Elements m1 to m2 of irank contain the ranks of the corresponding elements of rv. Note that the ranks are in the range m1 to m2: thus, if rvi is the first element in the rank order, iranki is set to m1.
2:     ifail int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:
On entry,m2<1,
On entry,order is not 'A' or 'D'.
An unexpected error has been triggered by this routine. Please contact NAG.
Your licence key may have expired or may not have been installed correctly.
Dynamic memory allocation failed.


Not applicable.

Further Comments

The average time taken by the function is approximately proportional to n×logn, where n=m2-m1+1.


This example reads a list of double numbers and ranks them in ascending order.
function m01da_example

fprintf('m01da example results\n\n');

rv = [5.3     4.6     7.8     1.7     5.3     9.9 ...
      3.2     4.3     7.8     4.5     1.2     7.6];

m1 = int64(1);
order = 'Ascending';
[irank, ifail] = m01da(rv, m1, order);

fprintf('   Data   Ranks\n\n');
for i = 1:numel(rv)

m01da example results

   Data   Ranks

    5.3      7
    4.6      6
    7.8     10
    1.7      2
    5.3      8
    9.9     12
    3.2      3
    4.3      4
    7.8     11
    4.5      5
    1.2      1
    7.6      9

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Chapter Introduction
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