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NAG Toolbox: nag_sort_realvec_rank (m01da)

Purpose

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

Syntax

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

Description

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 1010. The ranking is stable: equal elements preserve their ordering in the input data.

References

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

Parameters

Compulsory Input Parameters

1:     rv(m2) – double array
m2, the dimension of the array, must satisfy the constraint m2m1m2m1.
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 > 0m1>0.
3:     order – string (length ≥ 1)
If order = 'A'order='A', the values will be ranked in ascending (i.e., nondecreasing) order.
If order = 'D'order='D', into descending order.
Constraint: order = 'A'order='A' or 'D''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: m2m1m2m1.

Input Parameters Omitted from the MATLAB Interface

None.

Output Parameters

1:     irank(m2) – 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 rv(i)rvi is the first element in the rank order, irank(i)iranki is set to m1.
2:     ifail – int64int32nag_int scalar
ifail = 0ifail=0 unless the function detects an error (see [Error Indicators and Warnings]).

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
On entry,m2 < 1m2<1,
orm1 < 1m1<1,
orm1 > m2m1>m2.
  ifail = 2ifail=2
On entry,order is not 'A' or 'D'.

Accuracy

Not applicable.

Further Comments

The average time taken by the function is approximately proportional to n × log(n)n×log(n), where n = m2m1 + 1n=m2-m1+1.

Example

function nag_sort_realvec_rank_example
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] = nag_sort_realvec_rank(rv, m1, order)
 

irank =

                    7
                    6
                   10
                    2
                    8
                   12
                    3
                    4
                   11
                    5
                    1
                    9


ifail =

                    0


function m01da_example
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)
 

irank =

                    7
                    6
                   10
                    2
                    8
                   12
                    3
                    4
                   11
                    5
                    1
                    9


ifail =

                    0



PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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