nag_sort_intmat_rank_columns (m01dk) ranks columns n1 to n2 of a matrix, using the data in rows m1 to m2 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

m1 + 1

, and so on up to row m2.

nag_sort_intmat_rank_columns (m01dk) 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 columns 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: $im (ldm, n2)$ – int64int32nag_int array: ldm, the first dimension of the array, must satisfy the constraint $ldm \geq m2$ .
Rows m1 to m2 of columns n1 to n2 of im must contain integer data to be ranked.
2: $m1$ – int64int32nag_int scalar: The index of the first row of im to be used.

Constraint: $m1 > 0$ .
3: $n1$ – int64int32nag_int scalar: The index of the first column of im to be ranked.

Constraint: $n1 > 0$ .
4: $order$ – string (length ≥ 1): If $order ='A'$ , the columns 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 first dimension of the array im.
The index of the last row of im to be used.

Constraint: $m2 \geq m1$ .
2: $n2$ – int64int32nag_int scalar: Default: the second dimension of the array im.
The index of the last column of im to be ranked.

Constraint: $n2 \geq n1$ .

Output Parameters

1: $irank (n2)$ – int64int32nag_int array: Elements n1 to n2 of irank contain the ranks of the corresponding columns of im. Note that the ranks are in the range n1 to n2: thus, if the $i$ th column of im is the first in the rank order, $irank (i)$ is set to n1.
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:

$ifail = 1$

On entry,	$m2 < 1$ ,
or	$n2 < 1$ ,
or	$m1 < 1$ ,
or	$m1 > m2$ ,
or	$n1 < 1$ ,
or	$n1 > n2$ ,
or	$ldm < m2$ .

$ifail = 2$

On entry,

order is not 'A' or 'D'.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

The average time taken by the function is approximately proportional to

n \times \log (n)

, where

n = n2 - n1 + 1

Example

This example reads a matrix of integers and ranks the columns in descending order.

Open in the MATLAB editor: m01dk_example

function m01dk_example


fprintf('m01dk example results\n\n');

im = [int64(5),4,3,2,2,1,9,4,4,2,2,1;
               3,8,2,5,5,6,9,8,9,5,4,1;
               9,1,6,1,2,4,8,1,2,2,6,2];

m1 = int64(1);
n1 = int64(1);
order = 'Descending';

[irank, ifail] = m01dk( ...
                        im, m1, n1, order);

fprintf('Data\n');
for i = 1:size(im,1)
  fprintf('%5d',im(i,:));
  fprintf('\n');
end
fprintf('\nRanks\n');
fprintf('%5d',irank);
fprintf('\n');

m01dk example results

Data
    5    4    3    2    2    1    9    4    4    2    2    1
    3    8    2    5    5    6    9    8    9    5    4    1
    9    1    6    1    2    4    8    1    2    2    6    2

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

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox