Natural-Order Filename Sort

Natural-order sort of filenames or filepaths, with customizable numeric format.

To sort all of the strings in a cell array use NATSORT:
http://www.mathworks.com/matlabcentral/fileexchange/34464-customizable-natural-order-sort
To sort the rows of a cell array of strings use NATSORTROWS:
http://www.mathworks.com/matlabcentral/fileexchange/47433-natural-order-row-sort

### Summary ###

Alphanumeric sort of a cell array of strings (1xN char), where the strings are filenames or filepaths. Sorts the strings taking into account the values of any numeric substrings occurring within those strings. Compare for example:

A = {'a2.txt', 'a10.txt', 'a1.txt'};
sort(A)
ans = 'a1.txt' 'a10.txt' 'a2.txt'
natsortfiles(A)
ans = 'a1.txt' 'a2.txt' 'a10.txt'

By default NATSORTFILES simply treats all consecutive digits as integer values, however number recognition can be controlled by a regular expression: this allows decimal digits, +/- sign, exponent, binary, octal, or hexadecimal notation, and more. There are also options for controlling the sort direction and case sensitivity. See NATSORT for details.

NATSORTFILES does not perform a naive natural-order sort, but sorts the filenames and file extensions separately to ensure a dictionary sort, where shorter filenames always sort before longer ones. Likewise filepaths are split at each file-separator character, and each level of the file hierarchy is sorted separately.

### Example with DIR and Cell Array ###

D = 'C:\Test';
S = dir(fullfile(D,'*.txt'));
N = natsortfiles({S.name});
for k = 1:numel(N)
fullfile(D,N{k})
end

### File Dependency ###

The natural-order sort is provided by the function NATSORT (File Exchange 34464). All of NATSORT's optional inputs are also supported by NATSORTFILES, e.g.: to define a regular expression that matches the numeric substrings, select case sensitivity, etc.

### Explanation ###

The dot/period character has ASCII value 46, which means with a standard sort all of the characters with values 0:45 (including !"#$%&'()*+,- and space) will be sort before the period character. Because the period is used as the file separator character, applying a standard sort to filenames can result in some longer filenames sorting before shorter filenames, as shown here:

B = {'test_new.m'; 'test-old.m'; 'test.m'};
sort(B)
ans =
'test-old.m'
'test.m'
'test_new.m'

Sorting the filenames and file extensions separately allows the filenames to be sorted into dictionary order, with shorter names before longer names:

natsortfiles(B)
ans =
'test.m'
'test-old.m'
'test_new.m'

NATSORTFILES performs this together with a natural-order sort, so the values of any numeric substrings are also taken into account in the sort:

C = {'test2.m'; 'test10-old.m'; 'test.m'; 'test10.m'; 'test1.m'};
sort(C) % Wrong numeric order:
ans =
'test.m'
'test1.m'
'test10-old.m'
'test10.m'
'test2.m'
natsortfiles(C) % Correct numeric order, shorter names before longer:
ans =
'test.m'
'test1.m'
'test2.m'
'test10.m'
'test10-old.m'

### Filepaths Too! ###

This problems also affects filepaths, where the path separator character can affect the sort order. Without taking into account the file-separator character longer directory names can sort before shorter ones, and files and directories are mixed together:

D = {'A2-old\test.m';'A10\test.m';'A2\test.m';'A1archive.zip';'A1\test.m'};
sort(D) % Wrong numeric order, and '-' sorts before '\':
ans =
'A10\test.m'
'A1\test.m'
'A1archive.zip'
'A2-old\test.m'
'A2\test.m'

NATSORTFILES sorts shorter directory names sort before longer (just like a dictionary), and preserves the subdirectory hierarchy:

natsortfiles(D) % Shorter names before longer:
ans =
'A1archive.zip'
'A1\test.m'
'A2\test.m'
'A2-old\test.m'
'A10\test.m'

Because '\' is treated as a character, a naive sort mixes the subdirectory hierarchy, and longer directory names may come before shorter ones.