## The module "sortable2index" of the Mastrave modelling library

Daniele de Rigo

The file sortable2index.m is part of Mastrave.

Mastrave is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

Mastrave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Mastrave. If not, see http://www.gnu.org/licenses/.

#### Function declaration

[ indices, cardinality, glossary, freqs ] =
sortable2index( sortable               ,
mode     = 'ascending' )



#### Description

Floating point values and cells of strings can be sorted but not used as indices. @sortable2index remaps (total-ordered) sortable collections into positive integers preserving their order. In case of sparse matrices, the mapping replaces only nonzeros. Each index of indices represents an element of sortable which may occur several times in sortable . To each occurrence of the same value corresponds the same index -- as a consequence total ordering in sorting elements is required to preserve bijectivity between values and indices (e.g. despite ::sortable::, complex numbers are not ::tsortable:: allowing only partial ordering and therefore they cannot be indexed by this function). The set of these correspondences is returned in the vector or cell of strings glossary , whose length is the cardinality of the indices set. The number of occurrences of sortable elements which correspond to each index is returned by freqs . The particular way in which indices are generates can be governed using the optional mode input argument (if omitted, its default value is 'ascending').

If sortable elements are all (cell-arrays of) strings or of real numbers, you may consider to use instead of this function its specialized versions which respectively are @cellstr2index and @real2index .

#### Input arguments


sortable                ::tsortable::
Cell array of strings or numerical matrix.

mode                    ::string::
Criterion for generating indices from
sortable . (Default: 'ascending').
Valid modes are:

mode      │      meaning
───────────────┼─────────────────────────────────
'ascending' │ Indices are generated by
'--ascending' │ associating to each element of
│  sortable  the position of its
│ first occurrence in the set of
│  sortable  elements sorted in
│ ascending order.
───────────────┼─────────────────────────────────
'descending' │ Indices are generated by
'--descending' │ associating to each element of
│  sortable  the position of its
│ first occurrence in the set of
│  sortable  elements sorted in
│ descending order.
───────────────┼─────────────────────────────────
'forward'   │ Indices are generated by
'--forward'   │ associating to each element of
│  sortable  the position of its
│ first occurrence in the set of
│  sortable  elements.
───────────────┼─────────────────────────────────
'backward'  │ Indices are generated by
'--backward'  │ associating to each element of
│  sortable  the position of its
│ first occurrence in the set of
│  sortable  elements listed
│ in reverse order.
───────────────┼─────────────────────────────────
'random'    │ Indices are generated by
'--random'    │ associating to each element of
│  sortable  the position of its
│ first occurrence in the set of
│  sortable  elements randomly
│ shuffled.



#### Example of usage


% Behavior with different classes of  sortable
m{1}          = { 'foobar' , 'bar' , '' , 'quux' , 'foo' , 'bar' };
m{2}          = { 'foobar' };
m{3}          =   'foobar';
m{4}          = ceil( randn(1,15)*5 )/2;
m{4}([2 5])   = nan;
m{4}([4 8])   = inf;
m{4}([10])    = 0;
nulls_id      = find( 0 == m{4} )
rows          = ceil(rand(1,15)*1000)
cols          = ceil(rand(1,15)*10)
vals          = m{4}; vals(nulls_id)=-1
m{5}          = sparse( rows, cols, vals, 1100, 20 ); m{5}(10)=0;
m{6}          = { };
m{7}          = '';
m{8}          = [];
m{9}          = sparse(    0 ,  0 );
m{10}         = sparse( 1100 , 15 )
for i=1:numel(m)
fprintf( 1 , '\n\nm{%d} class is %s:\n', i , class(m{i}) );
disp( m{i} );
[idx, len, g] = sortable2index( m{i} )
end

% How  mode  affects the generated indices
idx           = sortable2index( m{4} , 'ascending'  )
idx           = sortable2index( m{4} , 'descending' )
idx           = sortable2index( m{4} , 'forward'    )
idx           = sortable2index( m{4} , 'backward'   )
idx           = sortable2index( m{4} , 'random'     )
idx           = sortable2index( m{4} , 'random'     )


See also:
real2index, cellstr2index, cell2sparse

Keywords:
conversion, cell-array, sortable, indices

Version: 0.4.1

#### Support

The Mastrave modelling library is committed to provide reusable and general - but also robust and scalable - modules for research modellers dealing with computational science.  You can help the Mastrave project by providing feedbacks on unexpected behaviours of this module.  Despite all efforts, all of us - either developers or users - (should) know that errors are unavoidable.  However, the free software paradigm successfully highlights that scientific knowledge freedom also implies an impressive opportunity for collectively evolve the tools and ideas upon which our daily work is based.  Reporting a problem that you found using Mastrave may help the developer team to find a possible bug.  Please, be aware that Mastrave is entirely based on voluntary efforts: in order for your help to be as effective as possible, please read carefully the section on reporting problems.  Thank you for your collaboration.

Copyright (C) 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 Daniele de Rigo