## The module "mat2multi" of the Mastrave modelling library

Daniele de Rigo

The file mat2multi.m is part of Mastrave.

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#### Function declaration

multi_array = mat2multi( matrix, dim, siz )



#### Description

Some functions are defined for matrices but not for multidimensional arrays (md-arrays). mat2multi allows to create md-arrays from matrices which can be processed even with ill-expandable functions operating column by column. This is done without using explicit loops, which would be interpreted and possibly inefficient loops. Column-wise operations by default apply to the columns of a matrix as if the matrix were a vector of column vectors. This class of functions includes reductions (in the APL sense) such as sum(.), prod(.); and scans (in the APL sense) such as cumsum(.), cumprod(.). The aforementioned basic functions extend to md-arrays, however some user-defined functions may not allow the same. mat2multi converts a matrix of size:.
[ n dim prod([n1 .. n dim -1 n dim +1 nk]) ] into a k-dimensional array multi_array of size siz :
[ n1 ... n dim ... nk ] as if multi_array were a collection of vectors having n dim elements each and being stored in the nd-array along its dim dimension.

The function multi2mat can produce from a given md-array a matrix suitable to be reversed by mat2multi.

#### Input arguments


matrix            ::matrix,!sparse::
Numeric, charachter or cell-array matrix (whose number
of dimensions cannot exceed 2).

dim               ::scalar_natural_nonzero::
Dimension of  multi_array  to which each  matrix
column vector must belong.

siz               ::numel,row_vector::
Vector whose elements are the desired cardinality of
each dimension of  multi_array .



#### Example of usage


% Basic usage:
mda     = zeros( 3, 4, 2);
mda(:)  = 1:numel( mda )

% 4x2 vectors of 3 elements each
dim     = 1
multi2mat( mda , dim )

% 3x2 vectors of 4 elements each
dim     = 2
multi2mat( mda , dim )

% 3x4 vectors of 2 elements each
dim     = 3
multi2mat( mda , dim )

% Reverse the conversion:
[ mat , siz ] = multi2mat( mda , dim );
mat2multi( mat , dim , siz )

% Scan example using cumsum:
scan1   = cumsum( mda , dim )
scan2   = mat2multi( cumsum( mat , 1 ) , dim , siz )
scan1  == scan2

% Reduction example using sum:
red1    = sum( mda , dim )
red_siz = siz; red_siz( dim ) = 1
red2    = mat2multi( sum( mat , 1 ) , dim , red_siz )
red1   == red2


See also:
multi2mat, mdeal

Keywords:
multidimensional-array, smart reshape, column-wise

Version: 0.2.5

#### 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