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

**Daniele de Rigo**

#### Copyright and license notice of the function mat2multi

Copyright © 2005,2006,2007,2008,2009,2010,2011 Daniele de Rigo

The file mat2multi.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

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

`of size`

**multi_array**`:`

**siz**`[ n1 ... n`as if

`... nk ]`**dim**`were a collection of vectors having n`

**multi_array**`elements each and being stored in the nd-array along its`

**dim**`dimension.`

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

#### Input arguments

matrixNumeric, charachter or cell-array matrix (whose number of dimensions cannot exceed 2).::matrix,!sparse::dimDimension of::scalar_natural_nonzero::to which eachmulti_arraycolumn vector must belong.matrixsizVector whose elements are the desired cardinality of each dimension of::numel,row_vector::.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.