The unchecked module "mat2multi_" of the Mastrave modelling library

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.

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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

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