The unchecked module "multi2mat_" of the Mastrave modelling library
Copyright © 2005,2006,2007,2008,2009,2010,2011 Daniele de Rigo
The file multi2mat_.m is part of Mastrave.
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[ matrix, siz ] = multi2mat_( multi_array, dim )
Some functions are defined for matrices but not for multidimensional arrays
multi2mat_ allows to deal with md-arrays even with those ill-expandable
functions which operate 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. multi2mat_ converts a
k-dimensional array multi_array of size siz :
[ n1 ... n dim ... nk ] into a matrix of size:
[ n dim prod([n1 .. n dim -1 n dim +1 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 mat2multi_ can reverse the conversion.
multi_array ::numcellstring,!sparse:: Numeric multidimensional array, vector, matrix or string, or (multidimensional) cell-array of strings. dim ::scalar_natural_nonzero:: Dimension of multi_array to which each matrix column vector must belong.
% 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: mat2multi, mdeal Keywords: multidimensional-array, smart reshape, column-wise Version: 0.2.5
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