The module "mat2multi" of the Mastrave modelling library
Copyright © 2005,2006,2007,2008,2009,2010,2011 Daniele de Rigo
The file mat2multi.m is part of Mastrave.
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multi_array = mat2multi( matrix, dim, siz )
Some functions are defined for matrices but not for multidimensional 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
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.
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 .
% 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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