Asked by Michael Ransom
on 16 Mar 2019

I have a problem that requires assigning values to an array of arbitrary dimensions.

For a given integer j, I pre-allocate a regular j-dimensional array such that

where are integers for . Such an array in MATLAB looks like:

Array = NaN.*ones( repmat( d , 1 , j ) ) ;

The problem is assigning values for elements in this array. Specifically, given are vectors of length , I require all combinations of element-wise multiplication for each of these vectors, where each result is assigned to .

For the simplest case , assuming vectors are stored in cell-arrays, I can do this quite easily using loops:

for m = 1:d

for n = 1:d

Array( m , n ) = v{ 1 }( m ).*v{ 2 }( n ) ;

end

end

But, a "psudeo-code" implementation with j loops would look something like:

for m( 1 ) = 1:d

...

for m( j ) = 1:d

Array( m( 1 ) , ... , m( j ) ) = v{ 1 }( m( j ) ).* ... .*v{ j }( m( j ) ) ;

end

...

end

The indexing of now becomes variable, which I have had no success in implementing.

Does there exist a way of assigning values to an array of arbitrary dimensions in MATLAB in this manner, or perhaps a neater method?

Answer by per isakson
on 17 Mar 2019

Edited by per isakson
on 18 Mar 2019

Accepted Answer

"The problem I have is to be able to this with an arbitrary value of j." I think value2arrayND does that. It takes a cell array, {dim1,dim2,dim3,...}, and returns an array, the size of which is [dim1,dim2,dim3,...]. value2array2D and value2array3D are based on the code of your comment. They are used to produce expected values.

>> a2 = value2array2D( );

>> aN2 = value2arrayND( {5,5} );

>> aN2-a2

ans =

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

>> a3 = value2array3D( );

>> aN3 = value2arrayND( {5,5,5} );

>> aN3(:,:,3)-a3(:,:,3)

ans =

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

where

function array = value2arrayND( d )

rng('default'); % for reproducing rand;

N = length(d);

v = cell( 1, N );

for jj = 1 : N

v{ jj } = rand( d{jj}, 1 );

end

array = nan(d{:});

nel = numel( array );

sz = [d{:}];

dim = cell( 1, N );

for ii = 1 : nel

[dim{:}] = ind2sub( sz, ii );

array(ii) = prod( arrayfun( @(jj) v{jj}(dim{jj}), 1:N, 'uni',true ) );

end

end

and

function array = value2array3D( )

rng('default'); % for reproducing rand;

d = { 5, 5, 5 }; % vector length; arbitrary

v{ 1 } = rand( d{1}, 1 ); % vector 1

v{ 2 } = rand( d{2}, 1 ); % vector 2

v{ 3 } = rand( d{3}, 1 ); % vector 3

array = nan(d{:});

for p = 1 : d{1}

for q = 1 : d{2}

for r = 1 : d{3}

array( p, q, r ) = v{ 1 }( p ).*v{ 2 }( q ).*v{ 3 }( r );

end

end

end

end

and

function array = value2array2D( )

rng('default'); % for reproducing rand;

d = { 5, 5 }; % vector length; arbitrary

v{ 1 } = rand( d{1}, 1 ); % vector 1

v{ 2 } = rand( d{2}, 1 ); % vector 2

array = nan(d{:});

for m = 1 : d{1}

for n = 1 : d{2}

array( m, n ) = v{ 1 }( m ).*v{ 2 }( n );

end

end

end

Michael Ransom
on 17 Mar 2019

This is exactly what I was after. A few rearrangements:

clear; clc;

rng = ('default'); % for reproducing rand

d = 5; % vector length

j = 3; % arbitrary value

v = cell( 1 , j ) ;

for m = 1:j

v{ m } = rand( d , 1 ); % vectors 1,...,j

end

Array = value2arrayND( d , j , v ) ;

followed by the function you provided in your answer with a few tweaks:

function Array = value2arrayND( d , j , v )

Array = NaN.*ones( repmat( d , 1 , j ) );

nel = numel( Array );

sz = size( Array );

dim = cell( 1 , j );

for ii = 1:nel

[dim{:}] = ind2sub( sz, ii );

Array( ii ) = prod( arrayfun( @(jj) v{jj}(dim{jj}), 1:length(v), 'uni',true ) );

end

end

Many thanks!

dpb
on 17 Mar 2019

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## 4 Comments

## dpb (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/450451-assigning-values-to-an-array-of-arbitrary-dimensions-in-matlab#comment_681882

## Michael Ransom (view profile)

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## Walter Roberson (view profile)

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## Michael Ransom (view profile)

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