Code covered by the BSD License

### Highlights from EXPAND

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# EXPAND

by

### Matt Fig (view profile)

23 Jun 2009 (Updated )

Replicate and tile each element of an array.

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

File Information
Description

EXPAND(A,SZ), for array A and vector SZ replicates each element of A by SZ. The results are tiled into an array in the same order as the elements of A, so that the result is size: size(A).*SZ.

Therefore the number of elements of SZ must equal the number of dimensions of A, or in MATLAB syntax:

length(size(A))==length(SZ)

must be true.
The result will have the same number of dimensions as does A.
There is no restriction on the number of dimensions for input A.

Examples:

>> A = [1 2;3 4]
A =
1 2
3 4
>> expand(A,[2 1])
ans =
1 2
1 2
3 4
3 4
>> expand(A,[2 2])
ans =
1 1 2 2
1 1 2 2
3 3 4 4
3 3 4 4

Please email me if bugs are found in the code. Thanks.

Acknowledgements

Replicate inspired this file.

MATLAB release MATLAB 7.4 (R2007a)
05 Mar 2015 Nike Dattani

### Nike Dattani (view profile)

I've been using EXPAND for a number of years, and it's part of my open source software FeynDyn for numerically calculating Feynman integrals.

Regarding Yair Altman's comment below:
Have the speed and memory of EXPAND been retested now?

I'm wondering if I should scrap EXPAND from my software.

Also, MATLAB has it's own EXPAND in the Symbolic Toolbox for expanding expressions like (x+y)^2.

Thanks for the input.

13 Jul 2013 Yair Altman

### Yair Altman (view profile)

Now that R2013b has finally incorporated Bruno's efficient implementation (FEX 24499) into the built-in KRON function, I expect the balance of performance and memory to shift in favor of KRON. Of course, expand will continue to be better for anyone still using R2013a or earlier.

24 Jun 2009 Matt Fig

### Matt Fig (view profile)

Another reason I bypassed kron is illustrated here:

http://i217.photobucket.com/albums/cc229/spamanon/tester_output-2.png

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24 Jun 2009 us

### us (view profile)

just like jos, i also felt at first that this - admittedly sleek engine - was more or less a KRON clone; but then your timing convinced me that there was clearly more to it...
however, i think you should at least mention KRON in a
statement...
us

24 Jun 2009 Matt Fig

### Matt Fig (view profile)

Hello Jos,

There are a couple of reasons I bypassed kron. The main reason is that expand, even with error checking etc., is faster on my machine(s):

A = reshape(randperm(24),6,4);
SZ = [300,400];
tic
T = expand(A,SZ);
toc %Elapsed time is 0.043622 seconds.
tic
T2 = kron(A,ones(SZ));
toc %Elapsed time is 0.082535 seconds.

For
A = reshape(randperm(144),18,8);
SZ = [300,400];
expand is .25 vs. .78 seconds for kron. 2007b win xp.

expand also works for your second example.
Thanks.

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24 Jun 2009 Jos (10584)

### Jos (10584) (view profile)

Why not simply
kron(A,eyes(SZ))

or, for non-numerical arrays,
X = {'a' 'b' ; [1:3] []}
X(kron(reshape(1:numel(X),size(X)), ones(2,3)))
%ans =
% 'a' 'a' 'a' 'b' 'b' 'b'
% 'a' 'a' 'a' 'b' 'b' 'b'
% [1x3 double] [1x3 double] [1x3 double] [] [] []
% [1x3 double] [1x3 double] [1x3 double] [] [] []

It can be expanded to the ND case using reshape etc ...

Good help though!

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