# Expand

Sean's pick this week is Expand by Matt Fig.

### Background

Matt Fig is one of MATLAB Central's top contributors. Even though he's been on hiatus for over two years, he's still the 10th highest contributor on Answers and the 14th most downloaded author on the File Exchange.

### Expand

My pick today is a contribution of Matt's that made an appearance somewhere in the code base for my Master's thesis. I was working with large 3-dimensional CT images and computation speed was important. Here's what it does:

x = magic(3)
xexpanded = expand(x,[3 2])
x =
8     1     6
3     5     7
4     9     2
xexpanded =
8     8     1     1     6     6
8     8     1     1     6     6
8     8     1     1     6     6
3     3     5     5     7     7
3     3     5     5     7     7
3     3     5     5     7     7
4     4     9     9     2     2
4     4     9     9     2     2
4     4     9     9     2     2


As you can see x has been expanded thrice along rows and twice along columns ([3 2]). Expand also works along N-dimensional arrays but does have a limitation that the expansion must match the number of dimensions. This can be circumvented with a second call to repmat to expand along higher dimensions.

### Kron

The 2-dimensional expand operation has always been possible with kron, but it requires creating a ones matrix and, at least back in my grad school era, was slower than expand. Since I was working with 3-dimensional images, this was not an option.

xkron = kron(x,ones(3,2))
xkron =
8     8     1     1     6     6
8     8     1     1     6     6
8     8     1     1     6     6
3     3     5     5     7     7
3     3     5     5     7     7
3     3     5     5     7     7
4     4     9     9     2     2
4     4     9     9     2     2
4     4     9     9     2     2


### R2015a Introduces repelem

Starting in R2015a, which shipped the first week of March, there is a new function that does the same thing as expand and more built in to MATLAB: meet repelem.

xrep = repelem(x,3,2)
xrep =
8     8     1     1     6     6
8     8     1     1     6     6
8     8     1     1     6     6
3     3     5     5     7     7
3     3     5     5     7     7
3     3     5     5     7     7
4     4     9     9     2     2
4     4     9     9     2     2
4     4     9     9     2     2


And into three dimensions:

xrep3 = repelem(x,3,1,2)
xrep3(:,:,1) =
8     1     6
8     1     6
8     1     6
3     5     7
3     5     7
3     5     7
4     9     2
4     9     2
4     9     2
xrep3(:,:,2) =
8     1     6
8     1     6
8     1     6
3     5     7
3     5     7
3     5     7
4     9     2
4     9     2
4     9     2


repelem on a vector can also vary the number of repeats, very nice for building up a vector or run length encoding.

v123 = repelem([2 4 7],1:3)
v123 =
2     4     4     7     7     7


### R2015a Other

Browsing through the release notes for R2015a and having had the opportunity to beat on the R2015a Prerelease, here are a few of my other favorite new features:

• discretize - similar to histcounts or histc but skips the histogram counting part.
• Array Size Limitation - Helps accidentally creating large arrays that would cause you to run out of RAM.
• Tab Complete for Object Authoring - Finally!
• ismembertol and uniquetol - ismember and unique with tolerance; these will save me a few calls to discretize.

Thanks Matt for providing the expand functionality; it has been very useful for nearly 6 years!

Give expand, repelem, and R2015a a try and let us know what you think about any of them here or leave a comment for Matt.

Published with MATLAB® R2015a

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