MATLAB: Are leading singleton dimensions not dropped when displaying size of multidimensional arrays

arraydimensionsdroppedleadingMATLABmatrixmultidimensionalsingletonsize;squeezetrailing

When displaying sizes of multidimensional arrays, the SIZE function retains the leading singleton dimensions, but drops the trailing singleton dimensions.

For example, consider the following multidimensional array:

for i=1:160
   myArr(:,:,i) = ones(128);
end
size(myArr(:,:,1))

For the array 'myArr', the SIZE function returns

 ans =
    128   128

However the commands:

size(myArr(:,1,:))
size(myArr(1,:,:))

return

 ans =
    128     1   160
 ans =
      1   128   160

respectively.

Best Answer

This is the expected behavior of multidimensional arrays.

Leading singleton dimensions are not dropped because they cannot be added on the fly (without a call to the RESHAPE function) to maintain memory integrity. However, trailing singleton dimensions are dropped because leaving them out will not affect memory integrity.

If the leading singleton dimensions are not required, the SQUEEZE function can be used. Hence for the example considered, the commands:

size(squeeze(myArr(:,1,:)))
size(squeeze(myArr(1,:,:)))

yield the results:

respectively, without displaying the singleton dimensions.

For more information regarding the SQUEEZE function, enter the following at the MATLAB Command Prompt:

doc squeeze

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MATLAB: What does squeeze() do in MATLAB

Squeeze is a useful tool to help compress dimensions of a multidimensional array when you have performed some operations. Let me give you a couple of examples as to why it is useful.

Suppose we have a 3 dimensional array.

A = rand(2,3,4);
size(A)
ans = 1×3
     2     3     4

Now suppose we wanted to extract some plane of the array? Thus to form A(1,:,:)? This should be 2-dimensional thing, right?

A(1,:,:)
ans = 
ans(:,:,1) =

    0.5894    0.7875    0.8829


ans(:,:,2) =

    0.8349    0.4246    0.8329


ans(:,:,3) =

    0.9120    0.3446    0.5253


ans(:,:,4) =

    0.8350    0.9092    0.3368

Hmm. It is not. At least, that does not look like a 2-dimensional array. In fact, MATLAB thinks it is 3-d still.

size(A(1,:,:))
ans = 1×3
     1     3     4

Or, suppose we wanted to form the mean, on the SECOND dimension of A?

mean(A,2)
ans = 
ans(:,:,1) =

    0.7533
    0.4986


ans(:,:,2) =

    0.6975
    0.6879


ans(:,:,3) =

    0.5940
    0.6914


ans(:,:,4) =

    0.6937
    0.7024
size(mean(A,2))
ans = 1×3
     2     1     4

So in both cases, I started with a 3-dimensional array, operated on it in a way that logically SHOULD have produced a 2-d array.

Squeeze fixes the problem, by dropping out those spurious singleton dimensions. That is,

squeeze(A(1,:,:))
ans = 3×4
    0.5894    0.8349    0.9120    0.8350
    0.7875    0.4246    0.3446    0.9092
    0.8829    0.8329    0.5253    0.3368
●
size(squeeze(A(1,:,:)))
ans = 1×2
     3     4
squeeze(mean(A,2))
ans = 2×4
    0.7533    0.6975    0.5940    0.6937
    0.4986    0.6879    0.6914    0.7024
size(squeeze(mean(A,2)))
ans = 1×2
     2     4

This allows you to get the result you wanted, in the shape you would have expected.

There is one small caveat to remember. All arrays in MATLAB are treated as if they have infinitely many trailing singleton dimensions. So a scalar is actually an array of size 1x1x1x1x1x1x1x1..., and a vector an array of size Nx1x1x1x1..., or 1xNx1x1x1x1... MATLAB never reports those trailing singleton dimensions however, at least not beyond the second dimension. (This is probably a consequence of requiring backwards compatibility all the way back to version 1 when possible, when MATLAB did not have multidimensional arrays at all.) So we see:

V = 1:3;
size(V)
ans = 1×2
     1     3
●
size(V.')
ans = 1×2
     3     1
●
S = 2;
size(S)
ans = 1×2
     1     1
●

Logically, if we apply squeeze to a scalar, we still have a scalar.

size(squeeze(S))
ans = 1×2
     1     1
size(squeeze(V.'))
ans = 1×2
     3     1
●
size(squeeze(V))
ans = 1×2
     1     3
●

So the only thing to remember is that squeeze does not convert a 1x3 vector into a 3x1 vector. (In my eyes, I disagree with the design of squeeze in that respect, but I did not write the code.)

W = A(1,1,:)
W = 
W(:,:,1) =

    0.5894


W(:,:,2) =

    0.8349


W(:,:,3) =

    0.9120


W(:,:,4) =

    0.8350

So W is a vector, but stored in a 3-dimensional form. It has size 1x1x4.

size(W)
ans = 1×3
     1     1     4
●
size(squeeze(W))
ans = 1×2
     4     1
●

So be careful when squeezing vectors, as it is not always perfectly consistent. At least not in my eyes.

Having read all of that, you should now be a master of the squeeze.

MATLAB: “Matrix Dimensions must agree”

t is used to build r, but it is not the same length as phi.

Best Answer

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MATLAB: What does squeeze() do in MATLAB

MATLAB: “Matrix Dimensions must agree”

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