Question

I have a loop in MATLAB that fills a cell array in my workspace (2011b, Windows 7, 64 bit) with the following entries:

my_array = 
    [1x219 uint16]
    [         138]
    [1x0   uint16] <---- row #3
    [1x2   uint16]
    [1x0   uint16]
    []             <---- row #6
    [         210]
    [1x7   uint16]
    [1x0   uint16]
    [1x4   uint16]
    [1x0   uint16]
    [         280]
    []
    []
    [         293]
    [         295]
    [1x2   uint16]
    [         298]
    [1x0   uint16]
    [1x8   uint16]
    [1x5   uint16]

Note that some entries hold [], as in row #6, while others hold [1x0] items, as in row #3.

1. Is there any difference between them? (other than the fact that MATLAB displays them differently). Any differences in how MATLAB represents them in memory?
2. If the difference is only about how MATLAB internally represents them, why should the programmer be aware of this difference ? (i.e. why display them differently?). Is it a (harmless) bug? or is there any benefit in knowing that such arrays are represented differently?

Answer 1

In most cases (see below for an exception) there is no real difference. Both are considered “empty”, since at least one dimension has a size of 0. However, I wouldn’t call this a bug, since as a programmer you may want to see this information in some cases.

Say, for example, you have a 2-D matrix and you want to index some rows and some columns to extract into a smaller matrix:

>> M = magic(4)  %# Create a 4-by-4 matrix

M =
    16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1

>> rowIndex = [1 3];  %# A set of row indices
>> columnIndex = [];  %# A set of column indices, which happen to be empty
>> subM = M(rowIndex,columnIndex)

subM =
   Empty matrix: 2-by-0

Note that the empty result still tells you some information, specifically that you tried to index 2 rows from the original matrix. If the result just showed [], you wouldn’t know if it was empty because your row indices were empty, or your column indices were empty, or both.

The Caveat…

There are some cases when an empty matrix defined as [] (i.e. all of its dimensions are 0) may give you different results than an empty matrix that still has some non-zero dimensions. For example, matrix multiplication can give you different (and somewhat non-intuitive) results when dealing with different kinds of empty matrices. Let’s consider these 3 empty matrices:

>> a = zeros(1,0);  %# A 1-by-0 empty matrix
>> b = zeros(0,1);  %# A 0-by-1 empty matrix
>> c = [];          %# A 0-by-0 empty matrix

Now, let’s try multiplying these together in different ways:

>> b*a

ans =
     []  %# We get a 0-by-0 empty matrix. OK, makes sense.

>> a*b

ans =
     0   %# We get a 1-by-1 matrix of zeroes! Wah?!

>> a*c

ans =
   Empty matrix: 1-by-0  %# We get back the same empty matrix as a.

>> c*b

ans =
   Empty matrix: 0-by-1  %# We get back the same empty matrix as b.

>> b*c
??? Error using ==> mtimes
Inner matrix dimensions must agree.  %# The second dimension of the first
                                     %#   argument has to match the first
                                     %#   dimension of the second argument
                                     %#   when multiplying matrices.

Getting a non-empty matrix by multiplying two empty matrices is probably enough to make your head hurt, but it kinda makes sense since the result still doesn’t really contain anything (i.e. it has a value of 0).