What is a simple way to check if a collection of vectors all have the same number of elements

I am look for a nice simple way to check if a collection of vectors all have the same number of elements. For example this might be used to validate some inputs to a function, or otherwise check compatibility before performing other operations.

Here's my current approach, which works, but I wonder if someone has simpler way of doing the same thing

a = rand(3,1);
b = rand(3,1);
c = rand(4,1);
d = rand(3,1);
vecs = {a,b,c,d};
n = cellfun(@numel,vecs);
if any(n(1)~=n)
    error('all vectors must be same length')
end

all vectors must be same length

[Torsten]

Why not renaming a,b,c and d to vecs{1},vecs{2},vecs{3} and vecs{4} ? Should make things easier ...

[Bruno Luong]

I'm half serious but:

The simplest way? IMO just don't do any check, just rely on MATLAB, if any operation on vecs with incompatible sizes will imply error, just let MATLAB throw an error instead of

error('all vectors must be same length')

Answer 1

[Bruno Luong]

if any(n(1)~=n)

The above will crash if your cell is empty.

IMO

if any(diff(n))

is a more robust test. Thus you can do the test in a single statement

if any(diff(cellfun(@numel,vecs)))
   % ...
end

And last but not least, if performance matters, use this

if any(diff(cellfun('prodofsize',vecs)))
   % ...
end

instead of @numel.

Here is why

vecs = arrayfun(@(x) zeros(randi(10),1), 1:1e6, 'unif', 0);
timeit(@()cellfun(@numel, vecs),1)

ans = 0.7885

timeit(@()cellfun('prodofsize', vecs),1)

ans = 0.0098

[Jon]

Thanks, very much, I will look into this too. Away for a week, no MATLAB, but will review again when I get back

Answer 2

[Walter Roberson]

a = rand(3,1);
b = rand(3,1);
c = rand(4,1);
d = rand(3,1);
vecs = {a,b,c,d};


n = cellfun(@numel,vecs,'uniform',0);
if ~isequal(n{:})
        error('all vectors must be same length')
end

all vectors must be same length

[Dyuman Joshi]

Using 'length' instead of @numel might have some benefit (in certain circumstances).

[Stephen23]

@Dyuman Joshi: can you give an example? In general the advice given on this forum is to avoid LENGTH due to its changing dimensions without warning... a behavior that is certainly the cause of a few threads on this forum.

[Dyuman Joshi]

The idea behind my comment is that, that the use of some functions being slower than using the function names as strings for cellfun, such as for length, isempty etc.

I am aware of the consensus of the community for length and I personally advocate for the use of numel over length as well.

But in some obscure case, it might have some benefit.

Edit - @Bruno has implemented another such function - 'prodofsize' in their answer, and you can see that there is significant performance difference.

[Walter Roberson]

L = randi([0 10], 1, 50);
vecs = arrayfun(@(L) rand(1,L), L, 'uniform', 0);

timeit( @() cellfun(@numel,vecs,'uniform',0), 1)

ans = 4.3728e-05

timeit( @() num2cell(cellfun('length',vecs)), 1)

ans = 8.9095e-06

There is an oddity that when you pass a character vector for the function name, cellfun does not accept any options such as uniformoutput

The difference in timings above is not large on an absolute scale, so one should wonder whether the difference is within measurement error -- but it was pretty consistent here on MATLAB answers over several experiments

[Jon]

@Walter Roberson That's neat, I didn't realize that isequal could take a variable number of input arguments, e.g. n{:},

I also thought about, using a try catch block something like below. I think my original approach (incorporating Walter's suggested modifications), seems cleaner than the try-catch. Maybe this is just a subjective issue, but wondered whether anyone has any thoughts on comparing the two ways and which approach is "better".

a = rand(3,1);
b = rand(3,1);
c = rand(4,1);
d = rand(3,1);
try
    M = horzcat(a(:),b(:),c(:),d(:))
catch 
    error('all vectors must be same length')
end

all vectors must be same length

[Jon]

Also, a very good answer, and good discussion, but I could only accept one. Thanks for all of your help.