CODEWITHSUNDEEP
matlabvectorization
Mikhail Poda
Mikhail Poda

Reputation: 5831

Vectorized operations on cell arrays

This post was triggered by following discussion on whether cell arrays are "normal arrays" and that vectorizaton does not work for cell arrays.

I wonder why following vectorization syntax is not implemented in MATLAB, what speaks against it:

>> {'hallo','matlab','world'} == 'matlab'
??? Undefined function or method 'eq' for input arguments of type 'cell'.

internally it would be equivalent to

[{'hallo'},{'matlab'},{'world'}] == {'matlab'}

because MATLAB knows when to cast, following works:

[{'hallo','matlab'},'world']

Cell array is an array of pointers. If both left and right side point to equal objects, isequal('hallo','hallo') returns as expected true, then why MATLAB still does not allow topmost example?

I know I can use strmatch or cellfun.

SUMMARY:

Upvotes: 8

Views: 9888

Answers (4)

abcd
abcd

Reputation: 42225

Firstly, == is not the same as isequal. The function that gets called when you use == is eq, and the scope of each of those is different.

For e.g., in eq(A,B), if B is a scalar, the function checks each element of A for equality with B and returns a logical vector. 

eq([2,5,4,2],2)

ans =

     1     0     0     1

However, isequal(A,B) checks if A is identically equal to B in all aspects. In other words, MATLAB cannot tell the difference between A and B. Doing this for the above example:

isequal([2,5,4,2],2)

ans =

     0

I think what you really intended to ask in the question, but didn't, is:

"Why is == not defined for cell arrays?"

Well, a simple reason is: Cells were not intended for such use. You can easily see how implementing such a function for cells can quickly get complicated when you start considering individual cases. For example, consider 

{2,5,{4,2}}==2

What would you expect the answer to be? A reasonable guess would be 

ans = {1,0,0}

which is fair. But let's say, I disagree. Now I'd like the equality operation to walk down nested cells and return 

ans = {1,0,{0,1}}

Can you disagree with this interpretation? Perhaps not. It's equally valid, and in some cases that's the behavior you want.

This was just a simple example. Now add to this a mixture of nested cells, different types, etc. within the cell and think about handling each of those corner cases. It quickly becomes a nightmare for the developers to implement such a functionality that can be satisfactorily used by everyone.

So the solution is to overload the function, implementing only the specific functionality that you desire, for use in your application. MATLAB provides a way to do that too, by creating an @cell directory and defining an eq.m for use with cells the way you want it. Ramashalanka has demonstrated this in his answer.

Upvotes: 7

Oliver Charlesworth
Oliver Charlesworth

Reputation: 272467

This is not unique to strings. Even the following does not work:

{ 1, 2, 3 } == 2

Cell arrays are not the same as "normal" arrays: they offer different syntax, different semantics, different capabilities, and are implemented differently (an extra layer of indirection).

Consider if == on cell arrays were defined in terms of isequal on an element-by-element basis. So, the above example would be no problem. But what about this?

{ [1 0 1], [1 1 0] } == 1

The resulting behaviour wouldn't be terribly useful in most circumstances. And what about this?

1 == { 1, 2, 3 }

And how would you define this? (I can think of at least three different interpretations.)

{ 1, 2, 3 } == { 4, 5, 6 }

And what about this?

{ 1, 2, 3 } == { { 4, 5, 6 } }

Or this?

{ 1, 2, 3 } == { 4; 5; 6 }

Or this?

{ 1, 2, 3 } == { 4, 5 }

You could add all sorts of special-case handling, but that makes the language less consistent, more complex, and less predictable.

Upvotes: 2

Ramashalanka
Ramashalanka

Reputation: 8854

There are many things that would seem natural for MATLAB to do that they have chosen not to. Perhaps they don't want to consider many special cases (see below). You can do it yourself by overloading. If you make a directory @cell and put the following in a new function eq.m:

function c = eq(a,b)
if iscell(b) && ~iscell(a)
    c = eq(b,a);
else
    c = cell(size(a));
    for n = 1:numel(c)
        if iscell(a) && iscell(b)
            c{n} = isequal(a{n},b{n});
        else
            c{n} = isequal(a{n},b);
        end
    end
end

Then you can do, e.g.:

>> {'hallo','matlab','world'} == 'matlab'
ans =     [0]    [1]    [0]

>> {'hallo','matlab','world'} == {'a','matlab','b'}
ans =     [0]    [1]    [0]

>> {'hallo','matlab','world'} == {'a','dd','matlab'}
ans =     [0]    [0]    [0]

>>  { 1, 2, 3 } == 2
ans =     [0]    [1]    [0]

But, even though I considered a couple of cases in my simple function, there are lots of things I didn't consider (checking cells are the same size, checking a multi-element cell against a singleton etc etc).

I used isequal even though it's called with eq (i.e. ==) since it handles {'hallo','matlab','world'} == 'matlab' better, but really I should consider more cases.

(EDIT: I made the function slightly shorter, but less efficient)

Upvotes: 5

DanielHsH
DanielHsH

Reputation: 4453

The reason for this problem is: cell arrays can store different types of variables in different cells. Thus the operator == can't be defined well for the entire array. It is even possible for a cell to contain another cell, further exacerbating the problem.

Think of {4,'4',4.0,{4,4,4}} == '4'. what should be the result? Each type evaluates in different way.

Upvotes: 1

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