Why doesn't [] ~=1 yield logical one?

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I'm using matlab r2012B, because the computer is old and disconnected from internet and it runs my experiment and is not to be updated.
I have the following:
a = [];
if a ~= 1
Now i ask myself, will the message 'a~=1' be printed? the answer is obviously yes. Why? because the expression 'a~=1' is clearly True. It is True that [] is not equal to 1. one is the number 1, and the other, is NOT the number 1. If I
If this threw an error, I would accept that. That seems reasonable.
Therefore, there must be some reason that this doesn't behave like I expect. What is that reason? Why does it behave the same way for a = 'string' (which evaluates to 0, makes sense) or a = {} (which throws an error, also reasonable).

Accepted Answer

John D'Errico
John D'Errico on 22 May 2021
Edited: John D'Errico on 23 May 2021
This has always been true as I recall, probably so since the mid-1980's, when I learned MATLAB.
Note that the result is an EMPTY arrray. Suppose we had performed the test:
a = 1;
x = 0:3;
x ~= a
ans = 1×4 logical array
1 0 1 1
We have compared the scalar value a to EVERY element in the vector x. 3 of the 4 values were not equal, and the other is equal. So we get a completely expected result, true where x is not equal to 1.
The same applies to a vector of length 0, thus an empty vector. Try this comparison:
y = [];
y ~= a
ans = 0×0 empty logical array
Again, every element in y is compared to a. Since there are no elements in y, the result is an empty vector.
Your problem is in how you view an empty array. It is NOT a scalar. That is
whos a x y
Name Size Bytes Class Attributes a 1x1 8 double x 1x4 32 double y 0x0 0 double
We see that y is not the same size as a. So while the comparison to x performs a scalar expansion, the same comparison to y results in a scalar expansion of a, to be the same size and shape as y: EMPTY.
We cannot compare a scalar value to y (an empty array) and expect a result that is either true or false. By the way, this is why the function isempty has been around since the dark ages.
Now, how does this work for a string? I'm not certain what you intended there.
If we do this:
str = '';
str == '1'
ans = 0×0 empty logical array
Then we get the same behavior with an empty string as with an empty array. If we try to compare a non-empty string to an ampty array, it will throw an error.
str = 'string';
str == ''
Error using ==
Arrays have incompatible sizes for this operation.
As you can see, I cannot compare a string VECTOR to an empty array, so it throws an error. I cannot expand an empty array. It is NOT a scalar.
Again, I think you are viewing an empty array as if it is a scalar. It is not so. Likewise, you cannot compare a scalar to a cell array, empty or NOT! But that is not the same issue. Comparisons are not defined like this for a cell array:
{} == 1
Operator '==' is not supported for operands of type 'cell'.
Paul on 23 May 2021
In r2012b, would the results from my code snippet be any different? It seems to me that
y ~= a
would still return empty in accordance with your third bullet, and
y ~= x
would presumably throw an error because it's not covered by bullets 1-3.
I realize that based on the OP's restriction to r2012b I shouldn't have brought post-r2012b features into the discussion. I'm just curious if I understand what that older behavior is.

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