Addition of non-uniform dimensional matrices

While writing a code for my research paper, the below Matlab operation since did not gave an error, I wasn't able to get the desired results. As per mathematics rules, for addition and subtraction, the 2 matrices should have the same dimensions.

1 - Why Matlab is not giving an error for addition or subtraction of below matrices?

2 - What is the advantage of allowing such an operation?

A=[1, 2, 3, 4];

B = [1; 2; 3;4];

C = A - B is calculated by Matlab.

Similarly the below operation also doesn't land into any errors, something strange.

D = [1, 2, 3, 4];

E = [1; 2; 3];

F = D-E;

G = E-D

Answer 1

[Walter Roberson]

"As per mathematics rules, for addition and subtraction, the 2 matrices should have the same dimensions."

No, what mathematics tell us that if 2 matrices do have the same dimensions, that the result of those operations should be such-and-such. Mathematics has nothing to say about the outcome of those operations on two dissimilar arrays.

Including that mathematics has nothing to say about the outcome of (for example) 1 + [3, 4, 5], which is the addition of two dissimilar arrays. It is convenient that MATLAB automatically interprets this as 1*[1, 1, 1] + [3, 4, 5] . And sometimes it is convenient that MATLAB automatically interprets [1; 2] + [3, 4, 5] as [1; 2] * [1 1 1] + [1;1] * [3, 4, 5]

The change to operations does not affect any calculation for which the array dimensions does match. The change affects only calculations for which the array dimensions does not match. And the change is that it now gives a meaningful and not unreasonable result instead of giving an error message.

There are times when I am writing code when I wish the operations would give an error message for unmatched dimension, that perhaps they had given a different form to the new functionality, such as calling it #+ and $- or something like that -- times when I do not expect the operation to be taking place and want the debugging help. But that does not mean that the new operations are wrong in any way, just that the interface to them is not optimal taking into account that size mismatches are somewhat common and automatic expansion is not always desirable.

Answer 2

[Star Strider]

‘1 - Why Matlab is not giving an error for addition or subtraction of below matrices?’

Beginning in R2016b, MATLAB automatically expands matrix arguments. Previously, this required bsxfun (that I still prefer, and that I use in my Answers here).

‘2 - What is the advantage of allowing such an operation?’

You have ow joined many of us here who asked the same thing in the last year or so.

[Ihsan Ullah]

I think this is very vague. They must have a valid justification for it. Lets wait for sometime and if we do not get a convincing answer here then it will be better to take it up with the support team.

[Star Strider]

Agreed.

However we have not gotten a convincing answer in the last year.

[Ihsan Ullah]

Hi, So below is the reply I got from Matlab Technical team. Your comments are appreciated on this, so we may take the same up with them,

Hello Ihsan,

My name is RXXXXXXXX and I am writing in reference to your Technical Support Case #029XXXXX regarding 'Addition of non-uniform dimensional matrices'.

I understand that you notice discrepancies with matrix operations in MATLAB and the expected result mathematically.

Your observation is spot on that mathematically the result you expect is not the output MATLAB displays/evaluates. This feature "Implicit Expansion" was introduced in R2016b and is described as:

Implicit expansion is a generalization of scalar expansion. With scalar expansion, a scalar expands to be the same size as another array to facilitate element-wise operations. With implicit expansion, the element-wise operators and functions listed here can implicitly expand their inputs to be the same size, as long as the arrays have compatible sizes. Two arrays have compatible sizes if, for every dimension, the dimension sizes of the inputs are either the same or one of them is 1.

Additional information is available at:

https://www.mathworks.com/help/matlab/matlab_prog/compatible-array-sizes-for-basic-operations.html

https://blogs.mathworks.com/loren/2016/10/24/matlab-arithmetic-expands-in-r2016b/

The decision to introduce this feature and thought process behind the same is described to an extent in the following blog post:

https://blogs.mathworks.com/loren/2016/11/10/more_thoughts_about_implicit_expansion/

In the example provided by you: D=[1,2,3,4]; E=[1;2;3];

The solution (D-E) can be considered equivalent to expanding each of D and E to (3 x 4) matrices. i.e.D = [1,2,3,4;1,2,3,4;1,2,3,4] and E=[1,1,1,1;2,2,2,2;3,3,3,3] and then performing element wise subtraction to get the result displayed by MATLAB.

I do understand that this is significantly different from mathematical rules and I do acknowledge that this may break some existing code and/or will require understanding of this behavior to get the desired results.

Please let me know if this addresses you concerns and questions. In case you have additional questions or concerns, please do not hesitate to reach out to me. I will be happy to re-open the case and assist you further.

Once again, I apologize for the inconvenience this has caused you and thank you for providing feedback.

Sincerely,

RXXXXXXXX KXXXXX

MathWorks Technical Support Department

[Star Strider]

If I actually had a vote (unfortunately I don’t), I would vote to revert to the mathematically correct operations, and require the bsxfun function if expansion were necessary. (The bsxfun function is much more efficient than using repmat. It is not difficult to learn to use it correctly and appropriately.)

We are voices crying in the wilderness, unfortunately.

[John D'Errico]

Everyone is different. Personally, I tend to like the automatic scalar dimension expansion. I think once you get used to it, it makes for nice clean looking code, easy to read.

But that is what makes the world an interesting place.

[Ihsan Ullah]

Thank you everyone for the interest shown here.

@Star Strider, I replied to Matlab technical support team earlier (combining your words with mine) and to reconsider the operation. I m sharing their response as below,

Hello Ihsan,

Thank you for the detailed response.

I acknowledge your point of view and agree with the concerns you have put forth regarding 'Implicit Expansion'. It would be useful for both new users and experts alike to be provided with a warning and if possible, to switch "off" this feature. Hence, I have relayed your feedback to the Development team and apprised them of your opinion and the difficulties this features introduces into your workflows. They may consider including these enhancements in a future release of MATLAB.

Thank you once again for your feedback and help in improving MATLAB!

Best,

RXXXXXX

[Star Strider]

@Ihsan Ullah — Thank you for your efforts in having MathWorks reconsider this. A ‘switch’ to turn off ‘implicit expansion’ would be welcome.