Adding vectors of different sizes... works now? Can this be suppressed?

In previous versions of matlab, adding two vectors of different sizes would result in an error (this would align with rules of matrix addition).

For example:

[ 1 2 3 4] + [1 2 3 4]'

ans =

     2     3     4     5
     3     4     5     6
     4     5     6     7
     5     6     7     8
     

For example:

[ 1 2 3 4] + [1 2 3 4 5]'

ans =

     2     3     4     5
     3     4     5     6
     4     5     6     7
     5     6     7     8
     6     7     8     9

Is there a way to suppress this new "feature"?

[Stephen23]

"Is there a way to suppress this new "feature"?"

No. See:

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

You might also be interested in these discussions:

https://www.mathworks.com/matlabcentral/discussions/general/848046-what-parts-of-matlab-would-you-not-miss/2578956#reply_2578956

https://www.mathworks.com/matlabcentral/answers/383533-how-do-i-avoid-getting-fooled-by-implicit-expansion

https://www.mathworks.com/matlabcentral/answers/2018036-bsxfun-vs-implicit-expansion

[Jeff Glusman]

Ugh. Definitely would not miss this "feature" -- I must've not caught this in earlier releases.

Thank you!

[John D'Errico]

People don't like change. But that is life. Things change.

I recall how, long ago, in the days before we had personal computers on our desks, we had terminals, connected to a mainframe. And one day, the operating system changed, and we all had to learn the new stuff. God there was an uproar. It was terrible! Before long, we were used to the new stuff, and you know, the old ways were really way worse.

As I said, things change. And once we get used to the new rules being there, we find out these new capabilities are actually really nice. Very handy.

What you will find is, once you get used to the idea, that older tools like BSXFUN, REPMAT, even MESHGRID are no longer needed for many tasks. You will see just how kludgy the BSXFUN interface seems.

It just takes a little time.

[James Tursa]

@John D'Errico +1

Personally, I love this feature. I even wish that * would have been implemented with automatic implicit expansion as well instead of having to call pagemtimes. Same for the other page"etc" functions.

[Star Strider]

It’s called ‘automatiic implicit expansion’ and appeared first in R2014b. Previously, it was necessary to use bsxfun to get that result.

[John D'Errico]

We had many lengthy discussions about BSXFUN, before it was introduced. At the time, implicit expansion was brought up as an alternative, but it never got any traction, AT THE TIME. I think they eventually realized that BSXFUN was nice, but not truly a good solution, and that implicit expansion was just better.

As @James Tursa said, I also truly love and appreciate this, and use it frequently.

Answer 1

[Walter Roberson]

There is no way to suppress implicit expansion.

Consider by the way that

3 + eye(4)

ans = 4×4

4 3 3 3 3 4 3 3 3 3 4 3 3 3 3 4

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also breaks the rules of matrix addition, since size(3) is not the same as size(eye(4))

Likewise

3 * eye(4)

ans = 4×4

3 0 0 0 0 3 0 0 0 0 3 0 0 0 0 3

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breaks the rules of matrix multiplication, since size(3,2) is not the same as size(eye(4),1) ["inner dimensions" do not match.]

[Jeff Glusman]

That's always been allowable though since it's a scalar being multiplied/added to a matrix (while breaking the rules of matrix math, it felt like scalars were treated as the same size as the matrix being added/multiplied).

Adding an Nx3 and an Mx1 makes zero sense and I am just puzzled by the decision to compute it at all.

[Voss]

N = 4;
M = 5;
rand(N,3)+rand(M,1)

Arrays have incompatible sizes for this operation.

[Jeff Glusman]

Sorry, Nx3 and Mx1 were just selected randomly - examples above stand - Nx1 + 1xM and Nx3 + 1x3 work:

[1 2 3; 4 5 6] + [1 2 3]

ans = 2×3

2 4 6 5 7 9

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[1 2 3] + [ 1 2 3 4]'

ans = 4×3

2 3 4 3 4 5 4 5 6 5 6 7

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[Walter Roberson]

See by the way the discussion at https://blogs.mathworks.com/loren/2016/11/10/more_thoughts_about_implicit_expansion/

[Paul]

Scalar multiplication is well defined mathematically; 3*eye(4) doesn't break any rules.

[Walter Roberson]

Scalar multiplication ought to be incompatible with the * matrix multiplication operator. The number of columns of the scalar does not match the number of rows of the matrix. It ought to be necessary to expand the scalar to a diagonal matrix first.

a = magic(3)

a = 3×3

8 1 6 3 5 7 4 9 2

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diag([3 3 3]) * a 

ans = 3×3

24 3 18 9 15 21 12 27 6

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●

3 * a

ans = 3×3

24 3 18 9 15 21 12 27 6

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[Paul]

That's an interesting take. Are there any sources/references that say that scalar multiplication with a matrix (or vector) is not defined because of the dimensional inconsistency?

[Walter Roberson]

It is the definition of algebraic matrix multiplication: you have to have M x N multiplied by N x P, forming an M x P result.

[Paul]

Are you suggesting that

a) scalar multiplication with a matrix (or vector) is not defined as a mathematical operation

or

b) scalar multiplication with a matrix is defined as a mathematical operation but shouldn't be

or

c) scalar multiplication with a matrix is well-defined mathematically but in Matlab scalar multiplication with a matrix should only be implemented with times, .* and attempts to multiply a scalar with a matrix with mtimes, * should throw an error,

or

d) something else?

I'm genuinely confused as to your position ...

[Stephen23]

"Are there any sources/references that say that scalar multiplication with a matrix (or vector) is not defined because of the dimensional inconsistency?"

All sources which teach/define matrix multiplication (note that MTIMES is defined in its documentation as "Matrix multiplication", not "Scalar multiplication").

For example, the 2nd sentence here https://en.wikipedia.org/wiki/Matrix_multiplication states "For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix" (bold added).

Or Wolfram Mathworld https://mathworld.wolfram.com/MatrixMultiplication.html which states "Therefore, in order for matrix multiplication to be defined, the dimensions of the matrices must satisfy (nxm)(mxp) = (nxp) where (axb) denotes a matrix with a rows and b columns" (bold added).

MATLAB's * operator has never fulfilled this requirement with a scalar and a non-scalar matrix. In other words, MATLAB is not mathematics (never was, never will be).

[Paul]

I see now in this comment that @Walter Roberson was referring to Matlab's implementation of mtimes, *. Don't know how I missed that on first read.

[Walter Roberson]

Right. If we are going to insist that MATLAB obey the "rules" on matrix addition, then we need to insist that MATLAB obey the "rules" on matrix multiplication as well, by making it invalid to mtimes() a scalar by a matrix, and making it invalid to plus() a scalar and a matrix.