# Would a BSXFUN operator family be a good idea?

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I don't think the pipe symbol '|' is being used for anything in MATLAB syntax. Would it be a good idea to use it to make a family of BSXFUN operators? For example, instead of

C=bsxfun(@times,A,B)

C=bsxfun(@plus,A,B)

you could do things like

C=A|*B;

C=A|+B;

##### 4 Comments

Walter Roberson
on 2 Jun 2013

APL referred to this as "Generalized Outer Product", and relates it closely to APL's "Generalized Inner Product".

APL's outer product syntax is

o.OPERATOR

where o is (in APL character set) a raised small circle, and OPERATOR is a dyadic (binary) operator.

APL's inner product syntax is

OPERATOR1.OPERATOR2

where OPERATOR2 is a dyadic (binary) operator, and OPERATOR1 is a "reduction operator" (that is, reduces an array by one dimension, such as by summing along rows.) +.x (raised multiplication) is APL's matrix multiplication: form the outer product and then sum along a dimension.

It would be nice if MATLAB too applied some systematism to the way that it used operators. For example, MATLAB could start by defining "." as prefix that could be applied to any binary operator, so that instead of .^ and .* and ./ being separate operators specially parsed, that instead they became part of a general rule -- that dot could be followed by a function name or an operator (whose formal name was substituted), or perhaps even an anonymous function, to form a new binary operator.

To be consistent with existing MATLAB usage, the formal name of the new binary operator would be formed from the name of the existing operator but with the leading character dropped (mtimes -> times, mpower -> power, mrdivide -> rdivide). My instinct is that that would not be the best practice going forward. I have not yet come up with a good solution that applies to objects as well.

Oh dang, we already have THIS.THAT syntax in place, don't we? THIS being an object and THAT being either a method or property. Sigh, so much for using . as the generalized extension signaler. Maybe # then.. hmmm, that's used for pragmas such as %#function and %#eml but perhaps there is no real syntactical overlap there... unless of course we can define "%" as being an operator :)

"#" is used as the comment introducer in numerous shells, and some other languages.

I thought I remembered encountering "$" in the first column as indicating comments in FORTRAN, but if I did then it must have been non-standard (WATFOR maybe). "c" and "C" and "*" and "!" (Fortran 90) are what it uses. Ummm, maybe my mind has wandered back to JCL again :-(

### Answers (3)

Walter Roberson
on 2 Jun 2013

Edited: Walter Roberson
on 2 Jun 2013

Pipe is "or"

Unused symbols are: back-quote (`), octothorp (#), dollar-sign ($), and question-mark (?). Oh yes, and double-quote (")

Jan
on 2 Jun 2013

Knut
on 2 Jun 2013

Edited: Knut
on 2 Jun 2013

I occasionally use the kron() function, and I probably should use bsxfun() more. What I seem to be banging my head up against: I saw the light with MATLAB when I grasped the beauty and compactness of regular 2-d oriented array/vectorization. The fact that it tended to make my MATLAB scripts faster did not hurt either.

Recently, I am feeling constrained: for the kind of stuff that I am doing, MATLAB vectorization can only take me so far. I believe that what I am longing for is tensor math. Is this a direction that TMW will/should head for, or is it too exotic/hard to make fast libraries/something else?

I'd like to write:

a = ones(2,4,3);

g = cat(3,1,2,3);

%1. short-hand for:

%for t = 1:3,

% R1(:,:,t)=a(:,:,t)*g(t);

%end

R1 = a.*g;

R1(:,:,1) =

1 1 1 1

1 1 1 1

R1(:,:,2) =

2 2 2 2

2 2 2 2

R1(:,:,3) =

3 3 3 3

3 3 3 3

%2. short-hand for:

%R2 = zeros(2,4);

%for t = 1:3,

% R2=R2+a(:,:,t)*g(t);

%end

R2 = a*g;

R2 =

6 6 6 6

6 6 6 6

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