matlabFunction: Why the extra ".0" and why only sometimes?

f = @(x)2.^x.*x.^2

f = function_handle with value:
    @(x)2.^x.*x.^2

f = sym(f)

f = 

f = matlabFunction(f)

f = function_handle with value:
    @(x)2.0.^x.*x.^2

While functionally irrelevant, it makes formulae difficult to read. Why does it happen, and why only sometimes? More importantly, is there any way to stop it?

Answer 1

[John D'Errico]

Does it really, really, really matter? Actually, there is a (subtle) reason for the 2.0.

You should recognize there is some potential ambiguity in the subexpression

2.*x

Was that intended to be seen as the number 2. multiplied by x using the .* operator, or the integer 2, multipled, using the * operator? And yes, you might decide the difference is not relevant. But might it be relevant? For example:

x = 1:5;

How should this line be evaluated?

x*2.*x'

ans = 5×5

2 4 6 8 10 4 8 12 16 20 6 12 18 24 30 8 16 24 32 40 10 20 30 40 50

In terms of the order of operations, MATLAB will multiply x. by 2. Then it needs to multiply that result by the vector transpose(x). But should it use the .* operator? Or the * operator? That is, should the result be:

(x*2).*(x')

ans = 5×5

2 4 6 8 10 4 8 12 16 20 6 12 18 24 30 8 16 24 32 40 10 20 30 40 50

In MATLAB, this operation would yield a 5x5 array. But the alternative would be written as

(x*2.) * (x')

ans = 110

And that operation yields a scalar.

The thing is, it very much matters how you interprret that line. Now, consider the expression:

x*2.0.*x

Now there can be no ambiguity, since we know that 2.0 is the number 2. AND that the operator that follows is the .* operator.

Looking at the code you have, again, the 2.0 should always eliminate any confusion.

[James Akula]

If you are suggesting that it really doesn't matter, you are right about that 😏. Mainly, I was just curious and, as it is a little inaesthetic and does make functions longer (and therefore sometimes more difficult to read) I was wondering if there was, in fact, some method to the madness. I suspected there must be.

It would still be nice to turn it off, however, since I don't think 2. is actually a valid way to write a number, other than at the end of a sentance, as in, "The dogs numbered 2." Even then, the real grammarists would probably say it must be a number ten or higher, as in "The dogs numbered two, but the cats numbered 11."

That is a discussion for another board, though.

(Perhaps there is some place in the world of mathematics where you do put a decimal with no digits after.)

[per isakson]

Yes, in Fortran, 2. is interpreted as a floating point number and 2 an integer. Back in the seventies, the first version of Matlab was based on Fortran.

[John D'Errico]

The problem is, 2. is an entirely valid way to write a number. You may not love it. As Per points out, some languages use that as a way to distinguish an integer from a floating point number. MATLAB does not really care in that respect, because 2 and 2. are both used to represent the same number, in both cases stored in a double. Regardless, MATLAB needs to use that form to resolve an ambiguity in MATLAB. If the cost lies in some people not liking the way it looks, it was a choice TMW made and therefore something we need to accept. Oh well.

[James Akula]

Thank you both for the interesting comments. Just knowing there's a reason makes it less frustrating to see. That said, I'm not sure the real reason has been identified. At least, I don't think its the only reason. Are all the instances of ".0" in the below really disambiguating things? Maybe I misunderstand, but I think not.

syms x

f = 2 + 2*x + 2*x^2 + 2^(x - 2) + 2^(2 - x)

f = 

f = matlabFunction(f)

f = function_handle with value:
    @(x)x.*2.0+2.0.^(x-2.0)+2.0.^(-x+2.0)+x.^2.*2.0+2.0

f = sym(f)

f = 

f = simplify(f, 'Steps', 6400)

f = 

f = matlabFunction(f)

f = function_handle with value:
    @(x)x.*2.0+cosh((log(2.0).*(x-2.0))./2.0).^2.*4.0+x.^2.*2.0

f = sym(f)

f = 

f = matlabFunction(f)

f = function_handle with value:
    @(x)x.*2.0+x.^2.*2.0+cosh(x.*3.465735902799726e-1-6.931471805599453e-1).^2.*4.0

Lots of "interesting" decisions being made there WRT representing values in numerical vs. symbolic space, including when to put, and not to put, a decimal.