Help with using summation functions in matlab (Trying to create an atomic scatter function)

Hello, I am trying to create a matlab script that calculates an atomic scattering factor dependent on a,b,s,z where z is the atomic number, a and b are a 4 term array I will be getting from my course textbook, and s is sin(theta)/lambda which I will be calculating by hand as part of my homework. Not sure why I am having this difficulty but it seems my matlab is much ruster than I thought, but I would rather do this than an excel spreadsheet.

Equation should look something like:

My code currently looks like this:

function f = f(z,s,a,b)

f =(z^2)-41.78214*(s.^2)*symsum(a.*(exp(1).^-b.*(s.^2)),[a,b],[1 4]);

end

Varaible are curently:

When I remove the summation I get an answer (woohoo!), but when i try to use the summation it really gives me the error:

>> Scatteringfactor(z,s,a,b);

Error: File: Scatteringfactor.m Line: 3 Column: 67

Unbalanced or unexpected parenthesis or bracket.

I suspect I am misusing the symsum function or there is a smarter way of doing this.

Answer 1

[Clifton Whittaker]

Already noticed I put Z square in the front where I didn't need that. Fixed that part, but yeah that of course doesn't impact my summation.

Answer 2

[Steven Lord]

There are no symbolic variables in the function you posted, so symsum isn't the right tool for this job. Instead, just use sum.

x = 1:10;
y = sum(x)

You also should use exp(x) rather than exp(1).^x.

[Clifton Whittaker]

Ok so I replaced symsum with sum and now have the following:

function f = f(z,s,a,b)
    f =(z)-41.78214*(s^2)*sum(a*(exp(1).^-b*(s.^2)),[a,b]);
end

Now I am being told that the inner matrix dimension do not match?

both a and b are a 4 element array and z and s are defined.

Is this still issues with my sum function?

[Guillaume]

Is s scalar or a matrix? In the same function you have both s^2 and s.^2. If s is a square matrix, the two will produce very different results. Of course, if s is a non-square matrix, s^2 is an error (but s.^2 is fine). For scalars there's no difference between the two but it's very sloppy to mix the two notations.

Similarly, if a, b and s are vectors/matrices, it's not clear if you meant to use matrix multiplication * or memberwise multiplication .*.

Mix up between .^ and ^ and between .* and * are most likely the reason for the error.

The brackets around the (z) are also puzzling. They don't do anything useful.

Finally, it's not clear why you're passing [a, b] as a 2nd input to sum. The second input of sum is the dimension to operate along. I strongly suspect that neither a or b are valid dimension (i.e. scalar positive integers).

Answer 3

[Guillaume]

function scatterfactor = calculatescatteringfactor(Z, s, a, b)
    assert(numel(s) == 1, 's must be scalar');
    assert(isequal(size(a), size(b)), 'a and b must be the same size');
    assert(numel(Z) == 1, 'Z must be scalar');
   
    scatterfactor = Z - 41.78214 * s^2 * sum(a .* exp(-b .* s^2));
end

is the correct syntax for this function.