Symbolic Piecewise Addition Issue

Hello, I'm working on a script that calculates the deflection of beams, and thus I'm using singularity functions, essentially piecewise polynomials that 'switch on' at a certain point. There is a very odd issue I'm finding when I add two together. Here is the function I call to create them in the first place:

function func = singz(coeff, order, center)
    %%% Creates a singularity function (symbolic)
    syms f(z)
    f(z) = piecewise(z < center, 0, z >= center, coeff*(z - center)^order);
end

I've attached below the variables I'm about to use. For reference, A, B, and C are real symbolic variables, and L is a positive symbolic variable.

Here are the two initial functions:

>> testfunc

testfunc(z) =

piecewise(z < 0, 0, z < L, -A, symtrue, - A - B)

and

>> singz(-testmag, 0, testloc)

ans =

piecewise(z < 2*L, 0, symtrue, -C)

The first is actually a composite of two singularity functions, but their addition had no issue, for some reason.

Here's what happens when I add the two above:

>> testfunc + singz(-testmag, 0, testloc)

ans(z) =

piecewise(z < 0, 0, z < L & in(z, 'real'), -A, z < L, - A - C, z < 2*L, - A - B, symtrue, - A - B - C)

For some reason, I get an 'in(z,....' But the primary issue is this 'z < L, - A - C' term. It makes absolutely no sense in my mind. I am aware that I can assume z to be real and simplify. The result is:

> simplify(Sy)

ans(z) =

piecewise(z < 0, 0, z < L, -A, z < L, - A - C, z < 2*L, - A - B, symtrue, - A - B - C)

I know that the 'correct' '-A' term is first and will thus be evaluated, but the other term shouldn't be there in the first place. I don't trust that this order will magically work out every time that I want to run this program.

Thank you in advance; any help would be greatly appreciated.

Answer 1

[Austin]

I figured it out. It was the 'singz' function:

function func = singz(coeff, order, center)

%%% Creates a singularity function (symbolic)

syms z real

func(z) = piecewise(z < center, 0, z >= center, coeff*(z - center)^order);

end

Apparently I needed to declare z within the function. I'm guessing this helped MATLAB 'see' the z's as the same dependent variable? Very odd issue, I'm sure returning a symbolic function gives issues in general.

Thank you for the help!

Answer 2

[Paul]

Seems to work here.

How does the singz function work insofar as the output argument, func, is not defined inside the function.

syms z A B C L real
assumeAlso(L,'positive');
testfunc(z) = piecewise(z < 0, 0, z < L, -A, symtrue, - A - B)
fsingz(z)    = piecewise(z < 2*L, 0, symtrue, -C)

testfunc(z) + fsingz(z)
% in case symbolic output not rendering, long standing issue on Answers
char(ans)

ans = 'piecewise(z < 0, 0, z < L, -A, z < 2*L, - A - B, symtrue, - A - B - C)'

[Austin]

Apologies on the 'func' part, I think that I deleted that line while trying to fix something. I added back in 'func = f'. Regardless, I double-checked just now and the issue still persists.

>> syms A B C L real

>> assumeAlso(L, 'positive');

>> testfunc = singz(-A, 0, 0) + singz(-B, 0, L)

testfunc =

piecewise(z < 0, 0, z < L, -A, symtrue, - A - B)

>> testfunc + singz(-C, 0, 2*L)

ans =

piecewise(z < 0, 0, z < L & in(z, 'real'), -A, z < L, - A - C, z < 2*L, - A - B, symtrue, - A - B - C)

It happens, even if I separate them out:

>> testfunc2 = singz(-C, 0, 2*L)

testfunc2 =

piecewise(z < 2*L, 0, symtrue, -C)

>> testfunc + testfunc2

ans =

piecewise(z < 0, 0, z < L & in(z, 'real'), -A, z < L, - A - C, z < 2*L, - A - B, symtrue, - A - B - C)

[Walter Roberson]

syms A B C L real
assumeAlso(L, 'positive');
testfunc = singz(-A, 0, 0) + singz(-B, 0, L)

Output argument "func" (and possibly others) not assigned a value in the execution with "solution>singz" function.

testfunc + singz(-C, 0, 2*L)

testfunc2 = singz(-C, 0, 2*L)
 
testfunc + testfunc2
 
function func = singz(coeff, order, center)
    %%% Creates a singularity function (symbolic)
    syms f(z)
    f(z) = piecewise(z < center, 0, z >= center, coeff*(z - center)^order);
end

[Walter Roberson]

R2024b does not have the in(z,'real')

syms A B C L real
assumeAlso(L, 'positive');
testfunc = singz(-A, 0, 0) + singz(-B, 0, L);
disp(char(testfunc))

piecewise(z < 0, 0, z < L & 0 <= z, -A, L <= z, - A - B)

testfunc + singz(-C, 0, 2*L);
disp(char(ans))

piecewise(z < 0, 0, z < L & 0 <= z, -A, L <= z & z < 2*L, - A - B, 2*L <= z, - A - B - C)

testfunc2 = singz(-C, 0, 2*L);
disp(char(testfunc2))

piecewise(z < 2*L, 0, 2*L <= z, -C)

 
testfunc + testfunc2;
disp(char(ans))

piecewise(z < 0, 0, z < L & 0 <= z, -A, L <= z & z < 2*L, - A - B, 2*L <= z, - A - B - C)

 
function func = singz(coeff, order, center)
    %%% Creates a singularity function (symbolic)
    syms f(z)
    func(z) = piecewise(z < center, 0, z >= center, coeff*(z - center)^order);
end

[Austin]

I just updated to 2024b and it still didn't work. I tried what you did, but the results are slightly different for the domains:

>> syms A B C L real

assumeAlso(L, 'positive');

testfunc = singz(-A, 0, 0) + singz(-B, 0, L);

disp(char(testfunc))

piecewise(z < 0, 0, z < L, -A, symtrue, - A - B)

It defines -A at z<L, not z in [0,L]. Not sure what would cause this.

Maybe it isn't recognizing that they are the same 'z'?