how drop near zero imaginary terms from symbolic result?

I'm doing some symbolic matrix manipulations with complex valued matrices. Some of my results are as below.

Zaa*(1 + 3i/36028797018963968) + Zab*(1 + 3i/36028797018963968)

Is there a way to tell Matlab to ignore those near zero imaginary results so the answer will be reported simply as,

Zaa + Zab

[Jamie Steel]

Does the real function not work? I.e.

Zaa*real(1 + 3i/36028797018963968) + Zab*real(1 + 3i/36028797018963968)

Or, if you mean only when the imaginary part is near zero, how about

tolerance = 1e-6;

z = result % e.g. 1 + 3i/36028797018963968

if imag(z) < tolerance

z = real(z)

end

[John D'Errico]

@Jamie Steel - the use of a tolerance does not apply here, because the imaginary pary of that number is NOT a number, but in fact still symbolic. Worse, if Zaa and Zab may themselves be complex, then you get a messier result than you expected.

syms Zaa Zab
term = Zaa*(1 + 3i/36028797018963968) + Zab*(1 + 3i/36028797018963968);
imag(term)

ans = 

[Jamie Steel]

@John D'Errico Ah I see, perhaps I misinterpreted the expression - I assumed the symbols were only Zaa and Zab, and that the following complex number z was some numerical result multiplying them. That is horribly messy though! My experience with symbolic manipulation is certainly limited enough such that I've never run into trouble like that thankfully

[Russell]

Thank you. That is better than nothing, but is ugly.

I tried the following and it sorta works too. Wish better way to do it directly.

vpa(term,2)

ans =

Zaa*(1.0 + 8.3e-17i) + Zab*(1.0 + 8.3e-17i)

Answer 1

[Moksh]

Hi Russell,

I understand that you are attempting to eliminate the imaginary part in the intermediate term if it is close to zero, as shown in the example provided.

You can utilize the "abs" and "imag" functions in MATLAB to obtain the magnitude of the imaginary part. By comparing this magnitude with a threshold value, which can be adjusted as needed, you can determine if the imaginary part is sufficiently close to zero.

Here is an example code:

syms Zaa Zab

% Get the imaginary part in z
z = 1 + 3i/36028797018963968;
imag_z = imag(z);
tol = 1e-5;

% Ignore the imaginary part in z if it is near zero
if abs(imag_z) < tol
    z = real(z);
end

% Define the main result
Z = Zaa * z + Zab * z;
disp(Z)

For more understanding about the above used functions, please refer to the following documentation:

• imag: https://in.mathworks.com/help/matlab/ref/imag.html
• abs: https://in.mathworks.com/help/matlab/ref/abs.html

Hope this information helps!

Best Regards,

Moksh Aggarwal

[Dyuman Joshi]

You are treating z as a numeric variable, which is not the case here as OP is dealing with symbolic variables.

This has been clarified above as well (1 year ago by @John D'Errico) - https://in.mathworks.com/matlabcentral/answers/1790480-how-drop-near-zero-imaginary-terms-from-symbolic-result#comment_2338445