Calculation of abs() and angle() of a symbolic expression - strange behaviour

Hi.

I have come across some strange behaviour of the abs() and angle() function in symbolic calculations:

The first result is as expected. The second should be calculated with equal ease as

but matlab just rewrites the expression using the | | sign.

Similar behaviour applies to the angle function

Why is this happening and how to force matlab to do the calculation also in the second case?

Marek

[Govind KM]

Hi Marek,

I am able to reproduce this in MATLAB R2024b for abs but not for angle. Do you have a similiar example for the same behaviour using angle?

[Marek Golebiowski]

Hi,

thanks for your interest in the topic.

Here is an example:

The correct result should be -atan2(LR,R+1), yet matlab again rewrites the expression

best

Marek

Answer 1

[Govind KM]

Hi Marek,

When a symbolic expression is defined, it undergoes some internal simplification before being displayed. For some cases, additional simplification steps can be required to get a simpler result. The simplify method can be used to perform further simplication on a symbolic expression. Here is sample code for the provided example:

syms R real positive
syms L real positive

%Specify the number of simplification steps using the 'Steps' option
%Use the 'All' option to return all equivalent results
exp1=simplify(abs(R+1i*L*R+1),'All',true,'Steps',10), disp(char(exp1))

[((R + 1)^2 + L^2*R^2)^(1/2); (2*R + R^2 + L^2*R^2 + 1)^(1/2)]

exp2=simplify(abs(R+1i*L*R+L),'All',true,'Steps',10), disp(char(exp2))

[abs(L + R + L*R*1i); ((L + R)^2 + L^2*R^2)^(1/2); (L^2 + R^2 + L^2*R^2 + 2*L*R)^(1/2)]

The desired result can be selected as needed:

desiredExp=exp2(2), disp(char(desiredExp))

((L + R)^2 + L^2*R^2)^(1/2)

The PreferReal option can be used to favor the selection of expressions containing real values over the ones containing complex values:

simplify(abs(R+1i*L*R+L),'Steps',10,'Criterion','PreferReal'), disp(char(ans))

((L + R)^2 + L^2*R^2)^(1/2)

A similar approach can be followed for the angle function.

More details on the simplify method and its options can be found in the following documentation:

https://www.mathworks.com/help/symbolic/sym.simplify.html#namevaluepairs

Hope this is helpful!

[Marek Golebiowski]

thank you.

that solves the problem

Marek