MATLAB: How to change a Function by a Variable

change of variablesMATLABSymbolic Math Toolbox

How can I change a MATLAB function with a variable? (They are symbolic equations.)

Assume that I have an equation of "A*sin(phi)+B*cos(phi)". I want to replace "sin(phi)" by "2*x/(1+x^2)" , and "cos(phi)" should by replaced by "2*x/(1+x^2)" ? (Notice that x=tan (phi/2) , therefore sin(phi)=2*x/(1+x^2), and cos(phi)=2*x/(1+x^2) ) .

The final symboic equation should look :

"A*2*x/(1+x^2) + B*2*x/(1+x^2)"

syms A B phi x
equation_current=A*sin(phi)+B*cos(phi)
% ??? Some unknown operations ???
equation_new=A*2*x/(1+x^2)  +  B*2*x/(1+x^2)

Best Answer

Ercan, here you go, for the first term:

syms phi x A B
eq = A*sin(phi) + B*cos(phi)
eq = subs(eq,sin(phi),2*x/(1+x^2))

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You can carry on symbolic calculations. Read about diff.

https://www.mathworks.com/help/symbolic/diff.html

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Hello Ashmika,

You do have a symbolic solution for h, which goes to show that symbolic solutions are not always the ideal.

There are eight solutions in all. Each one contains, among other things, a roots function, the roots of a 4th degree polynomial in z

roots(z^4 + z^3*A(r,phi) + z^2*B(r,phi) +... D(r,phi), z, k)

where the coefficents A(r,phi) etc are complicated functions of r and phi. Here z is just a dummy variable, and the roots are determined by the coefficients A,B,C,D. Four distinct roots are indicated by cycling k through 1,2,3,4 as you can see at the end of each of the first four very long lines of code.

That's four solutions. The other four solutions have the same values for the roots, the only difference being that the expression at the beginning of each line

2*r^2*cos(phi + pi/3)

has positive sign for the first four solutions and negative sign for the last four solutions.

The four roots are merely indicated by the index k. Since this is a polynomial of degree four, it is possible to write each of the four roots explicitly in terms of A,B,C,D but if you think you have long expressions now, those expressions might be several times longer.

A symblic expression that takes up a page of text begins to lose its effectiveness. You can still do calculaton by plugging values or even more symbolic epressions into them, but at some point one might consider just doing a numerical calculation from the beginning.

Best Answer

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