Solution of implicit function

Hi,

I have an equation for example x^2+y^2-16=0 . How can I get all of x and y value for this equation. Of course I can write it y=sqrt(16-x^2). But what if this equation is more complex. I tried something with solve command on matlab but i didn't achive. can u help me?

[Matt J]

How can I get all of x and y value for this equation.

There are infinite pairs x,y that solve your example equation. I think you really mean, "how can I get y for a given x?"

[Cengiz Görkem DENGIZ]

Yes i try it for x values. x=linspace (0,4,101) with solve command but it takes too much time for complex problem. Also i can plot with it ezplot. I want to get this plot data. But not from plot. First calculate data then plot.

Answer 1

[Matt J]

If analytical solutions exist, then SOLVE would be the thing to use.

If analytical solutions don't exist, then you would have to search numerically for a solution using FZERO or FSOLVE.

[Cengiz Görkem DENGIZ]

Solve command take too much time. For example i want to find it for x=linspace (0,4,101). How could i calculate y values for x values easily and rapidly.

[Matt J]

Once you have solved the equation symbolically, you could convert it to a vectorized anonymous function,

    >> x=sym('x'); f=sqrt(16-x^2)

    f =

    (16 - x^2)^(1/2)

    >> fa=str2func(['@(x)' char(vectorize(f))])

    fa = 

        @(x)(16-x.^2).^(1./2)

    >> tic;fa(linspace(0,1,401));toc
    Elapsed time is 0.000538 seconds.

Seems pretty fast to me.

[Cengiz Görkem DENGIZ]

Yes you are right. But my equation is not simple like that.

s1^2/s0^2-c*s1*s2/s0/s90+s2^2/s90^2+((p+q)-(p*s1+q*s2)/sb)*s1*s2/s0/s90-su^2=0

Here s1 and s2 are variables. The others are constant.

[Walter Roberson]

So you solve() for s1 and get two results (two branches of a quadratic.) And you matlabFunction() that; do the parts individually if you need to. Then substitute in the s2 values.

[Cengiz Görkem DENGIZ]

Could you show me a little example?

[Walter Roberson]

c = rand; s90 = rand; p = rand; q = rand; sb = rand; su = rand;   %in other words you need numeric values for them

syms s1 s2
eqn = s1^2/s0^2-c*s1*s2/s0/s90+s2^2/s90^2+((p+q)-(p*s1+q*s2)/sb)*s1*s2/s0/s90-su^2;
sols = solve(eqn, s1);

f1 = matlabFunction(sols(1), s2);
f2 = matlabFunction(sols(2), s2);

S2 = linspace(-50,50);

plot(S2, f1(S2), S2, f2(S2));