Why is there a jagged line when I plot this function?

Hi guys,

I am trying to plot an implicit function and am getting strange results. I understand the smooth part of the function, but not the jagged part. Why is the jagged part there at all? Also, what can I do to eliminate it?

Here's the code:

f1=(@(x,y) (5.*y.^(1./2) -3)./(2.5.*y.^(1./2)+2.5.*x.^(1./2)-3)-y);
fimplicit(f1,[0 4 0 4],'black')

Answer 1

[tmarske]

It's because fimplicit is using too few evaluation points, resulting in too coarse an interpolation (by default it uses 151). You can override this using the 'MeshDensity' argument:

f1=(@(x,y) (5.*y.^(1./2) -3)./(2.5.*y.^(1./2)+2.5.*x.^(1./2)-3)-y);
fimplicit(f1,[0 4 0 4],'black', 'MeshDensity', 5000)

[econogist]

Thanks for your response tmarske. So how can I eliminate that part of the plot completely? I don't want it to be smooth or jagged, I want to try to get rid of it entirely.

[Walter Roberson]

What would you expect the result to look like? There are two lower-branch solutions for each x, and at some point they become equal and cross; what would you discard?

[econogist]

I expected it to look like it does in the attachment done here in Desmos. Why does it look different here compared to Matlab?

[Walter Roberson]

Ah, what is happening is that your function has a discontinuity in it, and what fimplicit is detecting is not a zero but rather a sign change.

[econogist]

Thanks for that! I see what you mean. So is there anyway I can get rid of that part of the plot completely? I tried limiting the range, but that gets rid of the part I want as well.

[Walter Roberson]

If you have the symbolic toolbox, you can solve f1 for x in term of y to get a single x for each y. you can then linspace() for y and put those through the equation to derive x, and then plot(x,y)

Answer 2

[econogist]

I do have the symbolic toolbox. I'm trying to do what you said but still having some trouble as I'm new to matlab. I think I'm on the right track, but it's coming up with an error message.

Here is what I have so far:

syms x y
eqn=(5.*y.^(1/2) -3)./(2.5.*x.^(1./2)+2.5.*y.^(1/2)-3)==y;
S=solve(eqn, x);
y=linspace(0,100);
plot(S,y)

[Walter Roberson]

plot(subs(S), y)

[econogist]

Thank you! This worked great!