How to plot "f(x,y) = x^2 * y" function in matlab?

I am a beginner, so I am familiar with matlab. I am trying to plot a function: f(x, y) = x^2 * y, but it looks like something wrong. I am also trying another way but it looks different with a result I got from Google. Is there anybody have experience this problem, help me please?

The method I am trying is: x = rcost, y = rsint -> f(r, t) = r^2 * cos^2(t) * r * sin(t)

    ra = linspace(-2.0, 2.0);
    theta = linspace(-0.5*pi, 0.5*pi);
    [TH, RA] = meshgrid(theta, ra);
    F = RA.^3 * cos(TH) * cos(TH) * sin(TH);
    surf(TH,RA,F);
    shading interp;

[sixwwwwww]

Dear Minh, Can you share screen shot of expected out?

[Image Analyst]

linspace takes 3 arguments, not 2. Anyway, see my answer below, which follows your original method, not the Google trig method.

[the cyclist]

linspace() can accept two arguments. It will default to 100 generated points.

Answer 1

[Image Analyst]

Try this:

x = linspace(-2.0, 2.0, 50);
y = linspace(-2.0, 2.0, 50);
[xm, ym] = meshgrid(x, y);
fxy = xm.^2 .* ym;
surf(fxy);

% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);

It gives you almost exactly what you want. You just have to rotate the viewpoint of the axis. I trust you can do this.

[Minh Phuoc]

thank you. I got it.

[Minh Phuoc]

I want to visualize the Lagrange Multiplier for f(x, y) = x^2 * y, with x, y lie on the circle around the origin with radius is square root of 3, g(x, y) = x^2 + y^2 - 3. So I can plot the f function but it is too large and the circle is too small. Do you know how to scale or resize it like this image?

My result is:

The Matlab source code is:

    x = linspace(-2.0, 2.0, 50);
    y = linspace(-2.0, 2.0, 50);
    [xm, ym] = meshgrid(x, y);
    fxy = xm.^2 .* ym;
    surf(fxy);
    shading interp;
    hold all;
    theta = linspace(0, 2*pi);
    [xmc, ymc] = pol2cart(theta, sqrt(3));
    plot3(xmc, ymc, xmc+ymc);

Answer 2

[the cyclist]

I expect you are doing a matrix multiplication where you had actually wanted an element-by-element multiplication. Try this line instead:

F = RA.^3 .* cos(TH) .* cos(TH) .* sin(TH);

Notice how I modified your multiplications.

[Minh Phuoc]

I tried it, but it still does not work. This is the output.

The expected output is