Help with Basic 2D Contour Plot

I am trying to get this contour plot to work. This is a simple example so I can figure out how to do it before applying it to trickier equations.

I have this function saved in a separate .m file:

function a = triarea(x,y)
a = x.^3-2.*x-5+y.^2;
end

The main script calls this function:

for s=[0:1:3],
    for t=[0:1:3],
        q=triarea(s,t)
    end
end

This displays the range of values for q (one after the other, ideally I'd like them as one matrix upon completion but don't know how to do that).

What I want to do is a contour plot where the x-axis is the s variable and the y-axis is the t variable and q is represented as the contour i.e. varying in colour depending on it's value at each s,t point.

How do I do this?

It says that the contour variable Z must be at least a 2x2 matrix but I have only one value at each s,t point.

Answer 1

[Friedrich]

Hi,

don't use a loop. Use meshgrid:

s=[0:1:3]
t=[0:1:3]

[X,Y]  = meshgrid(s,t)
Z =triarea(X,Y);
contour(X,Y,Z)

This works as long the function triarea accepts matrices as input like it does in your example. Also you don't need to care about s and t (they dont need the same length and the values also doesn't matter).

s=-pi:0.1:pi;
t = 10:0.1:20;

[X,Y]  = meshgrid(s,t)
Z =triarea(X,Y);
contour(X,Y,Z)

Answer 2

[John Doe]

Will this work for you?

q = zeros(4);
for s=[0:1:3],
    for t=[0:1:3],
        q(t+1,s+1)=triarea(s,t)
    end
end

Note that this will only work if t and s contain only integers. If they do not:

s = [0:0.1:3];
t = [0:0.1:3];

q = zeros(length(s));

for i = 1:length(s)
  for j = 1:length(t)
    q(i,j) = triarea(s(i),t(j));
  end
end

- Rob

Answer 3

[James]

Thanks for your answers. Huge leap forward in my work.

I now get the values of q displayed as a matrix:

Z =

      -5    -6    -1    16
      -4    -5     0    17
      -1    -2     3    20
       4     3     8    25

I also have a contour plot of q in terms of s,t which looks like this:

http://postimg.org/image/4o31o2qrz/

So all seems good. Apart from that contour plot (the colours) don't seem to correspond to the matrix values (i.e. I thought top left be most blue and bottom left most red, and that doesn't seem to be the case).

Answer 4

[John Doe]

Follow the instructions from Friedrich, but flip the matrix around before you plot it.

Now, Z(1,1) is in the origin, Z(1,2) is in (0,1), Z(3,3) is in (2,2) etc. As you go downwards in Z, you move upwards on the Y-axis (in the plot).

ZZ = flipud(Z);

Answer 5

[James]

I have used Friedrich's code and got that contour plot.

If I flip Z before I plot it:

[X,Y]  = meshgrid(s,t);
Z =triarea(X,Y);
ZZ=flipud(Z)
contourf(X,Y,ZZ);

This displays the matrix as it should be but also flips the contour plot!

If I plot is as before i.e. plot Z then put 'ZZ=flipud(Z)' after I can see the matrix that corresponds correctly to the contour plot.

I could live with remembering that one of either the plot or the matrix is flipped but sure there must be a tweak to fix it. Quite an odd problem.