Element wise conditional evaluation of a function over a meshgrid

I created a 2-D mesh using meshgrid. Now, I want to evaluate a function over this mesh based on the elements of mesh i.e., if the mesh elements are equal then evaluate expression1 else evaluate expression2.

a=linspace(1,2,2);
b=linspace(1,3,3);
[A,B]=meshgrid(a,b)

fact(A,B,0.1)

function f = fact(m,n,lam)
    if m==n
        f=m.*(n+2)+lam;
    else
        f=0;
    end
end

The above just gives me the matrices A and B and 0 from the else statement. I want it to compare the elements of "m" and "n" and evaluate the "if" part if they are the same. I tried using bsxfun(@eq,m,n) instead of m==n. It gives the same result, 0 from the else part. Below is the output.

A =

     1     2
     1     2
     1     2


B =

     1     1
     2     2
     3     3


ans =

     0

Instead, evaluating the following code (no if statement) over the mesh does give me the expected result of the function values over the entire mesh.

a=linspace(1,2,2);
b=linspace(1,3,3);
[A,B]=meshgrid(a,b)

fact(A,B,0.1)

function f = fact(m,n,lam)

        f=m.*(n+2)+lam;
end

gives

A =

     1     2
     1     2
     1     2


B =

     1     1
     2     2
     3     3


ans =

    3.1000    6.1000
    4.1000    8.1000
    5.1000   10.1000

The output I am looking for should look like

3.1000      0
0           8.1000
0           0

Answer 1

[Matt J]

f = (A==B) .* (A.*(B+2)+lam);

[Adamya Goyal]

Wow. Thank you! This looks like magic. ??

[Matt J]

You're welcome, but please Accept-click the answer to indicate that it worked.

[James Browne]

That is pretty awesome! Nice work!

Answer 2

[James Browne]

Hello, I believe that I have developed a solution for you:

a=linspace(1,2,2);
b=linspace(1,3,3);
[A,B] = meshgrid(a,b)
fact(A,B,0.1)
function f = fact(m,n,lam)
f = zeros(size(n,1), size(n,2));
for i = 1:size(n,1)
    for j = 1:size(n,2)
        if m(i,j) == n(i,j)
            f(i,j) = m(i,j)*(n(i,j)+2)+lam;
        else
            f(i,j)=0;
        end
    end
end
end

Hope this at least helps =)

[Adamya Goyal]

Yes. Thank you so much. But, I want to avoid using loops and keep it "vectorized" if possible. Because the mesh I am going to use this for is going to be huge (~10000x10000 or larger).