Solve equation with 2 variables being vectors

Example C=@(A,B) A+B*A A=[1 2 3] B=[4 2 6]

I want C to be a matrix of all possible solutions

Right now I have C as a function and A and B as user inputs

Is there any easier way than writing a loop?

Clarification: C is a very complicated equation with a 2 variables that can have multiple inputs. I want to know all possible solutions. Is there a way to get all possible solutions without nesting loops. I'm making a contour map of 2 inputs and 2 outputs.

[Justin]

What do you mean by possible solutions? Do you mean adding only one number from one to only one number to the other one and finding each answer?

Can you explain what the goal of this operation is or some other background?

[Nicole]

bsxfun does not work because I have 4 variables, c and a are system dependent constants, Ff and Xi are inputs.

Xf=solve(Ff==2*c*a*(Xf/Xi-Xi^2/Xf^2),Xf);

Xf=Xf(1);

Xfs=matlabFunction(Xf);

where Xfs=@(Ff,Xi,a,c)

[Justin]

You should be able to put an array into a symbolic variable and solve for each value of that array. That means you could define Ff and Xi using the meshgrid method in my answer below. You could:

[Xi, Ff] = meshgrid(Xi, Ff)

and then solve with the values of Xi and Ff that are returned which should give you every possible combination.

Answer 1

[Justin]

Edited for clarification:

This may do the trick. It has a loop but only one for implementing the function. After it is run the a, b, and c should hopefully be everything you need.

A=[1 2 3];
B=[4 2 6];
[a, b] = meshgrid(A, B);

for i = 1:length(p)
  c(i) = C(a(i), b(i));
end

Let me know how that works.

_______________________________________________

OLD STUFF:

I'm not sure if I understand the question right but bsxfun may be useful. bsxfun automatically extends an array along a singleton dimension to match the other array's size. You could use it to get the results you want (I think).

A=[1 2 3];
B=[4 2 6];
bsxfun(@plus, A, B')
ans =
   5     6     7
   3     4     5
   7     8     9

Answer 2

[Matt J]

C=bsxfun(@(A,B) A+B.*A, A(:),B(:).')