Create a function that interpolates matrix values

My problem is the following:

Suppose we have a matrix A. I want to interpret the matrix entries A(i,j) as the values of a function f(x,y) on a lattice in R^2, that is A(i,j)=f(i,j) for all i,j on the lattice.

Is it possible to define such a function f as a Matlab function?

That is, given a matrix A, I want to define a function of the continuous variable (x,y) which somehow interpolates between the values of A (for my purposes, it could even be a piecewise constant function).

Answer 1

[Thiago Henrique Gomes Lobato]

Yes, sure. Something like this should do the trick:

% Your tabular function
A = [1,2;
     3,4];
 
 % Your values
 x = 1.5;
 y = 1.1;
 
 res = ftable(x,y,A)
 
 function funVal = ftable(x,y,A)
 
 % Find the index in the matrix
 Xx(1) = floor(x);
 Xx(2) = ceil(x);
 
 if Xx(1)== Xx(2)
     Xx(2) = Xx(2)+1;
 end
 
 Yy(1) = floor(y);
 Yy(2) = ceil(y);
 
 if Yy(1)== Yy(2)
     Yy(2) = Yy(2)+1;
 end
 
 % Get the matrix values
 V = A(Xx,Yy);
 
 % Mesh grid and interpolate
 [X,Y] = meshgrid(Xx,Yy);
 funVal = interp2(X,Y,V,x,y);
 end
 
 res =

    1.7000