Multidimensional data storage and interpolation

Question

I have a function (so to speak, i actually have data with this characteristic) with one variable x and several parameters a, b and c, so y = f(x, a, b, c). Now i want to interpolate within families of parameters (for example for variations of a).

I'm currently doing this for data with one parameter (here, y is the data matrix)

% generate variable and data
x = linspace(0, 1, 100);
a = [0, 1]; % parameter
for i = 1:length(a)
    y(:, i) = x.^2 + a(i);
end
% interpolate:
yi = interp1(a, y.', 0.5);

This works fine, but how do i expand this to more dimensions?

My current data format is like this: Each column of my data matrix represents one specific set of parameters, so for example:

0 0 0 0
1 1 1 1
2 2 2 2
3 3 3 3

where the first column denotes a = 0, b = 0, the second a = 1, b = 0, the third a = 0, b = 1 and the last a = 1, b = 1 (values are just for clarification, this is not on purpose binary. Also, the data columns are obviously not the same).

This data format is just the consequence of my data aquisition scheme, but i'm happy to change this into something more useful. Whatever works.

Answer 1

Works well for me:

% generate variable and data
x = linspace(0, 1, 100);
a = [0, 1, 2]; % parameter
b = [3, 4, 5]; % parameter
c = [6, 7, 8]; % parameter

% Create grid
[X,A,B,C]=ndgrid(x,a,b,c);

% define function
foo = @(x,p1,p2,p3) p1.*x.^2 + p2.*x + p3;

% evaluate function
Y = foo(X,A,B,C);

% interpolate:
yi = interpn(X,A,B,C,Y,x,1,4,6);