Simultaneously interpolating over multiple rows of a matrix.

I have a matrix ("mat") of size N*M where each row is defined over a grid ("grid"), and I would like to obtain interpolated values ("vals") over a subset of rows of length K ("ind1") over a query vector ("qvec"). This is part of a larger iterative routine, where the size and elements of ind1 and the elements of mat and qvec change each iteration. I'm currently using a for-loop over the subset of rows, interpolating one at time. Here is a simplified example:

K = length(ind1);
vals_temp   = zeros(N,1);

for ii = 1:K
    ind2                 = ind1(ii); 
    vals_temp(ind2,1)     = interp1(grid,mat(ind2,:),qvec(ind2)); 
end

vals     = vals_temp(vals_temp>0);
 

I would like to be able to do this without a loop because this is very time consuming. I’m thinking that I can use interpn over the entire subset ind1, but I’m having trouble figuring out how to make the inputs conformable. Any help would be appreciated.

Answer 1

[Matt J]

This might be better,

e=1:K;

F=griddedInterpolant(mat(ind1,:),{e,grid});

vals_temp = F(e,qvec);

[Brandon]

I get this error:

Error using griddedInterpolant

Sample values must be of type double or single.

[Brandon]

it appears the inputs to griddedInterpolant above are reversed:

F=griddedInterpolant({e,grid},mat(ind1,:));

Now there is about a 6% improvement in computational time. Thanks!

Answer 2

[Matt J]

V=mat.';

vals_temp   = interp1(grid,V(:,ind1),qvec); 

[Brandon]

Thanks for you help. I think that something might still be missing, as this gives me a K*K matrix instead of a K length vector.

[Matt J]

Is the length of qvec also K?

[Brandon]

I just need to take the diagonals of that K*K matrix to get what i'm looking for. Thanks a lot!

[Matt J]

OK, but wait, now you're doing K^2 interpolation operations instead of K operations. Are you finding this to be faster regardless?

[Brandon]

Computation time is actually about 5% longer. Any other suggestions?