interpolate value of 3D points on a meshgrid with a CUSTOM FUNCTION

% particle to mesh interpolation function (NOT ARBITRARY)
H = 3/pi/rCut^2;
u = @(r) H*(1-r/rCut).*(r.^2<=rCut^2);
    
for k = 1:length(ptcls.q)
            r = sqrt((X - ptcls.x(1, k)).^2 + (Y - ptcls.x(2, k)).^2 + (Z - ptcls.x(3, k)).^2);
            rho_lr = rho_lr + ptcls.q(k)*u(r);
end

I want to speed up this simple loop where ptcls.q is the value I want to interpolate, X,Y,Z are the points of a meshgrid and ptcls.x is the 3D scattered position of particles inside the mesh. I cannot use scatteredInterpolant function since is slow and does not fit the math behind the problem, any idea on how to speed up the calculation?

Answer 1

[Torsten]

I don't understand why you use ptcls.q on the right-hand side of an equation (thus as known) if you want to interpolate it.

Assuming ptcls.q is a row vector, the loop can easily be replaced by

r = sqrt((X - ptcls.x(1, :)).^2 + (Y - ptcls.x(2, :)).^2 + (Z - ptcls.x(3, :)).^2);
H = 3/pi/rCut^2;
u = H*(1-r/rCut).*(r.^2<=rCut^2);
rho_lr = sum(ptcls.q.*u)

[Andrea Somma]

I want to interpolate a scattered field with points x y z stored inside ptcls.x with value ptcls.q (scalar) on a mesh with a meshgrid X,Y,Z. The problem is I cant use matrix operations of matlab since the mesh is a 64x64x64 and the particles are 100k, I cant store a r 3D matrix of that size

[Andrea Somma]

r is acrually the distances from a point to each node of the mesh

[Torsten]

The problem is I cant use matrix operations of matlab since the mesh is a 64x64x64 and the particles are 100k, I cant store a r 3D matrix of that size

If you can't store it, then you will have to use a loop over the 100000 particles. Here, your r will only have 64x64x64 elements in each cycle of the loop.

[Andrea Somma]

Yes that's exactly what I sent, my question was if there is a smart way to select nodes of the mesh in order to reduce the numer of calculations with a matlab function

[Torsten]

Yes that's exactly what I sent, my question was if there is a smart way to select nodes of the mesh in order to reduce the numer of calculations with a matlab function

How should this be possible ? For each particle, you have to "order" the (X,Y,Z) coordinates with respect to their distance to the particle position in order to interpolate. And in order to achieve this, given a particle, you have to evaluate r for each triple (X,Y,Z).

[Andrea Somma]

Since the particle has coordinates x,y,z and the grid X,Y,Z with linear spacing you can in some way extract a subset of XYZ by the next node of the mesh i = floor(x/hX) and neighbours inside hx*n_neighbours > rCut, where hX is the grid spacing. Then performing the interpolation only on that subset of nodes, I supposed that matlab had a sort of nearest neighbours algorithm to do that