Interpolation value from 3D matrices - matlab

Question

With 3 vectors and 3 functions, I'm building 3 result matrices. Here's a short and simplified example of what I'm actually doing:
xVec = -0.2:0.05:0.2; % Vector 1
yVec = 0:0.1:0.4; % Vector 2
zVec = 1:3; % Vector 3
[X,Y,Z] = meshgrid(xVec,yVec,zVec);
R1 = (X.^2+Y.^2)./sqrt(Z); % Result matrix 1
R2 = sin(X.^2+Y.^2)./exp(Z); % Result matrix 2
R3 = cos(X.^2+Y.^(1/2)).*(Z.^(1/2)); % Result matrix 3
As of now, I'm calling 6 times the interp1 MATLAB function in order to interpolate (linearly) the 3 result matrices for a specific set of xVec, yVec and zVec values (e.g. xVec = 0.012, yVec = 0.37, and zVec = 1.45). I'm using the interp1 function as I was not able to find a better way of solving this (I think this could be possible with interp2 or interp3 MATLAB functions). By running the MATLAB profiler, I found that the calls to interp1 are taking a lot of time. Hence, I would like to know if there is a faster way of doing this (e.g. using less calls by using the interp2 or interp3 MATLAB function, or maybe even merging my 3 result matrices in a multidimensional array)?

Answer 1

As suggested in the comments, you can use gridded griddedInterpolant. I do not think that there is a standard procedure in MATLAB for optimisation of the interpolation of vector fields (although I did not look thoroughly enough to state this for a fact). Thus, I think you will have to use a different griddedInterpolant for each individual function R1, R2 and R3.
%% griddedInterpolant
[X, Y, Z] = ndgrid(xVec, yVec, zVec);
R1 = (X.^2+Y.^2)./sqrt(Z);
F = griddedInterpolant(X, Y, Z, R1, 'cubic');
figure
subplot(121)
s = slice(Y, X, Z, R1, 0.2, [-0.1 0.1], 2);
set(s, 'EdgeColor', 'none');
for n = 1 : length(s)
set(s(n),'alphadata', get(s(n), 'cdata'), 'facealpha', 'flat')
end
xlabel('y');
ylabel('x');
zlabel('z');
view([-130 30]);
title('Original data');
xqVec = linspace(min(xVec), max(xVec), numPoints); % Vector 1 interpolant
yqVec = linspace(min(yVec), max(yVec), numPoints); % Vector 2 interpolant
zqVec = linspace(min(zVec), max(zVec), numPoints); % Vector 3 interpolant
[Xq, Yq, Zq] = ndgrid(xqVec, yqVec, zqVec);
tic
R1q = F(Xq, Yq, Zq);
toc
subplot(122)
s = slice(Yq, Xq, Zq, R1q, 0.2, [-0.1 0.1], 2);
set(s, 'EdgeColor', 'none');
for n=1:length(s)
set(s(n), 'alphadata', get(s(n), 'cdata'), 'facealpha', 'flat')
end
xlabel('y');
ylabel('x');
zlabel('z');
view([-130 30]);
title('Gridded interpolant');
%% Query at a point
disp(['R1 at [0 0.21 2.1] is ' num2str(F(0, 0.21, 2.1))])