Unfortunately, there will be a separate look-up for each call. The only thing I can think of is to find the bounding box yourself and then use INTERPN to do the linear interpolation without needing to find it. Something like this.
function [r1,r2,r3] = interpn3times(x1,x2,x3,x4,F1,F2,F3,xi1,xi2,xi3,xi4)
b1 = getBracket(x1,xi1);
b2 = getBracket(x2,xi2);
b3 = getBracket(x3,xi3);
b4 = getBracket(x4,xi4);
r1 = interpn(x1(b1),x2(b2),x3(b3),x4(b4),F1(b1,b2,b3,b4),xi1,xi2,xi3,xi4);
r2 = interpn(x1(b1),x2(b2),x3(b3),x4(b4),F2(b1,b2,b3,b4),xi1,xi2,xi3,xi4);
r3 = interpn(x1(b1),x2(b2),x3(b3),x4(b4),F3(b1,b2,b3,b4),xi1,xi2,xi3,xi4);
function b = getBracket(v,x)
L = length(v);
if x >= v(end)
b = [L-1,L];
elseif x <= v(1)
b = [1,2];
else
i = interp1(v,1:L,x,'previous');
b = [i,i+1];
end
I've tested this with exactly one test case, so obviously this is a no guarantees, use at your own risk type of thing, and I'm not sure it will actually be faster to do it this way than just to call INTERPN and let it do the look-ups three times. But that's the only thing that came to mind other than hacking the generated C code.
