MATLAB: Interpolating n-dimensional functions

Question

I have a function which takes six variables and gives a single numerical value, newfn(a,b,c,d,e,f,), although most will only take a small range of values, and want to create a grid where I vary these variables and then be able to interpolate values between the grid. As I understand it I need to make the grid for reference data first, for the sake of quick computation say it is something like:

[alist,blist,clist,dlist,elist,flist]=ndgrid([1:2:10],[0.1:0.1:0.5],[0,2],[1.1,1.2,1.3],[10,20,30],3);

then find the reference values:

refdata=newfn(alist,blist,clist,dlist,elist,flist)

then suppose our grid of values to interpolate to is given by

[nag,nbg,ncg,ndg,neg,nfg]=ndgrid([1:10],[0.1:0.1:0.5],[0:2],[1.1,1.2,1.3],[10,15,20,25,30],3);

Then I thought I'd be able to use griddatan like this:

intrpldata=griddatan([ag,bg,cg,dg,eg,fg],refdata,[nag,nbg,ncg,ndg,neg,nfg])

but this isn't working, so I'm going badly wrong somewhere?

Answer 1

First, IF you have a complete gridded lattice, then you don't want to use griddatan. That is DEFINITELY a BAD idea. Why? Because griddatan will try to tessellate that domain. It thinks you have a scattered set of data, and has no idea how things are related. The result would be very slow at best, and for no good reason. Actually, tit would be a good reason - you want to use the wrong tool in griddatan.

The actual failure of griddatan there is because you are calling it incorrectly. But since this is the wrong tool to use in the first place, just use the correct tool.

Instead, you need to use a tool like griddedInterpolant, or interpn. Either will work, although if you wish to use interpn, then you need to create the grid using meshgrid, not ndgrid. Since you have used ndgrid there, then use griddedInterpolant.