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I have a question related to an interpolation process. My data set is given in the following way:

An array Y which contains several vectors as follows:

Y = [Y1; Y2; Y3; Y4; Y5; Y6; .... Y32];

Each of these vector is defined as: Y1 = [0,0,0,0,0], Y2 = [0,0,0,0,1],....

Then, every Y_i vector has an evaluated parameter. For instance, V(Y1) = 80, V(Y2) = 90 leading to a vector V whose length is 32.

My goal is to get the value for any configuration of the Y vector, for example, xq = [0,0,0.5,0,1].

I tried it via the interpn function as follows:

vq = interpn(Y,V,xq,'linear');

Where,

[x1,x2,x3,x4,x5] = ndgrid(0:0.5:1);

xq = [x1(:) x2(:) x3(:) x4(:) x5(:)];

But I obtained an error using griddedInterpolant/subsref -> "The input data has inconsistent size".

Is it possible to carry out this kind of interpolation? Thanks in advance.

Guillaume
on 26 Nov 2019

TLDR: The Y and xq you've constructed work for scatteredInterpolant but not for griddedInterpolant which uses a different format.

interpn expects gridded data in a full grid format, which is not what your Y represents, at least in its current form. To represent gridded data, you would have to pass either 5 vectors (each [0 1] it sounds) or 5 5-D matrices

Assuming your Y truly represents all distincts point of a full grid (which it should be if you have 32 values) you can transform your input data into the format required by interpn (or griddedInterpolant which I would recommend over interpn):

griddedvalues = accumarray(Y + 1, V); %only works if Y values are integers. + 1 to make the 0 valid indices

You can then create your interpolant with

interpolant = griddedInterpolant(repmat({[0 1]}, 1, 5), griddedvalues);

and query it as

result = interpolant(x1, x2, x3, x4, x5)

Unfortunately, with gridded interpolant (and interpn you can't pass the query point in the xq format you created.

---

The syntax you've used however works with scatteredInterpolant.

interpolant = scatteredInterpolant(Y, V);

result = interpolant(xq)

scatteredInterpolant is probably slower than griddedInterpolant for properly gridded data but it's certainly easier to use with your Y and xq.

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