Interpolation between three sets of data

I have three Arrays(Column Vector?) of Speed vs. Position for three different voltages (9V, 13.5V and 16V). Each array contains a speed for every position (2387 values). I would like to make a lookup table with the position and voltage as inputs and the speed value as output. For that, I would like to interpolate the speed vs. position arrays for the voltages in between the three that I already have. That should result in speed vs position arrays for 9v, 10v, 11v - 16v. Is this possible?

The interpolation methods in the help section only show how to interpolate along the x-axis (in this case the Position values) while in my case, I have three sets of data separated by voltage and want to interpolate in between these sets.

Perhaps a multidimensional array could be used?

Any help would be greatly appreciated.

Answer 1

[Andrei Bobrov]

Let your data S (Speed) V (voltages):

V = [9, 13.5, 16];
S = randi(20,10,3);

Solution:

n = 1:size(S,1);
[ii,jj] = ndgrid(n,V);
F = griddedInterpolant(ii,jj,S,'cubic');

[i2,Vnew] = ndgrid(n,[9 10 11 16]);

out = F(i2,Vnew);

or with griddata:

n = 1:size(S,1);
[ii,jj] = ndgrid(n,V);
[i2,Vnew] = ndgrid(n,[9 10 11 16]);

out = griddata(ii,jj,S,i2,Vnew);

[Sami Al-Abbar]

Thank you for your answer. I have a question though.

for S, should I replace randi(20,10,3); with my three variables corresponding with 9 13.5 and 6 from the workspace?

I tried that and my "out" was filled with NAN's.

Could you perhaps explain your solution so that I understand what is being done at each step?

Also, matlab gave the following errors:

"Error using griddedInterpolant The grid vectors do not define a grid of points that match the given values."

"Warning: The 'cubic' method requires the grid to have a uniform spacing. Switching the method from 'cubic' to 'spline' because this condition is not met."

Thank you in advance!

EDIT:

I got it to work with your edit with griddata! Thank you very much!

[Andrei Bobrov]

Please try variant with griddata. Now I do not have access to MATLAB, only an Octave. And please attach example of your data.

[Sami Al-Abbar]

Okay, I have now interpolated the data from 9-16V in increments of 0.5V. I have done this for 25C, -20C and 85C. Now I wish to interpolate in the same method but in the third dimension in order to get a 4d matrix.

I have this so far:

   V = [9, 13.5, 16];
  SRT = [RT9VCor,RT13_5VCor,RT16VCor];
  SLT = [LT9VCor,LT13_5VCor,LT16VCor];
  SHT = [HT9VCor,HT13_5VCor,HT16VCor];

n = 1:size(SRT,1);
[ii,jj] = ndgrid(n,V);
[i2,Vnew] = ndgrid(n,[9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16]);
RTout = griddata(ii,jj,SRT,i2,Vnew);
LTout = griddata(ii,jj,SLT,i2,Vnew);
HTout = griddata(ii,jj,SHT,i2,Vnew);

Everything above works so far. Now I want to interpolate these results for the different temperatures.

T = [-20, 25, 85];
S = cat(3,LTout,RTout,HTout);

n1 = 1:size(S,1);
[ii1,jj1] = ndgrid(n1,T);
[i21,Tnew] = ndgrid(n,-20:1:85);
Vout = griddata(ii1,jj1,S,i21,Tnew);

Since I dont quite understand what the ii and jj are doing, I also dont know how to adjust them for a third dimension. The griddata also needs to be adjusted but I dont know what to change. These are the error messages:

"Error using griddata (line 93) X,Y and XI,YI cannot be arrays of dimension greater than two."

"Error in Data_Analysis (line 56) Vout = griddata(ii1,jj1,S,i21,Tnew);"

(The Data itself consists of RPM values per mm. There are 2387 data points which correspond to the Position and each point has an RPM value)

Thank you in advance.

[Andrei Bobrov]

n = 1:size(SLT,1);
[i0,j0,k0] = ndgrid(n,[9,13.5,16],[-20,25,85]);
S = cat(3,SLT,SRT,SHT);
[i1,j1,k1] = ndgrid(n,9:.5:16,-20:85);

Vout0 = griddatan([i0(:),j0(:),k0(:)],S(:),[i1(:),j1(:),k1(:)]);
Vout = reshape(Vout0,size(i1));

[Sami Al-Abbar]

Thank you very much!

I spent most of yesterday afternoon and this morning trying to figure this out by reading the help section and using trial and error.

I got close enough to know the griddatan needed a 2387x15x106 values but I didnt know how to use ndgrid to achieve this. Thanks again for your solution.

Answer 2

[Alka Nair]

Hi, Interpolation can also be done for multidimensional data. Please refer to the documentation page for INTERP2 and INTERP3 at the following locations:

http://www.mathworks.com/help/matlab/ref/interp2.html

and

http://www.mathworks.com/help/matlab/ref/interp3.html