griddedInterpolant error "Interpolation requires at least two sample points for each grid dimension."

I'm systematically getting this error trying to use griddedInterpolant. Here's a simple example:

bp1 = [0:1:10];

bp2 = [5:0.5:10];

bp3 = [2:0.1:3];

tv = bp1.*bp3+bp2.^2

f=griddedInterpolant(bp1,bp2,bp3,tv)

But I get the error:

Error using griddedInterpolant

Interpolation requires at least two sample points for each grid dimension.

What have I missed?

Answer 1

[Voss]

The points (bp1, bp2, bp3) in 3d space do not form a grid. They are equally-spaced points along a line segment from (0,5,2) to (10,10,3).

You can use ndgrid to construct a set of points that form a grid from your bp1, bp2, bp3 vectors.

bp1 = 0:1:10;
bp2 = 5:0.5:10;
bp3 = 2:0.1:3;
% tv = bp1.*bp3+bp2.^2;

[BP1,BP2,BP3] = ndgrid(bp1,bp2,bp3);

TV = BP1.*BP3+BP2.^2;

f=griddedInterpolant(BP1,BP2,BP3,TV)

f = 
  griddedInterpolant with properties:

            GridVectors: {[0 1 2 3 4 5 6 7 8 9 10]  [5 5.5000 6 6.5000 7 7.5000 8 8.5000 9 9.5000 10]  [2 2.1000 2.2000 2.3000 2.4000 2.5000 2.6000 2.7000 2.8000 2.9000 3]}
                 Values: [11×11×11 double]
                 Method: 'linear'
    ExtrapolationMethod: 'linear'

[Dave Hall]

First, thanks for pointing out that I hadn't created a grid! (doh!) Second, thanks for pointing me to "ndgrid". That was not so obvious. The challenge will be adapting my real problem, which is a 5 parameter data set with 22000 lines. But I think what you've shown can be applied. I'll let you know if it doesn't work.

[Stephen23]

Another approach which does not create large arrays BP1, BP2, BP3, is to simply RESHAPE the vectors to have the correct orientations (note that RESHAPE is a very efficient command):

BP1 = reshape(0:1:10,   [],1,1);
BP2 = reshape(5:0.5:10, 1,[],1);
BP3 = reshape(2:0.1:3,  1,1,[]);
TV = BP1.*BP3+BP2.^2;
f = griddedInterpolant({BP1(:),BP2(:),BP3(:)},TV)

f = 
  griddedInterpolant with properties:

            GridVectors: {[11×1 double]  [11×1 double]  [11×1 double]}
                 Values: [11×11×11 double]
                 Method: 'linear'
    ExtrapolationMethod: 'linear'

[Dave Hall]

The challenge I have is: my results vector is the result of simulation of the 22000 combinations of bp1, bp2, bp3, bp4 and bp5. How do I go about creating the equivalent of TV above? In other words, I have a spreadsheet that looks like:

0 59 18 0 50 4805.37

0 59 18 0 150 4806.96

0 59 18 0 250 4806.96

0 59 18 0 350 4806.96

0 59 18 0.2 50 4811.76

0 59 18 0.2 150 4817.66

0 59 18 0.2 250 4817.67

Definining bp1, bp2, bp3, bp4 and bp5 (columns 1-5) is pretty clear, but what do I do with the last column, result vector tv?

[Stephen23]

Either call RESHAPE on each column of data.

Or simply call SCATTEREDINTERPOLANT and let it do the work for you.

[Dave Hall]

Unfortunately, scatteredInterpolant is limited to 3 parameters. I'll try to reshape each parameter plus the result vector.

Answer 2

[Star Strider]

The interpn function could be an option. You will need to experiment with the ndgrid function to determine how best to reshape the first 5 columns of your data to conform to it (if they indeed need reshaping — they may not) and then do the interpolation. I am not certain how easy it would be to make sense of the results, much less plot them, since everything in this universe is limited to 3 spatial dimensions and time, last I heard.

If you only want to interpolate specific points or ranges of points within the limits of the original vectors (so not extrapolating), interpn could do what you want.