How to speed up a 2D interpolation in MATLAB?

I am reading a table from excel which I am using as the basis for a 2D interpolation, I've included an image of the table with the x, y and output variables shown with the sensitive data omitted for reference.

I have sensor data for position and velocity, with the variable names Raw_Position and Raw_Velocity respetively, that are used to interpolate the Output0 value at a given positon and velocity. The sensor data is in the format of n rows and m columns.

Currently I am achieving this using two interp1 functions inside nested for loops that repeat the calculation for every row and column of the sensor data but this is very slow and my script is taking several minutes to run for a large data set. Is there a way to speed up this process with the interp2 function or something similar?

Answer 1

[Paul]

A single call to interp2 should do the trick

Position0 = 1:4;
Velocity0 = 1:5;
Output0 = Position0.' + Velocity0;
RawPosition =[1 2;3 4;1 2]; RawVelocity = [2 3;4 5;1 2];
Output = interp2(Velocity0,Position0,Output0,RawVelocity,RawPosition)

Output = 3×2

3 5 7 9 2 4

% check
RawPosition + RawVelocity

ans = 3×2

3 5 7 9 2 4

[Jack Smith]

Hi Paul,

This worked for me for inputs in a single row format but my inputs are actually arrays with 1000 rows and 100 columns. I believe I need to put the interp2 function within two for loops and interpolate the value of Output0 for each row in column 1, then column 2 and so on. This is where I am having dificulties.

I've copied my code below. The x and y axis are switched compared to the sketch I posted before.

for i = size(Position0,1) %rows

for j = size(Position0,2) %columns

Output(i,j) = interp2(Position0,Velocity0,Output0,RawPosition(i,j),RawVelocity(i,j));

end

end

[Paul]

Hi Jack,

As I showed, the RawPosition and RawVelocity inputs to interp2 can be arrays. In my example they were both 3 x 2, as was the output.

Also, according to our sketch Position0 corresponds to rows of Output0 and Velocity0 corresponds to the columns of Output0. In interp2, the x-coordinate corresponds to the columns and the y-coordinate the rows, which is why in my example I had Velocity as x and Postion as y.

[Jack Smith]

Thanks Paul, after swicthing the position and velocity variables this has worked for me now.