MATLAB: Expanding and interpolating between sequential values in a nx2 matrix

interpolationloopsMATLABvectorization

Hello,
I wish to linearly interpolate between sequential values in a given sorted 2xn matrix and a integer or non-integer sub-interval spacing value. For instance:
Given
[1 3; 2 6; 3 1; 4 9]
and an interpolation interval of, say, 0.5 (or any other value less than the minimum spacing between sequential values in column 1)
I hope to return an expanded nx2 matrix containing:
[1 3; 1.5 4.5; 2 6; 2.5 3.5; 3 1; 3.5 5; 4 9]
Note: The first column does not have to possess equally-spaced values.
I have written a function to do this using looping and it works quite well. However, when the input matrix exceeds 10,000 rows and the sub-interval is less than 0.5 the efficiency of my function drops off very quickly.
Does anyone know of a way to accomplish this goal using vectorization operations so that I can avoid using – or minimize – looping in my function?
Thank you in advance.
David

Best Answer

One possible method:
x0 = [1 3; 2 6; 3 1; 4 9]; % Original array
interval = 0.5;
xi = [min(x0(:,1)):interval:max(x0(:,1))]'; % Define new spacing by interval
yi = interp1(x0(:,1),x0(:,2),xi); % Interpolated values at new spacing
newArray = [xi yi]; % New array
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