Expanding and interpolating between sequential values in a nx2 matrix

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

Answer 1

[the cyclist]

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

Answer 2

[Paulo Silva]

m=[1 3; 2 6; 3 1; 4 9];
mm=interp2(m);
mm(:,2)=[];  %remove the midle column
mm %your result

[Fangjun Jiang]

That is interesting, Paulo! Where did you get that interp2(m) with one input argument?

[Paulo Silva]

The Gods of Mathworks leave these presents for us to find :)

Found it by chance but has you can see there's a problem, one extra column must be removed from the result and that slows the code, also it doesn't work properly for other interval values than 0.5

[Fangjun Jiang]

Okay, I just want to understand how it treats the single input argument which is a 2-D array. If there is no available document, I guess I can go play and figure.

[Paulo Silva]

edit interp2 and see the magic inside :)

[Fangjun Jiang]

Got it. Thank you, Paulo! Honestly I can't vote for your solution though!

Answer 3

[David]

Thank you guys. All of your input was very helpful. I'm somewhat new to Matlab and am just beginning to pick a part its intricacies.

David