Correlation of vector data, currently as x and y in two waves

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Hi,

I have two waves containing the x and y components of a set of vectors (representing particle trajectories) evenly spaced in time. I have scaled each wave separately by the time step, and I can determine the autocorrelation of each wave separately and these can be combined in a couple of ways, bu not to my best satisfaction.

More desirable however, would be to directly determine the autocorrelation of the vectors themselves. The correlation of two vectors separated by a time lag can be determined by taking the dot product of the two vectors.

Given the two waves of x and y components, how do I convert it to a vector wave (assuming that such a thing is present in Igor), then how do I determine the autocorrelation of the resulting wave?

Any help is appreciated.

Thanks,

nan0guy
Hello nanoguy,

there is no such thing as a vector wave in Igor. There are only 1D, 2D, 3D, and 4D waves.

Which means that you will have to choose your own convention for a vector wave. I believe that in your case a reasonable option would be to use a 2D wave with two columns, and as many rows as you have vectors. For example:
x1 y1
x2 y2
x3 y3
x4 y4
... and so on.

This is purely convention: you choose that your vectors will be represented this way, but it makes no difference to Igor – Igor sees only ordinary waves.

There are a number of ways to calculate the scalar product from such a setup. For speed I'd typically recommend MatrixOP:
wave MyVectorWave
MatrixOP /O W_ScalarProduct = sum(col(MyVectorWave, 0) * col(MyVectorWave, 1))

which will return the result in W_ScalarProduct, a wave with only 1 point.

To introduce varying time lags, take a look at the rotateRows and shiftVector functions in the MatrixOP documentation.

April 12, 2012 at 05:23 am - Permalink

741 wrote:
Hello nanoguy,

there is no such thing as a vector wave in Igor. There are only 1D, 2D, 3D, and 4D waves.


Well, there *is* the complex wave, which to my mind is at least a good *storage* format for a set of x/y vectors, even supporting conversion between cartesian and polar representations.

But yes, autocorrelation of complex waves isn't a function that's built into Igor.

--Jim Prouty
Software Engineer, WaveMetrics, Inc.

April 13, 2012 at 10:55 am - Permalink