Cross correlation using mathdotnet

Question

I have recently started using Mathdotnet Numerics statistical package to do data analysis in c#.

I am looking for the cross correlation function. Does Mathdotnet have an API for this?

Previously I have been using MATLAB xcorr or Python numpy.correlate . So I am looking for a C# equivalent of these.

I have looked through their documentation but it isn't very straightforward. https://numerics.mathdotnet.com/api/

Answer 1

Correlation can be calculated by any of the methods from MathNet.Numerics.Statistics.Correlation , like Pearson or Spearman . But if you're looking for results like the ones provided by Matlab's xcorr or autocorr , then you have to manually calculate the correlation using those methods for each lag/delay value between your input samples. Notice this example includes both, cross and auto correlation.

double fs = 50; //sampling rate, Hz
double te = 1; //end time, seconds
int size = (int)(fs * te); //sample size

var t = Enumerable.Range(0, size).Select(p => p / fs).ToArray();
var y1 = t.Select(p => p < te / 2 ? 1.0 : 0).ToArray();
var y2 = t.Select(p => p < te / 2 ? 1.0 - 2*p : 0).ToArray();

var r12 = StatsHelper.CrossCorrelation(y1, y2); // Y1 * Y2
var r21 = StatsHelper.CrossCorrelation(y2, y1); // Y2 * Y1
var r11 = StatsHelper.CrossCorrelation(y1, y1); // Y1 * Y1 autocorrelation

StatsHelper:

public static class StatsHelper
{
    public static LagCorr CrossCorrelation(double[] x1, double[] x2)
    {
        if (x1.Length != x2.Length)
            throw new Exception("Samples must have same size.");

        var len = x1.Length;
        var len2 = 2 * len;
        var len3 = 3 * len;
        var s1 = new double[len3];
        var s2 = new double[len3];
        var cor = new double[len2];
        var lag = new double[len2];

        Array.Copy(x1, 0, s1, len, len);
        Array.Copy(x2, 0, s2, 0, len);

        for (int i = 0; i < len2; i++)
        {
            cor[i] = Correlation.Pearson(s1, s2);
            lag[i] = i - len;
            Array.Copy(s2,0,s2,1,s2.Length-1);
            s2[0] = 0;
        }

        return new LagCorr { Corr = cor, Lag = lag };
    }
}

LagCorr:

public class LagCorr
{
    public double[] Lag { get; set; }
    public double[] Corr { get; set; }
}

---

EDIT: Adding Matlab comparison results:

clear;
step=0.02;
t=[0:step:1-step];
y1=ones(1,50);
y1(26:50)=0;
y2=[1-2*t];
y2(26:50)=0;

[cor12,lags12]=xcorr(y1,y2);
[cor21,lags21]=xcorr(y2,y1);
[cor11,lags11]=xcorr(y1,y1);
[cor22,lags22]=xcorr(y2,y2);

subplot(2,3,1);
plot(t,y1);
title('Y1');
axis([0 1 -0.5 1.5]);

subplot(2,3,2);
plot(lags12,cor12);
title('Y1*Y2');
axis([-30 30 0 15]);

subplot(2,3,3);
plot(lags11,cor11);
title('Y1*Y1');
axis([-30 30 0 30]);

subplot(2,3,4);
plot(t,y2);
title('Y2');
axis([0 1 -0.5 1.5]);

subplot(2,3,5);
plot(lags21,cor21);
title('Y2*Y1');
axis([-30 30 0 15]);

subplot(2,3,6);
plot(lags22,cor22);
title('Y2*Y2');
axis([-30 30 0 10]);

Answer 2

I have tried the above solution with a sine wave that was shifted backwards by 20 time units with respect to a first sine wave. It gave me the correct result that the maximum of the correlation is at -20 (see below). One could discuss whether its appropriate to apply a zero padding, the zeros are not usually part of the signal. The MATLAB cross-correlation is not normalized the same way, it's not a "Pearson correlation" as in the example above.

The definition of the MATLAB cross-correlation is different: for scaling option "none" its a convolution with the time reversed signal. There are also various scaling options but none of them gives the same result as the Pearson correlation: matlab definition of xcorr

My result: cross correlation of sin(n*0.1) with sin(n*0.1 - 20*0.1) using the example above: