使用Mathdotnet进行互相关 [英] Cross correlation using mathdotnet

问题描述

我最近开始使用Mathdotnet Numerics统计软件包在c#中进行数据分析.

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

我正在寻找互相关函数. Mathdotnet是否为此提供API?

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

以前，我一直在使用MATLAB xcorr或Python numpy.correlate.因此，我正在寻找与这些等效的C#.

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

我仔细阅读了他们的文档，但这不是很简单. https://numerics.mathdotnet.com/api/

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

推荐答案

可以使用MathNet.Numerics.Statistics.Correlation中的任何方法(例如Pearson或Spearman)来计算相关性.但是，如果要查找Matlab的xcorr或autocorr提供的结果，则必须使用这些方法针对输入样本之间的每个滞后/延迟值手动计算相关性.请注意，此示例同时包含交叉和自动相关.

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; }
}

---

编辑:添加 Matlab 比较结果:

---

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]);

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