Correlation of two arrays in C#

Question

Having two arrays of double values, I want to compute correlation coefficient (single double value, just like the CORREL function in MS Excel). Is there some simple one-line

Answer 1

You can have the values in separate lists at the same index and use a simple Zip.

var fitResult = new FitResult();
var values1 = new List<int>();
var values2 = new List<int>();

var correls = values1.Zip(values2, (v1, v2) =>
                                       fitResult.CorrelationCoefficient(v1, v2));

A second way is to write your own custom implementation (mine isn't optimized for speed):

public double ComputeCoeff(double[] values1, double[] values2)
{
    if(values1.Length != values2.Length)
        throw new ArgumentException("values must be the same length");

    var avg1 = values1.Average();
    var avg2 = values2.Average();

    var sum1 = values1.Zip(values2, (x1, y1) => (x1 - avg1) * (y1 - avg2)).Sum();

    var sumSqr1 = values1.Sum(x => Math.Pow((x - avg1), 2.0));
    var sumSqr2 = values2.Sum(y => Math.Pow((y - avg2), 2.0));

    var result = sum1 / Math.Sqrt(sumSqr1 * sumSqr2);

    return result;
}

Usage:

var values1 = new List<double> { 3, 2, 4, 5 ,6 };
var values2 = new List<double> { 9, 7, 12 ,15, 17 };

var result = ComputeCoeff(values1.ToArray(), values2.ToArray());
// 0.997054485501581

Debug.Assert(result.ToString("F6") == "0.997054");

Another way is to use the Excel function directly:

var values1 = new List<double> { 3, 2, 4, 5 ,6 };
var values2 = new List<double> { 9, 7, 12 ,15, 17 };

// Make sure to add a reference to Microsoft.Office.Interop.Excel.dll
// and use the namespace

var application = new Application();

var worksheetFunction = application.WorksheetFunction;

var result = worksheetFunction.Correl(values1.ToArray(), values2.ToArray());

Console.Write(result); // 0.997054485501581

Answer 2

Math.NET Numerics is a well-documented math library that contains a Correlation class. It calculates Pearson and Spearman ranked correlations: http://numerics.mathdotnet.com/api/MathNet.Numerics.Statistics/Correlation.htm

The library is available under the very liberal MIT/X11 license. Using it to calculate a correlation coefficient is as easy as follows:

using MathNet.Numerics.Statistics;

...

correlation = Correlation.Pearson(arrayOfValues1, arrayOfValues2);

Good luck!

Answer 3

Public Function Correlation(ByRef array1() As Double, ByRef array2() As Double) As Double
    'siehe https://stackoverflow.com/questions/17447817/correlation-of-two-arrays-in-c-sharp

    'der hier errechnete "Pearson correlation coefficient" muss noch quadriert werden, um R-Squared zu erhalten, siehe
    'https://en.wikipedia.org/wiki/Coefficient_of_determination


    Dim array_xy(array1.Length - 1) As Double
    Dim array_xp2(array1.Length - 1) As Double
    Dim array_yp2(array1.Length - 1) As Double

    Dim i As Integer
    For i = 0 To array1.Length - 1
        array_xy(i) = array1(i) * array2(i)
    Next i
    For i = 0 To array1.Length - 1
        array_xp2(i) = Math.Pow(array1(i), 2.0)
    Next i
    For i = 0 To array1.Length - 1
        array_yp2(i) = Math.Pow(array2(i), 2.0)
    Next i


    Dim sum_x As Double = 0
    Dim sum_y As Double = 0
    Dim EinDouble As Double

    For Each EinDouble In array1
        sum_x += EinDouble
    Next
    For Each EinDouble In array2
        sum_y += EinDouble
    Next

    Dim sum_xy As Double = 0
    For Each EinDouble In array_xy
        sum_xy += EinDouble
    Next

    Dim sum_xpow2 As Double = 0
    For Each EinDouble In array_xp2
        sum_xpow2 += EinDouble
    Next

    Dim sum_ypow2 As Double = 0
    For Each EinDouble In array_yp2
        sum_ypow2 += EinDouble
    Next

    Dim Ex2 As Double = Math.Pow(sum_x, 2.0)
    Dim Ey2 As Double = Math.Pow(sum_y, 2.0)

    Dim ReturnWert As Double
    ReturnWert = (array1.Length * sum_xy - sum_x * sum_y) / Math.Sqrt((array1.Length * sum_xpow2 - Ex2) * (array1.Length * sum_ypow2 - Ey2))
    Correlation = ReturnWert
End Function

Answer 4

In order to calculate Pearson product-moment correlation coefficient

http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient

You can use this simple code:

  public static Double Correlation(Double[] Xs, Double[] Ys) {
    Double sumX = 0;
    Double sumX2 = 0;
    Double sumY = 0;
    Double sumY2 = 0;
    Double sumXY = 0;

    int n = Xs.Length < Ys.Length ? Xs.Length : Ys.Length;

    for (int i = 0; i < n; ++i) {
      Double x = Xs[i];
      Double y = Ys[i];

      sumX += x;
      sumX2 += x * x;
      sumY += y;
      sumY2 += y * y;
      sumXY += x * y;
    }

    Double stdX = Math.Sqrt(sumX2 / n - sumX * sumX / n / n);
    Double stdY = Math.Sqrt(sumY2 / n - sumY * sumY / n / n);
    Double covariance = (sumXY / n - sumX * sumY / n / n);

    return covariance / stdX / stdY; 
  }

Answer 5

If you don't want to use a third party library, you can use the method from this post (posting code here for backup).

public double Correlation(double[] array1, double[] array2)
{
    double[] array_xy = new double[array1.Length];
    double[] array_xp2 = new double[array1.Length];
    double[] array_yp2 = new double[array1.Length];
    for (int i = 0; i < array1.Length; i++)
    array_xy[i] = array1[i] * array2[i];
    for (int i = 0; i < array1.Length; i++)
    array_xp2[i] = Math.Pow(array1[i], 2.0);
    for (int i = 0; i < array1.Length; i++)
    array_yp2[i] = Math.Pow(array2[i], 2.0);
    double sum_x = 0;
    double sum_y = 0;
    foreach (double n in array1)
        sum_x += n;
    foreach (double n in array2)
        sum_y += n;
    double sum_xy = 0;
    foreach (double n in array_xy)
        sum_xy += n;
    double sum_xpow2 = 0;
    foreach (double n in array_xp2)
        sum_xpow2 += n;
    double sum_ypow2 = 0;
    foreach (double n in array_yp2)
        sum_ypow2 += n;
    double Ex2 = Math.Pow(sum_x, 2.00);
    double Ey2 = Math.Pow(sum_y, 2.00);

    return (array1.Length * sum_xy - sum_x * sum_y) /
           Math.Sqrt((array1.Length * sum_xpow2 - Ex2) * (array1.Length * sum_ypow2 - Ey2));
}

Answer 6

In my tests, both @Dmitry Bychenko's and @keyboardP's code postings above resulted in generally the same correlations as Microsoft Excel over a handful of manual tests I did, and did not need any external libraries.

e.g. Running this once (data for this run listed at the bottom):

@Dmitry Bychenko: -0.00418479432051121

@keyboardP:______-0.00418479432051131

MS Excel:_________-0.004184794

Here is a test harness:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace TestCorrel {
    class Program {

        static void Main(string[] args) {

            Random rand = new Random(DateTime.Now.Millisecond);

            List<double> x = new List<double>();
            List<double> y = new List<double>();

            for (int i = 0; i < 100; i++) {

                x.Add(rand.Next(1000) * rand.NextDouble());
                y.Add(rand.Next(1000) * rand.NextDouble());

                Console.WriteLine(x[i] + "," + y[i]);
            }

            Console.WriteLine("Correl1: " + Correl1(x, y));
            Console.WriteLine("Correl2: " + Correl2(x, y));
        }

        public static double Correl1(List<double> x, List<double> y) {

            //https://stackoverflow.com/questions/17447817/correlation-of-two-arrays-in-c-sharp
            if (x.Count != y.Count)
                return (double.NaN); //throw new ArgumentException("values must be the same length");

            double sumX = 0;
            double sumX2 = 0;
            double sumY = 0;
            double sumY2 = 0;
            double sumXY = 0;

            int n = x.Count < y.Count ? x.Count : y.Count;

            for (int i = 0; i < n; ++i) {

                Double xval = x[i];
                Double yval = y[i];

                sumX += xval;
                sumX2 += xval * xval;
                sumY += yval;
                sumY2 += yval * yval;
                sumXY += xval * yval;
            }

            Double stdX = Math.Sqrt(sumX2 / n - sumX * sumX / n / n);
            Double stdY = Math.Sqrt(sumY2 / n - sumY * sumY / n / n);
            Double covariance = (sumXY / n - sumX * sumY / n / n);

            return covariance / stdX / stdY;
        }

        public static double Correl2(List<double> x, List<double> y) {

            double[] array_xy = new double[x.Count];
            double[] array_xp2 = new double[x.Count];
            double[] array_yp2 = new double[x.Count];

            for (int i = 0; i < x.Count; i++)
                array_xy[i] = x[i] * y[i];
            for (int i = 0; i < x.Count; i++)
                array_xp2[i] = Math.Pow(x[i], 2.0);
            for (int i = 0; i < x.Count; i++)
                array_yp2[i] = Math.Pow(y[i], 2.0);
            double sum_x = 0;
            double sum_y = 0;
            foreach (double n in x)
                sum_x += n;
            foreach (double n in y)
                sum_y += n;
            double sum_xy = 0;
            foreach (double n in array_xy)
                sum_xy += n;
            double sum_xpow2 = 0;
            foreach (double n in array_xp2)
                sum_xpow2 += n;
            double sum_ypow2 = 0;
            foreach (double n in array_yp2)
                sum_ypow2 += n;
            double Ex2 = Math.Pow(sum_x, 2.00);
            double Ey2 = Math.Pow(sum_y, 2.00);

            double Correl = 
            (x.Count * sum_xy - sum_x * sum_y) /
            Math.Sqrt((x.Count * sum_xpow2 - Ex2) * (x.Count * sum_ypow2 - Ey2));

            return (Correl);
        }
    }
}

Data for the example numbers above:

287.688269702572,225.610842817282
618.9313498167,177.955550192835
25.7778882802361,27.6549569366756
140.847984766051,714.618547504125
438.618761728806,533.48764902702
481.347431274758,214.381256273194
21.6406916848573,393.559209519792
135.30397563209,158.419851317732
334.314685154853,814.275162949821
764.614904770914,50.1435267264692
42.8179292282173,47.8631582287434
237.216836650491,370.488416981179
388.849658539449,134.961087643151
305.903013161804,441.926902444068
10.6625048679591,369.567569480076
36.9316453891488,24.8947204607049
2.10067253471383,491.941975629861
7.94887068492774,573.037801189831
341.738006353722,653.497146697015
98.8424873439793,475.215988045193
272.248712629196,36.1088809138671
122.336823399801,169.158256422336
9.32281673202422,631.076001565473
201.118425176068,803.724831627554
415.514343714115,64.248651454341
227.791637123,230.512133914284
25.3438658925443,396.854282886188
596.238994411304,72.543763144195
230.239735877253,933.983901697669
796.060099040186,689.952468971234
9.30882684202344,269.22063744125
16.5005430148451,8.96549091859045
536.324005148524,358.829873788557
519.694526420764,17.3212184707267
552.628357889423,12.5541588051962
210.516099897454,388.57537739937
141.341571405689,268.082028986924
503.880356335491,753.447006912645
515.494990213539,444.451280259737
973.8670776076,168.922799013985
85.7111146094795,36.3784999169309
37.2147129193017,108.040356312432
504.590177939548,50.3934166889607
482.821039277511,888.984586256083
5.52549206350255,156.717087003271
405.833169031345,394.099059180868
459.249365587835,11.68776424494
429.421127440604,314.216759666901
126.908422469584,331.907062556551
62.1416232716952,3.19765723645578
4.16058817699579,604.04046284223
484.262182311277,220.177370167886
58.6774453314382,339.09660232677
463.482149892246,199.181594849183
344.128297473829,268.531428258182
0.883430369609702,209.346384477963
77.9462970131758,255.221325168955
583.629439312792,235.557751925922
358.409186083083,376.046612200349
81.2148325150902,10.7696774717279
53.7315618049966,274.171515094196
111.284646992239,130.174321939319
317.280491961763,338.077288461885
177.454564264722,7.53587801919127
69.2239431670047,233.693477620228
823.419546454875,0.111916855029723
23.7174749401014,200.989081544331
44.9598299125022,102.633862571155
74.1602278468945,292.485449988155
130.11182449251,23.4682153367755
243.088760058903,335.807090202722
13.3974915991526,436.983231269281
73.3900805168739,252.352352472186
592.144630201228,92.3395205570103
57.7306153447044,47.1416798900541
522.649018382024,584.427794722108
15.3662010204821,60.1693953262499
16.8335716728277,851.401980430541
33.9869734449251,0.930781653584345
116.66608504982,146.126050951949
92.8896130355492,711.765618208687
317.91980889529,322.186540377413
44.8574470732629,209.275617858058
751.201537871362,37.935519233316
161.817758424588,2.83156183493862
531.64078452142,79.1750782491523
114.803219681048,283.106988439852
123.472725123853,154.125248027558
89.9276725453919,63.4626924192825
105.623296753328,111.234188702067
435.72981759707,23.7058234576629
259.324810619152,69.3535200857341
719.885234421531,381.086239833891
24.2674900099018,198.408173349876
57.7761600361095,146.52277489124
77.4594609157459,710.746080866431
636.671781979814,538.894185951396
56.6035279932448,58.2563265684323
485.16099039333,427.849954283261
91.9552873247095,576.92944263617