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Statistics.Covariance Method (TDenseMtxVec, TDenseMtxVec, TMtx, boolean)

Calculate the variance-covariance matrix (Result), assuming vectors X and Y are two variable and their elements are the observations.

C#
public Covariance(TDenseMtxVec X, TDenseMtxVec Y, TMtx Result, bool NormN);

X and Y can be two vectors or matrices of equal size. In first case two vectors are treated as two variables, X values as first variable observables, Y vector values as second variable observabled. In second case two matrices are treated as two variables X and Y, all X values as X variable observables and all Y values as Y variable observables. 

For column-vector valued random variables X and Y with respective expected values mu and nu, and respective scalar components m and n, the covariance is defined to be the m×n matrix called the covariance matrix: 

 

 

Calculate the covariance matrix from two vectors representing two variables.

using Dew.Math;
using Dew.Stats.Units;
namespace Dew.Examples
{
  private void Example()
  {
    Vector data1 = new Vector(0);
    Vector data2 = new Vector(0);
    Matrix cov = new Matrix(0,0);
    data1.SetIt(false,new double[] {1,2,3});
    data2.SetIt(false,new double[] {5,5.5});
    Statistics.Covariance(data1,data2,cov,false);
    // cov = [1.00000000, -2.00000000,
    //          -2.00000000, 6.083333334]
  }
}
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