public void CenteringTest()
{
double[,] C2 = Matrix.Centering(2);
Assert.IsTrue(Matrix.IsEqual(C2, new double[, ] {
{ 0.5, -0.5 },
{ -0.5, 0.5 }
}));
double[,] X =
{
{ 1, 5, 2, 0 },
{ 6, 2, 3, 100 },
{ 2, 5, 8, 2 },
};
double[,] CX = Matrix.Centering(3).Multiply(X); // Remove means from rows
double[,] XC = X.Multiply(Matrix.Centering(4)); // Remove means from columns
double[] colMean = Tools.Mean(X, 1);
double[] rowMean = Tools.Mean(X, 0);
Assert.IsTrue(rowMean.IsEqual(new double[] { 3.0, 4.0, 4.3333, 34.0 }, 0.001));
Assert.IsTrue(colMean.IsEqual(new double[] { 2.0, 27.75, 4.25 }, 0.001));
double[,] Xr = X.Subtract(rowMean, 0); // Remove means from rows
double[,] Xc = X.Subtract(colMean, 1); // Remove means from columns
Assert.IsTrue(Matrix.IsEqual(XC, Xc));
Assert.IsTrue(Matrix.IsEqual(CX, Xr, 0.00001));
double[,] S1 = XC.Multiply(X.Transpose());
double[,] S2 = Xc.Multiply(Xc.Transpose());
double[,] S3 = Tools.Scatter(X, colMean, 1);
Assert.IsTrue(Matrix.IsEqual(S1, S2));
Assert.IsTrue(Matrix.IsEqual(S2, S3));
}
