public void CovarianceMatrixNormalCaseNonSquareMoreRowsTest2()
{
PCA p = new PCA();
double[,] matrixArr = new double[10, 2]
{
{ 1.507, 0.988 },
{ 2.107, -9.312 },
{ 1.407, 1.798 },
{ 1.397, 2.098 },
{ -9.563, 1.988 },
{ 0.797, 0.888 },
{ 2.607, 0.488 },
{ -0.493, 1.588 },
{ 0.627, -0.412 },
{ -0.393, -0.112 }
};
double[,] expectation = new double[2, 2] {
{ 12.25722333, -3.41102889 },
{ -3.41102889, 11.44519556 }
};
matrixArr = p.CovarianceMatrix(matrixArr);
CollectionAssert.AreEqual(expectation,
matrixArr,
new Comparer(floatingPointTolerance));
}
public void CovarianceMatrixNormalCaseNonSquareMoreRowsTest()
{
PCA p = new PCA();
double[,] matrixArr = new double[10, 2] {
{ 0.69, 0.49 },
{ -1.31, -1.21 },
{ 0.39, 0.99 },
{ 0.09, 0.29 },
{ 1.29, 1.09 },
{ 0.49, 0.79 },
{ 0.19, -0.31 },
{ -0.81, -0.81 },
{ -0.31, -0.31 },
{ -0.71, -1.01 }
};
double[,] expectation = new double[2, 2] {
{ 0.6165555556, 0.6154444444 },
{ 0.6154444444, 0.7165555556 }
};
matrixArr = p.CovarianceMatrix(matrixArr);
CollectionAssert.AreEqual(expectation,
matrixArr,
new Comparer(floatingPointTolerance));
}
public void CovarianceMatrixNormalCaseSquareTest()
{
PCA p = new PCA();
double[,] matrixArr = new double[9, 9] {
{ -3617, 7121, -1770, -3850, -5723, 8288, 1787, 5367, -1375 },
{ -1733, 722, 946, 5770, -399, -5187, -4681, 9403, 3872 },
{ -3925, -1839, 6520, 2019, 6463, -8250, -6075, -1832, 2983 },
{ 6100, -3915, -1382, -9308, -4979, 8051, -533, 5281, 9673 },
{ 1243, -919, 9893, -3647, -2795, 1933, 4824, 33, 8109 },
{ -6118, -9715, 8984, -1367, 4956, 6600, -4139, -2693, 4956 },
{ 4136, -664, 5962, 4935, -6293, 8180, -5666, -7926, 9214 },
{ 2202, 8521, -4741, 5402, 9037, 4987, -4376, -7846, 4644 },
{ -3823, -1998, -3350, 570, -7444, 8243, 7435, 2623, 6424 }
};
double[,] expectation = new double[9, 9];
// array generated by maple
expectation[0, 0] = 0.176053975000000000e8;
expectation[0, 1] = 0.457826837500000000e7;
expectation[0, 2] = -0.399328887499999953e7;
expectation[0, 3] = -0.331221700000000093e7;
expectation[0, 4] = -0.627830337500000000e7;
expectation[0, 5] = 0.7003523e7;
expectation[0, 6] = -0.186999875000000000e7;
expectation[0, 7] = -0.4798844e7;
expectation[0, 8] = 0.986533037500000000e7;
expectation[1, 0] = 0.457826837500000000e7;
expectation[1, 1] = 0.301754470277777761e8;
expectation[1, 2] = -0.182812283888888881e8;
expectation[1, 3] = 0.848513673611111008e7;
expectation[1, 4] = 0.186260465277778334e7;
expectation[1, 5] = 0.428261597222222248e6;
expectation[1, 6] = 0.823882833333333256e6;
expectation[1, 7] = -0.153511636111111194e7;
expectation[1, 8] = -0.885727530555555597e7;
expectation[2, 0] = -0.399328887499999953e7;
expectation[2, 1] = -0.182812283888888881e8;
expectation[2, 2] = 0.308733886944444440e8;
expectation[2, 3] = -0.117307893055555481e7;
expectation[2, 4] = 0.462695686111111008e7;
expectation[2, 5] = -0.106785538611111101e8;
expectation[2, 6] = -0.589139766666666698e7;
expectation[2, 7] = -0.852483606944444589e7;
expectation[2, 8] = 0.435253290277777892e7;
expectation[3, 0] = -0.331221700000000093e7;
expectation[3, 1] = 0.848513673611111008e7;
expectation[3, 2] = -0.117307893055555481e7;
expectation[3, 3] = 0.259787679444444478e8;
expectation[3, 4] = 0.120599827361111119e8;
expectation[3, 5] = -0.124263529861111119e8;
expectation[3, 6] = -0.124783096666666660e8;
expectation[3, 7] = -0.119806404444444440e8;
expectation[3, 8] = -0.266636397222222295e7;
expectation[4, 0] = -0.627830337500000000e7;
expectation[4, 1] = 0.186260465277778334e7;
expectation[4, 2] = 0.462695686111111008e7;
expectation[4, 3] = 0.120599827361111119e8;
expectation[4, 4] = 0.378507245277777761e8;
expectation[4, 5] = -0.191299344027777798e8;
expectation[4, 6] = -0.184137604166666679e8;
expectation[4, 7] = -0.155837438611111119e8;
expectation[4, 8] = -0.572766680555555504e7;
expectation[5, 0] = 0.7003523e7;
expectation[5, 1] = 0.428261597222222248e6;
expectation[5, 2] = -0.106785538611111101e8;
expectation[5, 3] = -0.124263529861111119e8;
expectation[5, 4] = -0.191299344027777798e8;
expectation[5, 5] = 0.394546397777777761e8;
expectation[5, 6] = 0.127166160416666679e8;
expectation[5, 7] = -0.693834988888888806e7;
expectation[5, 8] = 0.558211630555555597e7;
expectation[6, 0] = -0.186999875000000000e7;
expectation[6, 1] = 0.823882833333333256e6;
expectation[6, 2] = -0.589139766666666698e7;
expectation[6, 3] = -0.124783096666666660e8;
expectation[6, 4] = -0.184137604166666679e8;
expectation[6, 5] = 0.127166160416666679e8;
expectation[6, 6] = 0.243410542500000000e8;
expectation[6, 7] = 0.108749302916666660e8;
expectation[6, 8] = 0.144274745833333372e7;
expectation[7, 0] = -0.4798844e7;
expectation[7, 1] = -0.153511636111111194e7;
expectation[7, 2] = -0.852483606944444589e7;
expectation[7, 3] = -0.119806404444444440e8;
expectation[7, 4] = -0.155837438611111119e8;
expectation[7, 5] = -0.693834988888888806e7;
expectation[7, 6] = 0.108749302916666660e8;
expectation[7, 7] = 0.357919496944444403e8;
expectation[7, 8] = -0.550449015277777798e7;
expectation[8, 0] = 0.986533037500000000e7;
expectation[8, 1] = -0.885727530555555597e7;
expectation[8, 2] = 0.435253290277777892e7;
expectation[8, 3] = -0.266636397222222295e7;
expectation[8, 4] = -0.572766680555555504e7;
expectation[8, 5] = 0.558211630555555597e7;
expectation[8, 6] = 0.144274745833333372e7;
expectation[8, 7] = -0.550449015277777798e7;
expectation[8, 8] = 0.120046551111111119e8;
matrixArr = p.MeanSubtraction(matrixArr);
matrixArr = p.CovarianceMatrix(matrixArr);
CollectionAssert.AreEqual(expectation,
matrixArr,
new Comparer(floatingPointTolerance));
}
public void CovarianceMatrixNormalCaseNonSquareMoreColumnsTest()
{
PCA p = new PCA();
double[,] matrixArr = new double[2, 10] {
{ 0.69, 0.49, -1.31, -1.21, 0.39, 0.99, 0.09, 0.29, 1.29, 1.09 },
{ 0.49, 0.79, 0.19, -0.31, -0.81, -0.81, -0.31, -0.31, -0.71, -1.01 }
};
double[,] expectation = new double[10, 10];
expectation[0, 0] = 0.199999999999999900e-1;
expectation[0, 1] = -0.299999999999999989e-1;
expectation[0, 2] = -0.149999999999999967e0;
expectation[0, 3] = -0.899999999999999689e-1;
expectation[0, 4] = 0.119999999999999996e0;
expectation[0, 5] = 0.179999999999999966e0;
expectation[0, 6] = 0.399999999999999939e-1;
expectation[0, 7] = 0.599999999999999839e-1;
expectation[0, 8] = 0.199999999999999956e0;
expectation[0, 9] = 0.209999999999999964e0;
expectation[1, 0] = -0.299999999999999989e-1;
expectation[1, 1] = 0.450000000000000122e-1;
expectation[1, 2] = 0.225000000000000033e0;
expectation[1, 3] = 0.135000000000000009e0;
expectation[1, 4] = -0.180000000000000049e0;
expectation[1, 5] = -0.270000000000000073e0;
expectation[1, 6] = -0.600000000000000117e-1;
expectation[1, 7] = -0.900000000000000105e-1;
expectation[1, 8] = -0.300000000000000044e0;
expectation[1, 9] = -0.315000000000000058e0;
expectation[2, 0] = -0.149999999999999967e0;
expectation[2, 1] = 0.225000000000000033e0;
expectation[2, 2] = 0.112500000000000000e1;
expectation[2, 3] = 0.675000000000000044e0;
expectation[2, 4] = -0.900000000000000133e0;
expectation[2, 5] = -0.135000000000000009e1;
expectation[2, 6] = -0.300000000000000044e0;
expectation[2, 7] = -0.449999999999999956e0;
expectation[2, 8] = -0.150000000000000000e1;
expectation[2, 9] = -0.157500000000000018e1;
expectation[3, 0] = -0.899999999999999689e-1;
expectation[3, 1] = 0.135000000000000009e0;
expectation[3, 2] = 0.675000000000000044e0;
expectation[3, 3] = 0.404999999999999971e0;
expectation[3, 4] = -0.540000000000000036e0;
expectation[3, 5] = -0.810000000000000053e0;
expectation[3, 6] = -0.179999999999999993e0;
expectation[3, 7] = -0.270000000000000018e0;
expectation[3, 8] = -0.899999999999999911e0;
expectation[3, 9] = -0.945000000000000062e0;
expectation[4, 0] = 0.119999999999999996e0;
expectation[4, 1] = -0.180000000000000049e0;
expectation[4, 2] = -0.900000000000000133e0;
expectation[4, 3] = -0.540000000000000036e0;
expectation[4, 4] = 0.720000000000000195e0;
expectation[4, 5] = 0.108000000000000029e1;
expectation[4, 6] = 0.240000000000000047e0;
expectation[4, 7] = 0.360000000000000042e0;
expectation[4, 8] = 0.120000000000000018e1;
expectation[4, 9] = 0.126000000000000023e1;
expectation[5, 0] = 0.179999999999999966e0;
expectation[5, 1] = -0.270000000000000073e0;
expectation[5, 2] = -0.135000000000000009e1;
expectation[5, 3] = -0.810000000000000053e0;
expectation[5, 4] = 0.108000000000000029e1;
expectation[5, 5] = 0.162000000000000011e1;
expectation[5, 6] = 0.360000000000000042e0;
expectation[5, 7] = 0.540000000000000036e0;
expectation[5, 8] = 0.180000000000000004e1;
expectation[5, 9] = 0.189000000000000012e1;
expectation[6, 0] = 0.399999999999999939e-1;
expectation[6, 1] = -0.600000000000000117e-1;
expectation[6, 2] = -0.300000000000000044e0;
expectation[6, 3] = -0.179999999999999993e0;
expectation[6, 4] = 0.240000000000000047e0;
expectation[6, 5] = 0.360000000000000042e0;
expectation[6, 6] = 0.800000000000000155e-1;
expectation[6, 7] = 0.119999999999999996e0;
expectation[6, 8] = 0.400000000000000022e0;
expectation[6, 9] = 0.420000000000000040e0;
expectation[7, 0] = 0.599999999999999839e-1;
expectation[7, 1] = -0.900000000000000105e-1;
expectation[7, 2] = -0.449999999999999956e0;
expectation[7, 3] = -0.270000000000000018e0;
expectation[7, 4] = 0.360000000000000042e0;
expectation[7, 5] = 0.540000000000000036e0;
expectation[7, 6] = 0.119999999999999996e0;
expectation[7, 7] = 0.179999999999999993e0;
expectation[7, 8] = 0.599999999999999978e0;
expectation[7, 9] = 0.630000000000000004e0;
expectation[8, 0] = 0.199999999999999956e0;
expectation[8, 1] = -0.300000000000000044e0;
expectation[8, 2] = -0.150000000000000000e1;
expectation[8, 3] = -0.899999999999999911e0;
expectation[8, 4] = 0.120000000000000018e1;
expectation[8, 5] = 0.180000000000000004e1;
expectation[8, 6] = 0.400000000000000022e0;
expectation[8, 7] = 0.599999999999999978e0;
expectation[8, 8] = 0.2e1;
expectation[8, 9] = 0.210000000000000009e1;
expectation[9, 0] = 0.209999999999999964e0;
expectation[9, 1] = -0.315000000000000058e0;
expectation[9, 2] = -0.157500000000000018e1;
expectation[9, 3] = -0.945000000000000062e0;
expectation[9, 4] = 0.126000000000000023e1;
expectation[9, 5] = 0.189000000000000012e1;
expectation[9, 6] = 0.420000000000000040e0;
expectation[9, 7] = 0.630000000000000004e0;
expectation[9, 8] = 0.210000000000000009e1;
expectation[9, 9] = 0.220500000000000007e1;
double[,] cpyMatrix = new double[2, 10];
matrixArr.CopyTo(cpyMatrix);
matrixArr = p.MeanSubtraction(matrixArr);
matrixArr = p.CovarianceMatrix(matrixArr);
CollectionAssert.AreEqual(expectation,
matrixArr,
new Comparer(floatingPointTolerance));
double[,] ourCov = matrixArr;
double[,] cov = cpyMatrix.Covariance();
CollectionAssert.AreEqual(expectation, cov, new Comparer(floatingPointTolerance));
}