// This method computes all principal angles using a sine based algorithm.
// Small angles are computed more accurately than larger angles
public static double[] getPrincipleAngles(DenseMatrix X, DenseMatrix Y) {
double[] s = new double[0];
if (X.numColumns() == 0 || Y.numColumns() == 0) return s;
DenseMatrix QX;
DenseMatrix QY;
// Orthonormalize X and Y
if (X.numColumns() < Y.numColumns()) { // Switch X and Y in this case
QX = Utilities.orth(Y);
QY = Utilities.orth(X);
} else {
QX = Utilities.orth(X);
QY = Utilities.orth(Y);
}
// Compute QY=QY-QX*(QX^T*QY)
DenseMatrix Z = new DenseMatrix(QX.numRows(), QY.numColumns());
DenseMatrix Temp1 = new DenseMatrix(QX.numColumns(), QX.numRows());
DenseMatrix Temp2 = new DenseMatrix(QX.numColumns(), QY.numColumns());
QX.transpose(Temp1); // Temp1=QX^T
Temp1.mult(QY, Temp2); // Temp2=Temp1*QY=QX^T*QY
QX.mult(Temp2, Z);
QY.add(-1D, Z);
// Now compute the singular values
try {
SVD svd = SVD.factorize(QY);
s = svd.getS();
} catch (NotConvergedException e) {
}
// Return angles in radians
for (int i = 0; i < s.length; ++i) s[i] = Math.asin(s[i]);
return s;
}
