/** {@inheritDoc} */
public RealMatrix getU() throws InvalidMatrixException {
if (cachedU == null) {
if (m >= n) {
// the tridiagonal matrix is Bt.B, where B is upper bidiagonal
final double[][] eData = eigenDecomposition.getV().getData();
final double[][] iData = new double[m][];
double[] ei1 = eData[0];
iData[0] = ei1;
for (int i = 0; i < n - 1; ++i) {
// compute B.E.S^(-1) where E is the eigenvectors matrix
// we reuse the array from matrix E to store the result
final double mi = mainBidiagonal[i];
final double si = secondaryBidiagonal[i];
final double[] ei0 = ei1;
ei1 = eData[i + 1];
iData[i + 1] = ei1;
for (int j = 0; j < n; ++j) {
ei0[j] = (mi * ei0[j] + si * ei1[j]) / singularValues[j];
}
}
// last row
final double lastMain = mainBidiagonal[n - 1];
for (int j = 0; j < n; ++j) {
ei1[j] *= lastMain / singularValues[j];
}
for (int i = n; i < m; ++i) {
iData[i] = new double[n];
}
cachedU = transformer.getU().multiply(MatrixUtils.createRealMatrix(iData));
} else {
// the tridiagonal matrix is B.Bt, where B is lower bidiagonal
cachedU = transformer.getU().multiply(eigenDecomposition.getV());
}
}
// return the cached matrix
return cachedU;
}
