/** {@inheritDoc} */
public RealMatrix getV() throws InvalidMatrixException {
if (cachedV == null) {
if (m >= n) {
// the tridiagonal matrix is Bt.B, where B is upper bidiagonal
cachedV = transformer.getV().multiply(eigenDecomposition.getV());
} else {
// the tridiagonal matrix is B.Bt, where B is lower bidiagonal
final double[][] eData = eigenDecomposition.getV().getData();
final double[][] iData = new double[n][];
double[] ei1 = eData[0];
iData[0] = ei1;
for (int i = 0; i < m - 1; ++i) {
// compute Bt.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 < m; ++j) {
ei0[j] = (mi * ei0[j] + si * ei1[j]) / singularValues[j];
}
}
// last row
final double lastMain = mainBidiagonal[m - 1];
for (int j = 0; j < m; ++j) {
ei1[j] *= lastMain / singularValues[j];
}
for (int i = m; i < n; ++i) {
iData[i] = new double[m];
}
cachedV = transformer.getV().multiply(MatrixUtils.createRealMatrix(iData));
}
}
// return the cached matrix
return cachedV;
}
/**
* Calculates the Singular Value Decomposition of the given matrix.
*
* @param matrix The matrix to decompose.
* @exception InvalidMatrixException (wrapping a {@link
* org.apache.commons.math.ConvergenceException} if algorithm fails to converge
*/
public SingularValueDecompositionImpl(RealMatrix matrix) throws InvalidMatrixException {
m = matrix.getRowDimension();
n = matrix.getColumnDimension();
cachedU = null;
cachedS = null;
cachedV = null;
cachedVt = null;
// transform the matrix to bidiagonal
transformer = new BiDiagonalTransformer(matrix);
mainBidiagonal = transformer.getMainDiagonalRef();
secondaryBidiagonal = transformer.getSecondaryDiagonalRef();
// compute Bt.B (if upper diagonal) or B.Bt (if lower diagonal)
mainTridiagonal = new double[mainBidiagonal.length];
secondaryTridiagonal = new double[mainBidiagonal.length - 1];
double a = mainBidiagonal[0];
mainTridiagonal[0] = a * a;
for (int i = 1; i < mainBidiagonal.length; ++i) {
final double b = secondaryBidiagonal[i - 1];
secondaryTridiagonal[i - 1] = a * b;
a = mainBidiagonal[i];
mainTridiagonal[i] = a * a + b * b;
}
// compute singular values
eigenDecomposition =
new EigenDecompositionImpl(mainTridiagonal, secondaryTridiagonal, MathUtils.SAFE_MIN);
singularValues = eigenDecomposition.getRealEigenvalues();
for (int i = 0; i < singularValues.length; ++i) {
final double si = singularValues[i];
singularValues[i] = (si < 0) ? 0.0 : Math.sqrt(si);
}
}