/**
* Gets the block diagonal matrix D of the decomposition.
* D is a block diagonal matrix.
* Real eigenvalues are on the diagonal while complex values are on
* 2x2 blocks { {real +imaginary}, {-imaginary, real} }.
*
* @return the D matrix.
*
* @see #getRealEigenvalues()
* @see #getImagEigenvalues()
*/
public RealMatrix getD()
{
if (cachedD == null)
{
// cache the matrix for subsequent calls
cachedD = MatrixUtils.CreateRealDiagonalMatrix(realEigenvalues);
for (int i = 0; i < imagEigenvalues.Length; i++)
{
if (Precision.compareTo(imagEigenvalues[i], 0.0, EPSILON) > 0)
{
cachedD.setEntry(i, i + 1, imagEigenvalues[i]);
}
else if (Precision.compareTo(imagEigenvalues[i], 0.0, EPSILON) < 0)
{
cachedD.setEntry(i, i - 1, imagEigenvalues[i]);
}
}
}
return(cachedD);
}
/**
* Computes the square-root of the matrix.
* This implementation assumes that the matrix is symmetric and positive
* definite.
*
* @return the square-root of the matrix.
* @throws MathUnsupportedOperationException if the matrix is not
* symmetric or not positive definite.
* @since 3.1
*/
public RealMatrix getSquareRoot()
{
if (!isSymmetric)
{
throw new Exception("MathUnsupportedOperationException");
}
double[] sqrtEigenValues = new double[realEigenvalues.Length];
for (int i = 0; i < realEigenvalues.Length; i++)
{
double eigen = realEigenvalues[i];
if (eigen <= 0)
{
throw new Exception("MathUnsupportedOperationException");
}
sqrtEigenValues[i] = Math.Sqrt(eigen);
}
RealMatrix sqrtEigen = MatrixUtils.CreateRealDiagonalMatrix(sqrtEigenValues);
RealMatrix v = getV();
RealMatrix vT = getVT();
return(v.multiply(sqrtEigen).multiply(vT));
}