/// <summary>
/// cholesky factorization
/// </summary>
/// <param name="A">hermitian matrix A. A must be a symmetric matrix.
/// Therefore the upper triangular part of A must be
/// <param name="throwException">throw an ILArgumentException if A
/// is found not to be positive definite.</param>
/// the (complex conjugate) of the lower triangular part. No check
/// is made for that! <br/>
/// The elements of A will not be altered.</param>
/// <returns>cholesky factorization</returns>
/// <remarks><para>if <paramref name="throwException"/> is true and
/// A is found not to be positive definite, an ILArgumentException
/// will be thrown and the operation will be canceled.</para>
/// <para> If <paramref name="throwException"/> is false, check the
/// return value's dimension to determine the success of the
/// operation (unless you are sure, A was positive definite).
/// If A was found not pos.def. the matrix returned
/// will be of dimension [k x k] and the result of the cholesky
/// factorization of A[0:k-1;0:k-1]. Here k is the first leading
/// minor of A which was found to be not positive definite. </para>
/// The factorization is carried out by use of the LAPACK functions
/// DPOTRF, ZPOTRF, SPOTRF or CPOTRF respectively. </remarks>
public static ILArray <fcomplex> chol(
ILArray <fcomplex> A, bool throwException)
{
if (!A.IsMatrix)
{
throw new ILArgumentSizeException("chol is defined for matrices only!");
}
int n = A.Dimensions[0], info = 0;
if (A.Dimensions[1] != n)
{
throw new ILArgumentException("chol: input matrix must be square!");
}
ILArray <fcomplex> ret = A.copyUpperTriangle(n);
Lapack.cpotrf('U', n, ret.m_data, n, ref info);
if (info < 0)
{
throw new ILArgumentException("chol: illegal parameter error.");
}
else if (info > 0)
{
// not pos.definite
if (!throwException)
{
if (info > 1)
{
int newDim = info - 1;
ret = A.copyUpperTriangle(newDim);
Lapack.cpotrf('U', newDim, ret.m_data, newDim, ref info);
if (info != 0)
{
throw new ILArgumentException("chol: the original matrix given was not pos. definit. An attempt to decompose the submatrix of order " + (newDim + 1).ToString() + " failed.");
}
return(ret);
}
else
{
return(ILArray <fcomplex> .empty(0, 0));
}
}
else
{
throw new ILArgumentException("chol: the matrix given is not positive definite!");
}
}
return(ret);
}
