#
# === Cholesky decomposition (>= GSL-1.10)
# A symmetric, positive definite square matrix <tt>A</tt> has 
# a Cholesky decomposition into a product of a lower triangular matrix 
# <tt>L</tt> and its transpose <tt>L^T</tt>.
# This is sometimes referred to as taking the square-root of a matrix. 
# The Cholesky decomposition can only be carried out when all the eigenvalues 
# of the matrix are positive. This decomposition can be used to convert the 
# linear system <tt>A x = b</tt> into a pair of triangular systems 
# <tt>L y = b, L^T x = y</tt>,
# which can be solved by forward and back-substitution. 
#
# ---
# * GSL::Linalg::Complex::Cholesky::decomp(A)
# * GSL::Linalg::Complex::cholesky_decomp(A)
#
#   Factorize the positive-definite square matrix <tt>A</tt> into the 
#   Cholesky decomposition <tt>A = L L^H</tt>.
#   On input only the diagonal and lower-triangular part of the matrix <tt>A</tt> 
#   are needed. The diagonal and lower triangular part of the returned matrix
#   contain the matrix <tt>L</tt>. The upper triangular part of the 
#   returned matrix contains L^T, and
#   the diagonal terms being identical for both L and L^T. 
#   If the input matrix is not positive-definite then the decomposition 
#   will fail, returning the error code <tt>GSL::EDOM</tt>. 
#
# ---
# * GSL::Linalg::Complex::Cholesky::solve(chol, b, x)
# * GSL::Linalg::Complex::cholesky_solve(chol, b, x)
#
#   Solve the system <tt>A x = b</tt> using the Cholesky decomposition 
#   of <tt>A</tt> into the matrix <tt>chol</tt> given by 
#   <tt>GSL::Linalg::Complex::Cholesky::decomp</tt>.
#
# ---
# * GSL::Linalg::Complex::Cholesky::svx(chol, x)
# * GSL::Linalg::Complex::cholesky_svx(chol, x)
#
#   Solve the system <tt>A x = b</tt> in-place using the Cholesky decomposition 
#   of <tt>A</tt> into the matrix <tt>chol</tt> given by 
#   <tt>GSL::Linalg::Complex::Cholesky::decomp</tt>. On input <tt>x</tt> 
#   should contain the right-hand side <tt>b</tt>, 
#   which is replaced by the solution on output. 
#
# {back}[link:files/rdoc/linalg_rdoc.html]
#
