Contents

#
# === 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:linalg_rdoc.html]
#

Version data entries

3 entries across 3 versions & 1 rubygems

Version	Path
rb-gsl-1.16.0.4	rdoc/cholesky_complex.rdoc
rb-gsl-1.16.0.3	rdoc/cholesky_complex.rdoc
rb-gsl-1.16.0.3.rc1	rdoc/cholesky_complex.rdoc