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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 |
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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 |