asa006, a FORTRAN77 code which computes the Cholesky factor of a positive definite symmetric matrix, by Michael Healy.
ASA006 is Applied Statistics Algorithm 6.
If A is a positive definite symmetric matrix, then there is an upper triangular matrix U with the property that
A = U' * UThe matrix U is known as the Cholesky factor of A, and can be used to easily solve linear systems involving A or compute the inverse of A.
The algorithm implemented here uses a compressed storage for both the matrix A and the factor U. This saves some storage, but can make computations a little awkward.
The computer code and data files described and made available on this web page are distributed under the MIT license
asa006 is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
ASA007, a FORTRAN77 library which computes the inverse of a symmetric positive definite matrix, and uses a version of ASA006 for for Cholesky factorization.
ASA047, a FORTRAN77 library which implements the Nelder-Mead minimization algorithm, and uses a version of ASA006 for Cholesky factorization.
LAPACK_EXAMPLES, a FORTRAN77 program which demonstrates the use of the LAPACK linear algebra library.
LINPACK, a FORTRAN77 library which includes routines for Cholesky factorization.
NL2SOL, a FORTRAN77 library which solves nonlinear least squares problems, and includes routines for Cholesky factorization.
PPPACK, a FORTRAN77 library which carries out piecewise polynomial interpolation and includes routines for Cholesky factorization.
Original FORTRAN77 version by Michael Healy; This version by John Burkardt.