FASTGL
Fast computation of Gauss-Legendre Quadrature Points and Weights

FASTGL is a Python library which carries out the fast computation of the K-th value and weight of an N-point Gauss-Legendre quadrature rule, by Ignace Bogaert.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

FASTGL is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

QUADRULE, a MATLAB library which contains information about quadrature rules, both as tabulated values, and as computational procedures.

TOMS655, a MATLAB library which computes the weights for interpolatory quadrature rules; this library is commonly called IQPACK, by Sylvan Elhay and Jaroslav Kautsky.

Reference:

1. Ignace Bogaert,
   Iteration-free computation of Gauss-Legendre quadrature nodes and weights,
   SIAM Journal on Scientific Computing,
   Volume 36, Number 3, 2014, pages A1008-1026.

Source Code:

• besseljzero.py, computes the kth zero of the J0(X) Bessel function.
• besselj1squared.py, computes the square of BesselJ(1, BesselZero(0,k)).
• glpair.py, computes the k-th Gauss-Legendre pair of an N-point rule.
• glpairs.py, computes the k-th Gauss-Legendre pair of an N-point rule.
• glpairtabulated.py, computes the k-th Gauss-Legendre pair of an N-point rule.
• legendre_theta.py, returns the K-th theta coordinate in an L point rule.
• legendre_weight.py, returns the K-th weight in an L point rule.
• timestamp.py, prints the current YMDHMS date as a time stamp.

Examples and Tests:

• fastgl_test.py, calls all the tests.
• fastgl_test.sh, runs all the tests.
• fastgl_test.txt, the output file.

You can go up one level to the Python source codes.