FASTGL
Fast computation of GaussLegendre Quadrature Points and Weights
FASTGL
is a Python library which
carries out the fast computation of the Kth value and weight of an
Npoint GaussLegendre 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:

Ignace Bogaert,
Iterationfree computation of GaussLegendre quadrature nodes and weights,
SIAM Journal on Scientific Computing,
Volume 36, Number 3, 2014, pages A10081026.
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 kth GaussLegendre pair of an Npoint rule.

glpairs.py,
computes the kth GaussLegendre pair of an Npoint rule.

glpairtabulated.py,
computes the kth GaussLegendre pair of an Npoint rule.

legendre_theta.py,
returns the Kth theta coordinate in an L point rule.

legendre_weight.py,
returns the Kth weight in an L point rule.

timestamp.py,
prints the current YMDHMS date as a time stamp.
Examples and Tests:
You can go up one level to
the Python source codes.
Last revised on 06 January 2016.