jacobi_rule, a Python code which generates a specific Gauss-Jacobi quadrature rule, based on user input.
The rule is written to three files for easy use as input to other programs.
The Gauss-Jacobi quadrature rule is used as follows:
Integral ( A <= x <= B ) (B-x)^alpha (x-A)^beta f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))a b
jacobi_rule ( order, alpha, beta, a, b, 'filename' )where
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
jacobi_rule is available in a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
alpert_rule, a Python code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.
ccn_rule, a Python code which returns a nested Clenshaw Curtis quadrature rule.
chebyshev1_rule, a Python code which returns a Gauss-Chebyshev type 1 quadrature rule.
chebyshev2_rule, a Python code which returns a Gauss-Chebyshev type 2 quadrature rule.
clenshaw_curtis_rule, a Python code which returns a Clenshaw Curtis quadrature rule.
gegenbauer_rule, a Python code which returns a Gauss-Gegenbauer quadrature rule.
gen_hermite_rule, a Python code which returns a generalized Gauss-Hermite quadrature rule.
gen_laguerre_rule, a Python code which returns a generalized Gauss-Laguerre quadrature rule.
hermite_rule, a Python code which returns a Gauss-Hermite quadrature rule.
jacobi_polynomial, a Python code which evaluates the Jacobi polynomial and associated functions.
laguerre_rule, a Python code which returns a Gauss-Laguerre quadrature rule.
legendre_rule, a Python code which returns a Gauss-Legendre quadrature rule.
line_felippa_rule, a Python code which returns a Felippa quadrature rule over the interior of a line segment in 1D.
patterson_rule, a Python code which returns a Gauss-Patterson quadrature rule.
quad_rule, a Python code which returns 1-dimensional quadrature rules.
truncated_normal_rule, a Python code which returns a quadrature rule for a normal probability density function (PDF), also called a Gaussian distribution, that has been truncated to [A,+oo), (-oo,B] or [A,B].