laguerre_rule, a Python code which generates a specific Gauss-Laguerre quadrature rule, based on user input.
The rule is written to three files for easy use as input to other programs.
The Gauss-Laguerre quadrature rule is used as follows:
Integral ( a <= x < +oo ) exp ( - b * ( x - a ) ) f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
laguerre_rule ( order, a, b, 'filename' )where
The computer code and data files described and made available on this web page are distributed under the MIT license
laguerre_rule 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.
alpert_rule, a Python code which returns 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_rule, a Python code which returns a Gauss-Jacobi 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 contains 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].