GEN_LAGUERRE_RULE, a C++ program which generates a specific generalized Gauss-Laguerre quadrature rule, based on user input.
The rule is written to three files for easy use as input to other programs.
The generalized Gauss-Laguerre quadrature rule is used as follows:
Integral ( A <= x < +oo ) |x-a|^alpha * exp(-b*(x-a)) f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
gen_laguerre_rule order alpha a b filenamewhere
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
GEN_LAGUERRE_RULE is available in a C++ version and a FORTRAN90 version and a MATLAB version.
CCN_RULE, a C++ program which defines a nested Clenshaw Curtis quadrature rule.
CHEBYSHEV1_RULE, a C++ program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
CHEBYSHEV2_RULE, a C++ program which can compute and print a Gauss-Chebyshev type 2 quadrature rule.
CLENSHAW_CURTIS_RULE, a C++ program which defines a Clenshaw Curtis quadrature rule.
GEGENBAUER_RULE, a C++ program which can compute and print a Gauss-Gegenbauer quadrature rule.
GEN_HERMITE_RULE, a C++ program which computes a generalized Gauss-Hermite quadrature rule.
HERMITE_RULE, a C++ program which computes a Gauss-Hermite quadrature rule.
JACOBI_RULE, a C++ program which computes a Gauss-Jacobi quadrature rule.
LAGUERRE_POLYNOMIAL, a C++ library which evaluates the Laguerre polynomial, the generalized Laguerre polynomial, and the Laguerre function.
LAGUERRE_RULE, a C++ program which computes a Gauss-Laguerre quadrature rule.
LATTICE_RULE, a C++ library which approximates M-dimensional integrals using lattice rules.
LEGENDRE_RULE, a C++ program which computes a Gauss-Legendre quadrature rule.
LEGENDRE_RULE_FAST, a C++ program which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.
LINE_FELIPPA_RULE, a C++ library which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.
PATTERSON_RULE, a C++ program which computes a Gauss-Patterson quadrature rule.
QUADRATURE_RULES, a dataset directory which contains sets of files that define quadrature rules over various 1D intervals or multidimensional hypercubes.
QUADRATURE_RULES_LAGUERRE, a dataset directory which contains triples of files defining Gauss-Laguerre quadrature rules.
QUADRULE, a C++ library which contains 1-dimensional quadrature rules.
TEST_INT, a C++ library which defines test integrands for 1D quadrature rules.
TEST_INT_LAGUERRE, a C++ library which defines test integrands for Gauss-Laguerre rules.
TRUNCATED_NORMAL_RULE, a C++ program which computes 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].