LAGUERRE_RULE_SS is a C++ program which generates a specific Gauss-Laguerre quadrature rule, based on user input, using a Stroud and Secrest rule.
The rule can be output as text in a standard programming language, or the data can be written to three files for easy use as input to other programs.
The Gauss-Laguerre quadrature rule is designed to approximate integrals on semi-infinite intervals. By default, this interval is [0,oo). If this default is not suitable, it is possible to redefine the abscissas and weights for the interval [A,oo) instead.
The Gauss-Laguerre quadrature assumes that the integrand we are considering has a form like:
Integral ( 0 <= x < +oo ) exp(-x) f(x) dxwhere the factor exp(-x) is regarded as a weight factor.
The standard Gauss-Laguerre quadrature rule is used as follows:
Integral ( 0 <= x < +oo ) exp(-x) f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
Although the standard rule is defined in terms of the product of the integral weight function exp(-x) and a function f(x), there may be cases when it is more convenient to think that we are simply approximating
Integral ( 0 <= x < +oo ) f(x) dx
The standard rule can easily be modified, by adjusting the weights, so that the computation can be done in this form. The program allows the user to specify, through the parameter OPTION, whether the standard rule is to be computed (OPTION=0), or the modified rule (OPTION=1).
The modified Gauss-Laguerre quadrature rule is used as follows:
Integral ( 0 <= x < +oo ) f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
laguerre_rule_ss order option outputwhere
Integral ( 0 <= x < +oo ) exp(-x) f(x) dxa 1 value requests the "modified" integration rule for
Integral ( 0 <= x < +oo ) f(x) dx
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
LAGUERRE_RULE_SS is available in a C++ version and a FORTRAN90 version and a MATLAB version.
CHEBYSHEV1_RULE, is a C++ program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
CHEBYSHEV2_RULE, is a C++ program which can compute and print a Gauss-Chebyshev type 2 quadrature rule.
CLENSHAW_CURTIS_RULE is a C++ program which defines a Clenshaw Curtis quadrature rule.
GEGENBAUER_RULE, is a C++ program which can compute and print a Gauss-Gegenbauer quadrature rule.
GEN_HERMITE_RULE, is a C++ program which can compute and print a generalized Gauss-Hermite quadrature rule.
GEN_LAGUERRE_RULE, is a C++ program which can compute and print a generalized Gauss-Laguerre quadrature rule.
HERMITE_RULE, is a C++ program which can compute and print a Gauss-Hermite quadrature rule.
INT_EXACTNESS, is a C++ program which checks the polynomial exactness of a 1-dimensional quadrature rule for a finite interval.
INT_EXACTNESS_LAGUERRE, is a C++ program which checks the polynomial exactness of a Gauss-Laguerre quadrature rule.
INTLIB is a FORTRAN90 library which contains routines for numerical estimation of integrals in 1D.
JACOBI_RULE, is a C++ program which can compute and print a Gauss-Jacobi quadrature rule.
LEGENDRE_RULE, is a C++ program which computes a Gauss-Legendre quadrature rule.
PATTERSON_RULE, is a C++ program which computes a Gauss-Patterson quadrature rule.
PRODUCT_FACTOR is a C++ program which constructs a product rule from distinct 1D factor rules.
PRODUCT_RULE is a C++ program which constructs a product rule from identical 1D factor rules.
QUADPACK is a FORTRAN90 library which contains routines for numerical estimation of integrals in 1D.
QUADRATURE_RULES is a dataset directory which contains sets of files that define quadrature rules over various 1D intervals or multidimensional hypercubes.
QUADRATURE_RULES_LAGUERRE is a dataset directory which contains triples of files defining standard Laguerre quadrature rules.
QUADRULE is a C++ library which contains 1-dimensional quadrature rules.
TANH_SINH_RULE, a C++ program which computes and writes out a tanh-sinh quadrature rule of given order.
TEST_INT is a FORTRAN90 library which defines functions that may be used as test integrands for quadrature rules in 1D.
TEST_INT_LAGUERRE is a C++ library which defines test integrands for integration over [A,+oo).
laguerre_rule_ss 4 0 C++
laguerre_rule_ss 4 0 F77
laguerre_rule_ss 4 0 F90
laguerre_rule_ss 4 1 F90
laguerre_rule_ss 8 0 MAT
laguerre_rule_ss 4 0 lag_o4
laguerre_rule_ss 4 0 lag_o4
laguerre_rule_ss 4 0 lag_o4
laguerre_rule_ss 4 1 lag_o4
laguerre_rule_ss 4 1 lag_o4
laguerre_rule_ss 4 1 lag_o4
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