GEN_HERMITE_RULE is a C++ program which generates a specific generalized Gauss-Hermite quadrature rule, based on user input.
The rule is written to three files for easy use as input to other programs.
The generalized Gauss Hermite quadrature rule is used as follows:
Integral ( -oo < x < +oo ) |x-a|^alpha * exp( - b * ( x - a)^2 ) f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
gen_hermite_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_HERMITE_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_LAGUERRE_RULE, a C++ program which computes a generalized Gauss-Laguerre quadrature rule.
HERMITE_RULE, a C++ program which computes a generalized Gauss-Hermite quadrature rule.
INT_EXACTNESS_GEN_HERMITE, a C++ program which checks the polynomial exactness of a generalized Gauss-Hermite quadrature rule.
JACOBI_RULE, a C++ program which computes a generalized Gauss-Jacobi quadrature rule.
LAGUERRE_RULE, a C++ program which computes a Gauss-Laguerre quadrature rule.
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PATTERSON_RULE, a C++ program which computes a Gauss-Patterson quadrature rule.
QUADRATURE_RULES_GEN_HERMITE, a dataset directory which contains triples of files defining generalized Gauss-Hermite quadrature rules.
QUADRULE, a FORTRAN90 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_HERMITE, a C++ library which defines test integrands that can be approximated using a Gauss-Hermite rule.
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].
gen_hermite_rule 4 1.0 0.0 1.0 gen_herm_o4_a1.0
gen_hermite_rule 4 1.0 0.0 1.0 gen_herm_o4_a1.0
gen_hermite_rule 4 1.0 0.0 1.0 gen_herm_o4_a1.0
You can go up one level to the C++ source codes.