chebyshev1_rule, a Python code which generates a specific Gauss-Chebyshev type 1 quadrature rule, based on user input.
The rule is written to three files for easy use as input to other programs.
The Gauss Chevbyshev type 1 quadrature rule is used as follows:
Integral ( A <= x <= B ) f(x) / sqrt ( ( x - A ) * ( B - x ) ) dx
is to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
chebyshev1_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
chebyshev1_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 can set up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.
ccn_rule, a Python code which defines a nested Clenshaw Curtis quadrature rule.
chebyshev_polynomial, a Python code which evaluates the Chebyshev polynomial and associated functions.
chebyshev1_exactness, a Python code which checks the polynomial exactness of a Gauss-Chebyshev type 1 quadrature rule.
chebyshev2_rule, a Python code which can compute and print a Gauss-Chebyshev type 2 quadrature rule.
clenshaw_curtis_rule, a Python code which defines a Clenshaw Curtis quadrature rule.
gegenbauer_rule, a Python code which can compute and print a Gauss-Gegenbauer quadrature rule.
gen_hermite_rule, a Python code which can compute and print a generalized Gauss-Hermite quadrature rule.
gen_laguerre_rule, a Python code which can compute and print a generalized Gauss-Laguerre quadrature rule.
hermite_rule, a Python code which can compute and print a Gauss-Hermite quadrature rule.
jacobi_rule, a Python code which can compute and print a Gauss-Jacobi quadrature rule.
laguerre_rule, a Python code which can compute and print a Gauss-Laguerre quadrature rule.
legendre_rule, a Python code which can compute and print a Gauss-Legendre quadrature rule.
line_felippa_rule, a Python code which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1d.
patterson_rule, a Python code which computes a Gauss-Patterson quadrature rule.
power_rule, a Python code which constructs a power rule, that is, a product quadrature rule from identical 1d factor rules.
quad_rule, a Python code which defines 1-dimensional quadrature rules.
truncated_normal_rule, a Python code 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].