patterson_rule, a Python code which generates a specific Gauss-Patterson quadrature rule.
The Gauss-Patterson quadrature is a nested family which begins with the Gauss-Legendre rules of orders 1 and 3, and then succesively inserts one new abscissa in each subinterval. Thus, after the second rule, the Gauss-Patterson rules do not have the super-high precision of the Gauss-Legendre rules. They trade this precision in exchange for the advantages of nestedness. This means that Gauss-Patterson rules are only available for orders of 1, 3, 7, 15, 31, 63, 127, 255 or 511.
The standard Gauss-Patterson quadrature rule is used as follows:
Integral ( A <= x <= B ) f(x) dx
is to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
The information on this web page is distributed under the MIT license.
patterson_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 sets up 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.
laguerre_rule, a Python code which returns a Gauss-Laguerre quadrature rule.
legendre_rule_fast, a Python code which uses a fast (order n) algorithm to compute a Gauss-Legendre quadrature rule of given order.
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 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].