python_rule, a Python code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as, a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).
The information on this web page is distributed under the MIT license.
python_rule is available in a C version and a C++ version and a Fortran77 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.
annulus_rule, a Python code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.
ccn_rule, a Python code which defines a Clenshaw Curtis Nested (CCN) quadrature rule.
chebyshev1_rule, a Python code which computes a Gauss-Chebyshev type 1 quadrature rule.
chebyshev2_rule, a Python code which computes a Gauss-Chebyshev type 2 quadrature rule.
circle_rule, a Python code which computes a quadrature rule for the unit circle in 2D, to approximate integrals of f(x,y) over the circumference of the circle of radius 1 and center (0,0).
clenshaw_curtis_rule, a Python code which defines a Clenshaw Curtis quadrature rule.
disk_rule, a Python code which computes a quadrature rule over the interior of a disk of radius R centered at the origin.
disk01_rule, a Python code which computes quadrature rules over the interior of the unit disk in 2D, with radius 1 and center (0,0).
gl_fast_rule, a Python code which carries out the rapid computation of the K-th value and weight of an N-point Gauss-Legendre quadrature rule, by Ignace Bogaert.
hermite_rule, a Python code which returns a Gauss-Hermite quadrature rule for estimating the integral of a function with density exp(-x^2) over the interval (-oo,+oo).
hexagon_stroud_rule, a Python code which returns one of four Stroud quadrature rules over the interior of the unit hexagon.
hexahedron_jaskowiec_rule, a Python code which returns a symmetric Jaskowiec quadrature rule for the hexahedron, with exactness up to total degree 21.
hexahedron_witherden_rule, a Python code which returns a symmetric Witherden quadrature rule for the hexahedron, with exactness up to total degree 11.
jacobi_rule, a Python code which returns a Gauss-Jacobi quadrature rule.
kronrod_rule, a Python code which computes a Gauss and Gauss-Kronrod pair of quadrature rules of arbitrary order, by Robert Piessens, Maria Branders.
laguerre_rule, a Python code which returns a Gauss-Laguerre quadrature rule for estimating the integral of a function with density exp(-x) over the interval [0,+oo).
legendre_rule, a Python code which returns a Gauss-Legendre quadrature rule for estimating the integral of a function with density rho(x)=1 over the interval [-1,+1].
line_ncc_rule, a Python code which computes a Newton Cotes Closed (NCC) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
patterson_rule, a Python code which returns a Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.
prism_jaskowiec_rule, a Python code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of a prism with triangular base, by Jan Jaskowiec, Natarajan Sukumar.
prism_witherden_rule, a Python code which returns a symmetric Witherden quadrature rule for a prism with triangular base, with exactness up to total degree 10.
pyramid_felippa_rule, a Python code which returns a Felippa quadrature rule for approximating integrals over the interior of a pyramid in 3D.
pyramid_jaskowiec_rule, a Python code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of a pyramid in 3D, by Jan Jaskowiec, Natarajan Sukumar.
pyramid_rule, a Python code which computes a conical product quadrature rule over the interior of the unit pyramid in 3D;
pyramid_witherden_rule, a Python code which returns a Witherden quadrature rule, with exactness up to total degree 10, over the interior of a pyramid.
quad_rule, a Python code which defines 1-dimensional quadrature rules.
quadrilateral_witherden_rule, a Python code which returns a symmetric Witherden quadrature rule for the quadrilateral, with exactness up to total degree 21.
simplex_gm_rule, a Python code which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or a simplex in M dimensions.
square_minimal_rule, a Python code which returns almost minimal quadrature rules, with exactness up to total degree 55, over the interior of the symmetric square in 2D, by Mattia Festa and Alvise Sommariva.
square_symq_rule, a Python code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of the square in 2D, by Hong Xiao and Zydrunas Gimbutas.
tetrahedron_arbq_rule, a Python code which returns quadrature rules, with exactness up to total degree 15, over the interior of a tetrahedron in 3D, by Hong Xiao and Zydrunas Gimbutas.
tetrahedron_felippa_rule, a Python code which returns a Felippa quadrature rule for approximating integrals over the interior of a tetrahedron in 3D.
tetrahedron_jaskowiec_rule, a Python code which returns quadrature rules, with exactness up to total degree 20, over the interior of a tetrahedron in 3D, by Jan Jaskowiec, Natarajan Sukumar.
tetrahedron_witherden_rule, a Python code which returns a symmetric Witherden quadrature rule for the tetrahedron, with exactness up to total degree 10.
triangle_symq_rule, a Python code which returns symmetric quadrature rules, with precision up to 50, over the interior of a triangle in 2D, by Hong Xiao and Zydrunas Gimbutas.
triangle_twb_rule, a Python code which generates a quadrature rule over the interior of a triangle in 2D, determined by Taylor, Wingate, and Bos.
triangle_witherden_rule, a Python code which returns a symmetric Witherden quadrature rule for the triangle, with exactness up to total degree 20.
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].
wedge_felippa_rule, a Python code which returns a Felippa quadrature rule for approximating integrals over the interior of the unit wedge in 3D.