circle_rule, an Octave code which computes quadrature rules 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).
The user specifies the value NT, the number of equally spaced angles. The program returns vectors T(1:NT) and W(1:NT), which define the rule Q(f).
Given NT and the vectors T and W, the integral I(f) of a function f(x,y) is estimated by Q(f) as follows:
q = 0.0
for i = 1, nt
x = cos ( t(i) )
y = sin ( t(i) )
q = q + w(j) * f ( x, y )
end
The computer code and data files described and made available on this web page are distributed under the MIT license
circle_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, an Octave code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.
annulus_rule, an Octave code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2d.
circle_arc_grid, an Octave code which computes points equally spaced along a circular arc;
circle_integrals, an Octave code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2d.
circle_monte_carlo, an Octave code which applies a monte carlo method to estimate the integral of a function on the circumference of the unit circle in 2d;
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disk_rule, an Octave code which computes quadrature rules over the interior of a disk in 2d.
pyramid_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3d.
pyramid_rule, an Octave code which computes a quadrature rule over the interior of the unit pyramid in 3d.
sphere_lebedev_rule, an Octave code which computes lebedev quadrature rules on the surface of the unit sphere in 3d.
square_felippa_rule, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a square in 2d.
stroud, an Octave code which defines quadrature rules for a variety of m-dimensional regions, including the interior of the square, cube and hypercube, the pyramid, cone and ellipse, the hexagon, the m-dimensional octahedron, the circle, sphere and hypersphere, the triangle, tetrahedron and simplex, and the surface of the circle, sphere and hypersphere.
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triangle_fekete_rule, an Octave code which defines fekete rules for quadrature or interpolation over the interior of a triangle in 2d.
triangle_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a triangle in 2d.
wedge_felippa_rule, an Octave code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3d.