circle_rule, a FORTRAN77 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 GNU LGPL 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.
circle_arc_grid, a FORTRAN77 program which computes points equally spaced along a circular arc;
circle_integrals, a FORTRAN77 library which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.
circle_monte_carlo, a FORTRAN77 library which applies a Monte Carlo method to estimate the integral of a function on the circumference of the unit circle in 2D;
CUBE_FELIPPA_RULE, a FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
DISK_RULE, a FORTRAN77 library which computes quadrature rules over the circumference of the unit circle in 2D.
PYRAMID_FELIPPA_RULE, a FORTRAN77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
PYRAMID_RULE, a FORTRAN77 program which computes a quadrature rule over the interior of the unit pyramid in 3D;
SPHERE_LEBEDEV_RULE, a FORTRAN77 library which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.
SQUARE_FELIPPA_RULE, a FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.
STROUD, a FORTRAN77 library 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.
TETRAHEDRON_FELIPPA_RULE, a FORTRAN77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
TRIANGLE_FELIPPA_RULE, a FORTRAN77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.
WEDGE_FELIPPA_RULE, a FORTRAN77 library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.