circle_rule, MATLAB code which computes quadrature rules for approximating integrals over the circumference of the unit circle in 2D.
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.
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