disk01_rule, a FORTRAN90 code which computes quadrature rules for approximating integrals over the interior of the unit disk in 2D.
The user specifies values NT and NR, where NT is the number of equally spaced angles, and NR controls the number of radial points. The program returns vectors T(1:NT), R(1:NR) and W(1:NR), which define the rule Q(f).
To use a rule that is equally powerful in R and T, typically, set NT = 2 * NR.
Given NT and NR, and the vectors T, R and W, the integral I(f) of a function f(x,y) is estimated by Q(f) as follows:
s = 0.0 do j = 1, nr do i = 1, nt x = r(j) * cos ( t(i) ) y = r(j) * sin ( t(i) ) s = s + w(j) * f ( x, y ) end do end do area = pi; q = area * s;
The computer code and data files described and made available on this web page are distributed under the MIT license
disk01_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
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