disk_rule, a Python code which computes a quadrature rule over the interior of the general disk in 2D, with radius RC and center (XC,YC).
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 center of the disk (XC,YC), and the radius of the disk RC. The program returns vectors W(NR*NT), X(NR*NT) and Y(NR*NT), 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, NR, and the quadrature vectors W, X, Y, the integral I(f) is estimated by Q(f) as follows:
s = 0.0
for k in range ( 0, nr * nt ):
s = s + w[k] * f(x[k],y[k])
area = pi * rc ** 2
q = area * s
The computer code and data files described and made available on this web page are distributed under the MIT license
disk_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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