# annulus_rule

annulus_rule, a Python code which computes a quadrature rule over the interior of the annulus in 2D, with center (XC,YC), inner radius R1 and outer radius R2.

The user specifies values NT and NR, where NT is the number of equally spaced angles, and NR controls the number of radial points.

To use a rule that is equally powerful in R and T, typically, set NT = 4 * NR.

### Languages:

annulus_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and codes:

alpert_rule, a Python code which can set up an alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

annulus_monte_carlo a Python code which uses the Monte Carlo method to estimate the integral of a function over the interior of a circular annulus in 2D.

disk_rule, a Pyton code which computes quadrature rules over the interior of the general disk in 2D.

disk01_rule, a Python code which computes quadrature rules over the interior of the unit disk in 2D.

line_ncc_rule, a Python code which computes a Newton Cotes Closed (NCC) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.

quadrule, a Python code which defines quadrature rules for approximating an integral over a 1D domain.

simplex_gm_rule, a Python code which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

square_minimal_rule, a Python code which returns "almost minimal" quadrature rules, with exactness up to total degree 55, over the interior of the symmetric square in 2D, by Mattia Festa and Alvise Sommariva.

truncated_normal_rule, a Python code which computes a quadrature rule for a normal distribution that has been truncated to [A,+oo), (-oo,B] or [A,B].

### Reference:

1. Philip Davis, Philip Rabinowitz,
Methods of Numerical Integration,
Second Edition,
Dover, 2007,
ISBN: 0486453391,
LC: QA299.3.D28.
2. Sylvan Elhay, Jaroslav Kautsky,
Algorithm 655: IQPACK, FORTRAN Subroutines for the Weights of Interpolatory Quadrature,
ACM Transactions on Mathematical Software,
Volume 13, Number 4, December 1987, pages 399-415.

### Source Code:

Last revised on 17 January 2020.