annulus_rule

annulus_rule, a C 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.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

annulus_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.

Related Data and Programs:

annulus_rule_test

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

c_rule, a C code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).

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:

• annulus_rule.sh, compiles the source code.
• annulus_rule.h, the include file.

• annulus_area.c, computes the area of a circular annulus in 2D.
• annulus_rule_compute.c, computes a quadrature rule for an annulus.
• disk01_monomial_integral.c, returns monomial integrals in the unit disk in 2D.
• imtqlx.c, diagonalizes a symmetric tridiagonal matrix.
• legendre_ek_compute.c, Legendre quadrature rule by the Elhay-Kautsky method.
• monomial_value.c, evaluates a monomial.
• r8_sign.c, returns the sign of an R8.
• r8vec_dot_product.c, returns the dot product of two R8VECs.
• r8vec_print.c, prints an R8VEC.
• r8vec_uniform_01_new.c, returns a unit pseudorandom R8VEC.
• r8vec3_print.c, prints an R8VEC3.
• rule_adjust.c, maps a quadrature rule from [A,B] to [C,D].
• timestamp.c, prints the current YMDHMS date as a time stamp.