ccn_rule, a Fortran90 code which generates a quadrature rule based on a nested set of points inspired by the Clenshaw Curtis quadrature rule.
The data defining the rule is written to three files for easy use as input to other codes.
The nested Clenshaw Curtis quadrature rule is used as follows:
Integral ( A <= x <= B ) f(x) dx
is to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
If the order of the CCN rule is 1, 3, 5, 9, 17, 33, or in general 2^L+1, then the rule is identical to the Clenshaw Curtis rule.
Otherwise, the rule is based on a subset of the points in the Clenshaw Curtis rule of next highest order in the sequence 2^L+1.
The CCN rule has no special accuracy properties, except that the rules of odd order are symmetric, and hence get one extra degree of precision. Moreover, the rules of even order have a single unpaired point which is assigned weight zero, so that it is equivalent to the immediately preceding rule of odd order.
ccn_rule n a b filenamewhere
The information on this web page is distributed under the MIT license.
ccn_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.
f90_rule, a Fortran90 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).