CCN_RULE is a C++ program 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 programs.
The nested Clenshaw Curtis quadrature rule is used as follows:
Integral ( A <= x <= B ) f(x) dxis 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 computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
CCN_RULE is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
CHEBYSHEV1_RULE, a C++ program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
CHEBYSHEV2_RULE, a C++ program which can compute and print a Gauss-Chebyshev type 2 quadrature rule.
CLENSHAW_CURTIS_RULE, a C++ program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
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HERMITE_RULE, a C++ program which can compute and print a Gauss-Hermite quadrature rule.
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LAGUERRE_RULE, a C++ program which can compute and print a Gauss-Laguerre quadrature rule.
LEGENDRE_RULE, a C++ program which can compute and print a Gauss-Legendre quadrature rule.
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PATTERSON_RULE, a C++ program which computes a Gauss-Patterson quadrature rule.
QUADRATURE_RULES_CCN, a dataset directory which contains quadrature rules for integration on [-1,+1], using a nested Clenshaw Curtis rule.
TANH_SINH_RULE, a C++ program which computes and writes out a tanh-sinh quadrature rule of given order.
TRUNCATED_NORMAL_RULE, a C++ program which computes a quadrature rule for a normal probability density function (PDF), also called a Gaussian distribution, that has been truncated to [A,+oo), (-oo,B] or [A,B].
CCN_09 is a nested Clenshaw Curtis rule of order 9, which will exactly match the standard Clenshaw Curtis rule.
ccn_rule 9 -1 +1 ccn_o9
ccn_rule 9 -1 +1 ccn_o9
ccn_rule 9 -1 +1 ccn_o9
You can go up one level to the C++ source codes.