QUADRULE_FAST
Efficient Quadrature Rule Implementation

QUADRULE_FAST is a MATLAB library which implements fast and efficient forms of several popular quadrature rules.

The quadrature rules are defined on the interval [-1,1], and assume there is no additional weighting factor in the data.

The fast implementations are exhibited and discussed in the papers by Trefethen and Waldvogel.

Related Data and Programs:

CLENSHAW_CURTIS_RULE, a MATLAB program which can compute Clenshaw Curtis rules for 1 dimensional or multidimensional problems.

FELIPPA, a MATLAB library which defines quadrature rules for lines, triangles, quadrilaterals, pyramids, wedges, tetrahedrons and hexahedrons.

PRODUCT_RULE, a MATLAB program which can create a multidimensional quadrature rule as a product of one dimensional rules.

QUADPACK, a FORTRAN90 library which contains a variety of routines for numerical estimation of integrals in 1D.

QUADRATURE_TEST, a MATLAB program which reads the definition of a multidimensional quadrature rule from three files, applies the rule to a number of test integrals, and prints the results.

QUADRULE, a MATLAB library which contains quadrature rules.

STROUD, a MATLAB library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

Reference:

1. Philip Davis, Philip Rabinowitz,
   Methods of Numerical Integration,
   Second Edition,
   Dover, 2007,
   ISBN: 0486453391,
   LC: QA299.3.D28.
2. Charles Clenshaw, Alan Curtis,
   A Method for Numerical Integration on an Automatic Computer,
   Numerische Mathematik,
   Volume 2, Number 1, December 1960, pages 197-205.
3. Lloyd Trefethen,
   Is Gauss Quadrature Better Than Clenshaw-Curtis?,
   SIAM Review,
   Volume 50, Number 1, 2008, pages 67-87.
4. Joerg Waldvogel,
   Fast Construction of the Fejer and Clenshaw-Curtis Quadrature Rules,
   BIT Numerical Mathematics,
   Volume 43, Number 1, 2003, pages 1-18.

Source Code:

• clenshaw_curtis_integrate.m applies a Clenshaw Curtis quadrature rule.
• clenshaw_curtis_integrate_fast.m applies a Clenshaw Curtis quadrature rule, using an efficient MATLAB implementation.
• clenshaw_curtis_rule_compute.m computes a Clenshaw Curtis quadrature rule.
• clenshaw_curtis_rule_set.m sets a Clenshaw Curtis quadrature rule by looking it up in a table.
• fejer1_integrate_fast.m applies a Fejer type 1 quadrature rule, using an efficient MATLAB implementation.
• fejer1_rule_compute.m computes a Fejer type 1 quadrature rule.
• fejer1_rule_set.m sets a Fejer type 1 quadrature rule by looking it up in a table.
• fejer2_integrate_fast.m applies a Fejer type 2 quadrature rule, using an efficient MATLAB implementation.
• fejer2_rule_compute.m computes a Fejer type 2 quadrature rule.
• fejer2_rule_set.m sets a Fejer type 2 quadrature rule by looking it up in a table.
• gauss_legendre_integrate_fast.m applies a Gauss-Legendre quadrature rule, using an efficient MATLAB implementation.
• gauss_legendre_rule_compute.m computes a Gauss Legendre quadrature rule.
• gauss_legendre_rule_set.m sets a Gauss Legendre quadrature rule by looking it up in a table.
• timestamp.m prints the current YMDHMS date as a time stamp.

Examples and Tests:

• quadrule_fast_test.m, a sample calling program.
• quadrule_fast_test.out, the output from a run of the sample program.
• quadrule_fast_test01.m, compares CLENSHAW_CURTIS_RULE_COMPUTE and CLENSHAW_CURTIS_RULE_SET.
• quadrule_fast_test02.m, tests CLENSHAW_CURTIS_RULE_COMPUTE.
• quadrule_fast_test03.m, tests CLENSHAW_CURTIS_INTEGRATE and CLENSHAW_CURTIS_INTEGRATE_FAST.
• quadrule_fast_test04.m, compares GAUSS_LEGENDRE_RULE_COMPUTE and GAUSS_LEGENDRE_RULE_SET.
• quadrule_fast_test05.m, tests GAUSS_LEGENDRE_RULE_COMPUTE.
• quadrule_fast_test06.m, tests GAUSS_LEGENDRE_INTEGRATE_FAST.
• quadrule_fast_test07.m, compares FEJER1_RULE_COMPUTE and FEJER1_RULE_SET.
• quadrule_fast_test08.m, tests FEJER1_RULE_COMPUTE.
• quadrule_fast_test09.m, tests FEJER1_INTEGRATE_FAST.
• quadrule_fast_test10.m, compares FEJER2_RULE_COMPUTE and FEJER2_RULE_SET.
• quadrule_fast_test11.m, tests FEJER2_RULE_COMPUTE.
• quadrule_fast_test12.m, tests FEJER2_INTEGRATE_FAST.
• f1.m, test integrand function #1.
• f2.m, test integrand function #2.
• f3.m, test integrand function #3.

You can go up one level to the MATLAB source codes.