NINTLIB
Multi-dimensional quadrature

NINTLIB is a library of C++ routines, using double precision arithmetic, for estimating integrals over multi-dimensional regions.

Please note that these routines are simple and academic. A good program for computing an integral in multiple dimensions must include error estimation and adaptivity. Simple straightforward approaches to reducing the error will cause a ruinous explosion in the number of function evaluations required.

Related Data and Programs:

CLENSHAW_CURTIS is a C++ library which can set up a Clenshaw Curtis quadrature grid in multiple dimensions.

FEKETE is a C++ library of routines for defining a Fekete rule for quadrature or interpolation over a triangle.

INTEGRAL_TEST is a FORTRAN90 executable program which tests the suitability of a set of N points for use in an equal-weight quadrature rule over the multi-dimensional unit hypercube.

INTLIB is a FORTRAN90 library of routines for estimating the integral of a function over a one-dimensional interval.

NINT_EXACTNESS is a C++ program which demonstrates how to measure the polynomial exactness of a multidimensional quadrature rule.

NINTLIB is also available in a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

PRODUCT_RULE is an executable C++ program which can create a multidimensional quadrature rule as a product of one dimensional rules.

QUADRULE is a C++ library of routines which define a variety of (mostly 1-dimensional) quadrature rules.

STROUD is a FORTRAN90 library of routines which define a variety of quadrature rules over various "interesting" geometric shapes.

TEST_NINT is a C++ library of routines that can be used to test multi-dimensional quadrature routines.

Reference:

1. Philip Davis, Philip Rabinowitz,
   Methods of Numerical Integration,
   Second Edition,
   Dover, 2007,
   ISBN: 0486453391,
   LC: QA299.3.D28.

Source Code:

• nintlib.C, the source code.
• nintlib.H, the include file.
• nintlib.csh, commands to compile the source code.

Examples and Tests:

• nintlib_prb.C, a sample problem.
• nintlib_prb.csh, commands to compile, link and run the sample problem.
• nintlib_prb.out, sample problem output.

List of Routines:

• BOX_ND estimates a multidimensional integral using a product rule.
• I4_HUGE returns a "huge" I4.
• I4_POWER returns the value of I^J.
• MONTE_CARLO_ND estimates a multidimensional integral using Monte Carlo.
• P5_ND estimates a multidimensional integral with a formula of exactness 5.
• R8_ABS returns the absolute value of an R8.
• R8_EPSILON returns the R8 roundoff unit.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• ROMBERG_ND estimates a multidimensional integral using Romberg integration.
• SAMPLE_ND estimates a multidimensional integral using sampling.
• SUM2_ND estimates a multidimensional integral using a product rule.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TUPLE_NEXT computes the next element of a tuple space.

You can go up one level to the C++ source codes.