NINTLIB
Multi-dimensional quadrature

NINTLIB is a FORTRAN90 library which estimates 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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

NINTLIB is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CUBPACK, a FORTRAN90 library which estimates the integral of a function over a collection of N-dimensional hyperrectangles and simplices.

FEKETE, a FORTRAN90 library which defines Fekete rules for interpolation or quadrature on a triangle.

INTEGRAL_TEST, a FORTRAN90 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, a FORTRAN90 library which estimates the integral of a function over a one-dimensional interval.

NINT_EXACTNESS, a FORTRAN90 program which measures the polynomial exactness of a multidimensional quadrature rule.

PRODUCT_RULE, a FORTRAN90 program which constructs a product rule from 1D factor rules.

QUADRATURE_RULES, a dataset directory which contains sets of files that define quadrature rules over various 1D intervals or multidimensional hypercubes.

QUADRULE, a FORTRAN90 library which defines a variety of (mostly 1-dimensional) quadrature rules.

SIMPACK, a FORTRAN77 library which approximates the integral of a function or vector of functions over a multidimensional simplex, or a region which is the sum of multidimensional simplexes.

STROUD, a FORTRAN90 library which defines a variety of quadrature rules over various "interesting" geometric shapes.

TEST_INT_2D, a FORTRAN90 library which defines test integrands for 2D quadrature rules.

TEST_NINT, a FORTRAN90 library which defines test functioins for multi-dimensional quadrature routines.

TESTPACK, a FORTRAN90 library which defines a set of integrands used to test multidimensional quadrature.

Reference:

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

Source Code:

• nintlib.f90, the source code.

Examples and Tests:

• nintlib_test.f90, a sample problem.
• nintlib_test.txt, the output file.

List of Routines:

• BOX_ND estimates a multidimensional integral using a product rule.
• MONTE_CARLO_ND estimates a multidimensional integral using Monte Carlo.
• P5_ND estimates a multidimensional integral using a formula of exactness 5.
• 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 FORTRAN90 source codes.