nintlib

nintlib, a MATLAB code 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 MIT license.

Languages:

nintlib is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

nintlib_test

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

quad_rule, a MATLAB code which defines a variety of (mostly 1-dimensional) quadrature rules.

quad_fast_rule, a MATLAB code which defines efficient versions of a few 1D quadrature rules.

stroud, a MATLAB code which defines quadrature rules over various interesting geometric shapes.

test_int_2d, a MATLAB code which defines test integrands for 2D quadrature rules.

test_nint, a MATLAB code which tests 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:

• box_nd.m, computes the integral of F(X) over a product box.
• monte_carlo_nd.m, computes a Monte Carlo estimate of an integral in a box.
• p5_nd.m, approximates the integral of F(X) over a product region.
• romberg_nd.m, approximates the integral of a F(X) over a product region.
• sample_nd.m, estimates the integral of F(X) over the multi-dimensional unit box.
• sum2_nd.m, computes the integral of F(X) over a multi-dimensional product region.
• tuple_next.m, computes the next element of a tuple space.