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Manuscript Title: CUBA - a library for multidimensional numerical integration

Authors: Thomas Hahn

Program title: CUBA

Catalogue identifier: ADVH_v1_3
Distribution format: tar.gz

Journal reference: Comput. Phys. Commun. 176(2007)712

Programming language: C.

Computer: Designed for: all platforms with an ISO C99 C compiler
Tested on: x86 (Linux/gcc), Alpha (Tru64 Unix/gcc), PowerPC (Mac OS X/gcc).

Operating system: Linux, Tru64 Unix, Mac OS X.

RAM: 1M words

Word size: 8 bits

Keywords: Multidimensional numerical integration, Monte Carlo methods, Cubature rules, Variance reduction.

PACS: 02.60.Jh, 02.70Uu.

Classification: 4.11.

Does the new version supersede the previous version?: Yes

Nature of problem:
Multidimensional numerical integrations, e.g. of phase spaces.

Solution method:
The CUBA library contains the four algorithms Vegas, Suave, Divonne, and Cuhre with the following characteristics:

Routine	Basic integration method	Algorithm type	Variance reduction
Vegas	Sobol quasi-random sample	Monte Carlo	importance sampling
Suave	Sobol quasi-random sample	Monte Carlo	globally adaptive subdivision
Divonne	Korobov quasi-random sample	Monte Carlo	stratified sampling
	or Sobol quasi-random sample	Monte Carlo	aided by methods from
	or cubature rules	deterministic	numerical optimisation
Cuhre	cubature rules	deterministic	globally adaptive subdivision

Reasons for new version:
User-requested improvements

Summary of revisions:
Version 1.3 adds versions of the integration routines where all number-of-points-like quantities are 64-bit integers (long long int in C, integer*8 in Fortran). This can become necessary in cases of slow convergence. The corresponding routine names are prefixed with "ll".

Unusual features:
Coherent interface in Fortran, C/C++, and Mathematica. Can integrate vector integrands.

Running time:
Varies greatly depending on the integrand and the chosen accuracy. Can range from seconds to days.