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Manuscript Title: Multidimensional automatic integrator (MDAI) - an efficient routine for automatic integration of functions of many variables.
Authors: W. Nazarewicz, M. Pindor
Program title: MDAI
Catalogue identifier: ACUI_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 31(1984)1
Programming language: Fortran.
Computer: NORD 100/500/50.
Operating system: SINTRAN III, SCOPE 3.4, NOS/BE 1.5.
RAM: 25K words
Word size: 60
Peripherals: disc.
Keywords: General purpose, Numerical, Quadrature, Multipole integrals, Subvolume adaptation, Korobov method, Product-gauss Legendre method.
Classification: 4.11.

Nature of problem:
Calculation of multidimensional integrals of quantum physics, quantum chemistry, etc.; for example calculation of the single particle overlap integrals, matrix elements of the many body Hamiltonian.

Solution method:
The integration volume is divided into subvolumes in order to concentrate the integration points where the integrand changes most rapidly. In each subvolume the product-Gauss-Legendre method or the Korobov method is used, as chosen by the user or by default. An option is included : if a required relative accuracy is not achieved for a predetermined limit on the number of the initial volume divisions, an intermediate information is sent to a mass-storage device, and the user can improve the result with the same program later, without repeating the calculations for subvolumes over which the integral has been satisfactorily performed.

Restrictions:
The program can be applied for integration of functions with a number of variables between 2 and 7. However, by relatively simple modifications (changing sizes of some COMMON blocks via the main program) the user can extend the program to higher dimensions.

Running time:
The running time depends strongly on the complexity of the function to be integrated and on the limit of integration volume divisions (declared by the user).