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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.

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).