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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_0Distribution 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). |

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