MONTE_CARLO_RULE
Monte Carlo Sampling Regarded as Quadrature Rule


MONTE_CARLO_RULE is a FORTRAN90 program which generates a dataset of N random M-dimensional points, regards it as a quadrature rule for the unit hypercube, and writes out three files of information.

Usage:

monte_carlo_rule m n s
where

The data is written to three files:

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

MONTE_CARLO_RULE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

POWER_RULE, a FORTRAN90 program which constructs a power rule, that is, a product quadrature rule from identical 1D factor rules.

QUADRATURE_RULES_UNIFORM, a dataset directory which contains quadrature rules for M-dimensional unit cubes, based on a uniform pseudorandom sequence. stored as a file of abscissas, a file of weights, and a file of region limits.

SPARSE_GRID_CC_DATASET, a FORTRAN90 program which creates a Clenshaw-Curtis sparse grid and write the data to three files.

SPARSE_GRID_GL_DATASET, a FORTRAN90 program which creates a Gauss-Legendre sparse grid and write the data to three files.

SPARSE_GRID_HERMITE_DATASET, a FORTRAN90 program which creates a Gauss-Hermite sparse grid and write the data to three files.

SPARSE_GRID_LAGUERRE_DATASET, a FORTRAN90 program which creates a Gauss-Laguerre sparse grid and write the data to three files.

SPARSE_GRID_MIXED_DATASET, a FORTRAN90 program which creates a sparse grid dataset based on a mixture of 1D rules.

SPARSE_GRID_OPEN_DATASET, a FORTRAN90 program which creates a sparse grid dataset based on open rules (Fejer 2, Gauss-Patterson, Newton-Cotes-Open).

Reference:

  1. Paul Bratley, Bennett Fox, Linus Schrage,
    A Guide to Simulation,
    Springer Verlag, pages 201-202, 1983.
  2. Bennett Fox,
    Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
    ACM Transactions on Mathematical Software,
    Volume 12, Number 4, pages 362-376, 1986.
  3. Donald Knuth,
    The Art of Computer Programming,
    Volume 2: Seminumerical Algorithms,
    Addison Wesley, 1969.

Source Code:

List of Routines:

You can go up one level to the FORTRAN90 source codes.


Last revised on 23 December 2011.