LATTICE_RULE is a FORTRAN90 library which approximates integrals in multiple dimensions using lattice rules.
The lattice rules are defined on the unit square, or in higher dimensions, on the unit hypercube.
Lattice rules are more suitable to integrands that are periodic, with period 1, in all variables. However, there are techniques that may be used when the integrand does not satisfy this requirement.
The performance of a lattice rule depends heavily on the choice of the generator vectors. Once the spatial dimension and the number of points have been chosen, there are techniques for finding a good generator vector.
The simplest lattice rules are called "rank 1" rules, and use a lattice generated by multiples of a single generator vector. More elaborate rules can be generated by using more generator vectors, up to the maximum, which is the dimension of the space.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
LATTICE_RULE is available in a C++ version and a FORTRAN90 version and a MATLAB version.
FAURE, a FORTRAN90 library which computes elements of a Faure quasirandom sequence.
GRID, a FORTRAN90 library which computes elements of a grid dataset.
HALTON, a FORTRAN90 library which computes elements of a Halton quasirandom sequence.
HAMMERSLEY, a FORTRAN90 library which computes elements of a Hammersley quasirandom sequence.
HEX_GRID, a FORTRAN90 library which computes elements of a hexagonal grid dataset.
HEX_GRID_ANGLE, a FORTRAN90 library which computes elements of an angled hexagonal grid dataset.
IHS, a FORTRAN90 library which computes elements of an improved distributed Latin hypercube dataset.
LATIN_CENTER, a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing center points.
LATIN_EDGE, a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing edge points.
LATIN_RANDOM, a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing points at random.
LCVT, a FORTRAN90 library which computes a latinized Centroidal Voronoi Tessellation.
NIEDERREITER2, a FORTRAN90 library which computes elements of a Niederreiter quasirandom sequence with base 2.
PRODUCT_RULE, a FORTRAN90 program which can create a multidimensional quadrature rule as a product of one dimensional rules.
QUADRATURE_RULES, a dataset directory which contains sets of files that define quadrature rules over various 1D intervals or multidimensional hypercubes.
QUADRULE, a FORTRAN90 library which defines a number of quadrature rules.
SOBOL, a FORTRAN90 library which computes elements of a Sobol quasirandom sequence.
STROUD, a FORTRAN90 library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.
TEST_NINT, a FORTRAN90 library which defines test functioins for multi-dimensional quadrature routines.
UNIFORM, a FORTRAN90 library which computes elements of a uniform pseudorandom sequence.
You can go up one level to the FORTRAN90 source codes.