SANDIA_SGMGG
Sparse Grid Mixed Growth, Generalized Construction

SANDIA_SGMGG is a FORTRAN90 library which contains some experimental code for the investigation of sparse grids constructed in a generalized fashion, in which the set of indices corresponding to a sparse grid is chosen in a generalized way, rather than being defined by a linear constraint.

The sparse grid is associated with a data structure, whose management is a significant part of the computation.

We assume we are working in a space of dimension ND. An index vector is a list of ND nonnegative integers, which represent the level of quadrature in each dimension. A single index vector can be used to construct a product rule.

A sparse grid can be thought of as a weighted summation of product rules; our represention of a sparse grid will then consist of a list of NI index vectors, which we can regard as an ND by NI array.

Not every collection of index vectors will be admissible. For our purposes, a collection of index vectors is admissible if each vector in the set is admissible. An index vector that is part of a collection is admissible if it is the 0 vector, or every vector formed by decrementing exactly one entry by 1 is an admissible vector in the set.

Here is an example of an admissible collection of index vectors in 2D:

        (0,3)
        (0,2) (1,2)
        (0,1) (1,1)
        (0,0) (1,0) (2,0) (3,0) (4,0)
      

Licensing:

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

Languages:

SANDIA_SGMGG is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

SGMGA, a FORTRAN90 library which creates sparse grids based on a mixture of 1D quadrature rules, allowing anisotropic weights for each dimension.

Reference:

1. Thomas Gerstner, Michael Griebel,
   Dimension-adaptive tensor-product quadrature,
   Computing,
   Volume 71, Number 1, August 2003, pages 65-87.

Source Code:

• sandia_sgmgg.f90, the source code.

Examples and Tests:

• sandia_sgmgg_test.f90, a sample calling program.
• sandia_sgmgg_test.txt, the output file.

List of Routines:

• I4_MODP returns the nonnegative remainder of I4 division.
• I4_WRAP forces an I4 to lie between given limits by wrapping.
• I4MAT_TRANSPOSE_PRINT prints an I4MAT, transposed.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• I4VEC_PRINT prints an I4VEC.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8VEC_INDEXED_HEAP_D creates a descending heap from an indexed R8VEC.
• R8VEC_INDEXED_HEAP_D_EXTRACT: extract from heap descending indexed R8VEC.
• R8VEC_INDEXED_HEAP_D_INSERT: insert value into heap descending indexed R8VEC.
• R8VEC_INDEXED_HEAP_D_MAX: maximum value in heap descending indexed R8VEC.
• SANDIA_SGMGG_COEF_INC2 computes tentative coefficient changes.
• SANDIA_SGMGG_COEF_NAIVE returns the combinatorial coefficients.
• SANDIA_SGMGG_NEIGHBOR_NAIVE returns the immediate forward neighbor vector.
• SGMGG_PRINT prints out an SGMGG data structure.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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