sandia_sgmgg

sandia_sgmgg, an Octave code 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 and an Octave version.

Related Data and Programs:

sandia_sgmgg_test

sgmga, a MATLAB 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:

• i4_modp.m, returns the nonnegative remainder of integer division;
• i4_wrap.m, forces an integer to lie between given limits;
• i4mat_transpose_print.m, prints an I4MAT, transposed;
• i4mat_transpose_print_some.m, prints some of an I4MAT, transposed;
• i4vec_print.m, prints an I4VEC;
• r8_uniform_01.m, returns a unit pseudorandom R8;
• r8vec_indexed_heap_d.m, creates a descending heap from an indexed R8VEC.
• r8vec_indexed_heap_d_extract.m, extract from heap descending indexed R8VEC.
• r8vec_indexed_heap_d_insert.m, insert value into heap descending indexed R8VEC.
• r8vec_indexed_heap_d_max.m, maximum value in heap descending indexed R8VEC.
• sandia_sgmgg_coef_inc2.m, computes tentative coefficient changes.
• sandia_sgmgg_coef_naive.m, returns the combinatorial coefficients.
• sandia_sgmgg_neighbor_naive.m, returns the immediate forward neighbor vector.
• sgmgg_print.m, prints out an SGMGG data structure.