SPARSE_GRID_DISPLAY
Plot Points in a Sparse Grid

SPARSE_GRID_DISPLAY is a MATLAB program which can read an ASCII file defining a set of points on a 2D or 3D sparse grid, and display a plot of those points, inside a plot frame of user-specified range [Rmin,Rmax].

SPARSE_GRID_DISPLAY was designed as a utility for the display of 2D or 3D sparse grids, but there's no real reason it can't be used to display other pointsets.

Usage:

sparse_grid_display ( 'file_name', rmin, rmax )

• 'file_name' is the name of the file containing the data points.
• rmin, rmax is the range in X, Y (and possibly Z) over which the plot is to be displayed. This is typically either [-1,1] or [0,1]. Some sparse grids don't include points on the boundary, so it is useful to be able to specify the plot range, and thus force the boundaries to show up, and to show up "in the same place" for multiple plots. Also, this feature allows you to zoom in on part of the grid, if you wish.

Licensing:

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

Related Data and Programs:

CC_DISPLAY is a MATLAB program which displays points on various grids derived from the Clenshaw Curtis rule.

GL_DISPLAY is a MATLAB program which displays points on various grids derived from the Gauss-Legendre rule.

NESTED_SEQUENCE_DISPLAY, a MATLAB program which displays a set of nested sequences.

QUADRATURE_RULES is a dataset directory which defines quadrature rules; a number of examples of sparse grid quadrature rules are included.

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

SMOLPACK is a C library which implements Novak and Ritter's method for estimating the integral of a function over a multidimensional hypercube using sparse grids.

SPARSE_GRID_CC is a datatset directory which contains some sample sparse grids from the Clenshaw Curtis rule.

SPARSE_GRID_F2 is a datatset directory which contains some sample sparse grids from the Fejer Type 2 rule.

SPARSE_GRID_GP is a datatset directory which contains some sample sparse grids from the Gauss Patterson rule.

SPARSE_GRID_NCC is a datatset directory which contains some sample sparse grids from the Newton Cotes Closed rule.

SPARSE_GRID_NCO is a datatset directory which contains some sample sparse grids from the Newton Cotes Open rule.

TOMS847 is a MATLAB program which uses sparse grids to carry out multilinear hierarchical interpolation. It is commonly known as SPINTERP, and is by Andreas Klimke.

XY is a data directory which contains some examples of 2D pointsets.

XY_DISPLAY is a MATLAB program which can read a file of coordinates of points, and display an image of the points in a MATLAB graphics window.

XY_DISPLAY_OPEN_GL is a C++ program which can read a file containing 2D point coordinates, and display an image of those points using Open GL.

Reference:

• Sergey Smolyak,
  Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions,
  Doklady Akademii Nauk SSSR,
  Volume 4, 1963, pages 240-243.

Source Code:

• sparse_grid_display.m, the source code.

Examples and Tests:

A 2D example:

• ../../datasets/sparse_grid_f2/f2_d2_level5.txt, a sample input file, containing 145 points in the region [-1,1]x[-1,1], associated with a Fejer Type 2 rule.
• ../../datasets/sparse_grid_f2/f2_d2_level5.png, the PNG image of the points.

A 3D example:

• ../../datasets/sparse_grid_ncc/ncc_d3_level3.txt, a sample input file, containing 69 points in the region [0,1]x[0,1]x[0,1], associated with a Newton Cotes Closed rule.
• ../../datasets/sparse_grid_ncc/ncc_d3_level3.png, PNG image of the points.

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