SPARSE_GRID_DISPLAY
Plot Points in a Sparse Grid

SPARSE_GRID_DISPLAY is a MATLAB M file 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]. The image is automatically saved to a PNG file.

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'

the name of the file containing the data points.

rmin, rmax

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.

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.

PNG is the format used for the output files that store the images created by this program.

POINTS_01_PLOT is a MATLAB program which can read a file of points in the unit square and make a plot.

POINTS_DISPLAY_MATLAB 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.

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

QUADRATURE_RULES is a dataset directory of files that define quadrature rules; a number of examples of sparse grid quadrature rules are included.

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

SPARSE_GRID_CC some sample sparse grids from the Clenshaw Curtis rule.

SPARSE_GRID_F1 some sample sparse grids from the Fejer Type 1 rule.

SPARSE_GRID_F2 some sample sparse grids from the Fejer Type 2 rule.

SPARSE_GRID_GP some sample sparse grids from the Gauss Patterson rule.

SPARSE_GRID_NCC some sample sparse grids from the Newton Cotes Closed rule.

SPARSE_GRID_NCO some sample sparse grids from the Newton Cotes Open rule.

SPARSE_GRID_NCOH some sample sparse grids from the Newton Cotes Open Half rule.

SPINTERP is a MATLAB library of routines by Andreas Klimke which use a sparse grid to perform multilinear hierarchical interpolation.

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

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:

The "main" program:

• sparse_grid_display.m, the main program.

• file_name_ext_swap.m, creates a new file name by changing the extension.
• s_tex_escape.m, modifies a string so that things that accidentally look like a TeX escape string are NOT interpreted as such.
• timestamp.m, prints the current YMDHMS date as a timestamp.

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.