box_plot_test

box_plot_test is a MATLAB program which calls box_plot to read a file of integer coordinates and associated colors, and make a plot, placing a unit box of the given color at each coordinate.

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:

box_plot, a MATLAB program which displays a box plot of data that consists of pairs of integers;

Source Code:

• box_plot_test.m calls all the tests.
• box_plot_test.sh runs all the tests.
• box_plot_test.txt the output file.

ADAPTIVE looks at the adaptive modification of a sparse grid rule in 2D.

• adaptive_1.txt, the coordinates and colors.
• adaptive_1.png,
• adaptive_2.txt, the coordinates and colors.
• adaptive_2.png,
• adaptive_3.txt, the coordinates and colors.
• adaptive_3.png,
• adaptive_4.txt, the coordinates and colors.
• adaptive_4.png,
• adaptive_5.txt, the coordinates and colors.
• adaptive_5.png,
• abc.png, steps 1 through 3 in one plot.
• de.png, steps 4 through 5 in one plot.
• abcde.png, steps 1 through 5 in one plot.

ALPHA_1.0_1.0 prints some of the 64 pairs of values on an 8 by 8 grid. Blue indicates "old" data, and red "new".

• alpha_1.0_1.0.txt, the coordinates and colors.
• alpha_1.0_1.0.png, a PNG image of a plot of the points.

ALPHA_1.0_1.5 prints some of the 64 pairs of values on an 8 by 8 grid. Blue indicates "old" data, and red "new".

• alpha_1.0_1.5.txt, the coordinates and colors.
• alpha_1.0_1.5.png, a PNG image of a plot of the points.

ALPHA_1.0_2.0 prints some of the 64 pairs of values on an 8 by 8 grid. Blue indicates "old" data, and red "new".

• alpha_1.0_2.0.txt, the coordinates and colors.
• alpha_1.0_2.0.png, a PNG image of a plot of the points.

BOXES suggests the monomials that are exactly integrated by a 2D Clenshaw-Curtis sparse grid of levels 0 through 4. Monomials added on this level are red, old ones are blue. A common 20x20 grid is used for all the plots.

• boxes_level0.txt, the coordinates and colors.
• boxes_level0.png, a PNG image of a plot of the points.
• boxes_level1.txt, the coordinates and colors.
• boxes_level1.png, a PNG image of a plot of the points.
• boxes_level2.txt, the coordinates and colors.
• boxes_level2.png, a PNG image of a plot of the points.
• boxes_level3.txt, the coordinates and colors.
• boxes_level3.png, a PNG image of a plot of the points.
• boxes_level4.txt, the coordinates and colors.
• boxes_level4.png, a PNG image of a plot of the points.

CC looks at the monomials that are exactly integrated by 2D Clenshaw-Curtis sparse grids of levels 0 through 6, using a common 35x35 grid.

• cc_level0.txt, the coordinates and colors.
• cc_level0.png,
• cc_level1.txt, the coordinates and colors.
• cc_level1.png,
• cc_level2.txt, the coordinates and colors.
• cc_level2.png,
• cc_level3.txt, the coordinates and colors.
• cc_level3.png,
• cc_level4.txt, the coordinates and colors.
• cc_level4.png,
• cc_level5.txt, the coordinates and colors.
• cc_level5.png,
• cc_level6.txt, the coordinates and colors.
• cc_level6.png, (note that the data in columns 0 and 1, and rows 0 and 1, goes off the scale, to 65).

CCS looks at the monomials that are exactly integrated by 2D Clenshaw-Curtis "Slow exponential" sparse grids of levels 0 through 6, using a common 35x35 grid. This is a variant of the Clenshaw Curtis rule that tries to delay the exponential growth of the orders. Differences only appear once level 4 has been reached.

• ccs_level0.txt, the coordinates and colors.
• ccs_level0.png,
• ccs_level1.txt, the coordinates and colors.
• ccs_level1.png,
• ccs_level2.txt, the coordinates and colors.
• ccs_level2.png,
• ccs_level3.txt, the coordinates and colors.
• ccs_level3.png,
• ccs_level4.txt, the coordinates and colors.
• ccs_level4.png,
• ccs_level5.txt, the coordinates and colors.
• ccs_level5.png,
• ccs_level6.txt, the coordinates and colors.
• ccs_level6.png,

CGW looks at the first eight rules in an anisotropic sparse grid that has double the growth in X as in Y:

• cgw_boxes_level0.txt, the coordinates and colors.
• cgw_boxes_level0.png,
• cgw_boxes_level1.txt, the coordinates and colors.
• cgw_boxes_level1.png,
• cgw_boxes_level2.txt, the coordinates and colors.
• cgw_boxes_level2.png,
• cgw_boxes_level3.txt, the coordinates and colors.
• cgw_boxes_level3.png,
• cgw_boxes_level4.txt, the coordinates and colors.
• cgw_boxes_level4.png,
• cgw_boxes_level5.txt, the coordinates and colors.
• cgw_boxes_level5.png,
• cgw_boxes_level6.txt, the coordinates and colors.
• cgw_boxes_level6.png,
• cgw_boxes_level7.txt, the coordinates and colors.
• cgw_boxes_level7.png,
• cgw_boxes_level8.txt, the coordinates and colors.
• cgw_boxes_level8.png,

CHECKERBOARD is a set of 64 pairs of integers and colors that correspond to a checkerboard.

• checkerboard.txt, the coordinates and colors.
• checkerboard.png, a PNG image of a plot of the points.

CLAY is a set of pairs of integers that record the basic method (1,1) in blue, some low order methods in green, and secondary refinements in red.

• clay.txt, the coordinates and colors.
• clay.png, a PNG image of a plot of the points.

F is a set of points that can make the letter F:

• f.txt, the coordinates and colors.
• f.png, a PNG image of a plot of the points.

GP looks at the monomials that are exactly integrated by 2D Gauss-Patterson sparse grids of levels 0 through 5, using a common 35x35 grid.

• gp_level0.txt, the coordinates and colors.
• gp_level0.png,
• gp_level1.txt, the coordinates and colors.
• gp_level1.png,
• gp_level2.txt, the coordinates and colors.
• gp_level2.png,
• gp_level3.txt, the coordinates and colors.
• gp_level3.png,
• gp_level4.txt, the coordinates and colors.
• gp_level4.png,
• gp_level5.txt, the coordinates and colors.
• gp_level5.png,

GPS looks at the monomials that are exactly integrated by 2D slow-growth Gauss-Patterson sparse grids of levels 0 through 5, using a common 35x35 grid.

• gps_level0.txt, the coordinates and colors.
• gps_level0.png,
• gps_level1.txt, the coordinates and colors.
• gps_level1.png,
• gps_level2.txt, the coordinates and colors.
• gps_level2.png,
• gps_level3.txt, the coordinates and colors.
• gps_level3.png,
• gps_level4.txt, the coordinates and colors.
• gps_level4.png,
• gps_level5.txt, the coordinates and colors.
• gps_level5.png,

SM symbolically displays the monomials that will be integrated precisely by a Smolyak sparse grid rule of given level if the 1D factor rules form a family of precisions at least 1, 3, 5, 7, 9, ...

• boxes_level0.txt, the coordinates and colors.
• sm_level0.png, a PNG image of a plot of the points.
• sm_level1.txt, the coordinates and colors.
• sm_level1.png, a PNG image of a plot of the points.
• sm_level2.txt, the coordinates and colors.
• sm_level2.png, a PNG image of a plot of the points.
• sm_level3.txt, the coordinates and colors.
• sm_level3.png, a PNG image of a plot of the points.
• sm_level4.txt, the coordinates and colors.
• sm_level4.png, a PNG image of a plot of the points.
• sm_level5.txt, the coordinates and colors.
• sm_level5.png, a PNG image of a plot of the points.

SPARSE is a sequence of plots that suggest how a sparse grid is put together in such a way as to capture all monomials up to a specific total degree.

• sparse1.txt, indicates the monomials to be captured.
• sparse1.png, a PNG image of a plot of the points.
• sparse2.txt, shows how a product rule would capture the monomials (and more).
• sparse2.png, a PNG image of a plot of the points.
• sparse3.txt, begins a sparse grid by adding Q(0x3).
• sparse3.png, a PNG image of a plot of the points.
• sparse4.txt, continues a sparse grid by adding Q(2x2).
• sparse4.png, a PNG image of a plot of the points.
• sparse5.txt, continues a sparse grid by subtracting Q(0x2).
• sparse5.png, a PNG image of a plot of the points.
• sparse6.txt, continues a sparse grid by adding Q(2x1).
• sparse6.png, a PNG image of a plot of the points.
• sparse7.txt, continues a sparse grid by subtracting Q(1x1).
• sparse7.png, a PNG image of a plot of the points.
• sparse8.txt, continues a sparse grid by adding Q(3,0).
• sparse8.png, a PNG image of a plot of the points.
• sparse9.txt, completes the sparse grid by subtracting Q(2x0).
• sparse9.png, a PNG image of a plot of the points.