**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.

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

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

- 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.

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

**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.