**box_display_test**,
a MATLAB code which
calls box_display(), which
creates a plot over a range of integer boxes, whose default color is
gray, but some of which can be painted red (new stuff) and some painted
blue (old stuff)

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

box_display, a MATLAB code which displays a box plot, over integer pairs of data, of a function defined by two formulas.

- box_display_test.m calls all the tests.
- box_display_test.sh runs all the tests.
- box_display_test.txt the output file.

- box_display_test01.m makes pictures of total degree polynomial indices at levels 1 to 7.
- box_display_test02.m makes pictures of maximum degree polynomial indices at levels 1 to 7.
- box_display_test03.m makes pictures of hyperbolic cross polynomial indices at levels 1 to 7.
- box_display_test04.m makes pictures of Smolyak Clenshaw Curtis polynomial indices at levels 1 to 7.
- box_display_test05.m displays the polynomial indices for methods that have just reached x^8 and y^8.
- box_display_test06.m displays the polynomial indices for methods that have just reached x^4 and y^8.

**TD** represents the total degree polynomials for which D1 + D2 <= L.
Blue indicates "old" data, and red "new".

**MD** represents the maximum degree polynomials for which
max ( D1, D2 ) <= L. Blue indicates "old" data, and red "new".

**HC** represents the hyperbolic cross polynomials for which (D1+1)*(D2+1) <= L.
Blue indicates "old" data, and red "new".

**CC** represents the Smolyak Clenshaw Curtis polynomials for which
log2(D1-1)+log2(D2-1) <= L.
Blue indicates "old" data, and red "new".

**DEGREE8** represents the monomials precisely integrated by
quadrature rules, assuming the quadrature rule is just powerful
enough to integrate x^8 and y^8.

- degree8_cc.png, for the level 3 sparse grid quadrature rule based on the Clenshaw-Curtis family with exponential growth.
- degree8_hyper.png, for the level 3 hyperbolic cross quadrature rule.
- degree8_max.png, for any quadrature rule with a precision that is exactly all monomoials of maximum degree 8 or less.
- degree8_total.png, for any quadrature rule with a precision that is exactly all monomoials of total degree 8 or less.

**DEGREE48** represents the monomials precisely integrated by
an anisotropic quadrature rule, assuming the quadrature rule is
just powerful enough to integrate x^4 and y^8. Our anisotropy
essentially weights the x exponent twice as much as y.

- degree48_cc.png, for an anisotropic sparse grid quadrature rule based on the Clenshaw-Curtis family with exponential growth.
- degree48_hyper.png, for a hyperbolic cross quadrature rule.
- degree48_max.png, for any quadrature rule with a precision that is exactly all monomoials of maximum weighted degree 8.
- degree48_total.png, for any quadrature rule with a precision that is exactly all monomoials of total weighted degree 8 or less.