box_display_test

box_display_test is a MATLAB program which calls box_display to create 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)

Licensing:

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

Related Data and Programs:

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

Source Code:

• 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".

• td1.png
• td2.png
• td3.png
• td4.png
• td5.png
• td6.png
• td7.png
• td8.png
• td9.png

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

• md1.png
• md2.png
• md3.png
• md4.png
• md5.png
• md6.png
• md7.png
• md8.png
• md9.png

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

• hc1.png
• hc2.png
• hc3.png
• hc4.png
• hc5.png
• hc6.png
• hc7.png

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

• cc1.png
• cc2.png
• cc3.png
• cc4.png
• cc5.png
• cc6.png
• cc7.png

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.