# 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)

### 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:

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.

Last revised on 02 December 2018.