cc_display

cc_display, a MATLAB code which displays the abscissas used in a 2D quadrature rule.

The current version only considers a single Clenshaw Curtis grid, in which the orders of the rule in the X and Y directions may differ.

Variations could be added, in which the points associated with an isotropic Smolyak rule would be displayed, or in which several sets of Clenshaw Curtis grids would be superimposed, or a Gauss-Legendre rule would be displayed.

Licensing:

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

Languages:

cc_display is available in a MATLAB version.

Related Data and Programs:

box_plot, a MATLAB code which can color in specified entries of a checkerboard, corresponding to pairs of integer data.

cc_display_test

circle_grid_display, a MATLAB code which reads a matrix of integers, and draws a corresponding grid of circles filled with color.

clenshaw_curtis_rule, a MATLAB code which defines a Clenshaw Curtis quadrature rule.

gl_display, a MATLAB code which displays a single Gauss Legendre product rule quadrature grid in 2D.

grid_display, a MATLAB code which can display a 2D or 3D grid or sparse grid.

nested_sequence_display, a MATLAB code which displays a set of nested sequences.

nintlib, a MATLAB code which contains routines for numerical estimation of integrals in multiple dimensions.

quadrule, a MATLAB code which contains quadrature rules.

stroud, a MATLAB code which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

tensor_grid_display, a MATLAB code which can display the grid points of a tensor product rule used for interpolation or quadrature, in 1D, 2D or 3D.

test_int, a MATLAB code which contains a number of functions that may be used as test integrands for quadrature rules in 1D.

test_nint, a MATLAB code which contains test integrands for quadrature rules in multiple dimensions.

triangle_fekete_rule, a MATLAB code which defines a Fekete rule for quadrature or interpolation over a triangle.

Reference:

1. Philip Davis, Philip Rabinowitz,
   Methods of Numerical Integration,
   Second Edition,
   Dover, 2007,
   ISBN: 0486453391,
   LC: QA299.3.D28.
2. Charles Clenshaw, Alan Curtis,
   A Method for Numerical Integration on an Automatic Computer,
   Numerische Mathematik,
   Volume 2, Number 1, December 1960, pages 197-205.
3. W Morven Gentleman,
   Algorithm 424: Clenshaw-Curtis Quadrature,
   Communications of the ACM,
   Volume 15, Number 5, May 1972, pages 353-355.
4. Lloyd Trefethen,
   Is Gauss Quadrature Better than Clenshaw-Curtis?
5. Joerg Waldvogel,
   Fast Construction of the Fejer and Clenshaw-Curtis Quadrature Rules,
   BIT Numerical Mathematics,
   Volume 43, Number 1, 2003, pages 1-18.

Source Code:

• cc_abscissa.m returns the I-th Clenshaw Curtis abscissa.
• cc_grid.m returns a multidimensional Clenshaw-Curtis grid.
• cc_grid_display.m displays a multidimensional Clenshaw-Curtis grid.
• cc_grids_animate.m displays a sequence of merged CC grids from order [1,1] to [A,B].
• cc_grids_constrained.m computes CC orders and grids satisfying a constraint.
• cc_grids_constrained_display.m displays grids generated by CC_GRIDS_CONSTRAINED.
• cc_grids_constrained_size.m computes CC orders and grids with a constraint.
• cc_grids_minmax.m computes CC orders and grids with Q_MIN <= Q <= Q_MAX.
• cc_grids_minmax_display.m displays grids generated by CC_GRIDS_MINMAX.
• cc_grids_minmax_size.m returns sizes for the CC_GRIDS_MINMAX.
• cc_level_compose_animate.m displays the individual CC grids that compose a given level.
• cc_level_to_order.m converts CC nesting levels to CC orders.
• cc_levels_constrained.m computes CC levels and grids satisfying a constraint.
• cc_levels_constrained_display.m displays grids generated by CC_LEVELS_CONSTRAINED.
• cc_levels_constrained_animate.m displays a sequence of grids generated by CC_LEVELS_CONSTRAINED.
• cc_levels_constrained_size.m computes sizes for CC_LEVELS_CONSTRAINED.
• cc_levels_minmax_animate.m displays a sequence of merged grids generated by CC_LEVELS_MINMAX.
• cc_levels_minmax_display.m displays grids generated by CC_LEVELS_MINMAX.
• cc_levels_minmax.m computes CC grids with LEVEL_MIN <= LEVEL <= LEVEL_MAX.
• cc_levels_minmax_size.m returns sizes for CC_LEVELS_MINMAX.
• comp_next.m computes the compositions of the integer N into K parts.
• compnz_next.m computes the compositions of the integer N into K nonzero parts.
• vec_gray_next.m computes the elements of a product space.
• vector_constrained_next4.m returns the "next" constrained vector.