CC_DISPLAY
Display 2D Quadrature Rules

CC_DISPLAY is a MATLAB program 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 GNU LGPL license.

Languages:

CC_DISPLAY is available in a MATLAB version.

Related Data and Programs:

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

cc_display_test

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

CLENSHAW_CURTIS_RULE, a MATLAB library which defines a Clenshaw Curtis quadrature rule.

FEKETE, a MATLAB library which defines a Fekete rule for quadrature or interpolation over a triangle.

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

GRID_DISPLAY, a MATLAB library which can display a 2D or 3D grid or sparse grid.

GRIDLINES, a MATLAB library which gives the user more control over drawing gridlines on a graph than the builtin "grid on" command.

INTLIB, a FORTRAN90 library which contains routines for numerical estimation of integrals in 1D.

NESTED_SEQUENCE_DISPLAY, a MATLAB program which displays a set of nested sequences.

NINTLIB, a MATLAB library which contains routines for numerical estimation of integrals in multiple dimensions.

QUADPACK, a FORTRAN90 library which contains routines for numerical estimation of integrals in 1D.

QUADRULE, a MATLAB library which contains quadrature rules.

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

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

TEST_NINT, a MATLAB library which contains a number of functions that may be used as test integrands for quadrature rules in multiple dimensions.

TOMS351, a FORTRAN77 library which estimates an integral using Romberg integration.

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.
• timestamp.m prints the current YMDHMS date as a time stamp.
• vec_gray_next.m computes the elements of a product space.
• vector_constrained_next4.m returns the "next" constrained vector.