GL_DISPLAY
Display 2D Gauss-Legendre Quadrature Rules

GL_DISPLAY, a MATLAB library which displays the abscissas used in a 2D Gauss-Legendre product quadrature rule.

Licensing:

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

Languages:

GL_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, a MATLAB library which displays a Clenshaw Curtis product rule quadrature grids in 2D.

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_test

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.

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

PLY_DISPLAY, a MATLAB program which displays an image of a 3D graphics file in PLY format;

QUADRULE, a MATLAB library which defines quadrature rules.

STROUD, a MATLAB library which defines 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.

Reference:

1. Philip Davis, Philip Rabinowitz,
   Methods of Numerical Integration,
   Second Edition,
   Dover, 2007,
   ISBN: 0486453391,
   LC: QA299.3.D28.
2. Lloyd Trefethen,
   Is Gauss Quadrature Better than Clenshaw-Curtis?

Source Code:

• 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.
• gl_grid.m returns a multidimensional Gauss Legendre grid in which any combination of 1D rules may be specified.
• gl_grid_display.m displays a multidimensional Gauss Legendre grid.
• gl_grid_square_display.m displays a 2D "square" Gauss Legendre grid.
• gl_grid_square.m returns a multidimensional Gauss Legendre grid in which all 1D rules have the same order.
• gl_grids_minmax.m computes all Gauss Legendre grids whose orders sum to Q between QMIN and QMAX.
• gl_grids_minmax_display.m displays all Gauss Legendre grids whose orders sum to Q between QMIN and QMAX.
• gl_grids_minmax_size.m computes the total size of all Gauss Legendre grids whose orders sum to Q between QMIN and QMAX.
• gl_level_to_order.m converts a GL level to a GL order.
• gl_levels_minmax.m computes all Gauss Legendre grids whose orders sum to LEVEL between LEVEL_MIN and LEVEL_MAX.
• gl_levels_minmax_display.m displays all Gauss Legendre grids whose orders sum to LEVEL between LEVEL_MIN and LEVEL_MAX.
• gl_levels_minmax_size.m computes the total size of all Gauss Legendre grids whose orders sum to LEVEL between LEVEL_MIN and LEVEL_MAX.
• i4_sign.m returns the sign of an integer.
• legendre_compute.m computes the points and weights of a Gauss-Legendre quadrature rule.
• timestamp.m prints the current YMDHMS date as a time stamp.
• tuple_next2.m computes the next element of an integer tuple space.
• vec_next.m computes the elements of a product space.