GL_DISPLAY
Display 2D Gauss-Legendre Quadrature Rules

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

Licensing:

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

Related Data and Programs:

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

CC_DISPLAY is a MATLAB library which displays a Clenshaw Curtis product rule quadrature grids in 2D.

CLENSHAW_CURTIS is a MATLAB library which defines a Clenshaw Curtis quadrature rule.

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

INTLIB is a FORTRAN90 library which defines routines for numerical estimation of integrals in 1D.

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

NINTLIB is a MATLAB library which defines routines for numerical estimation of integrals in multiple dimensions.

QUADPACK is a MATLAB library which defines routines for numerical estimation of integrals in 1D.

QUADRULE is a MATLAB library which defines quadrature rules.

SPARSE_GRID_DISPLAY is a MATLAB library which displays a sparse grid in 2D or 3D.

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

TEST_INT is a FORTRAN90 library which defines number of functions that may be used as test integrands for quadrature rules in 1D.

TOMS351 is 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. Lloyd Trefethen,
   Is Gauss Quadrature Better than Clenshaw-Curtis?

Tar File:

A GZIP'ed TAR file of the contents of this directory is available. This is only done as a convenience for users who want ALL the files, and don't want to download them individually. This is not a convenience for me, so don't be surprised if the tar file is somewhat out of date.

• gl_display_m_src.tar.csh the commands used to create the GZIP'ed TAR file.
• gl_display_m_src.tar.gz the GZIP'ed TAR file.

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.

Examples and Tests:

GL_GRID_SQUARE_DISPLAY displays Gauss-Legendre grids in which the orders of each dimension are equal.

• gl_grid_square_21x21.png, a PNG image of a 21 by 21 Gauss Legendre "square" grid.

GL_GRID_DISPLAY displays Gauss-Legendre grids in which the orders of each dimension are arbitrary.

• gl_grid_1x5.png, a PNG image of a 1 by 5 Gauss Legendre grid.
• gl_grid_5x3.png, a PNG image of a 5 by 3 Gauss Legendre grid.
• gl_grid_10x20.png, a PNG image of a 10 by 20 Gauss Legendre grid.

GL_GRIDS_MINMAX_DISPLAY displays all Gauss-Legendre grids in which the orders of each dimension sum to a value Q between QMIN and QMAX.

• gl_grids_minmax_2to5.png, a PNG image of Gauss Legendre grids with Q between 2 and 5.
• gl_grids_minmax_3to5.png, a PNG image of Gauss Legendre grids with Q between 3 and 5.
• gl_grids_minmax_4to5.png, a PNG image of Gauss Legendre grids with Q between 4 and 5.
• gl_grids_minmax_5to5.png, a PNG image of Gauss Legendre grids with Q between 5 and 5.

GL_LEVELS_MINMAX_DISPLAY displays all Gauss-Legendre grids in which the levels of each dimension sum to a value LEVEL between LEVEL_MIN and LEVEL_MAX.

• gl_levels_minmax_0to6.png, a PNG image of Gauss Legendre grids with LEVEL between 0 and 6.
• gl_levels_minmax_3to3.png, a PNG image of Gauss Legendre grids with LEVEL between 3 and 3.
• gl_levels_minmax_4to4.png, a PNG image of Gauss Legendre grids with LEVEL between 4 and 4.
• gl_levels_minmax_5to5.png, a PNG image of Gauss Legendre grids with LEVEL between 5 and 5.
• gl_levels_minmax_6to6.png, a PNG image of Gauss Legendre grids with LEVEL between 6 and 6.

You can go up one level to the MATLAB source codes.