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<html>
<head>
<title>
GL_DISPLAY - Display 2D Gauss-Legendre Quadrature Rules
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
GL_DISPLAY <br> Display 2D Gauss-Legendre Quadrature Rules
</h1>
<hr>
<p>
<b>GL_DISPLAY</b>
is a MATLAB library which
displays the abscissas used in a 2D Gauss-Legendre product quadrature rule.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>GL_DISPLAY</b> is available in
<a href = "../../m_src/gl_display/gl_display.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/box_plot/box_plot.html">
BOX_PLOT</a>,
a MATLAB program which
can color in specified entries of
a checkerboard, corresponding to pairs of integer data.
</p>
<p>
<a href = "../../m_src/cc_display/cc_display.html">
CC_DISPLAY</a>,
a MATLAB library which
displays a Clenshaw Curtis product rule quadrature grids in 2D.
</p>
<p>
<a href = "../../m_src/circle_grid_display/circle_grid_display.html">
CIRCLE_GRID_DISPLAY</a>,
a MATLAB program which reads a matrix of integers, and draws a corresponding
grid of circles filled with color.
</p>
<p>
<a href = "../../m_src/clenshaw_curtis_rule/clenshaw_curtis_rule.html">
CLENSHAW_CURTIS_RULE</a>,
a MATLAB library which
defines a Clenshaw Curtis quadrature rule.
</p>
<p>
<a href = "../../m_src/fekete/fekete.html">
FEKETE</a>,
a MATLAB library which
defines a Fekete rule for quadrature or interpolation over a triangle.
</p>
<p>
<a href = "../../m_src/grid_display/grid_display.html">
GRID_DISPLAY</a>,
a MATLAB library which
can display a 2D or 3D grid or sparse grid.
</p>
<p>
<a href = "../../m_src/gridlines/gridlines.html">
GRIDLINES</a>,
a MATLAB library which
gives the user more control over drawing gridlines on a graph
than the builtin "grid on" command.
</p>
<p>
<a href = "../../f_src/intlib/intlib.html">
INTLIB</a>,
a FORTRAN90 library which
defines routines for numerical estimation of integrals in 1D.
</p>
<p>
<a href = "../../m_src/nested_sequence_display/nested_sequence_display.html">
NESTED_SEQUENCE_DISPLAY</a>,
a MATLAB program which
displays a set of nested sequences.
</p>
<p>
<a href = "../../m_src/ply_display/ply_display.html">
PLY_DISPLAY</a>,
a MATLAB program which
displays an image of a 3D graphics file in PLY format;
</p>
<p>
<a href = "../../m_src/quadrule/quadrule.html">
QUADRULE</a>,
a MATLAB library which
defines quadrature rules.
</p>
<p>
<a href = "../../m_src/stroud/stroud.html">
STROUD</a>,
a MATLAB library which
defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D,
3D and N-dimensions.
</p>
<p>
<a href = "../../m_src/tensor_grid_display/tensor_grid_display.html">
TENSOR_GRID_DISPLAY</a>,
a MATLAB program which
can display the grid points of a tensor product rule used for
interpolation or quadrature, in 1D, 2D or 3D.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Philip Davis, Philip Rabinowitz,<br>
Methods of Numerical Integration,<br>
Second Edition,<br>
Dover, 2007,<br>
ISBN: 0486453391,<br>
LC: QA299.3.D28.
</li>
<li>
Lloyd Trefethen,<br>
Is Gauss Quadrature Better than Clenshaw-Curtis?
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "comp_next.m">comp_next.m</a>
computes the compositions of the integer N into K parts.
</li>
<li>
<a href = "compnz_next.m">compnz_next.m</a>
computes the compositions of the integer N into K nonzero parts.
</li>
<li>
<a href = "gl_grid.m">gl_grid.m</a>
returns a multidimensional Gauss Legendre grid in
which any combination of 1D rules may be specified.
</li>
<li>
<a href = "gl_grid_display.m">gl_grid_display.m</a>
displays a multidimensional Gauss Legendre grid.
</li>
<li>
<a href = "gl_grid_square_display.m">gl_grid_square_display.m</a>
displays a 2D "square" Gauss Legendre grid.
</li>
<li>
<a href = "gl_grid_square.m">gl_grid_square.m</a>
returns a multidimensional Gauss Legendre grid in
which all 1D rules have the same order.
</li>
<li>
<a href = "gl_grids_minmax.m">gl_grids_minmax.m</a>
computes all Gauss Legendre grids whose orders sum to Q between
QMIN and QMAX.
</li>
<li>
<a href = "gl_grids_minmax_display.m">gl_grids_minmax_display.m</a>
displays all Gauss Legendre grids whose orders sum to Q between
QMIN and QMAX.
</li>
<li>
<a href = "gl_grids_minmax_size.m">gl_grids_minmax_size.m</a>
computes the total size of all Gauss Legendre grids whose orders
sum to Q between QMIN and QMAX.
</li>
<li>
<a href = "gl_level_to_order.m">gl_level_to_order.m</a>
converts a GL level to a GL order.
</li>
<li>
<a href = "gl_levels_minmax.m">gl_levels_minmax.m</a>
computes all Gauss Legendre grids whose orders sum to LEVEL between
LEVEL_MIN and LEVEL_MAX.
</li>
<li>
<a href = "gl_levels_minmax_display.m">gl_levels_minmax_display.m</a>
displays all Gauss Legendre grids whose orders sum to LEVEL between
LEVEL_MIN and LEVEL_MAX.
</li>
<li>
<a href = "gl_levels_minmax_size.m">gl_levels_minmax_size.m</a>
computes the total size of all Gauss Legendre grids whose orders
sum to LEVEL between LEVEL_MIN and LEVEL_MAX.
</li>
<li>
<a href = "i4_sign.m">i4_sign.m</a>
returns the sign of an integer.
</li>
<li>
<a href = "legendre_compute.m">legendre_compute.m</a>
computes the points and weights of a Gauss-Legendre quadrature rule.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints the current YMDHMS date as a time stamp.
</li>
<li>
<a href = "tuple_next2.m">tuple_next2.m</a>
computes the next element of an integer tuple space.
</li>
<li>
<a href = "vec_next.m">vec_next.m</a>
computes the elements of a product space.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>GL_GRID_SQUARE_DISPLAY</b> displays Gauss-Legendre grids in which
the orders of each dimension are equal.
<ul>
<li>
<a href = "gl_grid_square_21x21.png">gl_grid_square_21x21.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
a 21 by 21 Gauss Legendre "square" grid.
</li>
</ul>
</p>
<p>
<b>GL_GRID_DISPLAY</b> displays Gauss-Legendre grids in which
the orders of each dimension are arbitrary.
<ul>
<li>
<a href = "gl_grid_1x5.png">gl_grid_1x5.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
a 1 by 5 Gauss Legendre grid.
</li>
<li>
<a href = "gl_grid_5x3.png">gl_grid_5x3.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
a 5 by 3 Gauss Legendre grid.
</li>
<li>
<a href = "gl_grid_10x20.png">gl_grid_10x20.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
a 10 by 20 Gauss Legendre grid.
</li>
</ul>
</p>
<p>
<b>GL_GRIDS_MINMAX_DISPLAY</b> displays all Gauss-Legendre grids in which
the orders of each dimension sum to a value Q between QMIN and QMAX.
<ul>
<li>
<a href = "gl_grids_minmax_2to5.png">gl_grids_minmax_2to5.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
Gauss Legendre grids with Q between 2 and 5.
</li>
<li>
<a href = "gl_grids_minmax_3to5.png">gl_grids_minmax_3to5.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
Gauss Legendre grids with Q between 3 and 5.
</li>
<li>
<a href = "gl_grids_minmax_4to5.png">gl_grids_minmax_4to5.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
Gauss Legendre grids with Q between 4 and 5.
</li>
<li>
<a href = "gl_grids_minmax_5to5.png">gl_grids_minmax_5to5.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
Gauss Legendre grids with Q between 5 and 5.
</li>
</ul>
</p>
<p>
<b>GL_LEVELS_MINMAX_DISPLAY</b> displays all Gauss-Legendre grids
in which the levels of each dimension sum to a value LEVEL
between LEVEL_MIN and LEVEL_MAX.
<ul>
<li>
<a href = "gl_levels_minmax_0to6.png">gl_levels_minmax_0to6.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
Gauss Legendre grids with LEVEL between 0 and 6.
</li>
<li>
<a href = "gl_levels_minmax_3to3.png">gl_levels_minmax_3to3.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
Gauss Legendre grids with LEVEL between 3 and 3.
</li>
<li>
<a href = "gl_levels_minmax_4to4.png">gl_levels_minmax_4to4.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
Gauss Legendre grids with LEVEL between 4 and 4.
</li>
<li>
<a href = "gl_levels_minmax_5to5.png">gl_levels_minmax_5to5.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
Gauss Legendre grids with LEVEL between 5 and 5.
</li>
<li>
<a href = "gl_levels_minmax_6to6.png">gl_levels_minmax_6to6.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
Gauss Legendre grids with LEVEL between 6 and 6.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 06 November 2006.
</i>
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