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<html>
<head>
<title>
QUAD_MESH_RCM - Reverse Cuthill-McKee Node Reordering
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
QUAD_MESH_RCM <br> Reverse Cuthill-McKee Node Reordering
</h1>
<hr>
<p>
<b>QUAD_MESH_RCM</b>
is a C++ program which
computes the reverse Cuthill-McKee (RCM) reordering for nodes in a mesh of 4-node
quadrilaterals.
</p>
<p>
The user supplies a node file and an element file, containing
the coordinates of the nodes, and the indices of the nodes that
make up each element.
</p>
<p>
The program reads the data, computes the adjacency information,
carries out the RCM algorithm to get the permutation, applies
the permutation to the nodes and elements, and writes out
new node and element files that correspond to the RCM permutation.
</p>
<p>
(Note that, internally, the program has to convert some data from
0-based to 1-based indexing in order to work with the RCM codes.
Aside from some inelegant coding, the user should not notice any
effects of this temporary adjustment.)
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>quad_mesh_rcm</b> <i>'prefix'</i>
</blockquote>
where <i>'prefix'</i> is the common file prefix:
<ul>
<li>
<i>'prefix'</i><b>_nodes.txt</b>, the node coordinates;
</li>
<li>
<i>'prefix'</i><b>_elements.txt</b>, the element definitions.
</li>
<li>
<i>'prefix'</i><b>_rcm_nodes.txt</b>, the reordered node coordinates;
</li>
<li>
<i>'prefix'</i><b>_rcm_elements.txt</b>, the reordered element definitions.
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and 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>QUAD_MESH_RCM</b> is available in
<a href = "../../cpp_src/quad_mesh_rcm/quad_mesh_rcm.html">a C++ version</a> and
<a href = "../../f_src/quad_mesh_rcm/quad_mesh_rcm.html">a FORTRAN version</a> and
<a href = "../../m_src/quad_mesh_rcm/quad_mesh_rcm.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/mesh_bandwidth/mesh_bandwidth.html">
MESH_BANDWIDTH</a>,
a C++ program which
returns the geometric bandwidth associated with a mesh of
elements of any order and in a space of arbitrary dimension.
</p>
<p>
<a href = "../../m_src/mesh_display/mesh_display.html">
MESH_DISPLAY</a>,
a MATLAB program which
reads data defining a polygonal mesh and displays it, with optional numbering.
</p>
<p>
<a href = "../../cpp_src/mesh_display_opengl/mesh_display_opengl.html">
MESH_DISPLAY_OPENGL</a>,
a C++ program which
reads files defining a polygonal mesh and displays an image using OpenGL.
</p>
<p>
<a href = "../../data/quad_mesh/quad_mesh.html">
QUAD_MESH</a>,
a data directory which
defines a format for storing meshes of quadrilaterals over a 2D region.
</p>
<p>
<a href = "../../cpp_src/quad_mesh/quad_mesh.html">
QUAD_MESH</a>,
a C++ library which
handles meshes of quadrilaterals over a 2D region;
</p>
<p>
<a href = "../../cpp_src/rcm/rcm.html">
RCM</a>,
a C++ library which
carries out reverse Cuthill-McKee computations.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_rcm/tet_mesh_rcm.html">
TET_MESH_RCM</a>,
a C++ program which
applies the reverse Cuthill-McKee reordering to a tetrahedral
mesh of nodes in 3D.
</p>
<p>
<a href = "../../cpp_src/triangulation_rcm/triangulation_rcm.html">
TRIANGULATION_RCM</a>,
a C++ program which
reads files describing a triangulation of nodes in 2D, and applies the RCM algorithm
to produce a renumbering of the triangulation with a reduced
bandwidth.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
HL Crane, Norman Gibbs, William Poole, Paul Stockmeyer,<br>
Algorithm 508:
Matrix Bandwidth and Profile Reduction,<br>
ACM Transactions on Mathematical Software,<br>
Volume 2, Number 4, December 1976, pages 375-377.
</li>
<li>
Marc deBerg, Marc Krevald, Mark Overmars,
Otfried Schwarzkopf,<br>
Computational Geometry,<br>
Springer, 2000,<br>
ISBN: 3-540-65620-0.
</li>
<li>
Alan George, Joseph Liu,<br>
Computer Solution of Large Sparse Positive Definite Matrices,<br>
Prentice Hall, 1981,<br>
ISBN: 0131652745,<br>
LC: QA188.G46
</li>
<li>
Norman Gibbs,<br>
Algorithm 509:
A Hybrid Profile Reduction Algorithm,<br>
ACM Transactions on Mathematical Software,<br>
Volume 2, Number 4, December 1976, pages 378-387.
</li>
<li>
Norman Gibbs, William Poole, Paul Stockmeyer,<br>
An Algorithm for Reducing the Bandwidth
and Profile of a Sparse Matrix,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 13, 1976, pages 236-250.
</li>
<li>
Joseph ORourke,<br>
Computational Geometry,<br>
Second Edition,<br>
Cambridge, 1998,<br>
ISBN: 0521649765,<br>
LC: QA448.D38.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "quad_mesh_rcm.cpp">
quad_mesh_rcm.cpp</a>,
the source code.
</li>
<li>
<a href = "quad_mesh_rcm.sh">
quad_mesh_rcm.sh</a>,
commands to compile, link, and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>HOLE</b> works with region of equal-sized squares, with some irregularities.
<ul>
<li>
<a href = "hole_output.txt">hole_output.txt</a>,
the printed output from the command <br>
"quad_mesh_rcm ( 'hole' )"
</li>
<li>
<a href = "hole_nodes.txt">hole_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "hole_elements.txt">hole_elements.txt</a>,
the element file.
</li>
<li>
<a href = "hole_rcm_nodes.txt">hole_rcm_nodes.txt</a>,
the RCM reordered node file.
</li>
<li>
<a href = "hole_rcm_elements.txt">hole_rcm_elements.txt</a>,
the RCM reordered element file.
</li>
<li>
<a href = "hole.png">hole.png</a>,
an image of the mesh.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for QUAD_MESH_RCM.
</li>
<li>
<b>ADJ_BANDWIDTH</b> computes the bandwidth of an adjacency matrix.
</li>
<li>
<b>ADJ_PERM_BANDWIDTH</b> computes the bandwidth of a permuted adjacency matrix.
</li>
<li>
<b>ADJ_SET_Q4_MESH</b> sets adjacencies in a triangulation.
</li>
<li>
<b>ADJ_SIZE_Q4_MESH</b> counts adjacencies in a Q4 mesh.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is true if two characters are equal, disregarding case.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>DEGREE</b> computes the degrees of the nodes in the connected component.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the columns in the first line of a file.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>GENRCM</b> finds the reverse Cuthill-Mckee ordering for a general graph.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of integer division.
</li>
<li>
<b>I4_SWAP</b> switches two I4's.
</li>
<li>
<b>I4_WRAP</b> forces an I4 to lie between given limits by wrapping.
</li>
<li>
<b>I4COL_COMPARE</b> compares columns I and J of an I4COL.
</li>
<li>
<b>I4COL_SORT_A</b> ascending sorts the columns of an I4COL.
</li>
<li>
<b>I4COL_SWAP</b> swaps two columns of an I4COL.
</li>
<li>
<b>I4MAT_DATA_READ</b> reads data from an I4MAT file.
</li>
<li>
<b>I4MAT_HEADER_READ</b> reads the header from an I4MAT file.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of an I4MAT, transposed.
</li>
<li>
<b>I4MAT_WRITE</b> writes an I4MAT file with no header.
</li>
<li>
<b>I4VEC_HEAP_D</b> reorders an array of integers into a descending heap.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>I4VEC_REVERSE</b> reverses the elements of an integer vector.
</li>
<li>
<b>I4VEC_SORT_HEAP_A</b> ascending sorts an array of integers using heap sort.
</li>
<li>
<b>LEVEL_SET</b> generates the connected level structure rooted at a given node.
</li>
<li>
<b>MESH_BASE_ZERO</b> ensures that the element definition is zero-based.
</li>
<li>
<b>NEIGHBOR_ELEMENTS_Q4_MESH</b> determines element neighbors in a Q4 mesh.
</li>
<li>
<b>PERM_CHECK</b> checks that a vector represents a permutation.
</li>
<li>
<b>PERM_INVERSE3</b> produces the inverse of a given permutation.
</li>
<li>
<b>R8COL_PERMUTE</b> permutes an R8COL in place.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads the data from an R8MAT file.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file with no header.
</li>
<li>
<b>RCM</b> renumbers a connected component by the reverse Cuthill McKee algorithm.
</li>
<li>
<b>ROOT_FIND</b> finds a pseudo-peripheral node.
</li>
<li>
<b>S_LEN_TRIM</b> returns the length of a string to the last nonblank.
</li>
<li>
<b>S_TO_I4</b> reads an I4 from a string.
</li>
<li>
<b>S_TO_I4VEC</b> reads an I4VEC from a string.
</li>
<li>
<b>S_TO_R8</b> reads an R8 from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>SORT_HEAP_EXTERNAL</b> externally sorts a list of items into ascending order.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 30 September 2009.
</i>
<!-- John Burkardt -->
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<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>