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<html>
<head>
<title>
TRIANGULATION_RCM - Reverse Cuthill-McKee Node Reordering
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGULATION_RCM <br> Reverse Cuthill-McKee Node Reordering
</h1>
<hr>
<p>
<b>TRIANGULATION_RCM</b>
is a FORTRAN90 program which
computes the Reverse Cuthill-McKee (RCM) reordering for nodes in a triangulation composed
of 3-node or 6-node triangles.
</p>
<p>
The user supplies a node file and a triangle file, containing
the coordinates of the nodes, and the indices of the nodes that
make up each triangle. Either 3-node or 6-node triangles may
be used.
</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 triangles, and writes out
new node and triangle files that correspond to the RCM permutation.
</p>
<p>
Note that the node file would normally contain exactly 2 values
on each line, namely the X and Y coordinates of the nodes.
However, this is not necessary. Extra information can be
included on each line, for instance, a "Z" coordinate. Each
line should include the same number of items, but all will be
permuted correctly together. The program does not actually
need to know the coordinates of the nodes, so in fact, ANY data
(as long as it is real numeric data) associated with the nodes
can be listed in the node file, and will be correctly permuted.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>triangulation_rcm</b> <i>prefix</i>
</blockquote>
where <i>prefix</i> is the common filename prefix:
<ul>
<li>
<i>prefix</i>_nodes.txt contains the node coordinates,
</li>
<li>
<i>prefix</i>_elements.txt contains the element definitions.
</li>
<li>
<i>prefix</i>_rcm_nodes.txt will contain the RCM node coordinates,
</li>
<li>
<i>prefix</i>_rcm_elements.txt will contain the RCM 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>TRIANGULATION_RCM</b> is available in
<a href = "../../cpp_src/triangulation_rcm/triangulation_rcm.html">a C++ version</a> and
<a href = "../../f_src/triangulation_rcm/triangulation_rcm.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangulation_rcm/triangulation_rcm.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/mesh_bandwidth/mesh_bandwidth.html">
MESH_BANDWIDTH</a>,
a FORTRAN90 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 = "../../f_src/quad_mesh_rcm/quad_mesh_rcm.html">
QUAD_MESH_RCM</a>,
a FORTRAN90 program which
computes the reverse Cuthill-McKee (RCM) reordering for nodes in a mesh of 4-node
quadrilaterals.
</p>
<p>
<a href = "../../f_src/rcm/rcm.html">
RCM</a>,
a FORTRAN90 library which
carries out reverse Cuthill-McKee computations.
</p>
<p>
<a href = "../../f_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a FORTRAN90 program which
triangulates a set of nodes whose coordinates are stored in a file.
</p>
<p>
<a href = "../../f_src/tet_mesh_rcm/tet_mesh_rcm.html">
TET_MESH_RCM</a>,
a FORTRAN90 library which
applies the reverse Cuthill-McKee reordering to a tetrahedral
mesh of nodes in 3D.
</p>
<p>
<a href = "../../c_src/triangle/triangle.html">
TRIANGLE</a>,
a C program which
computes a triangulation of a geometric region.
</p>
<p>
<a href = "../../f_src/triangulation/triangulation.html">
TRIANGULATION</a>,
a FORTRAN90 library which
carries out various operations on order 3 ("linear") or order 6
("quadratic") triangulations.
</p>
<p>
<a href = "../../f_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">
TRIANGULATION_BOUNDARY_NODES</a>,
a FORTRAN90 program which
reads data defining a triangulation, determines which nodes
lie on the boundary, and writes their coordinates to a file.
</p>
<p>
<a href = "../../f_src/triangulation_corner/triangulation_corner.html">
TRIANGULATION_CORNER</a>,
a FORTRAN90 program which
patches triangulations so that no triangle has two sides on the boundary.
</p>
<p>
<a href = "../../f_src/triangulation_delaunay_discrepancy/triangulation_delaunay_discrepancy.html">
TRIANGULATION_DELAUNAY_DISCREPANCY</a>,
a FORTRAN90 program which
measures the amount by which a triangulation fails the local Delaunay test;
</p>
<p>
<a href = "../../cpp_src/triangulation_display_opengl/triangulation_display_opengl.html">
TRIANGULATION_DISPLAY_OPENGL</a>,
a C++ program which
reads files defining a triangulation and displays an image
using Open GL.
</p>
<p>
<a href = "../../f_src/triangulation_histogram/triangulation_histogram.html">
TRIANGULATION_HISTOGRAM</a>,
a FORTRAN90 program which
computes histograms of data over a triangulation.
</p>
<p>
<a href = "../../f_src/triangulation_l2q/triangulation_l2q.html">
TRIANGULATION_L2Q</a>,
a FORTRAN90 program which
reads data defining a 3-node triangulation and generates
midside nodes and writes out the corresponding 6-node triangulation.
</p>
<p>
<a href = "../../f_src/triangulation_mask/triangulation_mask.html">
TRIANGULATION_MASK</a>,
a FORTRAN90 program which
takes an existing triangulation and deletes triangles and
their corresponding nodes as requested by the user.
</p>
<p>
<a href = "../../data/triangulation_order3/triangulation_order3.html">
TRIANGULATION_ORDER3</a>,
a data directory which
contains a description and
examples of order 3 triangulations.
</p>
<p>
<a href = "../../data/triangulation_order6/triangulation_order6.html">
TRIANGULATION_ORDER6</a>,
a data directory which
contains a description and
examples of order 6 triangulations.
</p>
<p>
<a href = "../../f_src/triangulation_orient/triangulation_orient.html">
TRIANGULATION_ORIENT</a>,
a FORTRAN90 program which
reads data defining a triangulation, makes sure that
every triangle has positive orientation, and if not, writes a
corrected triangle file.
</p>
<p>
<a href = "../../f_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a FORTRAN90 program which
reads data defining a triangulation and creates a
PostScript image of the nodes and triangles.
</p>
<p>
<a href = "../../f_src/triangulation_q2l/triangulation_q2l.html">
TRIANGULATION_Q2L</a>,
a FORTRAN90 program which
reads data defining a 6-node triangulation, and subdivides
each triangle into 4 3-node triangles, writing the resulting
triangulation to a file.
</p>
<p>
<a href = "../../f_src/triangulation_quad/triangulation_quad.html">
TRIANGULATION_QUAD</a>,
a FORTRAN90 program which
estimates the integral of a function over a triangulated region.
</p>
<p>
<a href = "../../f_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>,
a FORTRAN90 program which
reads data defining a triangulation and computes a number
of quality measures.
</p>
<p>
<a href = "../../f_src/triangulation_refine/triangulation_refine.html">
TRIANGULATION_REFINE</a>,
a FORTRAN90 program which
can be used to refine a triangulation.
</p>
<p>
<a href = "../../f_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html">
TRIANGULATION_TRIANGLE_NEIGHBORS</a>,
a FORTRAN90 program which
reads data defining a triangulation, determines the neighboring
triangles of each triangle, and writes that information to a file.
</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 = "triangulation_rcm.f90">triangulation_rcm.f90</a>, the source code.
</li>
<li>
<a href = "triangulation_rcm.sh">triangulation_rcm.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>TEST3</b> works with a 3-node triangulation:
<ul>
<li>
<a href = "test3_output.txt">test3_output.txt</a>,
the printed output from the command <br>
"triangulation_rcm test3"
</li>
<li>
<a href = "test3_nodes.txt">test3_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "test3_nodes.png">test3_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nodes created by TRIANGULATION_PLOT.
</li>
<li>
<a href = "test3_elements.txt">test3_elements.txt</a>,
the triangle file.
</li>
<li>
<a href = "test3_elements.png">test3_elements.png</a>,
an image of the triangles before the reordering.
</li>
<li>
<a href = "test3_rcm_nodes.txt">test3_rcm_nodes.txt</a>,
the RCM reordered node file.
</li>
<li>
<a href = "test3_rcm_nodes.png">test3_rcm_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the reordered nodes created by TRIANGULATION_PLOT.
</li>
<li>
<a href = "test3_rcm_elements.txt">test3_rcm_elements.txt</a>,
the RCM reordered triangle file.
</li>
<li>
<a href = "test3_rcm_elements.png">test3_rcm_elements.png</a>,
an image of the triangles after the reordering.
</li>
</ul>
</p>
<p>
<b>TEST6</b> works with a 6-node triangulation:
<ul>
<li>
<a href = "test6_output.txt">test6_output.txt</a>,
the printed output from the command <br>
"triangulation_rcm test6"
</li>
<li>
<a href = "test6_nodes.txt">test6_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "test6_nodes.png">test6_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the nodes created by TRIANGULATION_PLOT.
</li>
<li>
<a href = "test6_elements.txt">test6_elements.txt</a>,
the triangle file.
</li>
<li>
<a href = "test6_elements.png">test6_elements.png</a>,
an image of the triangles before the reordering.
</li>
<li>
<a href = "test6_rcm_nodes.txt">test6_rcm_nodes.txt</a>,
the RCM reordered node file.
</li>
<li>
<a href = "test6_rcm_nodes.png">test6_rcm_nodes.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the reordered nodes created by TRIANGULATION_PLOT.
</li>
<li>
<a href = "test6_rcm_elements.txt">test6_rcm_elements.txt</a>,
the RCM reordered triangle file.
</li>
<li>
<a href = "test6_rcm_elements.png">test6_rcm_elements.png</a>,
an image of the triangles after the reordering.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TRIANGULATION_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>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is a case insensitive comparison of two characters for equality.
</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>DTABLE_DATA_READ</b> reads data from a double precision table file.
</li>
<li>
<b>DTABLE_DATA_WRITE</b> writes data to a double precision table file.
</li>
<li>
<b>DTABLE_HEADER_READ</b> reads the header from a double precision table file.
</li>
<li>
<b>DTABLE_HEADER_WRITE</b> writes the header to a double precision table file.
</li>
<li>
<b>DTABLE_WRITE</b> writes a double precision table file.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_NAME_EXT_GET</b> determines the "extension" of a file name.
</li>
<li>
<b>FILE_NAME_EXT_SWAP</b> replaces the current "extension" of a file name.
</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>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4_SWAP</b> swaps two integer values.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
</li>
<li>
<b>I4ROW_COMPARE</b> compares two rows of an I4ROW.
</li>
<li>
<b>I4ROW_SORT_A</b> ascending sorts the rows of an I4ROW.
</li>
<li>
<b>I4ROW_SWAP</b> swaps two rows of an I4ROW.
</li>
<li>
<b>I4VEC_REVERSE</b> reverses the elements of an integer vector.
</li>
<li>
<b>ITABLE_DATA_READ</b> reads data from an integer table file.
</li>
<li>
<b>ITABLE_DATA_WRITE</b> writes data to an integer table file.
</li>
<li>
<b>ITABLE_HEADER_READ</b> reads the header from an integer table file.
</li>
<li>
<b>ITABLE_HEADER_WRITE</b> writes the header to an integer table file.
</li>
<li>
<b>ITABLE_WRITE</b> writes an integer table file.
</li>
<li>
<b>LEVEL_SET</b> generates the connected level structure rooted at a given node.
</li>
<li>
<b>PERM_CHECK</b> checks that a vector represents a permutation.
</li>
<li>
<b>PERM_INVERSE</b> produces the inverse of a given permutation.
</li>
<li>
<b>R8COL_PERMUTE</b> permutes an R8COL in place.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</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_BLANK_DELETE</b> removes blanks from a string, left justifying the remainder.
</li>
<li>
<b>S_INDEX_LAST_C</b> finds the LAST occurrence of a given character.
</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>
<li>
<b>TIMESTRING</b> writes the current YMDHMS date into a string.
</li>
<li>
<b>TRIANGULATION_ORDER3_ADJ_COUNT</b> counts adjacencies in a triangulation.
</li>
<li>
<b>TRIANGULATION_ORDER3_ADJ_SET</b> sets adjacencies in a triangulation.
</li>
<li>
<b>TRIANGULATION_ORDER3_NEIGHBOR_TRIANGLES</b> determines triangle neighbors.
</li>
<li>
<b>TRIANGULATION_ORDER6_ADJ_COUNT</b> counts adjacencies in a triangulation.
</li>
<li>
<b>TRIANGULATION_ORDER6_ADJ_SET</b> sets adjacencies in a triangulation.
</li>
<li>
<b>TRIANGULATION_ORDER6_NEIGHBOR_TRIANGLES</b> determines triangle neighbors.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 08 January 2007.
</i>
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