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<html>
<head>
<title>
TOMS790 - Bivariate Interpolation of Scattered Data
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS790 <br> Bivariate Interpolation of Scattered Data
</h1>
<hr>
<p>
<b>TOMS790</b>
is a FORTRAN77 library which
constructs an interpolant to scattered 2D data,
by Robert Renka.
</p>
<p>
<b>TOMS790</b> is similar to the algorithm employed in ACM TOMS algorithm 660,
but achieves cubic precision (where the previous algorithm was only quadratic)
and has C2 continuity.
</p>
<p>
<b>TOMS790</b> is ACM TOMS Algorithm 790.
</p>
<p>
The original, true, correct version of this ACM TOMS algorithm is available
in the TOMS subdirectory of
<a href = "http://www.netlib.org/">the NETLIB web site</a>.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TOMS790</b> is available in
<a href = "../../f77_src/toms790/toms790.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms790/toms790.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/rbf_interp/rbf_interp.html">
RBF_INTERP</a>,
a FORTRAN90 library which
defines and evaluates radial basis interpolants to multidimensional data.
</p>
<p>
<a href = "../../f_src/toms526/toms526.html">
TOMS526</a>,
a FORTRAN90 library which
interpolates scattered bivariate data,
This is ACM TOMS algorithm 526,
by Hiroshi Akima;
</p>
<p>
<a href = "../../f_src/toms660/toms660.html">
TOMS660</a>,
a FORTRAN90 library which
takes scattered 2D data and produces an interpolating function F(X,Y),
this is ACM TOMS algorithm 660,
called <b>qshep2d</b>,
by Robert Renka.
</p>
<p>
<a href = "../../f_src/toms661/toms661.html">
TOMS661</a>,
a FORTRAN90 library which
takes scattered 3D data and produces an interpolating function F(X,Y,Z),
this is ACM TOMS algorithm 661,
called <b>qshep3d</b>,
by Robert Renka.
</p>
<p>
<a href = "../../f_src/toms792/toms792.html">
TOMS792</a>
a FORTRAN90 library which
tests functions that interpolate scattered data in the plane;
by Robert Renka;
this is ACM TOMS algorithm 792.
</p>
<h3 align="center">
Author:
</h3>
<p>
Robert Renka
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Richard Franke,<br>
Scattered Data Interpolation: Tests of Some Methods,<br>
Mathematics of Computation,<br>
Volume 38, Number 157, January 1982, pages 181-200.
</li>
<li>
Robert Renka,<br>
Algorithm 790:
CSHEP2D: Cubic Shepard Method for Bivariate Interpolation of Scattered Data,<br>
ACM Transactions on Mathematical Software,<br>
Volume 25, Number 1, March 1999, pages 70-73.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "toms790.f">toms790.f</a>, the source code.
</li>
<li>
<a href = "toms790.sh">toms790.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>TOMS790_PRB1</b> is a program which can be run interactively, and allows
the user to specify the test data to be used, and other parameters.
<ul>
<li>
<a href = "toms790_prb1.f">toms790_prb1.f</a>,
a sample calling program.
</li>
<li>
<a href = "toms790_prb1.sh">toms790_prb1.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "toms790_prb1_input.txt">toms790_prb1_input.txt</a>,
the input file.
</li>
<li>
<a href = "toms790_prb1_output.txt">toms790_prb1_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
<b>TOMS790_PRB2</b> tests the package using data on a 20 by 20 uniform grid.
<ul>
<li>
<a href = "toms790_prb2.f">toms790_prb2.f</a>,
a sample calling program.
</li>
<li>
<a href = "toms790_prb2.sh">toms790_prb2.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "toms790_prb2_output.txt">toms790_prb2_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CSHEP2</b> defines a C2 function F(X,Y) interpolating scattered data.
</li>
<li>
<b>CS2VAL</b> evaluates an interpolant defined by CSHEP2.
</li>
<li>
<b>CS2GRD</b> returns the value and gradients of a function defined by CSHEP2.
</li>
<li>
<b>CS2HES</b> returns value, gradients and Hessian of a function defined by CSHEP2.
</li>
<li>
<b>GETNP2</b> gets the closest unmarked node to a specified point.
</li>
<li>
<b>GIVENS</b> constructs a Givens plane rotation.
</li>
<li>
<b>ROTATE</b> applies a Givens rotation.
</li>
<li>
<b>SETUP2</b> sets a row of a regression matrix to fit a cubic function to data.
</li>
<li>
<b>STORE2</b> creates a closest-point data structure given points in the plane.
</li>
<li>
<b>TESTDT</b> returns one of five sets of test nodes.
</li>
<li>
<b>TSTFN1</b> computes one of ten bivariate test functions.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f77_src.html">
the FORTRAN77 source codes</a>.
</p>
<hr>
<i>
Last revised on 13 August 2011.
</i>
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