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<html>
<head>
<title>
INTERP - Interpolation Routines
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
INTERP <br> Interpolation Routines
</h1>
<hr>
<p>
<b>INTERP</b>
is a C++ library which
takes a set of data associated with successive values of
a parameter, and produces an interpolating function which can
be evaluated over a continuous range of the parameter.
</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>INTERP</b> is available in
<a href = "../../c_src/interp/interp.html">a C version</a> and
<a href = "../../cpp_src/interp/interp.html">a C++ version</a> and
<a href = "../../f77_src/interp/interp.html">a FORTRAN77 version</a> and
<a href = "../../f_src/interp/interp.html">a FORTRAN90 version</a> and
<a href = "../../m_src/interp/interp.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/bernstein_polynomial/bernstein_polynomial.html">
BERNSTEIN_POLYNOMIAL</a>,
a C++ library which
evaluates the Bernstein polynomials,
useful for uniform approximation of functions;
</p>
<p>
<a href = "../../cpp_src/divdif/divdif.html">
DIVDIF</a>,
a C++ library which
uses divided differences to interpolate data.
</p>
<p>
<a href = "../../cpp_src/hermite/hermite.html">
HERMITE</a>,
a C++ library which
computes the Hermite interpolant, a polynomial that matches function values
and derivatives.
</p>
<p>
<a href = "../../cpp_src/lebesgue/lebesgue.html">
LEBESGUE</a>,
a C++ library which
is given a set of nodes in 1D, and
plots the Lebesgue function, and estimates the Lebesgue constant,
which measures the maximum magnitude of the potential error
of Lagrange polynomial interpolation, and which uses gnuplot
to make plots of the Lebesgue function.
</p>
<p>
<a href = "../../cpp_src/rbf_interp/rbf_interp.html">
RBF_INTERP</a>,
a C++ library which
defines and evaluates radial basis interpolants to multidimensional data.
</p>
<p>
<a href = "../../cpp_src/spline/spline.html">
SPLINE</a>,
a C++ library which
computes functions that approximate or interpolate data.
</p>
<p>
<a href = "../../cpp_src/test_approx/test_approx.html">
TEST_APPROX</a>,
a C++ library which
defines a number of test problems for approximation and interpolation.
</p>
<p>
<a href = "../../cpp_src/test_interp_1d/test_interp_1d.html">
TEST_INTERP_1D</a>,
a C++ library which
defines test problems for interpolation of data y(x),
depending on a 1D argument.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Samuel Conte, Carl deBoor,<br>
Elementary Numerical Analysis,<br>
Second Edition,<br>
McGraw Hill, 1972,<br>
ISBN: 07-012446-4,<br>
LC: QA297.C65.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "interp.cpp">interp.cpp</a>, the source code.
</li>
<li>
<a href = "interp.hpp">interp.hpp</a>, the source code.
</li>
<li>
<a href = "interp.sh">interp.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "interp_prb.cpp">interp_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "interp_prb.sh">interp_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "interp_prb_output.txt">interp_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CC_ABSCISSAS</b> computes the Clenshaw Curtis abscissas.
</li>
<li>
<b>CC_ABSCISSAS_AB</b> computes the Clenshaw Curtis abscissas for the interval [A,B].
</li>
<li>
<b>F1_ABSCISSAS</b> computes Fejer type 1 abscissas.
</li>
<li>
<b>F1_ABSCISSAS_AB</b> computes Fejer type 1 abscissas for the interval [A,B].
</li>
<li>
<b>F2_ABSCISSAS</b> computes Fejer Type 2 abscissas.
</li>
<li>
<b>F2_ABSCISSAS_AB</b> computes Fejer Type 2 abscissas for the interval [A,B].
</li>
<li>
<b>INTERP_LAGRANGE:</b> Lagrange polynomial interpolation to a curve in M dimensions.
</li>
<li>
<b>INTERP_LINEAR:</b> piecewise linear interpolation to a curve in M dimensions.
</li>
<li>
<b>INTERP_NEAREST:</b> Nearest neighbor interpolation to a curve in M dimensions.
</li>
<li>
<b>LAGRANGE_VALUE</b> evaluates the Lagrange polynomials.
</li>
<li>
<b>NCC_ABSCISSAS</b> computes the Newton Cotes Closed abscissas.
</li>
<li>
<b>NCC_ABSCISSAS_AB</b> computes the Newton Cotes Closed abscissas for [A,B].
</li>
<li>
<b>NCO_ABSCISSAS</b> computes the Newton Cotes Open abscissas.
</li>
<li>
<b>NCO_ABSCISSAS_AB</b> computes the Newton Cotes Open abscissas for [A,B].
</li>
<li>
<b>PARAMETERIZE_ARC_LENGTH</b> parameterizes data by pseudo-arclength.
</li>
<li>
<b>PARAMETERIZE_INDEX</b> parameterizes data by its index.
</li>
<li>
<b>R8MAT_EXPAND_LINEAR2</b> expands an R8MAT by linear interpolation.
</li>
<li>
<b>R8VEC_ASCENDS_STRICTLY</b> determines if an R8VEC is strictly ascending.
</li>
<li>
<b>R8VEC_BRACKET</b> searches a sorted R8VEC for successive brackets of a value.
</li>
<li>
<b>R8VEC_EXPAND_LINEAR</b> linearly interpolates new data into an R8VEC.
</li>
<li>
<b>R8VEC_EXPAND_LINEAR2</b> linearly interpolates new data into an R8VEC.
</li>
<li>
<b>R8VEC_SORTED_NEAREST</b> returns the nearest element in a sorted R8VEC.
</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 03 March 2014.
</i>
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