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<html>
<head>
<title>
PWL_APPROX_1D - Approximation in 1D using Piecewise Linear Functions
</title>
</head>
<body bgcolor="#eeeeee" link="#cc0000" alink="#ff3300" vlink="#000055">
<h1 align = "center">
PWL_APPROX_1D <br> Approximation in 1D using Piecewise Linear Functions
</h1>
<hr>
<p>
<b>PWL_APROX_1D</b>
is a MATLAB library which
defines and evaluates a piecewise linear function, using NC "control points",
which approximates a set of ND data points (x(i),y(i)).
</p>
<p>
<b>PWL_APPROX_1D</b> needs access to the R8LIB library.
The test code also needs access to the TEST_INTERP_1D library.
</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>PWL_APPROX_1D</b> is available in
<a href = "../../c_src/pwl_approx_1d/pwl_approx_1d.html">a C version</a> and
<a href = "../../cpp_src/pwl_approx_1d/pwl_approx_1d.html">a C++ version</a> and
<a href = "../../f77_src/pwl_approx_1d/pwl_approx_1d.html">a FORTRAN77 version</a> and
<a href = "../../f_src/pwl_approx_1d/pwl_approx_1d.html">a FORTRAN90 version</a> and
<a href = "../../m_src/pwl_approx_1d/pwl_approx_1d.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/bernstein_polynomial/bernstein_polynomial.html">
BERNSTEIN_POLYNOMIAL</a>,
a MATLAB library which
evaluates the Bernstein polynomials,
useful for uniform approximation of functions;
</p>
<p>
<a href = "../../m_src/lagrange_approx_1d/lagrange_approx_1d.html">
LAGRANGE_APPROX_1D</a>,
a MATLAB library which
defines and evaluates the Lagrange polynomial p(x) of degree m
which approximates a set of nd data points (x(i),y(i)).
</p>
<p>
<a href = "../../m_src/pwl_interp_1d/pwl_interp_1d.html">
PWL_INTERP_1D</a>,
a MATLAB library which
interpolates a set of data using a piecewise linear function.
</p>
<p>
<a href = "../../m_src/r8lib/r8lib.html">
R8LIB</a>,
a MATLAB library which
contains many utility routines using double precision real (R8) arithmetic.
</p>
<p>
<a href = "../../m_src/spline/spline.html">
SPLINE</a>,
a MATLAB library which
constructs and evaluates spline interpolants and approximants.
</p>
<p>
<a href = "../../m_src/test_approx/test_approx.html">
TEST_APPROX</a>,
a MATLAB library which
defines test problems for approximation,
provided as a set of (x,y) data.
</p>
<p>
<a href = "../../m_src/test_interp/test_interp.html">
TEST_INTERP</a>,
a MATLAB library which
defines a number of test problems for interpolation,
provided as a set of (x,y) data.
</p>
<p>
<a href = "../../m_src/test_interp_1d/test_interp_1d.html">
TEST_INTERP_1D</a>,
a MATLAB library which
defines test problems for interpolation of data y(x),
depending on a 2D argument.
</p>
<p>
<a href = "../../m_src/vandermonde_approx_1d/vandermonde_approx_1d.html">
VANDERMONDE_APPROX_1D</a>,
a MATLAB library which
finds a polynomial approximant to data of a 1D argument
by setting up and solving an overdetermined linear system for the polynomial coefficients,
involving the Vandermonde matrix.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Kendall Atkinson,<br>
An Introduction to Numerical Analysis,<br>
Prentice Hall, 1989,<br>
ISBN: 0471624896,<br>
LC: QA297.A94.1989.
</li>
<li>
Philip Davis,<br>
Interpolation and Approximation,<br>
Dover, 1975,<br>
ISBN: 0-486-62495-1,<br>
LC: QA221.D33
</li>
<li>
David Kahaner, Cleve Moler, Steven Nash,<br>
Numerical Methods and Software,<br>
Prentice Hall, 1989,<br>
ISBN: 0-13-627258-4,<br>
LC: TA345.K34.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "pwl_approx_1d.m">pwl_approx_1d.m</a>,
determines the control points and values to be used by a piecewise linear
approximant to given data.
</li>
<li>
<a href = "pwl_approx_1d_matrix.m">pwl_approx_1d_matrix.m</a>,
evaluates a matrix used to determine the control points.
</li>
<li>
<a href = "pwl_interp_1d.m">pwl_interp_1d.m</a>,
evaluates a piecewise linear interpolant.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
The test code requires the <b>test_interp_1d</b> library.
<ul>
<li>
<a href = "pwl_approx_1d_test.m">pwl_approx_1d_test.m</a>, calls all the tests;
</li>
<li>
<a href = "pwl_approx_1d_test_output.txt">pwl_approx_1d_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "pwl_approx_1d_test01.m">pwl_approx_1d_test01.m</a>,
plots a piecewise linear interpolant to
the original data, and the piecewise linear approximant.
</li>
</ul>
</p>
<p>
<b>pwl_approx_1d_test01()</b> uses nc evenly spaced control points to approximate
a set of nd data values.
<ul>
<li>
<a href = "p01_pwl_02_16.png.png">p01_pwl_02_16.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
16 data values for problem p01;
</li>
<li>
<a href = "p01_pwl_04_16.png.png">p01_pwl_04_16.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
16 data values for problem p01;
</li>
<li>
<a href = "p01_pwl_08_16.png.png">p01_pwl_08_16.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
16 data values for problem p01;
</li>
<li>
<a href = "p01_pwl_16_16.png.png">p01_pwl_16_16.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
16 data values for problem p01;
</li>
<li>
<a href = "p01_pwl_02_64.png.png">p01_pwl_02_64.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
64 data values for problem p01;
</li>
<li>
<a href = "p01_pwl_04_64.png.png">p01_pwl_04_64.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
64 data values for problem p01;
</li>
<li>
<a href = "p01_pwl_08_64.png.png">p01_pwl_08_64.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
64 data values for problem p01;
</li>
<li>
<a href = "p01_pwl_16_64.png.png">p01_pwl_16_64.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
64 data values for problem p01;
</li>
<li>
<a href = "p02_pwl_02_16.png.png">p02_pwl_02_16.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
16 data values for problem p02;
</li>
<li>
<a href = "p02_pwl_04_16.png.png">p02_pwl_04_16.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
16 data values for problem p02;
</li>
<li>
<a href = "p02_pwl_08_16.png.png">p02_pwl_08_16.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
16 data values for problem p02;
</li>
<li>
<a href = "p02_pwl_16_16.png.png">p02_pwl_16_16.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
16 data values for problem p02;
</li>
<li>
<a href = "p02_pwl_02_64.png.png">p02_pwl_02_64.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
64 data values for problem p02;
</li>
<li>
<a href = "p02_pwl_04_64.png.png">p02_pwl_04_64.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
64 data values for problem p02;
</li>
<li>
<a href = "p02_pwl_08_64.png.png">p02_pwl_08_64.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
64 data values for problem p02;
</li>
<li>
<a href = "p02_pwl_16_64.png.png">p02_pwl_16_64.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
64 data values for problem p02;
</li>
<li>
<a href = "p03_pwl_02_16.png.png">p03_pwl_02_16.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
16 data values for problem p03;
</li>
<li>
<a href = "p03_pwl_04_16.png.png">p03_pwl_04_16.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
16 data values for problem p03;
</li>
<li>
<a href = "p03_pwl_08_16.png.png">p03_pwl_08_16.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
16 data values for problem p03;
</li>
<li>
<a href = "p03_pwl_16_16.png.png">p03_pwl_16_16.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
16 data values for problem p03;
</li>
<li>
<a href = "p03_pwl_02_64.png.png">p03_pwl_02_64.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
64 data values for problem p03;
</li>
<li>
<a href = "p03_pwl_04_64.png.png">p03_pwl_04_64.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
64 data values for problem p03;
</li>
<li>
<a href = "p03_pwl_08_64.png.png">p03_pwl_08_64.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
64 data values for problem p03;
</li>
<li>
<a href = "p03_pwl_16_64.png.png">p03_pwl_16_64.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
64 data values for problem p03;
</li>
<li>
<a href = "p04_pwl_02_16.png.png">p04_pwl_02_16.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
16 data values for problem p04;
</li>
<li>
<a href = "p04_pwl_04_16.png.png">p04_pwl_04_16.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
16 data values for problem p04;
</li>
<li>
<a href = "p04_pwl_08_16.png.png">p04_pwl_08_16.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
16 data values for problem p04;
</li>
<li>
<a href = "p04_pwl_16_16.png.png">p04_pwl_16_16.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
16 data values for problem p04;
</li>
<li>
<a href = "p04_pwl_02_64.png.png">p04_pwl_02_64.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
64 data values for problem p04;
</li>
<li>
<a href = "p04_pwl_04_64.png.png">p04_pwl_04_64.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
64 data values for problem p04;
</li>
<li>
<a href = "p04_pwl_08_64.png.png">p04_pwl_08_64.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
64 data values for problem p04;
</li>
<li>
<a href = "p04_pwl_16_64.png.png">p04_pwl_16_64.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
64 data values for problem p04;
</li>
<li>
<a href = "p05_pwl_02_16.png.png">p05_pwl_02_16.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
16 data values for problem p05;
</li>
<li>
<a href = "p05_pwl_04_16.png.png">p05_pwl_04_16.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
16 data values for problem p05;
</li>
<li>
<a href = "p05_pwl_08_16.png.png">p05_pwl_08_16.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
16 data values for problem p05;
</li>
<li>
<a href = "p05_pwl_16_16.png.png">p05_pwl_16_16.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
16 data values for problem p05;
</li>
<li>
<a href = "p05_pwl_02_64.png.png">p05_pwl_02_64.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
64 data values for problem p05;
</li>
<li>
<a href = "p05_pwl_04_64.png.png">p05_pwl_04_64.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
64 data values for problem p05;
</li>
<li>
<a href = "p05_pwl_08_64.png.png">p05_pwl_08_64.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
64 data values for problem p05;
</li>
<li>
<a href = "p05_pwl_16_64.png.png">p05_pwl_16_64.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
64 data values for problem p05;
</li>
<li>
<a href = "p06_pwl_02_16.png.png">p06_pwl_02_16.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
16 data values for problem p06;
</li>
<li>
<a href = "p06_pwl_04_16.png.png">p06_pwl_04_16.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
16 data values for problem p06;
</li>
<li>
<a href = "p06_pwl_08_16.png.png">p06_pwl_08_16.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
16 data values for problem p06;
</li>
<li>
<a href = "p06_pwl_16_16.png.png">p06_pwl_16_16.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
16 data values for problem p06;
</li>
<li>
<a href = "p06_pwl_02_64.png.png">p06_pwl_02_64.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
64 data values for problem p06;
</li>
<li>
<a href = "p06_pwl_04_64.png.png">p06_pwl_04_64.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
64 data values for problem p06;
</li>
<li>
<a href = "p06_pwl_08_64.png.png">p06_pwl_08_64.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
64 data values for problem p06;
</li>
<li>
<a href = "p06_pwl_16_64.png.png">p06_pwl_16_64.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
64 data values for problem p06;
</li>
<li>
<a href = "p07_pwl_02_16.png.png">p07_pwl_02_16.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
16 data values for problem p07;
</li>
<li>
<a href = "p07_pwl_04_16.png.png">p07_pwl_04_16.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
16 data values for problem p07;
</li>
<li>
<a href = "p07_pwl_08_16.png.png">p07_pwl_08_16.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
16 data values for problem p07;
</li>
<li>
<a href = "p07_pwl_16_16.png.png">p07_pwl_16_16.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
16 data values for problem p07;
</li>
<li>
<a href = "p07_pwl_02_64.png.png">p07_pwl_02_64.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
64 data values for problem p07;
</li>
<li>
<a href = "p07_pwl_04_64.png.png">p07_pwl_04_64.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
64 data values for problem p07;
</li>
<li>
<a href = "p07_pwl_08_64.png.png">p07_pwl_08_64.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
64 data values for problem p07;
</li>
<li>
<a href = "p07_pwl_16_64.png.png">p07_pwl_16_64.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
64 data values for problem p07;
</li>
<li>
<a href = "p08_pwl_02_16.png.png">p08_pwl_02_16.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
16 data values for problem p08;
</li>
<li>
<a href = "p08_pwl_04_16.png.png">p08_pwl_04_16.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
16 data values for problem p08;
</li>
<li>
<a href = "p08_pwl_08_16.png.png">p08_pwl_08_16.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
16 data values for problem p08;
</li>
<li>
<a href = "p08_pwl_16_16.png.png">p08_pwl_16_16.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
16 data values for problem p08;
</li>
<li>
<a href = "p08_pwl_02_64.png.png">p08_pwl_02_64.png</a>,
a plot of the piecewise linear approximant with 2 control points approximating
64 data values for problem p08;
</li>
<li>
<a href = "p08_pwl_04_64.png.png">p08_pwl_04_64.png</a>,
a plot of the piecewise linear approximant with 4 control points approximating
64 data values for problem p08;
</li>
<li>
<a href = "p08_pwl_08_64.png.png">p08_pwl_08_64.png</a>,
a plot of the piecewise linear approximant with 8 control points approximating
64 data values for problem p08;
</li>
<li>
<a href = "p08_pwl_16_64.png.png">p08_pwl_16_64.png</a>,
a plot of the piecewise linear approximant with 16 control points approximating
64 data values for problem p08;
</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 modified on 18 August 2012.
</i>
<!-- John Burkardt -->
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