PWL_INTERP_1D
Piecewise Linear Interpolation in 1D

PWL_INTERP_1D is a C++ library which interpolates a set of data with a piecewise linear function, creating graphics files for processing by GNUPLOT.

The PWL_INTERP_1D test code needs the R8LIB and TEST_INTERP libraries.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

PWL_INTERP_1D is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BARYCENTRIC_INTERP_1D, a C++ library which defines and evaluates the barycentric Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i). The barycentric approach means that very high degree polynomials can safely be used.

CHEBYSHEV_INTERP_1D, a C++ library which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).

GNUPLOT, C++ programs which illustrate the use of the gnuplot graphics program.

LAGRANGE_INTERP_1D, a C++ library which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).

NEAREST_INTERP_1D, a C++ library which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

NEWTON_INTERP_1D, a C++ library which finds a polynomial interpolant to data using Newton divided differences.

PWL_APPROX_1D, a C++ library which approximates a set of data using a piecewise linear function.

PWL_INTERP_2D, a C++ library which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.

R8LIB, a C++ library which contains many utility routines using double precision real (R8) arithmetic.

RBF_INTERP_1D, a C++ library which defines and evaluates radial basis function (RBF) interpolants to 1D data.

SHEPARD_INTERP_1D, a C++ library which defines and evaluates Shepard interpolants to 1D data, based on inverse distance weighting.

TEST_INTERP, a C++ library which defines a number of test problems for interpolation, provided as a set of (x,y) data.

TEST_INTERP_1D, a C++ library which defines test problems for interpolation of data y(x), depending on a 2D argument.

VANDERMONDE_INTERP_1D, a C library which finds a polynomial interpolant to data y(x) of a 1D argument, by setting up and solving a linear system for the polynomial coefficients, involving the Vandermonde matrix.

Reference:

1. Kendall Atkinson,
   An Introduction to Numerical Analysis,
   Prentice Hall, 1989,
   ISBN: 0471624896,
   LC: QA297.A94.1989.
2. Philip Davis,
   Interpolation and Approximation,
   Dover, 1975,
   ISBN: 0-486-62495-1,
   LC: QA221.D33
3. David Kahaner, Cleve Moler, Steven Nash,
   Numerical Methods and Software,
   Prentice Hall, 1989,
   ISBN: 0-13-627258-4,
   LC: TA345.K34.

Source Code:

• pwl_interp_1d.cpp, the source code.
• pwl_interp_1d.hpp, the include file.

Examples and Tests:

• pwl_interp_1d_test.cpp, a sample calling program.
• pwl_interp_1d_test.txt, the output file.

The test program makes data files that can be used by GNUPLOT to create graphics:

• data1.txt
• interp1.txt
• commands1.txt
• plot1.png
• data2.txt
• interp2.txt
• commands2.txt
• plot2.png
• data3.txt
• interp3.txt
• commands3.txt
• plot3.png
• data4.txt
• interp4.txt
• commands4.txt
• plot4.png
• data5.txt
• interp5.txt
• commands5.txt
• plot5.png
• data6.txt
• interp6.txt
• commands6.txt
• plot6.png
• data7.txt
• interp7.txt
• commands7.txt
• plot7.png
• data8.txt
• interp8.txt
• commands8.txt
• plot8.png

List of Routines:

• PWL_BASIS_1D evaluates a 1D piecewise linear basis function.
• PWL_INTERP_1D evaluates the piecewise linear interpolant.

You can go up one level to the C++ source codes.