PWL_INTERP_1D
Piecewise Linear Interpolation in 1D

PWL_INTERP_1D is a MATLAB library which interpolates a set of data with a piecewise linear function.

PWL_INTERP_1D needs the R8LIB library. The test code also needs the TEST_INTERP library.

Licensing:

The computer code and data files described and 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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BARYCENTRIC_INTERP_1D, a MATLAB 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 MATLAB library which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).

LAGRANGE_INTERP_1D, a MATLAB 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 MATLAB library which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

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

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

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

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

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

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

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

VANDERMONDE_INTERP_1D, a MATLAB library which finds a polynomial interpolant to a function of 1D data 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_basis_1d.m, evaluates a piecewise linear interpolant basis function.
• pwl_interp_1d.m, evaluates a piecewise linear interpolant.

Examples and Tests:

The test code requires the test_interp library as well.

• pwl_interp_1d_test.m, calls all the tests;
• pwl_interp_1d_test_output.txt, the output file.
• pwl_interp_1d_test01.m, plots the basis functions to the data.
• pwl_interp_1d_test02.m, plots the piecewise linear basis functions for a given set of nodes.

pwl_interp_1d_test01() plots the piecewise linear interpolant to the data.

• p01_pwl.png, a plot of the piecewise linear interpolant for problem p01;
• p02_pwl.png, a plot of the piecewise linear interpolant for problem p02;
• p03_pwl.png, a plot of the piecewise linear interpolant for problem p03;
• p04_pwl.png, a plot of the piecewise linear interpolant for problem p04;
• p05_pwl.png, a plot of the piecewise linear interpolant for problem p05;
• p06_pwl.png, a plot of the piecewise linear interpolant for problem p06;
• p07_pwl.png, a plot of the piecewise linear interpolant for problem p07;
• p08_pwl.png, a plot of the piecewise linear interpolant for problem p08;

pwl_interp_1d_test02() plots the basis functions to the data.

• p01_pwl_basis.png, a plot of the basis functions for problem p01;
• p02_pwl_basis.png, a plot of the basis functions for problem p02;
• p03_pwl_basis.png, a plot of the basis functions for problem p03;
• p04_pwl_basis.png, a plot of the basis functions for problem p04;
• p05_pwl_basis.png, a plot of the basis functions for problem p05;
• p06_pwl_basis.png, a plot of the basis functions for problem p06;
• p07_pwl_basis.png, a plot of the basis functions for problem p07;
• p08_pwl_basis.png, a plot of the basis functions for problem p08;

You can go up one level to the MATLAB source codes.