TEST_INTERP_1D
Test Functions Y(X) for Interpolation of a 1D Argument

TEST_INTERP_1D is a MATLAB library which defines test functions y(x) that may be used to test interpolation algorithms involving a 1D argument x.

TEST_INTERP_1D requires access to a compiled copy of the R8LIB library.

Licensing:

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

Languages:

TEST_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_1D, a MATLAB library which interpolates a set of data using a piecewise linear interpolant.

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.

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

TEST_INTERP_2D, a MATLAB library which defines test problems for interpolation of data z(x,y), depending on a 2D argument.

TEST_INTERP_ND, a MATLAB library which defines test problems for interpolation of data z(x), depending on an M-dimensional argument.

VANDERMONDE_INTERP_1D, a MATLAB 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. Philip Davis,
   Interpolation and Approximation,
   Dover, 1975,
   ISBN: 0-486-62495-1,
   LC: QA221.D33

Source Code:

• p00_f.m, evaluates the function for any problem.
• p00_plot.m, creates a plot of any problem.
• p00_prob_num.m, returns the number of test problems.
• p00_title.m, prints the title for any problem.
• p01_f.m, returns the function for problem p01.
• p01_title.m, returns the title for problem p01.
• p02_f.m, returns the function for problem p02.
• p02_title.m, returns the title for problem p02.
• p03_f.m, returns the function for problem p03.
• p03_title.m, returns the title for problem p03.
• p04_f.m, returns the function for problem p04.
• p04_title.m, returns the title for problem p04.
• p05_f.m, returns the function for problem p05.
• p05_title.m, returns the title for problem p05.
• p06_f.m, returns the function for problem p06.
• p06_title.m, returns the title for problem p06.
• p07_f.m, returns the function for problem p07.
• p07_title.m, returns the title for problem p07.
• p08_f.m, returns the function for problem p08.
• p08_title.m, returns the title for problem p08.

Examples and Tests:

• test_interp_1d_test.m, a sample calling program.
• test_interp_1d_test01.m, calls P00_TITLE to print the title of each function.
• test_interp_1d_test02.m, calls P00_F to evaluate each function at sample points.
• test_interp_1d_test03.m, calls P00_PLOT to plot each function.
• test_interp_1d_test_output.txt, the output file.

test_interp_1d_test03 plots each function:

• p01_plot.png
• p02_plot.png
• p03_plot.png
• p04_plot.png
• p05_plot.png
• p06_plot.png
• p07_plot.png
• p08_plot.png

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