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

TEST_INTERP_1D is a FORTRAN90 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 FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BARYCENTRIC_INTERP_1D, a FORTRAN90 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.

BERNSTEIN_POLYNOMIAL, a FORTRAN90 library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

CHEBYSHEV_INTERP_1D, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 library which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

NEWTON_INTERP_1D, a FORTRAN90 library which finds a polynomial interpolant to data using Newton divided differences.

PWL_INTERP_1D, a FORTRAN90 library which interpolates a set of data using a piecewise linear function.

R8LIB, a FORTRAN90 library which contains many utility routines using double precision real (R8) arithmetic.

RBF_INTERP_1D, a FORTRAN90 library which defines and evaluates radial basis function (RBF) interpolants to 1D data.

SHEPARD_INTERP_1D, a FORTRAN90 library which defines and evaluates Shepard interpolants to 1D data, based on inverse distance weighting.

TEST_INTERP_2D, a FORTRAN90 library which defines test problems for interpolation of data z(x,y), depending on a 2D argument.

TEST_INTERP_ND, a FORTRAN90 library which defines test problems for interpolation of data z(x), depending on an M-dimensional argument.

VANDERMONDE_INTERP_1D, a FORTRAN90 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:

• test_interp_1d.f90, the source code.

Examples and Tests:

• test_interp_1d_test.f90, a sample calling program.
• test_interp_1d_test.txt, the output file.

List of Routines:

• P00_F evaluates the function for any problem.
• P00_PROB_NUM returns the number of problems.
• P00_TITLE returns the title of any problem.
• P01_F evaluates the function for problem p01.
• P01_TITLE returns the title of problem p01.
• P02_F evaluates the function for problem p01.
• P02_TITLE returns the title of problem p02.
• P03_F evaluates the function for problem p03.
• P03_TITLE returns the title of problem p03.
• P04_F evaluates the function for problem p04.
• P04_TITLE returns the title of problem p04.
• P05_F evaluates the function for problem p05.
• P05_TITLE returns the title of problem p05.
• P06_F evaluates the function for problem p06.
• P06_TITLE returns the title of problem p06.
• P07_F evaluates the function for problem p07.
• P07_TITLE returns the title of problem p07.
• P08_F evaluates the function for problem p08.
• P08_TITLE returns the title of problem p08.

You can go up one level to the FORTRAN90 source codes.