SHEPARD_INTERP_1D
Shepard Interpolation of 1D Data

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

SHEPARD_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:

SHEPARD_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.

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).

DIVDIF, a FORTRAN90 library which uses divided differences to compute the polynomial interpolant to a given set of data.

HERMITE, a FORTRAN90 library which computes the Hermite interpolant, a polynomial that matches function values and derivatives.

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 interpolant.

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_2D, a FORTRAN90 library which defines and evaluates Shepard interpolants to 2D data, based on inverse distance weighting.

SHEPARD_INTERP_ND, a FORTRAN90 library which defines and evaluates Shepard interpolants to multidimensional data, based on inverse distance weighting.

TEST_INTERP, a FORTRAN90 library which defines a number of test problems for interpolation, provided as a set of (x,y) data.

TEST_INTERP_1D, a FORTRAN90 library which defines test problems for interpolation of data y(x), depending on a 2D argument.

VANDERMONDE_INTERP_1D, a FORTRAN90 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. Richard Franke,
   Scattered Data Interpolation: Tests of Some Methods,
   Mathematics of Computation,
   Volume 38, Number 157, January 1982, pages 181-200.
2. Donald Shepard,
   A two-dimensional interpolation function for irregularly spaced data,
   ACM '68: Proceedings of the 1968 23rd ACM National Conference,
   ACM, pages 517-524, 1969.

Source Code:

• shepard_interp_1d.f90, the source code.

Examples and Tests:

• shepard_interp_1d_test.f90, a sample calling program.
• shepard_interp_1d_test.txt, the output file.

List of Routines:

• SHEPARD_BASIS_1D evaluates a 1D Shepard basis function.
• SHEPARD_INTERP_1D evaluates a 1D Shepard interpolant.

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