SHEPARD_INTERP_1D
Shepard Interpolation of 1D Data

SHEPARD_INTERP_1D is a MATLAB 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 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).

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

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

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

SHEPARD_INTERP_ND, a MATLAB library which defines and evaluates Shepard interpolants to multidimensional data, 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. 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_basis_1d.m, evaluates a Shepard basis function for 1D data.
• shepard_interp_1d.m, evaluates a Shepard interpolant to 1D data.

Examples and Tests:

Running these tests requires access to the test_interp library. Should that library be available in a directory at the same level, this can be accomplished with the command "addpath ( '../test_interp' )".

• shepard_interp_1d_test.m, calls all the tests;
• shepard_interp_1d_test_output.txt, the output file.
• shepard_interp_1d_test01.m, tests a particular set of data and a particular value of the exponent.

shepard_interp_1d_test01 plots the data and Shepard interpolants.

• p01_data.png, the data for problem p01 with a linear interpolant.
• p01_0_poly.png, the Shepard interpolant for problem p01 with P = 0.
• p01_1_poly.png, the Shepard interpolant for problem p01 with P = 1.
• p01_2_poly.png, the Shepard interpolant for problem p01 with P = 2.
• p01_4_poly.png, the Shepard interpolant for problem p01 with P = 4.
• p01_8_poly.png, the Shepard interpolant for problem p01 with P = 8.
• p02_data.png, the data for problem p02 with a linear interpolant.
• p02_0_poly.png, the Shepard interpolant for problem p02 with P = 0.
• p02_1_poly.png, the Shepard interpolant for problem p02 with P = 1.
• p02_2_poly.png, the Shepard interpolant for problem p02 with P = 2.
• p02_4_poly.png, the Shepard interpolant for problem p02 with P = 4.
• p02_8_poly.png, the Shepard interpolant for problem p02 with P = 8.
• p03_data.png, the data for problem p03 with a linear interpolant.
• p03_0_poly.png, the Shepard interpolant for problem p03 with P = 0.
• p03_1_poly.png, the Shepard interpolant for problem p03 with P = 1.
• p03_2_poly.png, the Shepard interpolant for problem p03 with P = 2.
• p03_4_poly.png, the Shepard interpolant for problem p03 with P = 4.
• p03_8_poly.png, the Shepard interpolant for problem p03 with P = 8.
• p04_data.png, the data for problem p04 with a linear interpolant.
• p04_0_poly.png, the Shepard interpolant for problem p04 with P = 0.
• p04_1_poly.png, the Shepard interpolant for problem p04 with P = 1.
• p04_2_poly.png, the Shepard interpolant for problem p04 with P = 2.
• p04_4_poly.png, the Shepard interpolant for problem p04 with P = 4.
• p04_8_poly.png, the Shepard interpolant for problem p04 with P = 8.
• p05_data.png, the data for problem p05 with a linear interpolant.
• p05_0_poly.png, the Shepard interpolant for problem p05 with P = 0.
• p05_1_poly.png, the Shepard interpolant for problem p05 with P = 1.
• p05_2_poly.png, the Shepard interpolant for problem p05 with P = 2.
• p05_4_poly.png, the Shepard interpolant for problem p05 with P = 4.
• p05_8_poly.png, the Shepard interpolant for problem p05 with P = 8.
• p06_data.png, the data for problem p06 with a linear interpolant.
• p06_0_poly.png, the Shepard interpolant for problem p06 with P = 0.
• p06_1_poly.png, the Shepard interpolant for problem p06 with P = 1.
• p06_2_poly.png, the Shepard interpolant for problem p06 with P = 2.
• p06_4_poly.png, the Shepard interpolant for problem p06 with P = 4.
• p06_8_poly.png, the Shepard interpolant for problem p06 with P = 8.
• p07_data.png, the data for problem p07 with a linear interpolant.
• p07_0_poly.png, the Shepard interpolant for problem p07 with P = 0.
• p07_1_poly.png, the Shepard interpolant for problem p07 with P = 1.
• p07_2_poly.png, the Shepard interpolant for problem p07 with P = 2.
• p07_4_poly.png, the Shepard interpolant for problem p07 with P = 4.
• p07_8_poly.png, the Shepard interpolant for problem p07 with P = 8.
• p08_data.png, the data for problem p08 with a linear interpolant.
• p08_0_poly.png, the Shepard interpolant for problem p08 with P = 0.
• p08_1_poly.png, the Shepard interpolant for problem p08 with P = 1.
• p08_2_poly.png, the Shepard interpolant for problem p08 with P = 2.
• p08_4_poly.png, the Shepard interpolant for problem p08 with P = 4.
• p08_8_poly.png, the Shepard interpolant for problem p08 with P = 8.

shepard_interp_1d_test02 plots the Shepard basis functions.

• p07_0_poly.png, the Shepard basis functions for problem p07 with P = 0.
• p07_1_poly.png, the Shepard basis functions for problem p07 with P = 1.
• p07_2_poly.png, the Shepard basis functions for problem p07 with P = 2.
• p07_4_poly.png, the Shepard basis functions for problem p07 with P = 4.
• p07_8_poly.png, the Shepard basis functions for problem p07 with P = 8.

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