SHEPARD_INTERP_1D
Shepard Interpolation of 1D Data

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

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

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

PWL_INTERP_1D, a Python library which interpolates a set of data using a piecewise linear interpolant.

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

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

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

VANDERMONDE_INTERP_1D, a Python 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. 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:

• p00_data.py, returns the data for any problem.
• p00_data_num.py, returns the number of data points for any problem.
• p00_dim_num.py, returns the spatial dimension for any problem.
• p00_prob_num.py, returns the number of test problems.
• r8mat_print.py, prints an R8MAT.
• r8mat_print_some.py, prints some of an R8MAT.
• r8mat_transpose_print.py, prints an R8MAT, transposed.
• r8mat_transpose_print_some.py, prints some of an R8MAT, transposed.
• r8vec_norm.py, computes the L2 norm of an R8VEC.
• r8vec_norm_affine.py, computes the L2 norm of the difference of two R8VEC's.
• r8vec_print.py, prints an R8VEC.
• r8vec_uniform_01.py, returns a random value in [0,1].
• r8vec_uniform_ab.py, returns a random value in [A,B].
• shepard_basis_1d.py, evaluates a Shepard basis function for 1D data.
• shepard_value_1d.py, evaluates a Shepard interpolant to 1D data.
• timestamp.py, prints the YMDHMS date as a timestamp.

Examples and Tests:

• shepard_interp_1d_test.py, calls all the tests;
• shepard_interp_1d_test.sh, runs all the tests;
• shepard_interp_1d_test.txt, the output file.

shepard_interp_1d_test01 plots the data and Shepard interpolants.

• p01_data.png, the data for problem p01 with a linear interpolant.
• p01_0.0_shepard.png, the Shepard interpolant for problem p01 with P = 0.
• p01_1.0_shepard.png, the Shepard interpolant for problem p01 with P = 1.
• p01_2.0_shepard.png, the Shepard interpolant for problem p01 with P = 2.
• p01_4.0_shepard.png, the Shepard interpolant for problem p01 with P = 4.
• p01_8.0_shepard.png, the Shepard interpolant for problem p01 with P = 8.
• p02_data.png, the data for problem p02 with a linear interpolant.
• p02_0.0_shepard.png, the Shepard interpolant for problem p02 with P = 0.
• p02_1.0_shepard.png, the Shepard interpolant for problem p02 with P = 1.
• p02_2.0_shepard.png, the Shepard interpolant for problem p02 with P = 2.
• p02_4.0_shepard.png, the Shepard interpolant for problem p02 with P = 4.
• p02_8.0_shepard.png, the Shepard interpolant for problem p02 with P = 8.
• p03_data.png, the data for problem p03 with a linear interpolant.
• p03_0.0_shepard.png, the Shepard interpolant for problem p03 with P = 0.
• p03_1.0_shepard.png, the Shepard interpolant for problem p03 with P = 1.
• p03_2.0_shepard.png, the Shepard interpolant for problem p03 with P = 2.
• p03_4.0_shepard.png, the Shepard interpolant for problem p03 with P = 4.
• p03_8.0_shepard.png, the Shepard interpolant for problem p03 with P = 8.
• p04_data.png, the data for problem p04 with a linear interpolant.
• p04_0.0_shepard.png, the Shepard interpolant for problem p04 with P = 0.
• p04_1.0_shepard.png, the Shepard interpolant for problem p04 with P = 1.
• p04_2.0_shepard.png, the Shepard interpolant for problem p04 with P = 2.
• p04_4.0_shepard.png, the Shepard interpolant for problem p04 with P = 4.
• p04_8.0_shepard.png, the Shepard interpolant for problem p04 with P = 8.
• p05_data.png, the data for problem p05 with a linear interpolant.
• p05_0.0_shepard.png, the Shepard interpolant for problem p05 with P = 0.
• p05_1.0_shepard.png, the Shepard interpolant for problem p05 with P = 1.
• p05_2.0_shepard.png, the Shepard interpolant for problem p05 with P = 2.
• p05_4.0_shepard.png, the Shepard interpolant for problem p05 with P = 4.
• p05_8.0_shepard.png, the Shepard interpolant for problem p05 with P = 8.
• p06_data.png, the data for problem p06 with a linear interpolant.
• p06_0.0_shepard.png, the Shepard interpolant for problem p06 with P = 0.
• p06_1.0_shepard.png, the Shepard interpolant for problem p06 with P = 1.
• p06_2.0_shepard.png, the Shepard interpolant for problem p06 with P = 2.
• p06_4.0_shepard.png, the Shepard interpolant for problem p06 with P = 4.
• p06_8.0_shepard.png, the Shepard interpolant for problem p06 with P = 8.
• p07_data.png, the data for problem p07 with a linear interpolant.
• p07_0.0_shepard.png, the Shepard interpolant for problem p07 with P = 0.
• p07_1.0_shepard.png, the Shepard interpolant for problem p07 with P = 1.
• p07_2.0_shepard.png, the Shepard interpolant for problem p07 with P = 2.
• p07_4.0_shepard.png, the Shepard interpolant for problem p07 with P = 4.
• p07_8.0_shepard.png, the Shepard interpolant for problem p07 with P = 8.
• p08_data.png, the data for problem p08 with a linear interpolant.
• p08_0.0_shepard.png, the Shepard interpolant for problem p08 with P = 0.
• p08_1.0_shepard.png, the Shepard interpolant for problem p08 with P = 1.
• p08_2.0_shepard.png, the Shepard interpolant for problem p08 with P = 2.
• p08_4.0_shepard.png, the Shepard interpolant for problem p08 with P = 4.
• p08_8.0_shepard.png, the Shepard interpolant for problem p08 with P = 8.

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