shepard_interp_1d
shepard_interp_1d,
a Python code 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 MIT 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 code 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 code 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 code 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 code which
interpolates a set of data using a piecewise constant interpolant
defined by the nearest neighbor criterion.
newton_interp_1d,
a python code which
finds a polynomial interpolant to data using newton divided differences.
pwl_interp_1d,
a python code which
interpolates a set of data using a piecewise linear interpolant.
rbf_interp_1d,
a python code which
defines and evaluates radial basis function (rbf) interpolants
to 1d data.
test_interp,
a python code which
defines a number of test problems for interpolation,
provided as a set of (x,y) data.
test_interp_1d,
a python code which
defines test problems for interpolation of data y(x),
depending on a 2d argument.
vandermonde_interp_1d,
a python code 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:

Richard Franke,
Scattered Data Interpolation: Tests of Some Methods,
Mathematics of Computation,
Volume 38, Number 157, January 1982, pages 181200.

Donald Shepard,
A twodimensional interpolation function for irregularly spaced data,
ACM '68: Proceedings of the 1968 23rd ACM National Conference,
ACM, pages 517524, 1969.
Source Code:
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.
Last modified on 03 July 2015.