NEAREST_INTERP_1D
Nearest Neighbor Interpolation in 1D

NEAREST_INTERP_1D, a MATLAB library which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.

NEAREST_INTERP_1D needs the R8LIB library. The test 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:

NEAREST_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 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).

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.

nearest_interp_1d_test

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

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_1D, a MATLAB library which defines and evaluates Shepard interpolants to 1D data, which are 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. Kendall Atkinson,
   An Introduction to Numerical Analysis,
   Prentice Hall, 1989,
   ISBN: 0471624896,
   LC: QA297.A94.1989.
2. Philip Davis,
   Interpolation and Approximation,
   Dover, 1975,
   ISBN: 0-486-62495-1,
   LC: QA221.D33
3. David Kahaner, Cleve Moler, Steven Nash,
   Numerical Methods and Software,
   Prentice Hall, 1989,
   ISBN: 0-13-627258-4,
   LC: TA345.K34.

Source Code:

• nearest_interp_1d.m, evaluates the nearest neighbor interpolant.
• timestamp.m, prints the YMDHMS date as a timestamp.

Examples and Tests:

• nearest_interp_1d_test.m, calls all the tests;
• nearest_interp_1d_test.sh, runs all the tests;
• nearest_interp_1d_test.txt, the output file.

• nearest_interp_1d_test01.m, evaluates the interpolant at some sample points.
• nearest_interp_1d_test02.m, tests plots a piecewise linear interpolant to the original data, and the nearest neighbor interpolant.

nearest_interp_1d_test01() plots a piecewise linear interpolant to the original data, and the nearest neighbor interpolant.

• p01_data.png, a plot of the data and piecewise linear interpolant for problem p01;
• p01_nearest.png, a plot of the nearest neighbor interpolant for problem p01;
• p02_data.png, a plot of the data and piecewise linear interpolant for problem p02;
• p02_nearest.png, a plot of the nearest neighbor interpolant for problem p02;
• p03_data.png, a plot of the data and piecewise linear interpolant for problem p03;
• p03_nearest.png, a plot of the nearest neighbor interpolant for problem p03;
• p04_data.png, a plot of the data and piecewise linear interpolant for problem p04;
• p04_nearest.png, a plot of the nearest neighbor interpolant for problem p04;
• p05_data.png, a plot of the data and piecewise linear interpolant for problem p05;
• p05_nearest.png, a plot of the nearest neighbor interpolant for problem p05;
• p06_data.png, a plot of the data and piecewise linear interpolant for problem p06;
• p06_nearest.png, a plot of the nearest neighbor interpolant for problem p06;
• p07_data.png, a plot of the data and piecewise linear interpolant for problem p07;
• p07_nearest.png, a plot of the nearest neighbor interpolant for problem p07;
• p08_data.png, a plot of the data and piecewise linear interpolant for problem p08;
• p08_nearest.png, a plot of the nearest neighbor interpolant for problem p08;