NEAREST_INTERP_1D
Nearest Neighbor Interpolation in 1D

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

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 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).

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 function.

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

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

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.

Source Code:

• nearest_interp_1d.m, evaluates the nearest neighbor interpolant.
• p00_data.py, returns the data for any problem.
• p00_data_num.py, returns the number of data points for any problem.
• p00_prob_num.py, returns the number of test problems.
• 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.
• r8vec2_print.py, prints a pair of R8VEC's.
• timestamp.py, prints the YMDHMS date as a timestamp.

Examples and Tests:

The test code requires the test_interp library as well.

• nearest_interp_1d.sh, runs all the tests;
• nearest_interp_1d.txt, the output file.

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

• p01_pwl.png, a plot of the data and piecewise linear interpolant for problem p01;
• p01_near.png, a plot of the nearest neighbor interpolant for problem p01;
• p02_pwl.png, a plot of the data and piecewise linear interpolant for problem p02;
• p02_near.png, a plot of the nearest neighbor interpolant for problem p02;
• p03_pwl.png, a plot of the data and piecewise linear interpolant for problem p03;
• p03_near.png, a plot of the nearest neighbor interpolant for problem p03;
• p04_pwl.png, a plot of the data and piecewise linear interpolant for problem p04;
• p04_near.png, a plot of the nearest neighbor interpolant for problem p04;
• p05_pwl.png, a plot of the data and piecewise linear interpolant for problem p05;
• p05_near.png, a plot of the nearest neighbor interpolant for problem p05;
• p06_pwl.png, a plot of the data and piecewise linear interpolant for problem p06;
• p06_near.png, a plot of the nearest neighbor interpolant for problem p06;
• p07_pwl.png, a plot of the data and piecewise linear interpolant for problem p07;
• p07_near.png, a plot of the nearest neighbor interpolant for problem p07;
• p08_pwl.png, a plot of the data and piecewise linear interpolant for problem p08;
• p08_near.png, a plot of the nearest neighbor interpolant for problem p08;

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