barycentric_interp_1d, a FORTRAN77 code which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i). Because a barycentric formulation is used, polynomials of very high degree can safely be used.
Efficient calculation of the barycentric polynomial interpolant requires that the function to be interpolated be sampled at points from a known family, for which the interpolation weights have been precomputed. Such families include
Note that in the Berrut/Trefethen reference, there is a significant
typographical error on page 510, where an adjustment is made in cases
where the polynomial is to be evaluated exactly at a data point.
The paper reads:
exact(xdiff==0) = 1;
but it should read
exact(xdiff==0) = j;
The code requires the R8LIB library. The test also requires the TEST_INTERP_1D library.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
barycentric_interp_1d is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
chebyshev_interp_1d, a FORTRAN77 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 FORTRAN77 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 FORTRAN77 library which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.
PWL_INTERP_1D, a FORTRAN77 library which interpolates a set of data using a piecewise linear interpolant.
R8LIB, a FORTRAN77 library which contains many utility routines using double precision real (R8) arithmetic.
RBF_INTERP_1D, a FORTRAN77 library which defines and evaluates radial basis function (RBF) interpolants to 1D data.
SHEPARD_INTERP_1D, a FORTRAN77 library which defines and evaluates Shepard interpolants to 1D data, based on inverse distance weighting.
SPLINE, a FORTRAN77 library which constructs and evaluates spline interpolants and approximants.
TEST_INTERP_1D, a FORTRAN77 library which defines test problems for interpolation of data y(x), depending on a 2D argument.
VANDERMONDE_INTERP_1D, a FORTRAN77 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.