# lagrange_interp_1d

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).

### Languages:

lagrange_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).

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 function.

rbf_interp_1d, a python code which defines and evaluates radial basis function (rbf) interpolants to 1d data.

shepard_interp_1d, a python code which defines and evaluates shepard interpolants to 1d data, based on inverse distance weighting.

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.

### Source Code:

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lagrange_interp_1d_test02() plots the data and Lagrange interpolant for Chebyshev spacing.

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