LAGRANGE_INTERP_1D
Polynomial Interpolation in 1D using Lagrange Polynomials

LAGRANGE_INTERP_1D is 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).

LAGRANGE_INTERP_1D needs the R8LIB library. The test uses the TEST_INTERP_1D library.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

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 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).

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

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_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:

lagrange_basis_1d.py, evaluates the Lagrange basis polynomials.
lagrange_value_1d.py, evaluates the Lagrange interpolant.
p00_f.py, evaluates the function for any problem.
p00_prob_num.py, returns the number of test problems.
p00_title.py, prints the title for any problem.
r8mat_print.py, prints an R8MAT.
r8mat_print_some.py, prints some of an R8MAT.
r8vec_cheby_extreme.py, creates Chebyshev Extreme values in [A,B].
r8vec_norm.py, computes the L2 norm of an R8VEC.
r8vec_norm_affine.py, computes the L2 norm of the difference of two R8VEC's.
r8vec_print.py, prints an R8VEC.
r8vec_uniform_ab.py, returns a scaled pseudorandom R8VEC.
r8vec2_print.py, prints a pair of R8VEC's.
timestamp.py, prints the YMDHMS date as a timestamp.

Examples and Tests:

lagrange_interp_1d_test.py, calls all the tests;
lagrange_interp_1d_test.sh, runs all the tests;
lagrange_interp_1d_test.txt, the output file.

Images for Problem 1:

Images for Problem p02:

Images for problem p03:

Images for problem p04:

Images for problem p05:

Images for problem p06:

Images for problem p07:

Images for problem p08:

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