PWL_INTERP_1D
Piecewise Linear Interpolation in 1D

PWL_INTERP_1D is a Python library which interpolates a set of data with a piecewise linear function.

Licensing:

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

Languages:

PWL_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).

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_2D, a Python library which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.

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:

• p00_data.py, returns the data for any problem.
• p00_data_num.py, returns the number of data points for any problem.
• p00_dim_num.py, returns the spatial dimension for any problem.
• p00_prob_num.py, returns the number of test problems.
• pwl_basis_1d.py, evaluates a piecewise linear interpolant basis function.
• pwl_value_1d.py, evaluates a piecewise linear interpolant.
• r8mat_print.py, prints an R8MAT.
• r8mat_print_some.py, prints some of an R8MAT.
• 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.
• r8vec_norm_affine.py, computes the L2 norm of the difference of two R8VEC's.
• r8vec_print.py, prints an R8VEC.
• r8vec_uniform_01.py, returns a unit pseudorandom 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:

• pwl_interp_1d_test.py, calls all the tests;
• pwl_interp_1d_test.sh, runs all the tests;
• pwl_interp_1d_test.txt, the output file.

pwl_interp_1d_test01() plots the piecewise linear interpolant to the data.

• p01_pwl.png
• p02_pwl.png
• p03_pwl.png
• p04_pwl.png
• p05_pwl.png
• p06_pwl.png
• p07_pwl.png
• p08_pwl.png

pwl_interp_1d_test02() plots the basis functions to the data.

• p01_pwl_basis.png
• p02_pwl_basis.png
• p03_pwl_basis.png
• p04_pwl_basis.png
• p05_pwl_basis.png,
• p06_pwl_basis.png
• p07_pwl_basis.png
• p08_pwl_basis.png

You can go up one level to the Python source codes.