PWL_INTERP_1D
Piecewise Linear Interpolation in 1D

PWL_INTERP_1D is a FORTRAN77 library which interpolates a set of data with a piecewise linear function, creating graphics files for processing by GNUPLOT.

The PWL_INTERP_1D test code needs the R8LIB and TEST_INTERP libraries.

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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BARYCENTRIC_INTERP_1D, a FORTRAN77 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 FORTRAN77 library which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).

GNUPLOT, FORTRAN77 programs which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.

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_APPROX_1D, a FORTRAN77 library which approximates a set of data using a piecewise linear function.

PWL_INTERP_2D, a FORTRAN77 library which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.

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.

TEST_INTERP, a FORTRAN77 library which defines a number of test problems for interpolation, provided as a set of (x,y) data.

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.

Reference:

1. Kendall Atkinson,
   An Introduction to Numerical Analysis,
   Prentice Hall, 1989,
   ISBN: 0471624896,
   LC: QA297.A94.1989.
2. Philip Davis,
   Interpolation and Approximation,
   Dover, 1975,
   ISBN: 0-486-62495-1,
   LC: QA221.D33
3. David Kahaner, Cleve Moler, Steven Nash,
   Numerical Methods and Software,
   Prentice Hall, 1989,
   ISBN: 0-13-627258-4,
   LC: TA345.K34.

Source Code:

• pwl_interp_1d.f, the source code.
• pwl_interp_1d.sh, BASH commands to compile the source code.

Examples and Tests:

• pwl_interp_1d_prb.f, a sample calling program.
• pwl_interp_1d_prb.sh, BASH commands to compile and run the sample program.
• pwl_interp_1d_prb_output.txt, the output file.

The test program makes files which can be used by GNUPLOT to create PNG plots:

• data01.txt
• interp01.txt
• commands01.txt
• plot01.png
• data02.txt
• interp02.txt
• commands02.txt
• plot02.png
• data03.txt
• interp03.txt
• commands03.txt
• plot03.png
• data04.txt
• interp04.txt
• commands04.txt
• plot04.png
• data05.txt
• interp05.txt
• commands05.txt
• plot05.png
• data06.txt
• interp06.txt
• commands06.txt
• plot06.png
• data07.txt
• interp07.txt
• commands07.txt
• plot07.png
• data08.txt
• interp08.txt
• commands08.txt
• plot08.png

List of Routines:

• PWL_BASIS_1D evaluates a 1D piecewise linear basis function.
• PWL_INTERP_1D evaluates the piecewise linear interpolant.

You can go up one level to the FORTRAN77 source codes.