TEST_INTERP_FUN
Interpolation Tests Based on Functions

TEST_INTERP_FUN is a FORTRAN90 library which can provide the values of certain functions that are useful for testing an interpolation algorithm using a varying number of points.

The related packages TEST_INTERP and TEST_APPROX provide discrete data sets of (x,y) pairs. However, when the convergence rate of an interpolation process is of interest, it is important to be able to sample an underlying but "unknown" function at an increasing number of points. This library provides a few functions which are known to cause problems for certain kinds of interpolation schemes.

The problems available include:

1. Runge example, f(x) = 1 / ( x * x + 1 ), [-5,5], p01_plot.png;
2. Bernstein example, f(x) = abs ( x ), [-1,1], p02_plot.png;
3. The Step function, p03_plot.png;
4. The Doppler function, p04_plot.png;
5. The Rabbit Ears function, p05_plot.png;

Licensing:

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

Languages:

TEST_INTERP_FUN is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CHEBYSHEV, a FORTRAN90 library which computes the Chebyshev interpolant/approximant to a given function over an interval.

DIVDIF, a FORTRAN90 library which includes many routines to construct and evaluate divided difference interpolants.

PPPACK, a FORTRAN90 library which implements Carl de Boor's piecewise polynomial functions, including, particularly, cubic splines.

RBF_INTERP, a FORTRAN90 library which defines and evaluates radial basis interpolants to multidimensional data.

SPLINE, a FORTRAN90 library which includes many routines to construct and evaluate spline interpolants and approximants.

TEST_APPROX, a FORTRAN90 library which defines test problems for approximation, provided as a set of (x,y) data.

TEST_INTERP, a FORTRAN90 library which defines a number of test problems for interpolation, provided as a set of (x,y) data.

TEST_INTERP_2D, a FORTRAN90 library which defines a number of test problems for interpolation in 2D, provided as functions v = f(x,y).

TEST_INTERP_4D, a FORTRAN90 library which defines a number of test problems for interpolation in 4D, provided as functions v = f(w,x,y,z).

TEST_INTERP_ND, a FORTRAN90 library which defines test problems for interpolation of data z(x), depending on an M-dimensional argument.

TOMS446, a FORTRAN90 library which manipulates Chebyshev series for interpolation and approximation;
this is a version of ACM TOMS algorithm 446, by Roger Broucke.

Reference:

1. Samuel Conte, Carl deBoor,
   Elementary Numerical Analysis,
   Second Edition,
   McGraw Hill, 1972,
   ISBN: 07-012446-4,
   LC: QA297.C65.
2. Carl deBoor,
   A Practical Guide to Splines,
   Springer, 2001,
   ISBN: 0387953663,
   LC: QA1.A647.v27.

Source Code:

• test_interp_fun.f90, the source code.

Examples and Tests:

• test_interp_fun_test.f90, a sample calling program.
• test_interp_fun_test.txt, the output file.

List of Routines:

• P00_FUN evaluates the function for any problem.
• P00_LIM returns the limits of the approximation interval for any problem.
• P00_PROB_NUM returns the number of problems.
• P00_STORY prints the "story" for any problem.
• P00_TITLE returns the title of any problem.
• P01_FUN evaluates the function for problem 1.
• P01_LIM returns the limits of the approximation interval for problem 1.
• P01_STORY prints the "story" for problem 1.
• P01_TITLE returns the title of problem 1.
• P02_FUN evaluates the function for problem 2.
• P02_LIM returns the limits of the approximation interval for problem 2.
• P02_STORY prints the "story" for problem 2.
• P02_TITLE returns the title of problem 2.
• P03_FUN evaluates the function for problem 3.
• P03_LIM returns the limits of the approximation interval for problem 3.
• P03_STORY prints the "story" for problem 3.
• P03_TITLE returns the title of problem 3.
• P04_FUN evaluates the function for problem 4.
• P04_LIM returns the limits of the approximation interval for problem 4.
• P04_STORY prints the "story" for problem 4.
• P04_TITLE returns the title of problem 4.
• P05_FUN evaluates the function for problem 5.
• P05_LIM returns the limits of the approximation interval for problem 5.
• P05_STORY prints the "story" for problem 5.
• P05_TITLE returns the title of problem 5.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.