TEST_INTERP_4D
Interpolation Tests Based on 4D Functions

TEST_INTERP_4D is a FORTRAN90 library which can provide the values of certain scalar functions of a 4D argument that are useful for testing an interpolation algorithm using a varying number of points.

The problems available include:

1. 4D Runge example, f(x) = 1 / ( w^2 + x^2 + y^2 + z^2 + 1 ), [-5,5]^4.
2. Press example, f(x) = 514.1890*exp(-2.0*norm(x-(0.3,0.3,0.3,0.3) * x(1)*x(2)*x(3)*x(4) * (1-x(1))*(1-x(2))*(1-x(3))*(1-x(4)) , [0,1]^4.

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_4D is available in a FORTRAN90 version.

Related Data and Programs:

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

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

TEST_INTERP_FUN, a FORTRAN90 library which defines a number of test problems for interpolation in 1D, provided as functions (x,f(x)).

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

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_4d.f90, the source code.

Examples and Tests:

• test_interp_4d_test.f90, a sample calling program.
• test_interp_4d_test.txt, the output file.

List of Routines:

• P00_4D evaluates the function for any problem.
• P00_LIM_2D returns the interpolation 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_4D evaluates the function for problem 1.
• P01_LIM_4D returns the interpolation interval for problem 1.
• P01_STORY prints the "story" for problem 1.
• P01_TITLE returns the title of problem 1.
• P02_4D evaluates the function for problem 2.
• P02_LIM_4D returns the interpolation interval for problem 2.
• P02_STORY prints the "story" for problem 2.
• P02_TITLE returns the title of problem 2.
• R8VEC_EVEN_SELECT returns the I-th of N evenly spaced values in [ XLO, XHI ].
• R8VEC_EVEN2_SELECT returns the I-th of N evenly spaced midpoint values.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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