TEST_INTERP_2D
Test Interpolation Data Z(X,Y) of a 2D Argument

TEST_INTERP_2D is a FORTRAN77 library which defines test problems for interpolation of data z(x,y)), depending on a 2D argument.

The test for TEST_INTERP_2D requires access to the R8LIB library.

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_2D 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:

LAGRANGE_INTERP_2D, a FORTRAN77 library which defines and evaluates the Lagrange polynomial p(x,y) which interpolates a set of data depending on a 2D argument that was evaluated on a product grid, so that p(x(i),y(j)) = z(i,j).

PADUA, a FORTRAN77 library which returns the points and weights for Padu sets, useful for interpolation in 2D. GNUPLOT is used to plot the points.

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_2D, a FORTRAN77 library which defines and evaluates radial basis function (RBF) interpolants to 2D data.

SHEPARD_INTERP_2D, a FORTRAN77 library which defines and evaluates Shepard interpolants to 2D data, based on inverse distance weighting.

TEST_INTERP_1D, a FORTRAN77 library which defines test problems for interpolation of data y(x), depending on a 1D argument.

TEST_INTERP_ND, a FORTRAN77 library which defines test problems for interpolation of data z(x), depending on an M-dimensional argument.

TOMS526, a FORTRAN77 library which interpolates scattered bivariate data, This is ACM TOMS algorithm 526, by Hiroshi Akima;

TOMS660, a FORTRAN77 library which takes scattered 2D data and produces an interpolating function F(X,Y), this is ACM TOMS algorithm 660, called qshep2d, by Robert Renka.

TOMS790, a FORTRAN77 library which computes an interpolating function to a set of scattered data in the plane; this library is commonly called CSHEP2D; by Robert Renka; this is ACM TOMS algorithm 790.

TOMS886, a FORTRAN77 library which defines the Padua points for interpolation in a 2D region, including the rectangle, triangle, and ellipse, by Marco Caliari, Stefano de Marchi, Marco Vianello. This is ACM TOMS algorithm 886.

VANDERMONDE_INTERP_2D, a FORTRAN77 library which finds a polynomial interpolant to data z(x,y) of a 2D argument by setting up and solving a linear system for the polynomial coefficients, involving the Vandermonde matrix.

Reference:

1. Richard Franke,
   A Critical Comparison of Some Methods for Interpolation of Scattered Data,
   Naval Postgraduate School Technical Report,
   NPS-53-79-003, 1979.
2. Robert Renka, Ron Brown,
   Algorithm 792: Accuracy Tests of ACM Algorithms for Interpolation of Scattered Data in the Plane,
   ACM Transactions on Mathematical Software,
   Volume 25, Number 1, March 1999, pages 78-94.
3. Donald Shepard,
   A two-dimensional interpolation function for irregularly spaced data,
   ACM '68: Proceedings of the 1968 23rd ACM National Conference,
   ACM, pages 517-524, 1969.

Source Code:

• test_interp_2d.f, the source code.
• test_interp_2d.sh, BASH commands to compile the source code.

Examples and Tests:

• test_interp_2d_prb.f, a sample calling program.
• test_interp_2d_prb.sh, BASH commands to compile and run the sample program.
• test_interp_2d_prb_output.txt, the output file.

List of Routines:

• F00_F0 returns the value of any function.
• F00_F1 returns first derivatives of any function.
• F00_F2 returns second derivatives of any function.
• F00_NUM returns the number of test functions available.
• F00_TITLE returns the title for any function.
• F01_F0 returns the value of function f01.
• F01_F1 returns first derivatives of function f01.
• F01_F2 returns second derivatives of function f01.
• F01_TITLE returns the title for function f01.
• F02_F0 returns the value of function 2.
• F02_F1 returns first derivatives of function 2.
• F02_F2 returns second derivatives of function 2.
• F02_TITLE returns the title for function 2.
• F03_F0 returns the value of function 3.
• F03_F1 returns first derivatives of function 3.
• F03_F2 returns second derivatives of function 3.
• F03_TITLE returns the title for function 3.
• F04_F0 returns the value of function 4.
• F04_F1 returns first derivatives of function 4.
• F04_F2 returns second derivatives of function 4.
• F04_TITLE returns the title for function 4.
• F05_F0 returns the value of function 5.
• F05_F1 returns first derivatives of function 5.
• F05_F2 returns second derivatives of function 5.
• F05_TITLE returns the title for function 5.
• F06_F0 returns the value of function 6.
• F06_F1 returns first derivatives of function 6.
• F06_F2 returns second derivatives of function 6.
• F06_TITLE returns the title for function 6.
• F07_F0 returns the value of function 7.
• F07_F1 returns first derivatives of function 7.
• F07_F2 returns second derivatives of function 7.
• F07_TITLE returns the title for function 7.
• F08_F0 returns the value of function 8.
• F08_F1 returns first derivatives of function 8.
• F08_F2 returns second derivatives of function 8.
• F08_TITLE returns the title for function 8.
• F09_F0 returns the value of function 9.
• F09_F1 returns first derivatives of function 9.
• F09_F2 returns second derivatives of function 9.
• F09_TITLE returns the title for function 9.
• F10_F0 returns the value of function f10.
• F10_F1 returns first derivatives of function f10.
• F10_F2 returns second derivatives of function f10.
• F10_TITLE returns the title for function f10.
• F11_F0 returns the value of function f11.
• F11_F1 returns first derivatives of function f11.
• F11_F2 returns second derivatives of function f11.
• F11_TITLE returns the title for function f11.
• F12_F0 returns the value of function f12.
• F12_F1 returns first derivatives of function f12.
• F12_F2 returns second derivatives of function f12.
• F12_TITLE returns the title for function f12.
• F13_F0 returns the value of function f13.
• F13_F1 returns first derivatives of function f13.
• F13_F2 returns second derivatives of function f13.
• F13_TITLE returns the title for function f13.
• G00_NUM returns the number of grids available.
• G00_SIZE returns the size for any grid.
• G00_TITLE returns the title for any grid.
• G00_XY returns the grid points for any grid.
• G01_SIZE returns the size for grid 1.
• G01_TITLE returns the title for grid 1.
• G01_XY returns the grid points for grid 1.
• G02_SIZE returns the size for grid 2.
• G02_TITLE returns the title for grid 2.
• G02_XY returns the grid points for grid 2.
• G03_SIZE returns the size for grid 3.
• G03_TITLE returns the title for grid 3.
• G03_XY returns the grid points for grid 3.
• G04_SIZE returns the size for grid 4.
• G04_TITLE returns the title for grid 4.
• G04_XY returns the grid points for grid 4.
• G05_SIZE returns the size for grid 5.
• G05_TITLE returns the title for grid 5.
• G05_XY returns the grid points for grid 5.

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