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TEST_INTERP_2D
Test Interpolation Data Z(X,Y) of a 2D Argument {#test_interp_2d-test-interpolation-data-zxy-of-a-2d-argument align="center"}

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

TEST_INTERP_2D requires access to the R8LIB library.

Licensing: {#licensing align="center"}

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

Languages: {#languages align="center"}

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: {#related-data-and-programs align="center"}

LAGRANGE_INTERP_2D, a C++ 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 C++ 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 C++ library which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.

R8LIB, a C++ library which contains many utility routines, using double precision real (R8) arithmetic.

RBF_INTERP_2D, a C++ library which defines and evaluates radial basis function (RBF) interpolants to 2D data.

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

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

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

TOMS886, a C++ 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 a C++ version of ACM TOMS algorithm 886.

VANDERMONDE_INTERP_2D, a C++ 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: {#reference align="center"}

  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: {#source-code align="center"}

Examples and Tests: {#examples-and-tests align="center"}

List of Routines: {#list-of-routines align="center"}

  • 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 1.
  • F01_F1 returns first derivatives of function 1.
  • F01_F2 returns second derivatives of function 1.
  • F01_TITLE returns the title for function 1.
  • 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 10.
  • F10_F1 returns first derivatives of function 10.
  • F10_F2 returns second derivatives of function 10.
  • F10_TITLE returns the title for function 10.
  • 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 C++ source codes.

Last revised on 05 October 2012.