14-Jun-2023 07:42:16

lagrange_interp_nd_test():
  MATLAB/Octave version 5.2.0
  Test lagrange_interp_nd().
  The r8lib() library is needed.

lagrange_interp_nd_test01():
  Interpolate in 1D, using orders.
  lagrange_interp_nd_grid() sets the interpolant.
  lagrange_interp_nd_value() evaluates it.

         Zinterp          Zexact      Error

        0.673338         0.67336    2.22e-05
        0.215019        0.215003    1.60e-05
        0.168692        0.168687    5.46e-06
        0.404501        0.404483    1.75e-05
       0.0077811      0.00778446    3.36e-06

lagrange_interp_nd_test02():
  Interpolate in 2D, using orders.
  lagrange_interp_nd_grid() sets the interpolant.
  lagrange_interp_nd_value() evaluates it.

         Zinterp          Zexact      Error

        0.898918        0.898875    4.35e-05
        0.540577        0.539872    7.05e-04
        0.798956        0.798562    3.94e-04
        0.210284        0.210815    5.31e-04
        0.949333        0.949378    4.56e-05

lagrange_interp_nd_test03():
  Interpolate in 3D, using orders.
  lagrange_interp_nd_grid() sets the interpolant.
  lagrange_interp_nd_value() evaluates it.

         Zinterp          Zexact      Error

        0.727392        0.725808    1.58e-03
        0.387407        0.390931    3.52e-03
        0.943282        0.943544    2.62e-04
        0.858566        0.858572    5.78e-06
        0.586791        0.584382    2.41e-03

lagrange_interp_nd_test04():
  Interpolate in 3D, using orders.
  Use a sequence of increasing orders.

  Level     Order   Average Error

      0         1    3.08e-02
      1        27    3.10e-03
      2       125    2.16e-04
      3       729    2.36e-06
      4      4913    8.28e-08
      5     35937    5.14e-10

lagrange_interp_nd_test05():
  Repeat test #1, using levels.
  lagrange_interp_nd_grid2() sets the interpolant.
  lagrange_interp_nd_value2() evaluates it.

         Zinterp          Zexact      Error

       0.0905898       0.0906006    1.07e-05
        0.487905        0.487907    2.19e-06
        0.818172        0.818161    1.08e-05
        0.369457        0.369434    2.31e-05
        0.552563        0.552581    1.76e-05

lagrange_interp_nd_test06():
  Repeat test #2, using levels.
  lagrange_interp_nd_grid2() sets the interpolant.
  lagrange_interp_nd_value2() evaluates it.

         Zinterp          Zexact      Error

        0.724082         0.72381    2.72e-04
        0.827623        0.828084    4.61e-04
        0.541938        0.541516    4.22e-04
        0.866625        0.867283    6.58e-04
        0.843611        0.844707    1.10e-03

lagrange_interp_nd_test07():
  Repeat test #3,  using levels.
  lagrange_interp_nd_grid2() sets the interpolant.
  lagrange_interp_nd_value2() evaluates it.

         Zinterp          Zexact      Error

         0.80553        0.805843    3.13e-04
        0.835015        0.835402    3.87e-04
        0.889897        0.889752    1.45e-04
        0.769025        0.768276    7.49e-04
        0.787649        0.787867    2.18e-04

lagrange_interp_nd_test08():
  Interpolate in 3D, using levels.
  Use a sequence of increasing levels.

  Level     Order   Average Error

      0         1    3.44e-02
      1        27    4.00e-03
      2       125    9.39e-05
      3       729    2.87e-06
      4      4913    5.17e-08
      5     35937    6.53e-10

lagrange_interp_nd_test09():
  Interpolate in 3D, using orders.
  Use a sequence of increasing orders.
  Use anisotropic resolution.
  The interpolant is a polynomial of degrees 3, 5, 2
  so our orders need to be at least 4, 6, 3 to match it.

  Level     Orders   Average Error

      0   1   1   1    8.23e-02
      1   2   1   1    7.09e-02
      2   1   2   1    6.80e-02
      3   1   1   2    8.47e-02
      4   4   2   2    3.77e-02
      5   2   4   2    7.23e-02
      6   2   2   4    1.01e-01
      7   2   2   4    1.01e-01
      8   6   4   4    8.98e-04
      9   4   6   4    1.06e-16
     10   4   4   6    8.98e-04

lagrange_interp_nd_test():
  Normal end of execution.

14-Jun-2023 07:42:46