Support interpolation from general-dimension tables

[hsinhaoHHuang]

Goal

• To resolve Support Mis_InterpolateFrom2D/3DTable() #403

• To perform linear interpolation for general rectilinear tables

Changes

• Add new functions for the calculation of interpolation

  • Mis_LinearInterpolate() for interpolation of 1D values
  • Mis_BilinearInterpolate() for interpolation of 2D values
  • Mis_TrilinearInterpolate() for interpolation of 3D values
  • Mis_MultilinearInterpolate() for interpolation of general nD values

• Add new functions for the interpolations from tables

  • Mis_InterpolateFrom2DTable() for interpolation from a 2D table
  • Mis_InterpolateFrom3DTable() for interpolation from a 3D table
  • Mis_InterpolateFrom_nDim_Table() for interpolation from a general nD table
  • Mis_InterpolateFrom_nDim_Table_withIdxL() for interpolation from a general nD table with the IdxL already known

• Replace the HaloMerger_Trilinear_Interpolation() and HaloMerger_Get_Value_From_HALO_IC_Data in src/TestProblem/ELBDM/HaloMerger/Init_TestProb_ELBDM_HaloMerger.cpp

  • Now, we convert the data into a double-precision array and prepare the coordinates arrays and call the Mis_InterpolateFrom_nDim_Table_withIdxL().
  • The method to deal with the boundary values (1/2 cell size) of the table changes from interpolation with zero to extending values from the surface.

• Some minor format adjustments in src/TestProblem/ELBDM/HaloMerger/Init_TestProb_ELBDM_HaloMerger.cpp

Verifications

• The Mis_InterpolateFromTable() for the soliton profile can return the same value as before in TestProblem/ELBDM/HaloMerger

• The projections of the initial conditions of TestProblem/ELBDM/HaloMerger are the same as before.

• All unit tests attached in Mis_InterpolateFromTable.cpp and Mis_LinearInterpolate.cpp pass.

  • The answers are calculated by the scipy.interpolate.RegularGridInterpolator
    For example,

    import numpy as np
    from scipy.interpolate import RegularGridInterpolator
    
    def f(x, y, z):
       return x*y*y*z
    
    Table_x = np.array( [ 1.0, 2.0, 3.0, 4.0 ] )
    Table_y = np.array( [ 2.0, 3.0 ] )
    Table_z = np.array( [ 4.0, 5.0, 8.0 ] )
    
    Mesh_x, Mesh_y, Mesh_z = np.meshgrid( Table_x, Table_y, Table_z, indexing='ij' )
    
    Table_f = f(Mesh_x, Mesh_y, Mesh_z)
    
    interp = RegularGridInterpolator( (Table_x, Table_y, Table_z), Table_f, method='linear', bounds_error=False, fill_value=None )
    print( interp( np.array( [xp, yp, zp] ) ) )

[barrytchiang]

Thank you again for expanding the array of interpolation functions in GAMER! All the edits, additions, and tests to the code itself look great to me. I've also tested it myself, and everything seems good.

All the comments I left are small things in the text descriptions in this PR. Once these are addressed, it is ready to be merged.

[hsinhaoHHuang]

@barrytchiang Thank you for reviewing and testing this PR.
I have fixed the grammatical errors you listed. Thank you for your careful checks!

[hyschive]

@hsinhaoHHuang This PR is neat! And good job in adding unit tests for all the newly introduced functionalities! I only have some minor comments before merging.

[hyschive]

@hsinhaoHHuang This PR is neat! And good job in adding unit tests for all the newly introduced functionalities! I only have some minor comments before merging.

[hsinhaoHHuang]

Thank you for all the suggestions! I have updated this PR accordingly.

[hyschive]

@hsinhaoHHuang Thanks for the careful revision. Good job!