Heterogeneous Sparse Grids

class SpectralToolbox.HeterogeneousSparseGrids.HSparseGrid(polys, Ns, tol=None, sdout=<_io.TextIOWrapper name='<stderr>' mode='w' encoding='UTF-8'>)

Bases: object

Heterogeneous Sparse Grid class

Constructor of Heterogeneous Sparse Grid object (this does not allocate the sparse grid)

Parameters:

• polys (list of Spectral1D.Poly1D) – orthogonal polynomials to be used as basis functions
• Ns (list of integers) – accuracy for each dimension. It can be a list of accuracies or a single accuracy, in which case uniform accuracy is assumed
• tol (float) – tolerance to be used when comparing points of the grid (optional, default=:py:func:Misc.machineEpsilon())
• sdout (stream) – default output stream for the class (optional,default=``sys.stderr``)

Note

one of the following must hold: len(polys)==len(Ns) or len(Ns)==1, in which case the same order is used for all the directions.

Example

>>> from SpectralToolbox import HeterogeneousSparseGrids as HSG
>>> pH = Spectral1D.Poly1D(Spectral1D.HERMITEP_PROB,None)
>>> pL = Spectral1D.Poly1D(Spectral1D.JACOBI,[0.0,0.0])
>>> polys = [pH,pL]
>>> Ns = [2,4]
>>> sg = HSG.HSparseGrid(polys,Ns)

Ns = []

polys = []

sdout = []

sparseGrid(heter=False)

Generates the full and partial sparse grids

Parameters:heter (bool) – if Ns is homogeneous, this parameter will force the output of the partial sparse grid as well Returns:tuple (XF,WF,X) containing:

• XF: full grid points
• WF: full grid weights
• X: partial grid points

Example

>>> (XF,W,X) = sg.sparseGrid()
[SG] Sparse Grid Generation [============================================] 100%
[SG] Sparse Grid Generation: 0.01s

sparseGridInterp(X, fX, XF)

Interpolate values of the Sparse Grid using 1D Polynomial interpolation along cuts.

Parameters:

• X (2d-array of floats) – partial grid on which a function has been evaluated
• fX (1d-array of floats) – values for the points in the partial grid
• XF (2d-array of floats) – full grid on which to interpolate

Returns:

fXF the interpolated values on the full grid

Return type:

1d-array of floats

..note:: The partial and full grid must be overlapping

Example

>>> fXF = sg.sparseGridInterp(X,fX,XF)
[SG] Sparse Grid Interpolation [=========================================] 100%
[SG] Sparse Grid Interpolation: 0.00s

tol = []