PrecomputedSparseFunction(self, *args, **kwargs)

Tensor symbol representing a sparse array in symbolic equations; unlike SparseFunction, PrecomputedSparseFunction uses externally-defined data for interpolation.


Name Type Description Default
name str Name of the symbol. required
npoint int Number of sparse points. required
grid Grid The computational domain from which the sparse points are sampled. required
r int Number of gridpoints in each Dimension to interpolate a single sparse point to. E.g. r=2 for linear interpolation. required
coordinates numpy.numpy.ndarray The coordinates of each sparse point. required
gridpoints numpy.numpy.ndarray An array carrying the reference grid point corresponding to each sparse point. Of all the gridpoints that one sparse point would be interpolated to, this is the grid point closest to the origin, i.e. the one with the lowest value of each coordinate Dimension. Must be a two-dimensional array of shape (npoint, grid.ndim). required
interpolation_coeffs numpy.numpy.ndarray An array containing the coefficient for each of the r^2 (2D) or r^3 (3D) gridpoints that each sparse point will be interpolated to. The coefficient is split across the n Dimensions such that the contribution of the point (i, j, k) will be multiplied by interp_coeffs[..., i]*interp_coeffs[...,j]*interp_coeffs[...,k]. So for r=6, we will store 18 coefficients per sparse point (instead of potentially 216). Must be a three-dimensional array of shape (npoint, grid.ndim, r). required
space_order int Discretisation order for space derivatives. 0
shape tuple of ints Shape of the object. (npoint,)
dimensions tuple of Dimension Dimensions associated with the object. Only necessary if the SparseFunction defines a multi-dimensional tensor. required
dtype - type Any object that can be interpreted as a numpy data type. np.float32
initializer callable or any object exposing the buffer interface Data initializer. If a callable is provided, data is allocated lazily. required
allocator MemoryAllocator Controller for memory allocation. To be used, for example, when one wants to take advantage of the memory hierarchy in a NUMA architecture. Refer to default_allocator.__doc__ for more information. required


The parameters must always be given as keyword arguments, since SymPy uses *args to (re-)create the Dimension arguments of the symbolic object.


Name Description
interpolation_coeffs The Precomputed interpolation coefficients.
is_SparseFunction bool(x) -> bool
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