PrecomputedSparseTimeFunction

PrecomputedSparseTimeFunction(self, *args, **kwargs)

Tensor symbol representing a space- and time-varying sparse array in symbolic equations; unlike SparseTimeFunction, PrecomputedSparseTimeFunction uses externally-defined data for interpolation.

Parameters

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	np.ndarray	The coordinates of each sparse point.	required
gridpoints	np.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	np.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
time_order	int	Discretisation order for time derivatives.	1
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	data - 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.	None
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

Notes

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

Attributes

Name	Description
is_SparseTimeFunction	bool(x) -> bool