SparseTimeFunction

SparseTimeFunction(*args, **kwargs)

Tensor symbol representing a space- and time-varying sparse array in symbolic equations.

Like SparseFunction, SparseTimeFunction carries multi-dimensional data that are not aligned with the computational grid. As such, each data value is associated some coordinates. A SparseTimeFunction provides symbolic interpolation routines to convert between TimeFunctions and sparse data points. These are based upon standard [bi,tri]linear interpolation.

Parameters

Name Type Description Default
name str Name of the symbol. required
npoint int Number of sparse points. required
nt int Number of timesteps along the time Dimension. required
grid Grid The computational domain from which the sparse points are sampled. required
coordinates np.ndarray The coordinates of each sparse point. 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. (nt, 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

Examples

Creation

>>> from devito import Grid, SparseTimeFunction
>>> grid = Grid(shape=(4, 4))
>>> sf = SparseTimeFunction(name='sf', grid=grid, npoint=2, nt=3)
>>> sf
sf(time, p_sf)

Inspection

>>> sf.data
Data([[0., 0.],
      [0., 0.],
      [0., 0.]], dtype=float32)
>>> sf.coordinates
sf_coords(p_sf, d)
>>> sf.coordinates_data
array([[0., 0.],
       [0., 0.]], dtype=float32)

Symbolic interpolation routines

>>> from devito import TimeFunction
>>> f = TimeFunction(name='f', grid=grid)
>>> exprs0 = sf.interpolate(f)
>>> exprs1 = sf.inject(f, sf)

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
forward Symbol for the time-forward state of the TimeFunction.
is_SparseTimeFunction bool(x) -> bool

Methods

Name Description
inject Generate equations injecting an arbitrary expression into a field.
interpolate Generate equations interpolating an arbitrary expression into self.

inject

inject(field, expr, u_t=None, p_t=None, implicit_dims=None)

Generate equations injecting an arbitrary expression into a field.

Parameters

Name Type Description Default
field Function Input field into which the injection is performed. required
expr expr - like Injected expression. required
u_t expr - like Time index at which the interpolation is performed. None
p_t expr - like Time index at which the result of the interpolation is stored. None
implicit_dims Dimension or list of Dimension An ordered list of Dimensions that do not explicitly appear in the injection expression, but that should be honored when constructing the operator. None

interpolate

interpolate(expr, u_t=None, p_t=None, increment=False, implicit_dims=None)

Generate equations interpolating an arbitrary expression into self.

Parameters

Name Type Description Default
expr expr - like Input expression to interpolate. required
u_t expr - like Time index at which the interpolation is performed. None
p_t expr - like Time index at which the result of the interpolation is stored. None
increment If True, generate increments (Inc) rather than assignments (Eq). False
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