TensorFunction

TensorFunction(self, *args, **kwargs)

Tensor valued Function represented as a Matrix. Each component is a Function or TimeFunction.

A TensorFunction and the classes that inherit from it takes the same parameters as a DiscreteFunction and additionally:

Parameters

Name	Type	Description	Default
name	str	Name of the symbol.	required
grid	Grid	Carries shape, dimensions, and dtype of the TensorFunction. When grid is not provided, shape and dimensions must be given. For MPI execution, a Grid is compulsory.	required
space_order	int or 3-tuple of ints	Discretisation order for space derivatives. space_order also impacts the number of points available around a generic point of interest. By default, space_order points are available on both sides of a generic point of interest, including those nearby the grid boundary. Sometimes, fewer points suffice; in other scenarios, more points are necessary. In such cases, instead of an integer, one can pass a 3-tuple (o, lp, rp) indicating the discretization order (o) as well as the number of points on the left (lp) and right (rp) sides of a generic point of interest.	1
shape	tuple of ints	Shape of the domain region in grid points. Only necessary if grid isn’t given.	required
dimensions	tuple of Dimension	Dimensions associated with the object. Only necessary if grid isn’t given.	required
dtype	devito.data - type	Any object that can be interpreted as a numpy data type.	np.float32
staggered	Dimension or tuple of Dimension or Stagger	Staggering of each component, needs to have the size of the tensor. Defaults to the Dimensions.	required
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
padding	int or tuple of ints	Allocate extra grid points to maximize data access alignment. When a tuple of ints, one int per Dimension should be provided.	required
symmetric	bool	Whether the tensor is symmetric or not.	True
diagonal	Bool	Whether the tensor is diagonal or not.	False

Attributes

Name	Description
is_diagonal	Whether the tensor is diagonal.
laplace	Laplacian of the TensorFunction.
space_dimensions	Spatial dimensions.
space_order	The space order for all components.

Methods

Name	Description
div	Divergence of the TensorFunction (is a VectorFunction).
laplacian	Laplacian of the TensorFunction with shifted derivatives and custom

div

div(shift=None, order=None, method='FD')

Divergence of the TensorFunction (is a VectorFunction).

Parameters

Name	Type	Description	Default
shift		Shift for the center point of the derivative in number of gridpoints	None
order		Discretization order for the finite differences. Uses func.space_order when not specified	None
method		Discretization method. Options are ‘FD’ (default) and ‘RSFD’ (rotated staggered grid finite-difference).	'FD'

laplacian

laplacian(shift=None, order=None)

Laplacian of the TensorFunction with shifted derivatives and custom FD order.

Each second derivative is left-right (i.e D^T D with D the first derivative ): (self.dx(x0=dim+shift*dim.spacing, fd_order=order)).dx(x0=dim-shift*dim.spacing, fd_order=order)

Parameters

Name	Type	Description	Default
shift		Shift for the center point of the derivative in number of gridpoints	None
order		Discretization order for the finite differences. Uses func.space_order when not specified	None