TensorFunction

class devito.types.TensorFunction(*args, **kwargs)

Bases: AbstractTensor

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 (str) – Name of the symbol.

• grid (Grid, optional) – 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.

• space_order (int or 3-tuple of ints, optional) – Discretisation order for space derivatives. Defaults to 1. 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.

• shape (tuple of ints, optional) – Shape of the domain region in grid points. Only necessary if grid isn’t given.

• dimensions (tuple of Dimension, optional) – Dimensions associated with the object. Only necessary if grid isn’t given.

• dtype (data-type, optional) – Any object that can be interpreted as a numpy data type. Defaults to np.float32.

• staggered (tuple of Dimension, optional) – Define how the TensorFunction is staggered.

• initializer (callable or any object exposing the buffer interface, optional) – Data initializer. If a callable is provided, data is allocated lazily.

• allocator (MemoryAllocator, optional) – 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.

• padding (int or tuple of ints, optional) –

  Deprecated since version shouldn’t: be used; padding is now automatically inserted.

  Allocate extra grid points to maximize data access alignment. When a tuple of ints, one int per Dimension should be provided.

• symmetric (bool, optional) – Whether the tensor is symmetric or not. Defaults to True.

• diagonal (Bool, optional) – Whether the tensor is diagonal or not. Defaults to False.

• staggered – Staggering of each component, needs to have the size of the tensor. Defaults to the Dimensions.

property is_diagonal

Whether the tensor is diagonal.

is_symmetric(simplify=True)

Check if matrix is symmetric matrix, that is square matrix and is equal to its transpose.

By default, simplifications occur before testing symmetry. They can be skipped using ‘simplify=False’; while speeding things a bit, this may however induce false negatives.

Examples

>>> from sympy import Matrix
>>> m = Matrix(2, 2, [0, 1, 1, 2])
>>> m
Matrix([
[0, 1],
[1, 2]])
>>> m.is_symmetric()
True

>>> m = Matrix(2, 2, [0, 1, 2, 0])
>>> m
Matrix([
[0, 1],
[2, 0]])
>>> m.is_symmetric()
False

>>> m = Matrix(2, 3, [0, 0, 0, 0, 0, 0])
>>> m
Matrix([
[0, 0, 0],
[0, 0, 0]])
>>> m.is_symmetric()
False

>>> from sympy.abc import x, y
>>> m = Matrix(3, 3, [1, x**2 + 2*x + 1, y, (x + 1)**2, 2, 0, y, 0, 3])
>>> m
Matrix([
[         1, x**2 + 2*x + 1, y],
[(x + 1)**2,              2, 0],
[         y,              0, 3]])
>>> m.is_symmetric()
True

If the matrix is already simplified, you may speed-up is_symmetric() test by using ‘simplify=False’.

>>> bool(m.is_symmetric(simplify=False))
False
>>> m1 = m.expand()
>>> m1.is_symmetric(simplify=False)
True

property space_dimensions

Spatial dimensions.

space_order

The space order for all components.