TensorSpace

class odl.space.base_tensors.TensorSpace(shape, dtype)

Bases: LinearSpace

Base class for sets of tensors of arbitrary data type.

A tensor is, in the most general sense, a multi-dimensional array that allows operations per entry (keep the rank constant), reductions / contractions (reduce the rank) and broadcasting (raises the rank). For non-numeric data type like object, the range of valid operations is rather limited since such a set of tensors does not define a vector space. Any numeric data type, on the other hand, is considered valid for a tensor space, although certain operations - like division with integer dtype - are not guaranteed to yield reasonable results.

Under these restrictions, all basic vector space operations are supported by this class, along with reductions based on arithmetic or comparison, and element-wise mathematical functions ("ufuncs").

See the Wikipedia article on tensors for further details. See also [Hac2012] "Part I Algebraic Tensors" for a rigorous treatment of tensors with a definition close to this one.

Note also that this notion of tensors is the same as in popular Deep Learning frameworks.

References

[Hac2012] Hackbusch, W. Tensor Spaces and Numerical Tensor Calculus. Springer, 2012.

Attributes:

complex_dtype

The complex dtype corresponding to this space's dtype.

complex_space

The space corresponding to this space's complex_dtype.

default_order

Default storage order for new elements in this space.

dtype

Scalar data type of each entry in an element of this space.

element_type

Type of elements in this space: Tensor.

examples

Return example random vectors.

field

Scalar field of numbers for this vector space.

impl

Name of the implementation back-end of this tensor set.

is_complex

True if this is a space of complex tensors.

is_real

True if this is a space of real tensors.

itemsize

Size in bytes of one entry in an element of this space.

nbytes

Total number of bytes in memory used by an element of this space.

ndim

Number of axes (=dimensions) of this space, also called "rank".

real_dtype

The real dtype corresponding to this space's dtype.

real_space

The space corresponding to this space's real_dtype.

shape

Number of scalar elements per axis.

size

Total number of entries in an element of this space.

Methods

astype(dtype)	Return a copy of this space with new dtype.
available_dtypes()	Return the set of data types available in this implementation.
contains_all(other)	Test if all elements in other are contained in this set.
contains_set(other)	Test if other is a subset of this set.
default_dtype([field])	Return the default data type for a given field.
dist(x1, x2)	Return the distance between x1 and x2.
divide(x1, x2[, out])	Return the pointwise quotient of x1 and x2
element([inp])	Create a LinearSpaceElement from inp or from scratch.
inner(x1, x2)	Return the inner product of x1 and x2.
lincomb(a, x1[, b, x2, out])	Implement out[:] = a * x1 + b * x2.
multiply(x1, x2[, out])	Return the pointwise product of x1 and x2.
norm(x)	Return the norm of x.
one()	Return a tensor of all ones.
zero()	Return a tensor of all zeros.

__init__(shape, dtype)

Initialize a new instance.

Parameters:

shapenonnegative int or sequence of nonnegative ints

Number of entries of type dtype per axis in this space. A single integer results in a space with rank 1, i.e., 1 axis.

dtype

Data type of elements in this space. Can be provided in any way the numpy.dtype constructor understands, e.g. as built-in type or as a string. For a data type with a dtype.shape, these extra dimensions are added to the left of shape.