Aliases:
tf.linalg.tensordot
tf.tensordot
tf.tensordot(
a,
b,
axes,
name=None
)
Defined in tensorflow/python/ops/math_ops.py
.
Tensor contraction of a and b along specified axes.
Tensordot (also known as tensor contraction) sums the product of elements
from a
and b
over the indices specified by a_axes
and b_axes
.
The lists a_axes
and b_axes
specify those pairs of axes along which to
contract the tensors. The axis a_axes[i]
of a
must have the same dimension
as axis b_axes[i]
of b
for all i
in range(0, len(a_axes))
. The lists
a_axes
and b_axes
must have identical length and consist of unique
integers that specify valid axes for each of the tensors.
This operation corresponds to numpy.tensordot(a, b, axes)
.
Example 1: When a
and b
are matrices (order 2), the case axes = 1
is equivalent to matrix multiplication.
Example 2: When a
and b
are matrices (order 2), the case
axes = [[1], [0]]
is equivalent to matrix multiplication.
Example 3: Suppose that \(a_{ijk}\) and \(b_{lmn}\) represent two
tensors of order 3. Then, contract(a, b, [[0], [2]])
is the order 4 tensor
\(c_{jklm}\) whose entry
corresponding to the indices \((j,k,l,m)\) is given by:
\( c_{jklm} = \sum_i a_{ijk} b_{lmi} \).
In general, order(c) = order(a) + order(b) - 2*len(axes[0])
.
Args:
a
:Tensor
of typefloat32
orfloat64
.b
:Tensor
with the same type asa
.axes
: Either a scalarN
, or a list or anint32
Tensor
of shape [2, k]. If axes is a scalar, sum over the last N axes of a and the first N axes of b in order. If axes is a list orTensor
the first and second row contain the set of unique integers specifying axes along which the contraction is computed, fora
andb
, respectively. The number of axes fora
andb
must be equal.name
: A name for the operation (optional).
Returns:
A Tensor
with the same type as a
.
Raises:
ValueError
: If the shapes ofa
,b
, andaxes
are incompatible.IndexError
: If the values in axes exceed the rank of the corresponding tensor.