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TensorFlow 1 version
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View source on GitHub
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Tensor contraction of a and b along specified axes and outer product.
tf.tensordot(
a, b, axes, name=None
)
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. Additionally
outer product is supported by passing axes=0.
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: When a and b are matrices (order 2), the case axes=0 gives
the outer product, a tensor of order 4.
Example 4: 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
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Tensor of type float32 or float64.
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b
|
Tensor with the same type as a.
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axes
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Either a scalar N, or a list or an int32 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 or Tensor the first and second row contain
the set of unique integers specifying axes along which the contraction is
computed, for a and b, respectively. The number of axes for a and
b must be equal. If axes=0, computes the outer product between a and
b.
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name
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A name for the operation (optional). |
Returns | |
|---|---|
A Tensor with the same type as a.
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Raises | |
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ValueError
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If the shapes of a, b, and axes are incompatible.
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IndexError
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If the values in axes exceed the rank of the corresponding tensor. |