Aliases:
tf.einsum
tf.linalg.einsum
tf.einsum(
equation,
*inputs,
**kwargs
)
Defined in tensorflow/python/ops/special_math_ops.py
.
A generalized contraction between tensors of arbitrary dimension.
This function returns a tensor whose elements are defined by equation
,
which is written in a shorthand form inspired by the Einstein summation
convention. As an example, consider multiplying two matrices
A and B to form a matrix C. The elements of C are given by:
C[i,k] = sum_j A[i,j] * B[j,k]
The corresponding equation
is:
ij,jk->ik
In general, the equation
is obtained from the more familiar element-wise
equation by
1. removing variable names, brackets, and commas,
2. replacing "*" with ",",
3. dropping summation signs, and
4. moving the output to the right, and replacing "=" with "->".
Many common operations can be expressed in this way. For example:
# Matrix multiplication
>>> einsum('ij,jk->ik', m0, m1) # output[i,k] = sum_j m0[i,j] * m1[j, k]
# Dot product
>>> einsum('i,i->', u, v) # output = sum_i u[i]*v[i]
# Outer product
>>> einsum('i,j->ij', u, v) # output[i,j] = u[i]*v[j]
# Transpose
>>> einsum('ij->ji', m) # output[j,i] = m[i,j]
# Batch matrix multiplication
>>> einsum('aij,ajk->aik', s, t) # out[a,i,k] = sum_j s[a,i,j] * t[a, j, k]
This function behaves like numpy.einsum
, but does not support:
- Ellipses (subscripts like
ij...,jk...->ik...
) - Subscripts where an axis appears more than once for a single input
(e.g.
ijj,k->ik
).
Args:
equation
: astr
describing the contraction, in the same format asnumpy.einsum
.*inputs
: the inputs to contract (each one aTensor
), whose shapes should be consistent withequation
.name
: A name for the operation (optional).
Returns:
The contracted Tensor
, with shape determined by equation
.
Raises:
ValueError
: If- the format of
equation
is incorrect, - the number of inputs implied by
equation
does not matchlen(inputs)
, - an axis appears in the output subscripts but not in any of the inputs,
- the number of dimensions of an input differs from the number of indices in its subscript, or
- the input shapes are inconsistent along a particular axis.
- the format of