|TensorFlow 1 version||View source on GitHub|
Tensor contraction over specified indices and outer product.
See Migration guide for more details.
tf.einsum( equation, *inputs, **kwargs )
Used in the notebooks
|Used in the guide|
Einsum allows defining Tensors by defining their element-wise computation.
This computation is defined by
equation, a shorthand form based on Einstein
summation. 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]
In general, to convert the element-wise equation into the
use the following procedure (intermediate strings for matrix multiplication
example provided in parentheses):
- remove variable names, brackets, and commas, (
ik = sum_j ij * jk)
- replace "*" with ",", (
ik = sum_j ij , jk)
- drop summation signs, and (
ik = ij, jk)
- move the output to the right, while 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] # Trace einsum('ii', m) # output[j,i] = trace(m) = sum_i m[i, i] # Batch matrix multiplication einsum('aij,ajk->aik', s, t) # out[a,i,k] = sum_j s[a,i,j] * t[a, j, k]
To enable and control broadcasting, use an ellipsis. For example, to perform batch matrix multiplication with NumPy-style broadcasting across the batch dimensions, use:
einsum('...ij,...jk->...ik', u, v)
strdescribing the contraction, in the same format as
*inputs: the inputs to contract (each one a
Tensor), whose shapes should be consistent with
**kwargs: - optimize: Optimization strategy to use to find contraction path using opt_einsum. Must be 'greedy', 'optimal', 'branch-2', 'branch-all' or 'auto'. (optional, default: 'greedy').
- name: A name for the operation (optional).
Tensor, with shape determined by
- the format of
- number of inputs or their shapes are inconsistent with
- the format of