|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 )
This function returns a tensor whose elements are defined by
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]
In general, the
equation is obtained from the more familiar element-wise
- removing variable names, brackets, and commas,
- replacing "*" with ",",
- dropping summation signs, and
- 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] # 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)
the inputs to contract (each one a