Einsum - 12


  • name: Einsum (GitHub)

  • domain: main

  • since_version: 12

  • function: False

  • support_level: SupportType.COMMON

  • shape inference: True

This version of the operator has been available since version 12.


An einsum of the form term1, term2 -> output-term produces an output tensor using the following equation

output[output-term] = reduce-sum( input1[term1] * input2[term2] )

where the reduce-sum performs a summation over all the indices occurring in the input terms (term1, term2) that do not occur in the output-term.

The Einsum operator evaluates algebraic tensor operations on a sequence of tensors, using the Einstein summation convention. The equation string contains a comma-separated sequence of lower case letters. Each term corresponds to an operand tensor, and the characters within the terms correspond to operands dimensions.

This sequence may be followed by “->” to separate the left and right hand side of the equation. If the equation contains “->” followed by the right-hand side, the explicit (not classical) form of the Einstein summation is performed, and the right-hand side indices indicate output tensor dimensions. In other cases, output indices are (implicitly) set to the alphabetically sorted sequence of indices appearing exactly once in the equation.

When a dimension character is repeated in the left-hand side, it represents summation along the dimension.

The equation may contain ellipsis (“…”) to enable broadcasting. Ellipsis must indicate a fixed number of dimensions. Specifically, every occurrence of ellipsis in the equation must represent the same number of dimensions. The right-hand side may contain exactly one ellipsis. In implicit mode, the ellipsis dimensions are set to the beginning of the output. The equation string may contain space (U+0020) character.


  • equation - STRING (required) :

    Einsum expression string.


Between 1 and 2147483647 inputs.

  • Inputs (variadic, heterogeneous) - T:



  • Output (heterogeneous) - T:

    Output tensor

Type Constraints

  • T in ( tensor(double), tensor(float), tensor(float16), tensor(int16), tensor(int32), tensor(int64), tensor(int8), tensor(uint16), tensor(uint32), tensor(uint64), tensor(uint8) ):

    Constrain input and output types to all numerical tensor types.