(l-onnx-doc-Einsum)=

# Einsum


(l-onnx-op-einsum-12)=

## Einsum - 12

### Version

- **name**: [Einsum (GitHub)](https://github.com/onnx/onnx/blob/main/docs/Operators.md#Einsum)
- **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**.

### Summary

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.

### Attributes

* **equation - STRING** (required) :

  Einsum expression string.

### Inputs

Between 1 and 2147483647 inputs.

- **Inputs** (variadic, heterogeneous) - **T**:

  Operands

### Outputs

- **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.