mindspore.ops.einsum

mindspore.ops.einsum(equation, *operands)

According to the Einstein summation Convention (Einsum), the product of the input tensor elements is summed along the specified dimension. You can use this operator to perform diagonal, reducesum, transpose, matmul, mul, inner product operations, etc.

Note

The sublist format is also supported. For example, ops.einsum(op1, sublist1, op2, sublist2, …, sublist_out). In this format, equation can be derived by the sublists which are made up of Python's Ellipsis and list of integers in [0, 52). Each operand is followed by a sublist and an output sublist is at the end.

Parameters

• equation (str) – Notation based on the Einstein summation convention, represent the operation you want to do. the value can contain only letters, commas, ellipsis and arrow. The letters represent input tensor dimension, commas represent separate tensors, ellipsis indicates the tensor dimension that you do not care about, the left of the arrow indicates the input tensors, and the right of it indicates the desired output dimension.

• operands (Tensor) – Input tensor used for calculation. The dtype of the tensor must be the same.

Returns

Tensor, the shape of it can be obtained from the equation , and the dtype is the same as input tensors.

Raises

• TypeError – If equation is invalid, or the equation does not match the input tensor.

• ValueError – If the number in sublist is not in [0, 52) in sublist format.

Supported Platforms:

GPU

Examples

>>> import mindspore
>>> import numpy as np
>>> from mindspore import Tensor, ops
>>> x = Tensor(np.array([1.0, 2.0, 4.0]), mindspore.float32)
>>> equation = "i->"
>>> output = ops.einsum(equation, x)
>>> print(output)
[7.]
>>> x = Tensor(np.array([1.0, 2.0, 4.0]), mindspore.float32)
>>> y = Tensor(np.array([2.0, 4.0, 3.0]), mindspore.float32)
>>> equation = "i,i->i"
>>> output = ops.einsum(equation, x, y)
>>> print(output)
[ 2. 8. 12.]
>>> x = Tensor(np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]), mindspore.float32)
>>> y = Tensor(np.array([[2.0, 3.0], [1.0, 2.0], [4.0, 5.0]]), mindspore.float32)
>>> equation = "ij,jk->ik"
>>> output = ops.einsum(equation, x, y)
>>> print(output)
[[16. 22.]
 [37. 52.]]
>>> x = Tensor(np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]), mindspore.float32)
>>> equation = "ij->ji"
>>> output = ops.einsum(equation, x)
>>> print(output)
[[1. 4.]
 [2. 5.]
 [3. 6.]]
>>> x = Tensor(np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]), mindspore.float32)
>>> equation = "ij->j"
>>> output = ops.einsum(equation, x)
>>> print(output)
[5. 7. 9.]
>>> x = Tensor(np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]), mindspore.float32)
>>> equation = "...->"
>>> output = ops.einsum(equation, x)
>>> print(output)
[21.]
>>> x = Tensor(np.array([1.0, 2.0, 3.0]), mindspore.float32)
>>> y = Tensor(np.array([2.0, 4.0, 1.0]), mindspore.float32)
>>> equation = "j,i->ji"
>>> output = ops.einsum(equation, x, y)
>>> print(output)
[[ 2. 4. 1.]
 [ 4. 8. 2.]
 [ 6. 12. 3.]]
>>> x = mindspore.Tensor([1, 2, 3, 4], mindspore.float32)
>>> y = mindspore.Tensor([1, 2], mindspore.float32)
>>> output = ops.einsum(x, [..., 1], y, [..., 2], [..., 1, 2])
>>> print(output)
[[1. 2.]
 [2. 4.]
 [3. 6.]
 [4. 8.]]