* cherry pick from #43397

* fix code

* [EinsumOp] Polish forward logic and backward logic for optimize (#42603)

* change logic for optimize

* modifty

* merge

* change einsum_v2 as default and add new flags: FLAG_einsum_opt=1|0 (#43010)

* [EinsumOp] Make EinsumOp support bfloat16. (#43085)

* change einsum_v2 as default and add new flags: FLAG_einsum_opt=1|0

* make EInsumOP support bf16

* add unittest for BF16

* add condition for test_BF16

* fix bugs

* fix

* change the backward api to fit einsum op

* Extend python einsum interface to make einsum_v2 support multi-operands and switch it to default.

* add opt_einsum dependence

* add yaml and support eager model

* fix by code review

* full api fix

* when out is None, go old dygraph mode

* by static check

* first version: support 2-inputs forwards. TODO: 1. backward  2. BroadCast  3. MultiVariable

* time out -> 120

* formatted.

* Remove dead code.

* Fix error message in the unit test.

* polish formats.

* [Einsum] fix bugs.

* [Einsum] correct output dimension errors due to single element tensors.

* [Einsum] format polish.

* OP dot: refactor CPU kernels and get better loop performance.

* Minor fix on code format.

* Fixed minor errors.

* Add new API: einsum

* Update the Einsum unit test.

One case failed with matmul_v2, where the dtype is int64:

a = np.arange(2 * 3 * 1).reshape(2, 3, 1)
b = np.arange(1)
paddle.einsum("...i, ...i", a, b)

* Test cases in test_einsum test floating point dtypes only.

As of now Paddle only supports float/double dtypes in matmul, which is
one of building blocks of this Einsum implementation. We decide not to
test einsum against other dtypes.

* Polish format.

* More formatting.

* Format...

* Einsum: improve test coverage.

* Einsum: bug fixes and more testcases for testing error messages

* Einsum: fix format..

* Einsum: fixed typo and format.

* Einsum: format again...

* Einsum: applied suggested changes.

* Einsum API: improve API documentation.

* Einsum API: apply suggested changes.

* Einsum API: Add dygraph only note.

* Einsum API: Add dygraph only note.

* Einsum API: fixed unittest.