* add unittest for einsum-v2-trace and diagonal

* repeat labels.

* einsum support repeated labels.

* forward is ok for diagonal and undiagonalized.
TODO: check backward is ok by our theorem.

* backward is ok!

* fix by PR suggestions.

* fix ci error

* fix ci error

* fix ci warning

* update config

* re-blacken python code

* temporarily disable date and diff_py_file

* skip a format

* trim trailing whitespace

* fix `.cmake-format.py`

* revert npu ut changes, avoid npu ci error

[CodeStyle] use np.testing.assert_allclose instead of self.assertTrue(np.allclose(...)) (part 2) (#45213)

* autofix (get ci log)

* retrigger ci

* fix test_gather_nd_op, wrong expected in dygraph

* fix test_activation_op, unpack static graph result

* fix test_auc_op, unpack static graph result

* fix test_bce_loss, unpack static graph result

* fix test_bce_with_logits_loss, unpack static graph result

* fix test_cond, unpack static graph result

* fix test_dygraph_weight_norm, wrong numpy reference when `axis=None`

* fix test_einsum, wrong matmul inputs

* fix test_elementwise_heaviside_op, unpack static graph result

* fix test_frac_api, unpack static graph result

* skip test_group_norm_op_v2, probably the wrong numpy reference

* fix test_imperative_double_grad, wrong subscript

* skip test_imperative_tensor_clear_gradient, ???

* skip test_layer_norm_op, probably the wrong numpy reference

* fix test_math_op_patch, unpack static graph results

* fix test_masked_select_op, unpack static graph results

* fix test_mse_loss, unpack static graph results

* fix test_multi_label_soft_margin_loss, unpack static graph results

* fix test_multi_dot_op, unpack static graph results

* fix test_nll_loss, unpack static graph results

* fix test_normalization_wrapper, unpack static graph results

* fix test_pass_builder, unpack static graph results

* fix test_prelu_op, possibly an extra comma

* fix test_psroi_pool_op, unpack static graph results

* fix test_queue, unpack static graph results

* fix test_reorder_lod_tensor, compare an item with a list

* fix test_rrelu_op, unpack static graph results

* fix test_searchsorted_op, unpack static graph results

* fix test_sigmoid_focal_loss, unpack static graph results

* fix test_smooth_l1_loss, unpack static graph results

* fix test_soft_margin_loss, unpack static graph results

* fix test_softmax2d, unpack static graph results

* fix test_square_error_cost, unpack static graph results

* fix test_tril_indices_op, unpack static graph results

* fix test_unsqueeze_op, mismatch numpy reference (axis)

* skip test_layers, `static_rlt` is missing an axis

* fix test_mnist, unpack PredictorTools result (also a list)

* fix test_build_strategy, unpack PredictorTools result

* fix test_mobile_net, unpack PredictorTools result

* fix test_resnet_v2, unpack PredictorTools result

* revert some changes

revert test_layers

revert test_group_norm_op_v2

revert test_layer_norm_op

revert test_imperative_tensor_clear_gradient

* fix test_normal, use flatten instead of reshape, (PR-CI-Windows-OPENBLAS)

* empty commit, trigger CI

[CodeStyle][NPU] use np.testing.assert_allclose instead of self.assertTrue(np.allclose(...)) (part 1) (#44988)

* autofix

* try resolve precision issues

* revert some changes

* clean some `err_msg`

* 0.0001 -> 1e-4

* update commented assert code

* try to fix some shape errors

* `numpy` -> `np`

* empty commit, trigger kunlun ci, test=kunlun

* empty commit, retrigger kunlun ci, test=kunlun

* empty commit, trigger kunlun ci, try fix npu memcpy_h2d, test=kunlun

* try fix npu import error, test=kunlun

einsum support complex and add unittest.

* use yapf to format all python file

* yapf exclude two unittests file for they rely on writing and reading file, and format will break them

* disable diff_py_file because too many diff files cause command following failed

* 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 logic for optimize

* modifty

* 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

* 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.