


import unittest

import numpy as np

from transformers.testing_utils import require_flax, require_tf, require_torch
from transformers.utils import (
    expand_dims,
    flatten_dict,
    is_flax_available,
    is_tf_available,
    is_torch_available,
    reshape,
    squeeze,
    transpose,
)


if is_flax_available():
    import jax.numpy as jnp

if is_tf_available():
    import tensorflow as tf

if is_torch_available():
    import torch



class 	__lowerCamelCase			(unittest.TestCase						):







       def 		snake_case_	(			self: List[Any]					):






            '''simple docstring'''




            __UpperCamelCase =			{
                'task_specific_params': {
                    'summarization': {'length_penalty': 1.0, 'max_length': 128, 'min_length': 12, 'num_beams': 4},
                    'summarization_cnn': {'length_penalty': 2.0, 'max_length': 142, 'min_length': 56, 'num_beams': 4},
                    'summarization_xsum': {'length_penalty': 1.0, 'max_length': 62, 'min_length': 11, 'num_beams': 6},
                }
            }
            __UpperCamelCase =			{
                'task_specific_params.summarization.length_penalty': 1.0,
                'task_specific_params.summarization.max_length': 128,
                'task_specific_params.summarization.min_length': 12,
                'task_specific_params.summarization.num_beams': 4,
                'task_specific_params.summarization_cnn.length_penalty': 2.0,
                'task_specific_params.summarization_cnn.max_length': 142,
                'task_specific_params.summarization_cnn.min_length': 56,
                'task_specific_params.summarization_cnn.num_beams': 4,
                'task_specific_params.summarization_xsum.length_penalty': 1.0,
                'task_specific_params.summarization_xsum.max_length': 62,
                'task_specific_params.summarization_xsum.min_length': 11,
                'task_specific_params.summarization_xsum.num_beams': 6,
            }

            self.assertEqual(flatten_dict(A_					),A_					)







       def 		snake_case_	(			self: List[Any]					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            self.assertTrue(np.allclose(transpose(A_					),x.transpose()					)					)

            __UpperCamelCase =			np.random.randn(3,4,5					)
            self.assertTrue(np.allclose(transpose(A_,axes=(1, 2, 0)					),x.transpose((1, 2, 0)					)					)					)







       @require_torch
       def 		snake_case_	(			self: List[Any]					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            __UpperCamelCase =			torch.tensor(A_					)
            self.assertTrue(np.allclose(transpose(A_					),transpose(A_					).numpy()					)					)

            __UpperCamelCase =			np.random.randn(3,4,5					)
            __UpperCamelCase =			torch.tensor(A_					)
            self.assertTrue(np.allclose(transpose(A_,axes=(1, 2, 0)					),transpose(A_,axes=(1, 2, 0)					).numpy()					)					)







       @require_tf
       def 		snake_case_	(			self: Tuple					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            __UpperCamelCase =			tf.constant(A_					)
            self.assertTrue(np.allclose(transpose(A_					),transpose(A_					).numpy()					)					)

            __UpperCamelCase =			np.random.randn(3,4,5					)
            __UpperCamelCase =			tf.constant(A_					)
            self.assertTrue(np.allclose(transpose(A_,axes=(1, 2, 0)					),transpose(A_,axes=(1, 2, 0)					).numpy()					)					)







       @require_flax
       def 		snake_case_	(			self: Any					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            __UpperCamelCase =			jnp.array(A_					)
            self.assertTrue(np.allclose(transpose(A_					),np.asarray(transpose(A_					)					)					)					)

            __UpperCamelCase =			np.random.randn(3,4,5					)
            __UpperCamelCase =			jnp.array(A_					)
            self.assertTrue(np.allclose(transpose(A_,axes=(1, 2, 0)					),np.asarray(transpose(A_,axes=(1, 2, 0)					)					)					)					)







       def 		snake_case_	(			self: Any					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            self.assertTrue(np.allclose(reshape(A_,(4, 3)					),np.reshape(A_,(4, 3)					)					)					)

            __UpperCamelCase =			np.random.randn(3,4,5					)
            self.assertTrue(np.allclose(reshape(A_,(12, 5)					),np.reshape(A_,(12, 5)					)					)					)







       @require_torch
       def 		snake_case_	(			self: Optional[Any]					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            __UpperCamelCase =			torch.tensor(A_					)
            self.assertTrue(np.allclose(reshape(A_,(4, 3)					),reshape(A_,(4, 3)					).numpy()					)					)

            __UpperCamelCase =			np.random.randn(3,4,5					)
            __UpperCamelCase =			torch.tensor(A_					)
            self.assertTrue(np.allclose(reshape(A_,(12, 5)					),reshape(A_,(12, 5)					).numpy()					)					)







       @require_tf
       def 		snake_case_	(			self: List[Any]					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            __UpperCamelCase =			tf.constant(A_					)
            self.assertTrue(np.allclose(reshape(A_,(4, 3)					),reshape(A_,(4, 3)					).numpy()					)					)

            __UpperCamelCase =			np.random.randn(3,4,5					)
            __UpperCamelCase =			tf.constant(A_					)
            self.assertTrue(np.allclose(reshape(A_,(12, 5)					),reshape(A_,(12, 5)					).numpy()					)					)







       @require_flax
       def 		snake_case_	(			self: Optional[int]					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            __UpperCamelCase =			jnp.array(A_					)
            self.assertTrue(np.allclose(reshape(A_,(4, 3)					),np.asarray(reshape(A_,(4, 3)					)					)					)					)

            __UpperCamelCase =			np.random.randn(3,4,5					)
            __UpperCamelCase =			jnp.array(A_					)
            self.assertTrue(np.allclose(reshape(A_,(12, 5)					),np.asarray(reshape(A_,(12, 5)					)					)					)					)







       def 		snake_case_	(			self: Optional[Any]					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(1,3,4					)
            self.assertTrue(np.allclose(squeeze(A_					),np.squeeze(A_					)					)					)

            __UpperCamelCase =			np.random.randn(1,4,1,5					)
            self.assertTrue(np.allclose(squeeze(A_,axis=2					),np.squeeze(A_,axis=2					)					)					)







       @require_torch
       def 		snake_case_	(			self: Dict					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(1,3,4					)
            __UpperCamelCase =			torch.tensor(A_					)
            self.assertTrue(np.allclose(squeeze(A_					),squeeze(A_					).numpy()					)					)

            __UpperCamelCase =			np.random.randn(1,4,1,5					)
            __UpperCamelCase =			torch.tensor(A_					)
            self.assertTrue(np.allclose(squeeze(A_,axis=2					),squeeze(A_,axis=2					).numpy()					)					)







       @require_tf
       def 		snake_case_	(			self: int					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(1,3,4					)
            __UpperCamelCase =			tf.constant(A_					)
            self.assertTrue(np.allclose(squeeze(A_					),squeeze(A_					).numpy()					)					)

            __UpperCamelCase =			np.random.randn(1,4,1,5					)
            __UpperCamelCase =			tf.constant(A_					)
            self.assertTrue(np.allclose(squeeze(A_,axis=2					),squeeze(A_,axis=2					).numpy()					)					)







       @require_flax
       def 		snake_case_	(			self: Tuple					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(1,3,4					)
            __UpperCamelCase =			jnp.array(A_					)
            self.assertTrue(np.allclose(squeeze(A_					),np.asarray(squeeze(A_					)					)					)					)

            __UpperCamelCase =			np.random.randn(1,4,1,5					)
            __UpperCamelCase =			jnp.array(A_					)
            self.assertTrue(np.allclose(squeeze(A_,axis=2					),np.asarray(squeeze(A_,axis=2					)					)					)					)







       def 		snake_case_	(			self: str					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            self.assertTrue(np.allclose(expand_dims(A_,axis=1					),np.expand_dims(A_,axis=1					)					)					)







       @require_torch
       def 		snake_case_	(			self: Tuple					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            __UpperCamelCase =			torch.tensor(A_					)
            self.assertTrue(np.allclose(expand_dims(A_,axis=1					),expand_dims(A_,axis=1					).numpy()					)					)







       @require_tf
       def 		snake_case_	(			self: List[Any]					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            __UpperCamelCase =			tf.constant(A_					)
            self.assertTrue(np.allclose(expand_dims(A_,axis=1					),expand_dims(A_,axis=1					).numpy()					)					)







       @require_flax
       def 		snake_case_	(			self: Optional[Any]					):






            '''simple docstring'''




            __UpperCamelCase =			np.random.randn(3,4					)
            __UpperCamelCase =			jnp.array(A_					)
            self.assertTrue(np.allclose(expand_dims(A_,axis=1					),np.asarray(expand_dims(A_,axis=1					)					)					)					)






'''simple docstring'''

import unittest

import numpy as np

def _SCREAMING_SNAKE_CASE (A    ,					A    ,					A    ,					A = None    ,					)			->			np.ndarray:






       """simple docstring"""







       lowercase__      =					np.shape(A			)
       lowercase__      =					np.shape(A			)
       lowercase__      =					np.shape(A			)

       if shape_a[0] != shape_b[0]:
              lowercase__      =					(
                  '''Expected the same number of rows for A and B. '''
                  f"Instead found A of size {shape_a} and B of size {shape_b}"
              )
              raise ValueError(A			)

       if shape_b[1] != shape_c[1]:
              lowercase__      =					(
                  '''Expected the same number of columns for B and C. '''
                  f"Instead found B of size {shape_b} and C of size {shape_c}"
              )
              raise ValueError(A			)

       lowercase__      =					pseudo_inv
       if a_inv is None:
              try:
                     lowercase__      =					np.linalg.inv(A			)
              except np.linalg.LinAlgError:
                     raise ValueError(
                         '''Input matrix A is not invertible. Cannot compute Schur complement.'''			)

       return mat_c - mat_b.T @ a_inv @ mat_b
class     __lowerCAmelCase		(unittest.TestCase	):





      '''simple docstring'''






      def  UpperCamelCase__						(self       :       Dict					):

             '''simple docstring'''







             lowercase__      =					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
             lowercase__      =					np.array([[0, 3], [3, 0], [2, 3]]					)
             lowercase__      =					np.array([[2, 1], [6, 3]]					)

             lowercase__      =					schur_complement(UpperCamelCase  ,		UpperCamelCase  ,		UpperCamelCase					)

             lowercase__      =					np.block([[a, b], [b.T, c]]					)

             lowercase__      =					np.linalg.det(UpperCamelCase					)
             lowercase__      =					np.linalg.det(UpperCamelCase					)
             lowercase__      =					np.linalg.det(UpperCamelCase					)

             self.assertAlmostEqual(UpperCamelCase  ,		det_a * det_s					)



      def  UpperCamelCase__						(self       :       Optional[int]					):

             '''simple docstring'''







             lowercase__      =					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
             lowercase__      =					np.array([[0, 3], [3, 0], [2, 3]]					)
             lowercase__      =					np.array([[2, 1], [6, 3]]					)

             with self.assertRaises(UpperCamelCase					):
                    schur_complement(UpperCamelCase  ,		UpperCamelCase  ,		UpperCamelCase					)






      def  UpperCamelCase__						(self       :       Union[str, Any]					):

             '''simple docstring'''







             lowercase__      =					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
             lowercase__      =					np.array([[0, 3], [3, 0], [2, 3]]					)
             lowercase__      =					np.array([[2, 1, 3], [6, 3, 5]]					)

             with self.assertRaises(UpperCamelCase					):
                    schur_complement(UpperCamelCase  ,		UpperCamelCase  ,		UpperCamelCase					)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 unittest.main()




