





'''simple docstring'''
import unittest

import numpy as np
def 				lowercase__   (   __lowercase						:  np.ndarray				,  __lowercase						:  np.ndarray				,  __lowercase						:  np.ndarray				,  __lowercase						:  np.ndarray | None = None				,  ) ->      np.ndarray:



       """simple docstring"""






       __UpperCamelCase       =  np.shape(__lowercase     )
       __UpperCamelCase       =  np.shape(__lowercase     )
       __UpperCamelCase       =  np.shape(__lowercase     )

       if shape_a[0] != shape_b[0]:
              __UpperCamelCase       =  (
                  '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(__lowercase     )

       if shape_b[1] != shape_c[1]:
              __UpperCamelCase       =  (
                  '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(__lowercase     )

       __UpperCamelCase       =  pseudo_inv
       if a_inv is None:
              try:
                     __UpperCamelCase       =  np.linalg.inv(__lowercase     )
              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      snake_case     (    unittest.TestCase       ):




 """simple docstring"""



 def        _lowerCamelCase					(       self       :							Tuple	):
        __UpperCamelCase       =  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
        __UpperCamelCase       =  np.array([[0, 3], [3, 0], [2, 3]]	)
        __UpperCamelCase       =  np.array([[2, 1], [6, 3]]	)

        __UpperCamelCase       =  schur_complement(__A							,	__A							,	__A	)

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

        __UpperCamelCase       =  np.linalg.det(__A	)
        __UpperCamelCase       =  np.linalg.det(__A	)
        __UpperCamelCase       =  np.linalg.det(__A	)

        self.assertAlmostEqual(__A							,	det_a * det_s	)






 def        _lowerCamelCase					(       self       :							int	):
        __UpperCamelCase       =  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
        __UpperCamelCase       =  np.array([[0, 3], [3, 0], [2, 3]]	)
        __UpperCamelCase       =  np.array([[2, 1], [6, 3]]	)

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






 def        _lowerCamelCase					(       self       :							List[Any]	):
        __UpperCamelCase       =  np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]	)
        __UpperCamelCase       =  np.array([[0, 3], [3, 0], [2, 3]]	)
        __UpperCamelCase       =  np.array([[2, 1, 3], [6, 3, 5]]	)

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    unittest.main()







'''simple docstring'''
import os

import numpy
import onnx
def 				lowercase__   (   __lowercase						:  Optional[int]				,  __lowercase						:  Union[str, Any]     ) ->      Dict:



       """simple docstring"""






       __UpperCamelCase       =  a.name
       __UpperCamelCase       =  b.name

       __UpperCamelCase       =  ''
       __UpperCamelCase       =  ''

       __UpperCamelCase       =  a == b

       __UpperCamelCase       =  name_a
       __UpperCamelCase       =  name_b

       return res
def 				lowercase__   (   __lowercase						:  int				,  __lowercase						:  int				,  __lowercase						:  List[Any]     ) ->      Optional[int]:



       """simple docstring"""






       for i, input_name in enumerate(node_proto.input     ):
              if input_name == name:
                     node_proto.input.insert(__lowercase				,  __lowercase     )
                     node_proto.input.pop(i + 1     )

       if node_proto.op_type == "If":
              _graph_replace_input_with(node_proto.attribute[0].g				,  __lowercase				,  __lowercase     )
              _graph_replace_input_with(node_proto.attribute[1].g				,  __lowercase				,  __lowercase     )
       if node_proto.op_type == "Loop":
              _graph_replace_input_with(node_proto.attribute[0].g				,  __lowercase				,  __lowercase     )
def 				lowercase__   (   __lowercase						:  int				,  __lowercase						:  List[Any]				,  __lowercase						:  Dict     ) ->      int:



       """simple docstring"""






       for n in graph_proto.node:
              _node_replace_input_with(__lowercase				,  __lowercase				,  __lowercase     )
def 				lowercase__   (   __lowercase						:  List[str]				,  __lowercase						:  Union[str, Any]				,  __lowercase						:  str     ) ->      Union[str, Any]:



       """simple docstring"""






       __UpperCamelCase       =  list(model.graph.initializer     )
       __UpperCamelCase       =  list(model_without_ext.graph.initializer     )
       for i, ref_i in ind_to_replace:
              assert inits_with_data[i].name == inits[i].name
              assert inits_with_data[ref_i].name == inits[ref_i].name
              assert i > ref_i

              __UpperCamelCase       =  inits[i].name
              __UpperCamelCase       =  inits[ref_i].name

              model_without_ext.graph.initializer.remove(inits[i]     )

              # for n in model.graph.node:
              _graph_replace_input_with(model_without_ext.graph				,  __lowercase				,  __lowercase     )


def 				lowercase__   (   __lowercase						:  Dict     ) ->      Union[str, Any]:



       """simple docstring"""






       __UpperCamelCase       =  os.path.dirname(__lowercase     )
       __UpperCamelCase       =  os.path.basename(__lowercase     )

       __UpperCamelCase       =  onnx.load(os.path.join(__lowercase				,  __lowercase     )     )

       __UpperCamelCase       =  list(model.graph.initializer     )

       __UpperCamelCase       =  set()
       __UpperCamelCase       =  {}
       __UpperCamelCase       =  []

       __UpperCamelCase       =  0

       for i in range(len(__lowercase     )     ):
              if i in dup_set:
                     continue

              for j in range(i + 1				,  len(__lowercase     )     ):
                     if j in dup_set:
                            continue
                     if _is_equal_tensor_proto(inits[i]				,  inits[j]     ):
                            dup_set.add(__lowercase     )
                            dup_set.add(__lowercase     )

                            __UpperCamelCase       =  inits[j].data_type
                            __UpperCamelCase       =  numpy.prod(inits[j].dims     )
                            if dtype == 1:
                                   mem_size *= 4
                            elif dtype == 6:
                                   mem_size *= 4
                            elif dtype == 7 or dtype == 11:
                                   mem_size *= 8
                            else:
                                   print('unexpected data type: '				,  __lowercase     )
                            total_reduced_size += mem_size

                            __UpperCamelCase       =  inits[i].name
                            __UpperCamelCase       =  inits[j].name

                            if name_i in dup_map:
                                   dup_map[name_i].append(__lowercase     )
                            else:
                                   __UpperCamelCase       =  [name_j]
                            ind_to_replace.append((j, i)     )

       print('total reduced size: '				,  total_reduced_size / 1024 / 1024 / 1024				,  'GB'     )

       __UpperCamelCase       =  sorted(__lowercase     )
       _remove_dup_initializers_from_model(__lowercase				,  __lowercase				,  __lowercase     )

       __UpperCamelCase       =  'optimized_' + model_file_name
       __UpperCamelCase       =  os.path.join(__lowercase				,  __lowercase     )
       onnx.save(__lowercase				,  __lowercase     )

       return new_model
