




'''simple docstring'''


import os

import numpy
import onnx



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					List[str] ,    UpperCamelCase__    :					int				):




     """simple docstring"""


     a_     :							Tuple     						=  a.name
     a_     :							int     						=  b.name

     a_     :							Union[str, Any]     						=  """"""
     a_     :							Optional[Any]     						=  """"""

     a_     :							Union[str, Any]     						=  a == b

     a_     :							int     						=  name_a
     a_     :							List[Any]     						=  name_b

     return res



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					Dict ,    UpperCamelCase__    :					Tuple ,    UpperCamelCase__    :					str				):




     """simple docstring"""


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

     if node_proto.op_type == "If":
          _graph_replace_input_with(node_proto.attribute[0].g ,    UpperCamelCase__ ,    UpperCamelCase__				)
          _graph_replace_input_with(node_proto.attribute[1].g ,    UpperCamelCase__ ,    UpperCamelCase__				)
     if node_proto.op_type == "Loop":
          _graph_replace_input_with(node_proto.attribute[0].g ,    UpperCamelCase__ ,    UpperCamelCase__				)



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					Union[str, Any] ,    UpperCamelCase__    :					Dict ,    UpperCamelCase__    :					Any				):




     """simple docstring"""


     for n in graph_proto.node:
          _node_replace_input_with(UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__				)



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					Dict ,    UpperCamelCase__    :					Optional[Any] ,    UpperCamelCase__    :					Optional[Any]				):




     """simple docstring"""


     a_     :							List[str]     						=  list(model.graph.initializer				)
     a_     :							Optional[Any]     						=  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

          a_     :							List[Any]     						=  inits[i].name
          a_     :							Dict     						=  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 ,    UpperCamelCase__ ,    UpperCamelCase__				)



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					List[str]				):




     """simple docstring"""


     a_     :							Dict     						=  os.path.dirname(UpperCamelCase__				)
     a_     :							List[str]     						=  os.path.basename(UpperCamelCase__				)

     a_     :							List[Any]     						=  onnx.load(os.path.join(UpperCamelCase__ ,    UpperCamelCase__				)				)

     a_     :							Optional[Any]     						=  list(model.graph.initializer				)

     a_     :							Dict     						=  set()
     a_     :							Optional[Any]     						=  {}
     a_     :							Optional[Any]     						=  []

     a_     :							str     						=  0

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

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

                    a_     :							int     						=  inits[j].data_type
                    a_     :							List[Any]     						=  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: """ ,    UpperCamelCase__				)
                    total_reduced_size += mem_size

                    a_     :							Dict     						=  inits[i].name
                    a_     :							str     						=  inits[j].name

                    if name_i in dup_map:
                         dup_map[name_i].append(UpperCamelCase__				)
                    else:
                         a_     :							Tuple     						=  [name_j]
                    ind_to_replace.append((j, i)				)

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

     a_     :							Tuple     						=  sorted(UpperCamelCase__				)
     _remove_dup_initializers_from_model(UpperCamelCase__ ,    UpperCamelCase__ ,    UpperCamelCase__				)

     a_     :							Dict     						=  """optimized_""" + model_file_name
     a_     :							str     						=  os.path.join(UpperCamelCase__ ,    UpperCamelCase__				)
     onnx.save(UpperCamelCase__ ,    UpperCamelCase__				)

     return new_model






'''simple docstring'''


from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
lowerCAmelCase_      :  List[Any]				     =  2_9979_2458

# Symbols
lowerCAmelCase_     ,   lowerCAmelCase_     ,   lowerCAmelCase_     ,   lowerCAmelCase_      :  Tuple				     =  symbols('ct x y z')



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					float				):




     """simple docstring"""


     if velocity > c:
          raise ValueError("""Speed must not exceed light speed 299,792,458 [m/s]!"""				)
     elif velocity < 1:
          # Usually the speed should be much higher than 1 (c order of magnitude)
          raise ValueError("""Speed must be greater than or equal to 1!"""				)

     return velocity / c



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					float				):




     """simple docstring"""


     return 1 / sqrt(1 - beta(UpperCamelCase__				) ** 2				)



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					float				):




     """simple docstring"""


     return np.array(
         [
             [gamma(UpperCamelCase__				), -gamma(UpperCamelCase__				) * beta(UpperCamelCase__				), 0, 0],
             [-gamma(UpperCamelCase__				) * beta(UpperCamelCase__				), gamma(UpperCamelCase__				), 0, 0],
             [0, 0, 1, 0],
             [0, 0, 0, 1],
         ]				)



def  _SCREAMING_SNAKE_CASE     (      UpperCamelCase__    :					float ,    UpperCamelCase__    :					np.ndarray | None = None				):




     """simple docstring"""


     if event is None:
          a_     :							str     						=  np.array([ct, x, y, z]				)  # Symbolic four vector
     else:
          event[0] *= c  # x0 is ct (speed of light * time)

     return transformation_matrix(UpperCamelCase__				) @ event


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # Example of symbolic vector:
 lowerCAmelCase_      :  Union[str, Any]				     =  transform(2997_9245)
 print('Example of four vector: ')
 print(f"ct' = {four_vector[0]}")
 print(f"x' = {four_vector[1]}")
 print(f"y' = {four_vector[2]}")
 print(f"z' = {four_vector[3]}")

 # Substitute symbols with numerical values
 lowerCAmelCase_      :  Tuple				     =  {ct: c, x: 1, y: 1, z: 1}
 lowerCAmelCase_      :  Optional[int]				     =  [four_vector[i].subs(sub_dict) for i in range(4)]

 print(f"\n{numerical_vector}")
