


from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray





def lowerCamelCase__      (						__lowerCamelCase	:							List[Any]	,   __lowerCamelCase	:							Tuple	,   __lowerCamelCase	:							Optional[int]	,   __lowerCamelCase	:							List[str]	,   ):







   '''simple docstring'''




   _UpperCAmelCase   ,	_UpperCAmelCase       :       List[Any]							   =coefficient_matrix.shape
   _UpperCAmelCase   ,	_UpperCAmelCase       :       str							   =constant_matrix.shape

   if rowsa != colsa:
      _UpperCAmelCase       :       List[str]							   =f"Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"
      raise ValueError(__lowerCamelCase							)

   if colsa != 1:
      _UpperCAmelCase       :       List[Any]							   =f"Constant matrix must be nx1 but received {rowsa}x{colsa}"
      raise ValueError(__lowerCamelCase							)

   if rowsa != rowsa:
      _UpperCAmelCase       :       Tuple							   =(
          'Coefficient and constant matrices dimensions must be nxn and nx1 but '
          f"received {rowsa}x{colsa} and {rowsa}x{colsa}"
      )
      raise ValueError(__lowerCamelCase							)

   if len(__lowerCamelCase							) != rowsa:
      _UpperCAmelCase       :       Dict							   =(
          'Number of initial values must be equal to number of rows in coefficient '
          f"matrix but received {len(__lowerCamelCase							)} and {rowsa}"
      )
      raise ValueError(__lowerCamelCase							)

   if iterations <= 0:
      raise ValueError('Iterations must be at least 1'							)

   _UpperCAmelCase       :       Dict							   =np.concatenate(
       (coefficient_matrix, constant_matrix)	,   axis=1							)

   _UpperCAmelCase   ,	_UpperCAmelCase       :       List[Any]							   =table.shape

   strictly_diagonally_dominant(__lowerCamelCase							)

   # Iterates the whole matrix for given number of times
   for _ in range(__lowerCamelCase							):
      _UpperCAmelCase       :       Dict							   =[]
      for row in range(__lowerCamelCase							):
         _UpperCAmelCase       :       str							   =0
         for col in range(__lowerCamelCase							):
            if col == row:
               _UpperCAmelCase       :       List[str]							   =table[row][col]
            elif col == cols - 1:
               _UpperCAmelCase       :       Tuple							   =table[row][col]
            else:
               temp += (-1) * table[row][col] * init_val[col]
         _UpperCAmelCase       :       int							   =(temp + val) / denom
         new_val.append(__lowerCamelCase							)
      _UpperCAmelCase       :       Dict							   =new_val

   return [float(__lowerCamelCase							) for i in new_val]





def lowerCamelCase__      (						__lowerCamelCase	:							Tuple							):







   '''simple docstring'''




   _UpperCAmelCase   ,	_UpperCAmelCase       :       str							   =table.shape

   _UpperCAmelCase       :       Union[str, Any]							   =True

   for i in range(0	,   __lowerCamelCase							):
      _UpperCAmelCase       :       Union[str, Any]							   =0
      for j in range(0	,   cols - 1							):
         if i == j:
            continue
         else:
            total += table[i][j]

      if table[i][i] <= total:
         raise ValueError('Coefficient matrix is not strictly diagonally dominant'							)

   return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
 import doctest

 doctest.testmod()





'''simple docstring'''






from __future__ import annotations

import bisect





def lowerCamelCase__      (						__lowerCamelCase	:							list[int]	,   __lowerCamelCase	:							int	,   __lowerCamelCase	:							int = 0	,   __lowerCamelCase	:							int = -1							):







   '''simple docstring'''




   if hi < 0:
      _UpperCAmelCase       :       int							   =len(__lowerCamelCase							)

   while lo < hi:
      _UpperCAmelCase       :       Dict							   =lo + (hi - lo) // 2
      if sorted_collection[mid] < item:
         _UpperCAmelCase       :       int							   =mid + 1
      else:
         _UpperCAmelCase       :       Union[str, Any]							   =mid

   return lo





def lowerCamelCase__      (						__lowerCamelCase	:							list[int]	,   __lowerCamelCase	:							int	,   __lowerCamelCase	:							int = 0	,   __lowerCamelCase	:							int = -1							):







   '''simple docstring'''




   if hi < 0:
      _UpperCAmelCase       :       str							   =len(__lowerCamelCase							)

   while lo < hi:
      _UpperCAmelCase       :       List[Any]							   =lo + (hi - lo) // 2
      if sorted_collection[mid] <= item:
         _UpperCAmelCase       :       Dict							   =mid + 1
      else:
         _UpperCAmelCase       :       Tuple							   =mid

   return lo





def lowerCamelCase__      (						__lowerCamelCase	:							list[int]	,   __lowerCamelCase	:							int	,   __lowerCamelCase	:							int = 0	,   __lowerCamelCase	:							int = -1							):







   '''simple docstring'''




   sorted_collection.insert(bisect_left(__lowerCamelCase	,   __lowerCamelCase	,   __lowerCamelCase	,   __lowerCamelCase							)	,   __lowerCamelCase							)





def lowerCamelCase__      (						__lowerCamelCase	:							list[int]	,   __lowerCamelCase	:							int	,   __lowerCamelCase	:							int = 0	,   __lowerCamelCase	:							int = -1							):







   '''simple docstring'''




   sorted_collection.insert(bisect_right(__lowerCamelCase	,   __lowerCamelCase	,   __lowerCamelCase	,   __lowerCamelCase							)	,   __lowerCamelCase							)





def lowerCamelCase__      (						__lowerCamelCase	:							list[int]	,   __lowerCamelCase	:							int							):







   '''simple docstring'''




   _UpperCAmelCase       :       Optional[int]							   =0
   _UpperCAmelCase       :       Any							   =len(__lowerCamelCase							) - 1

   while left <= right:
      _UpperCAmelCase       :       int							   =left + (right - left) // 2
      _UpperCAmelCase       :       Union[str, Any]							   =sorted_collection[midpoint]
      if current_item == item:
         return midpoint
      elif item < current_item:
         _UpperCAmelCase       :       Optional[Any]							   =midpoint - 1
      else:
         _UpperCAmelCase       :       int							   =midpoint + 1
   return None





def lowerCamelCase__      (						__lowerCamelCase	:							list[int]	,   __lowerCamelCase	:							int							):







   '''simple docstring'''




   _UpperCAmelCase       :       Any							   =bisect.bisect_left(__lowerCamelCase	,   __lowerCamelCase							)
   if index != len(__lowerCamelCase							) and sorted_collection[index] == item:
      return index
   return None





def lowerCamelCase__      (						__lowerCamelCase	:							list[int]	,   __lowerCamelCase	:							int	,   __lowerCamelCase	:							int	,   __lowerCamelCase	:							int							):







   '''simple docstring'''




   if right < left:
      return None

   _UpperCAmelCase       :       str							   =left + (right - left) // 2

   if sorted_collection[midpoint] == item:
      return midpoint
   elif sorted_collection[midpoint] > item:
      return binary_search_by_recursion(__lowerCamelCase	,   __lowerCamelCase	,   __lowerCamelCase	,   midpoint - 1							)
   else:
      return binary_search_by_recursion(__lowerCamelCase	,   __lowerCamelCase	,   midpoint + 1	,   __lowerCamelCase							)


if __name__ == "__main__":
 lowercase							=input('Enter numbers separated by comma:\n').strip()
 lowercase							=sorted(int(item) for item in user_input.split(','))
 lowercase							=int(input('Enter a single number to be found in the list:\n'))
 lowercase							=binary_search(collection, target)
 if result is None:
  print(F"""{target} was not found in {collection}.""")
 else:
  print(F"""{target} was found at position {result} in {collection}.""")

