"""simple docstring"""



from __future__ import annotations

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





def  SCREAMING_SNAKE_CASE							(  snake_case,   snake_case,   snake_case,   snake_case,   ):
     __snake_case		,						__snake_case				=				coefficient_matrix.shape
     __snake_case		,						__snake_case				=				constant_matrix.shape

     if rowsa != colsa:
          __snake_case				=				f"Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"
          raise ValueError(snake_case)

     if colsa != 1:
          __snake_case				=				f"Constant matrix must be nx1 but received {rowsa}x{colsa}"
          raise ValueError(snake_case)

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

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

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

     __snake_case				=				np.concatenate(
         (coefficient_matrix, constant_matrix),   axis=1)

     __snake_case		,						__snake_case				=				table.shape

     strictly_diagonally_dominant(snake_case)

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

     return [float(snake_case) for i in new_val]





def  SCREAMING_SNAKE_CASE							(  snake_case):
     __snake_case		,						__snake_case				=				table.shape

     __snake_case				=				True

     for i in range(0,   snake_case):
          __snake_case				=				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()





from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
SCREAMING_SNAKE_CASE:     Optional[int]									= 2_9_9_7_9_2_4_5_8

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


def 					_a							(					lowerCAmelCase )->	float:
		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 					_a							(					lowerCAmelCase )->	float:
		return 1 / sqrt(1 - beta(lowerCAmelCase ) ** 2 )


def 					_a							(					lowerCAmelCase )->	np.ndarray:
		return np.array(
		    [
		        [gamma(lowerCAmelCase ), -gamma(lowerCAmelCase ) * beta(lowerCAmelCase ), 0, 0],
		        [-gamma(lowerCAmelCase ) * beta(lowerCAmelCase ), gamma(lowerCAmelCase ), 0, 0],
		        [0, 0, 1, 0],
		        [0, 0, 0, 1],
		    ] )


def 					_a							(					lowerCAmelCase    ,						lowerCAmelCase = None )->	np.ndarray:
		# Ensure event is not empty
		if event is None:
				SCREAMING_SNAKE_CASE_					      =							np.array([ct, x, y, z] )  # Symbolic four vector
		else:
				event[0] *= c  # x0 is ct (speed of light * time)

		return transformation_matrix(lowerCAmelCase ) @ event


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						# Example of symbolic vector:
						SCREAMING_SNAKE_CASE:     int									= transform(2_9_9_7_9_2_4_5)
						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
						SCREAMING_SNAKE_CASE:     List[Any]									= {ct: c, x: 1, y: 1, z: 1}
						SCREAMING_SNAKE_CASE:     Optional[Any]									= [four_vector[i].subs(sub_dict) for i in range(4)]

						print(f"""\n{numerical_vector}""")