
from __future__ import annotations

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



def        UpperCamelCase    (							lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__ ,			):
					'''simple docstring'''
					lowercase	,						lowercase							=						coefficient_matrix.shape
					lowercase	,						lowercase							=						constant_matrix.shape

					if rowsa != colsa:
										lowercase							=						f'Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'
										raise ValueError(lowerCAmelCase__		)

					if colsa != 1:
										lowercase							=						f'Constant matrix must be nx1 but received {rowsa}x{colsa}'
										raise ValueError(lowerCAmelCase__		)

					if rowsa != rowsa:
										lowercase							=						(
										    '''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:
										lowercase							=						(
										    '''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'''		)

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

					lowercase	,						lowercase							=						table.shape

					strictly_diagonally_dominant(lowerCAmelCase__		)

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

					return [float(lowerCAmelCase__		) for i in new_val]



def        UpperCamelCase    (							lowerCAmelCase__		):
					'''simple docstring'''
					lowercase	,						lowercase							=						table.shape

					lowercase							=						True

					for i in range(0 ,			lowerCAmelCase__		):
										lowercase							=						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 math import sqrt
def 					_UpperCAmelCase      ( __lowerCamelCase   :       int = 1_00_00_00		)     ->					int:
  _snake_case					     =       0
  _snake_case					     =       0
  _snake_case					     =       42

  while num_cuboids <= limit:
    max_cuboid_size += 1
    for sum_shortest_sides in range(2 ,					2 * max_cuboid_size + 1		):
      if sqrt(sum_shortest_sides**2 + max_cuboid_size**2		).is_integer():
        num_cuboids += (
            min(__lowerCamelCase ,					sum_shortest_sides // 2		)
            - max(1 ,					sum_shortest_sides - max_cuboid_size		)
            + 1
        )

  return max_cuboid_size


if __name__ == "__main__":
 print(F"{solution() = }")



