





'''simple docstring'''





from __future__ import annotations

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





def    __UpperCamelCase      (    a,     a,     a,     a,     ) ->list[float]:
					lowerCamelCase__    ,		lowerCamelCase__       =       coefficient_matrix.shape
					lowerCamelCase__    ,		lowerCamelCase__       =       constant_matrix.shape

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

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

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

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

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

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

					lowerCamelCase__    ,		lowerCamelCase__       =       table.shape

					strictly_diagonally_dominant(a)

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

					return [float(a) for i in new_val]





def    __UpperCamelCase      (    a) ->bool:
					lowerCamelCase__    ,		lowerCamelCase__       =       table.shape

					lowerCamelCase__       =       True

					for i in range(0,     a):
										lowerCamelCase__       =       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()








def    __UpperCamelCase      (    a) ->float:
					return 10 - x * x





def    __UpperCamelCase      (    a,     a) ->float:
					# Bolzano theory in order to find if there is a root between a and b
					if equation(a) * equation(a) >= 0:
										raise ValueError("Wrong space!")

					lowerCamelCase__       =       a
					while (b - a) >= 0.0_1:
										# Find middle point
										lowerCamelCase__       =       (a + b) / 2
										# Check if middle point is root
										if equation(a) == 0.0:
															break
										# Decide the side to repeat the steps
										if equation(a) * equation(a) < 0:
															lowerCamelCase__       =       c
										else:
															lowerCamelCase__       =       c
					return c


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						print(bisection(-2, 5))
						print(bisection(0, 6))

