
def 						UpperCAmelCase			(	a_						)		->	int:







				"""simple docstring"""



				__A   			= len(a_						)
				__A   			= len(matrix[0]						)
				__A   			= min(a_		,   a_						)

				for row in range(a_						):
								# Check if diagonal element is not zero
								if matrix[row][row] != 0:
												# Eliminate all the elements below the diagonal
												for col in range(row + 1		,   a_						):
																__A   			= matrix[col][row] / matrix[row][row]
																for i in range(a_		,   a_						):
																				matrix[col][i] -= multiplier * matrix[row][i]
								else:
												# Find a non-zero diagonal element to swap rows
												__A   			= True
												for i in range(row + 1		,   a_						):
																if matrix[i][row] != 0:
																				__A			,							__A   			= matrix[i], matrix[row]
																				__A   			= False
																				break
												if reduce:
																rank -= 1
																for i in range(a_						):
																				__A   			= matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
												row -= 1

				return rank


if __name__ == "__main__":
					import doctest

					doctest.testmod()







"""simple docstring"""
from collections.abc import Callable

import numpy as np



def      __lowerCamelCase   (							a_     :		Callable ,   a_     :		float ,   a_     :		float ,   a_     :		float ,   a_     :		float							)			->      np.ndarray:
      __SCREAMING_SNAKE_CASE   :List[Any]						=  int(np.ceil((x_end - xa) / step_size							)							)
      __SCREAMING_SNAKE_CASE   :Optional[Any]						=  np.zeros((n + 1,)							)
      __SCREAMING_SNAKE_CASE   :int						=  ya
      __SCREAMING_SNAKE_CASE   :str						=  xa

      for k in range(a_							):
            __SCREAMING_SNAKE_CASE   :Optional[int]						=  y[k] + step_size * ode_func(a_ ,   y[k]							)
            x += step_size

      return y


if __name__ == "__main__":
  import doctest

  doctest.testmod()