

from typing import Any

import numpy as np





def 	__a     (      A__			:  np.ndarray       ):
    return np.array_equal(A__			,  matrix.conjugate().T       )





def 	__a     (      A__			:  np.ndarray			,  A__			:  np.ndarray       ):
    SCREAMING_SNAKE_CASE										=   v.conjugate().T
    SCREAMING_SNAKE_CASE										=   v_star.dot(A__       )
    assert isinstance(A__			,  np.ndarray       )
    return (v_star_dot.dot(A__       )) / (v_star.dot(A__       ))





def 	__a     (      ):
    SCREAMING_SNAKE_CASE										=   np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]       )
    SCREAMING_SNAKE_CASE										=   np.array([[1], [2], [3]]       )
    assert is_hermitian(A__       ), F"{a} is not hermitian."
    print(rayleigh_quotient(A__			,  A__       )       )

    SCREAMING_SNAKE_CASE										=   np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]       )
    assert is_hermitian(A__       ), F"{a} is not hermitian."
    assert rayleigh_quotient(A__			,  A__       ) == float(3       )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    tests()






'''simple docstring'''






import cva
import numpy as np




class  _A :

		def __init__(   self					:   Any  ,      __magic_name__					:   float  ,      __magic_name__					:   int			)					->    Optional[int]:


					"""simple docstring"""

					if k in (0.04, 0.06):
								__snake_case					:      List[str]							      =     k
								__snake_case					:      int							      =     window_size
					else:
								raise ValueError("""invalid k value"""			)

		def __str__(   self					:   Union[str, Any]			)					->    str:


					"""simple docstring"""

					return str(self.k			)

		def 	lowercase__     (   self					:   Dict  ,      __magic_name__					:   str			)					->    tuple[cva.Mat, list[list[int]]]:


					"""simple docstring"""

					__snake_case					:      Dict							      =     cva.imread(__magic_name__  ,      0			)
					__snake_case      ,     __snake_case					:      List[str]							      =     img.shape
					__snake_case					:      list[list[int]]							      =     []
					__snake_case					:      str							      =     img.copy()
					__snake_case					:      Tuple							      =     cva.cvtColor(__magic_name__  ,      cva.COLOR_GRAY2RGB			)
					__snake_case      ,     __snake_case					:      List[Any]							      =     np.gradient(__magic_name__			)
					__snake_case					:      Optional[Any]							      =     dx**2
					__snake_case					:      Tuple							      =     dy**2
					__snake_case					:      List[Any]							      =     dx * dy
					__snake_case					:      List[Any]							      =     0.04
					__snake_case					:      Tuple							      =     self.window_size // 2
					for y in range(__magic_name__  ,      h - offset			):
								for x in range(__magic_name__  ,      w - offset			):
											__snake_case					:      Dict							      =     ixx[
											    y - offset : y + offset + 1, x - offset : x + offset + 1
											].sum()
											__snake_case					:      Optional[int]							      =     iyy[
											    y - offset : y + offset + 1, x - offset : x + offset + 1
											].sum()
											__snake_case					:      str							      =     ixy[
											    y - offset : y + offset + 1, x - offset : x + offset + 1
											].sum()

											__snake_case					:      List[str]							      =     (wxx * wyy) - (wxy**2)
											__snake_case					:      Dict							      =     wxx + wyy
											__snake_case					:      List[str]							      =     det - k * (trace**2)
											# Can change the value
											if r > 0.5:
														corner_list.append([x, y, r]			)
														color_img.itemset((y, x, 0)  ,      0			)
														color_img.itemset((y, x, 1)  ,      0			)
														color_img.itemset((y, x, 2)  ,      2_55			)
					return color_img, corner_list


if __name__ == "__main__":
	__UpperCamelCase					    =	HarrisCorner(0.04, 3)
	__UpperCamelCase    ,		__UpperCamelCase					    =	edge_detect.detect("path_to_image")
	cva.imwrite("detect.png", color_img)


