
from itertools import product

from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uinta, zeros



def   _a  ( __UpperCamelCase							:	List[Any]						,__UpperCamelCase							:	Union[str, Any]     ):
			lowerCAmelCase__			:     Dict					   =      k_size // 2
			lowerCAmelCase__   ,					lowerCAmelCase__			:     Union[str, Any]					   =      mgrid[0 - center : k_size - center, 0 - center : k_size - center]
			lowerCAmelCase__			:     str					   =      1 / (2 * pi * sigma) * exp(-(square(__UpperCamelCase     ) + square(__UpperCamelCase     )) / (2 * square(__UpperCamelCase     ))     )
			return g



def   _a  ( __UpperCamelCase							:	Dict						,__UpperCamelCase							:	Any						,__UpperCamelCase							:	Tuple     ):
			lowerCAmelCase__   ,					lowerCAmelCase__			:     List[str]					   =      image.shape[0], image.shape[1]
			# dst image height and width
			lowerCAmelCase__			:     Tuple					   =      height - k_size + 1
			lowerCAmelCase__			:     Union[str, Any]					   =      width - k_size + 1

			# im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
			lowerCAmelCase__			:     Union[str, Any]					   =      zeros((dst_height * dst_width, k_size * k_size)     )
			lowerCAmelCase__			:     Any					   =      0
			for i, j in product(range(__UpperCamelCase     )						,range(__UpperCamelCase     )     ):
						lowerCAmelCase__			:     int					   =      ravel(image[i : i + k_size, j : j + k_size]     )
						lowerCAmelCase__			:     List[Any]					   =      window
						row += 1

			#  turn the kernel into shape(k*k, 1)
			lowerCAmelCase__			:     Union[str, Any]					   =      gen_gaussian_kernel(__UpperCamelCase						,__UpperCamelCase     )
			lowerCAmelCase__			:     Dict					   =      ravel(__UpperCamelCase     )

			# reshape and get the dst image
			lowerCAmelCase__			:     List[str]					   =      dot(__UpperCamelCase						,__UpperCamelCase     ).reshape(__UpperCamelCase						,__UpperCamelCase     ).astype(__UpperCamelCase     )

			return dst


if __name__ == "__main__":
							# read original image
							A__							: List[Any]     =       imread(r"""../image_data/lena.jpg""")
							# turn image in gray scale value
							A__							: Any     =       cvtColor(img, COLOR_BGR2GRAY)

							# get values with two different mask size
							A__							: Tuple     =       gaussian_filter(gray, 3, sigma=1)
							A__							: Any     =       gaussian_filter(gray, 5, sigma=0.8)

							# show result images
							imshow("""gaussian filter with 3x3 mask""", gaussianaxa)
							imshow("""gaussian filter with 5x5 mask""", gaussianaxa)
							waitKey()




"""simple docstring"""


def      __UpperCAmelCase       (      lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   0
  _UpperCAmelCase    			=   len(lowercase		)

  for i in range(n - 1		):
    for j in range(i + 1 ,lowercase		):
      if arr[i] > arr[j]:
        num_inversions += 1

  return num_inversions






def      __UpperCAmelCase       (      lowercase		):







  """simple docstring"""
  if len(lowercase		) <= 1:
    return arr, 0
  _UpperCAmelCase    			=   len(lowercase		) // 2
  _UpperCAmelCase    			=   arr[0:mid]
  _UpperCAmelCase    			=   arr[mid:]

  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   _count_cross_inversions(lowercase ,lowercase		)

  _UpperCAmelCase    			=   inversion_p + inversions_q + cross_inversions
  return c, num_inversions






def      __UpperCAmelCase       (      lowercase ,lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   []
  _UpperCAmelCase    			=   _UpperCAmelCase    			=   _UpperCAmelCase    			=   0
  while i < len(lowercase		) and j < len(lowercase		):
    if p[i] > q[j]:
      # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
      # These are all inversions. The claim emerges from the
      # property that P is sorted.
      num_inversion += len(lowercase		) - i
      r.append(q[j]		)
      j += 1
    else:
      r.append(p[i]		)
      i += 1

  if i < len(lowercase		):
    r.extend(p[i:]		)
  else:
    r.extend(q[j:]		)

  return r, num_inversion






def      __UpperCAmelCase       (      ):







  """simple docstring"""
  _UpperCAmelCase    			=   [10, 2, 1, 5, 5, 2, 11]

  # this arr has 8 inversions:
  # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

  _UpperCAmelCase    			=   count_inversions_bf(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)

  assert num_inversions_bf == num_inversions_recursive == 8

  print("""number of inversions = """ ,lowercase		)

  # testing an array with zero inversion (a sorted arr_1)

  arr_a.sort()
  _UpperCAmelCase    			=   count_inversions_bf(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)

  assert num_inversions_bf == num_inversions_recursive == 0
  print("""number of inversions = """ ,lowercase		)

  # an empty list should also have zero inversions
  _UpperCAmelCase    			=   []
  _UpperCAmelCase    			=   count_inversions_bf(lowercase		)
  _UpperCAmelCase			,					_UpperCAmelCase    			=   count_inversions_recursive(lowercase		)

  assert num_inversions_bf == num_inversions_recursive == 0
  print("""number of inversions = """ ,lowercase		)


if __name__ == "__main__":
    main()
