






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 		lowercase__  (				_UpperCamelCase       ,							_UpperCamelCase) ->			Union[str, Any]:
      """simple docstring"""

      UpperCamelCase					       =  k_size // 2
      UpperCamelCase					       =  mgrid[0 - center : k_size - center, 0 - center : k_size - center]
      UpperCamelCase					       =  1 / (2 * pi * sigma) * exp(-(square(_UpperCamelCase) + square(_UpperCamelCase)) / (2 * square(_UpperCamelCase)))
      return g
def 		lowercase__  (				_UpperCamelCase       ,							_UpperCamelCase       ,							_UpperCamelCase) ->			Optional[int]:
      """simple docstring"""

      UpperCamelCase					       =  image.shape[0], image.shape[1]
      # dst image height and width
      UpperCamelCase					       =  height - k_size + 1
      UpperCamelCase					       =  width - k_size + 1

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

      #  turn the kernel into shape(k*k, 1)
      UpperCamelCase					       =  gen_gaussian_kernel(_UpperCamelCase       ,							_UpperCamelCase)
      UpperCamelCase					       =  ravel(_UpperCamelCase)

      # reshape and get the dst image
      UpperCamelCase					       =  dot(_UpperCamelCase       ,							_UpperCamelCase).reshape(_UpperCamelCase       ,							_UpperCamelCase).astype(_UpperCamelCase)

      return dst


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

       # get values with two different mask size
       __magic_name__   :  int        =							gaussian_filter(gray, 3, sigma=1)
       __magic_name__   :  List[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()






from typing import Callable, Dict, Optional, Tuple

import torch
from torch import nn
from torch.distributions import (
    AffineTransform,
    Distribution,
    Independent,
    NegativeBinomial,
    Normal,
    StudentT,
    TransformedDistribution,
)

class __UpperCamelCase     (				_a		):






					'''simple docstring'''



					def __init__(				self				,      lowerCamelCase__				,      lowerCamelCase__=None				,      lowerCamelCase__=None				,      lowerCamelCase__=0						):
						UpperCAmelCase__:	Any									= 1.0 if scale is None else scale
						UpperCAmelCase__:	int									= 0.0 if loc is None else loc

						super().__init__(lowerCamelCase__				,      [AffineTransform(loc=self.loc				,      scale=self.scale				,      event_dim=lowerCamelCase__						)]						)





					@property
					def    _UpperCAmelCase    (				self						):
						return self.base_dist.mean * self.scale + self.loc





					@property
					def    _UpperCAmelCase    (				self						):
						return self.base_dist.variance * self.scale**2





					@property
					def    _UpperCAmelCase    (				self						):
						return self.variance.sqrt()

class __UpperCamelCase     (				nn.Module		):






					'''simple docstring'''



					def __init__(				self				,      lowerCamelCase__				,      lowerCamelCase__				,      lowerCamelCase__				,      **lowerCamelCase__						):
						super().__init__(**lowerCamelCase__						)
						UpperCAmelCase__:	Any									= args_dim
						UpperCAmelCase__:	List[str]									= nn.ModuleList([nn.Linear(lowerCamelCase__				,      lowerCamelCase__						) for dim in args_dim.values()]						)
						UpperCAmelCase__:	Any									= domain_map





					def    _UpperCAmelCase    (				self				,      lowerCamelCase__						):
						UpperCAmelCase__:	str									= [proj(lowerCamelCase__						) for proj in self.proj]

						return self.domain_map(*lowerCamelCase__						)

class __UpperCamelCase     (				nn.Module		):






					'''simple docstring'''



					def __init__(				self				,      lowerCamelCase__						):
						super().__init__()
						UpperCAmelCase__:	str									= function





					def    _UpperCAmelCase    (				self				,      lowerCamelCase__				,      *lowerCamelCase__						):
						return self.function(lowerCamelCase__				,      *lowerCamelCase__						)

class __UpperCamelCase     :






					'''simple docstring'''



					__magic_name__        =   42
					__magic_name__        =   42
					__magic_name__        =   42





					def __init__(				self				,      lowerCamelCase__ = 1						):
						UpperCAmelCase__:	str									= dim
						UpperCAmelCase__:	Any									= {k: dim * self.args_dim[k] for k in self.args_dim}





					def    _UpperCAmelCase    (				self				,      lowerCamelCase__						):
						if self.dim == 1:
							return self.distribution_class(*lowerCamelCase__						)
						else:
							return Independent(self.distribution_class(*lowerCamelCase__						)				,      1						)





					def    _UpperCAmelCase    (				self				,      lowerCamelCase__				,      lowerCamelCase__ = None				,      lowerCamelCase__ = None				,      ):
						UpperCAmelCase__:	Optional[Any]									= self._base_distribution(lowerCamelCase__						)
						if loc is None and scale is None:
							return distr
						else:
							return AffineTransformed(lowerCamelCase__				,      loc=lowerCamelCase__				,      scale=lowerCamelCase__				,      event_dim=self.event_dim						)





					@property
					def    _UpperCAmelCase    (				self						):
						return () if self.dim == 1 else (self.dim,)





					@property
					def    _UpperCAmelCase    (				self						):
						return len(self.event_shape						)





					@property
					def    _UpperCAmelCase    (				self						):
						return 0.0





					def    _UpperCAmelCase    (				self				,      lowerCamelCase__						):
						return ParameterProjection(
						    in_features=lowerCamelCase__				,      args_dim=self.args_dim				,      domain_map=LambdaLayer(self.domain_map						)				,      )





					def    _UpperCAmelCase    (				self				,      *lowerCamelCase__						):
						raise NotImplementedError()





					@staticmethod
					def    _UpperCAmelCase    (				lowerCamelCase__						):
						return (x + torch.sqrt(torch.square(lowerCamelCase__						) + 4.0						)) / 2.0

class __UpperCamelCase     (				_a		):






					'''simple docstring'''



					__magic_name__        =   {"df": 1, "loc": 1, "scale": 1}
					__magic_name__        =   StudentT





					@classmethod
					def    _UpperCAmelCase    (				cls				,      lowerCamelCase__				,      lowerCamelCase__				,      lowerCamelCase__						):
						UpperCAmelCase__:	Dict									= cls.squareplus(lowerCamelCase__						).clamp_min(torch.finfo(scale.dtype						).eps						)
						UpperCAmelCase__:	List[Any]									= 2.0 + cls.squareplus(lowerCamelCase__						)
						return df.squeeze(-1						), loc.squeeze(-1						), scale.squeeze(-1						)

class __UpperCamelCase     (				_a		):






					'''simple docstring'''



					__magic_name__        =   {"loc": 1, "scale": 1}
					__magic_name__        =   Normal





					@classmethod
					def    _UpperCAmelCase    (				cls				,      lowerCamelCase__				,      lowerCamelCase__						):
						UpperCAmelCase__:	str									= cls.squareplus(lowerCamelCase__						).clamp_min(torch.finfo(scale.dtype						).eps						)
						return loc.squeeze(-1						), scale.squeeze(-1						)

class __UpperCamelCase     (				_a		):






					'''simple docstring'''



					__magic_name__        =   {"total_count": 1, "logits": 1}
					__magic_name__        =   NegativeBinomial





					@classmethod
					def    _UpperCAmelCase    (				cls				,      lowerCamelCase__				,      lowerCamelCase__						):
						UpperCAmelCase__:	Dict									= cls.squareplus(lowerCamelCase__						)
						return total_count.squeeze(-1						), logits.squeeze(-1						)





					def    _UpperCAmelCase    (				self				,      lowerCamelCase__						):
						UpperCAmelCase__							,						UpperCAmelCase__:	str									= distr_args
						if self.dim == 1:
							return self.distribution_class(total_count=lowerCamelCase__				,      logits=lowerCamelCase__						)
						else:
							return Independent(self.distribution_class(total_count=lowerCamelCase__				,      logits=lowerCamelCase__						)				,      1						)





					def    _UpperCAmelCase    (				self				,      lowerCamelCase__				,      lowerCamelCase__ = None				,      lowerCamelCase__ = None						):
						UpperCAmelCase__							,						UpperCAmelCase__:	List[str]									= distr_args

						if scale is not None:
							# See scaling property of Gamma.
							logits += scale.log()

						return self._base_distribution((total_count, logits)						)