
import math
import sys

import cva
import numpy as np



def 	UpperCamelCase   (							lowerCAmelCase__			,      lowerCAmelCase__		):
					'''simple docstring'''
					# For applying gaussian function for each element in matrix.
					lowercase						     =						math.sqrt(lowerCAmelCase__		)
					lowercase						     =						1 / (sigma * math.sqrt(2 * math.pi		))
					return cons * np.exp(-((img / sigma) ** 2) * 0.5		)



def 	UpperCamelCase   (							lowerCAmelCase__			,      lowerCAmelCase__			,      lowerCAmelCase__			,      lowerCAmelCase__		):
					'''simple docstring'''
					lowercase						     =						kernel_size // 2
					return img[x - half : x + half + 1, y - half : y + half + 1]



def 	UpperCamelCase   (							lowerCAmelCase__			,      lowerCAmelCase__		):
					'''simple docstring'''
					# Creates a gaussian kernel of given dimension.
					lowercase						     =						np.zeros((kernel_size, kernel_size)		)
					for i in range(0			,      lowerCAmelCase__		):
										for j in range(0			,      lowerCAmelCase__		):
															lowercase						     =						math.sqrt(
															    abs(i - kernel_size // 2		) ** 2 + abs(j - kernel_size // 2		) ** 2		)
					return vec_gaussian(lowerCAmelCase__			,      lowerCAmelCase__		)



def 	UpperCamelCase   (							lowerCAmelCase__			,      lowerCAmelCase__			,      lowerCAmelCase__			,      lowerCAmelCase__			,      ):
					'''simple docstring'''
					lowercase						     =						np.zeros(img.shape		)
					lowercase						     =						get_gauss_kernel(lowerCAmelCase__			,      lowerCAmelCase__		)
					lowercase     ,						lowercase						     =						img.shape
					for i in range(kernel_size // 2			,      size_x - kernel_size // 2		):
										for j in range(kernel_size // 2			,      size_y - kernel_size // 2		):
															lowercase						     =						get_slice(lowerCAmelCase__			,      lowerCAmelCase__			,      lowerCAmelCase__			,      lowerCAmelCase__		)
															lowercase						     =						img_s - img_s[kernel_size // 2, kernel_size // 2]
															lowercase						     =						vec_gaussian(lowerCAmelCase__			,      lowerCAmelCase__		)
															lowercase						     =						np.multiply(lowerCAmelCase__			,      lowerCAmelCase__		)
															lowercase						     =						np.multiply(lowerCAmelCase__			,      lowerCAmelCase__		)
															lowercase						     =						np.sum(lowerCAmelCase__		) / np.sum(lowerCAmelCase__		)
															lowercase						     =						val
					return imga



def 	UpperCamelCase   (							lowerCAmelCase__		):
					'''simple docstring'''
					lowercase						     =						args[1] if args[1:] else '''../image_data/lena.jpg'''
					lowercase						     =						float(args[2]		) if args[2:] else 1.0
					lowercase						     =						float(args[3]		) if args[3:] else 1.0
					if args[4:]:
										lowercase						     =						int(args[4]		)
										lowercase						     =						kernel_size + abs(kernel_size % 2 - 1		)
					else:
										lowercase						     =						5
					return filename, spatial_variance, intensity_variance, kernel_size


if __name__ == "__main__":
							lowercase__  ,					lowercase__  ,					lowercase__  ,					lowercase__		:Any			  =   parse_args(sys.argv)
							lowercase__		:List[str]			  =   cva.imread(filename, 0)
							cva.imshow("input image", img)

							lowercase__		:List[str]			  =   img / 255
							lowercase__		:Optional[int]			  =   out.astype("float32")
							lowercase__		:List[str]			  =   bilateral_filter(out, spatial_variance, intensity_variance, kernel_size)
							lowercase__		:Optional[int]			  =   out * 255
							lowercase__		:Optional[int]			  =   np.uinta(out)
							cva.imshow("output image", out)
							cva.waitKey(0)
							cva.destroyAllWindows()






from __future__ import annotations

from decimal import Decimal

from numpy import array



def 	UpperCamelCase   (							lowerCAmelCase__		):
					'''simple docstring'''
					lowercase						     =						Decimal

					# Check if the provided matrix has 2 rows and 2 columns
					# since this implementation only works for 2x2 matrices
					if len(lowerCAmelCase__		) == 2 and len(matrix[0]		) == 2 and len(matrix[1]		) == 2:
										# Calculate the determinant of the matrix
										lowercase						     =						float(
										    d(matrix[0][0]		) * d(matrix[1][1]		) - d(matrix[1][0]		) * d(matrix[0][1]		)		)
										if determinant == 0:
															raise ValueError('''This matrix has no inverse.'''		)

										# Creates a copy of the matrix with swapped positions of the elements
										lowercase						     =						[[0.0, 0.0], [0.0, 0.0]]
										lowercase     ,						lowercase						     =						matrix[1][1], matrix[0][0]
										lowercase     ,						lowercase						     =						-matrix[1][0], -matrix[0][1]

										# Calculate the inverse of the matrix
										return [
										    [(float(d(lowerCAmelCase__		)		) / determinant) or 0.0 for n in row] for row in swapped_matrix
										]
					elif (
					    len(lowerCAmelCase__		) == 3
					    and len(matrix[0]		) == 3
					    and len(matrix[1]		) == 3
					    and len(matrix[2]		) == 3
					):
										# Calculate the determinant of the matrix using Sarrus rule
										lowercase						     =						float(
										    (
										        (d(matrix[0][0]		) * d(matrix[1][1]		) * d(matrix[2][2]		))
										        + (d(matrix[0][1]		) * d(matrix[1][2]		) * d(matrix[2][0]		))
										        + (d(matrix[0][2]		) * d(matrix[1][0]		) * d(matrix[2][1]		))
										    )
										    - (
										        (d(matrix[0][2]		) * d(matrix[1][1]		) * d(matrix[2][0]		))
										        + (d(matrix[0][1]		) * d(matrix[1][0]		) * d(matrix[2][2]		))
										        + (d(matrix[0][0]		) * d(matrix[1][2]		) * d(matrix[2][1]		))
										    )		)
										if determinant == 0:
															raise ValueError('''This matrix has no inverse.'''		)

										# Creating cofactor matrix
										lowercase						     =						[
										    [d(0.0		), d(0.0		), d(0.0		)],
										    [d(0.0		), d(0.0		), d(0.0		)],
										    [d(0.0		), d(0.0		), d(0.0		)],
										]
										lowercase						     =						(d(matrix[1][1]		) * d(matrix[2][2]		)) - (
										    d(matrix[1][2]		) * d(matrix[2][1]		)
										)
										lowercase						     =						-(
										    (d(matrix[1][0]		) * d(matrix[2][2]		)) - (d(matrix[1][2]		) * d(matrix[2][0]		))
										)
										lowercase						     =						(d(matrix[1][0]		) * d(matrix[2][1]		)) - (
										    d(matrix[1][1]		) * d(matrix[2][0]		)
										)
										lowercase						     =						-(
										    (d(matrix[0][1]		) * d(matrix[2][2]		)) - (d(matrix[0][2]		) * d(matrix[2][1]		))
										)
										lowercase						     =						(d(matrix[0][0]		) * d(matrix[2][2]		)) - (
										    d(matrix[0][2]		) * d(matrix[2][0]		)
										)
										lowercase						     =						-(
										    (d(matrix[0][0]		) * d(matrix[2][1]		)) - (d(matrix[0][1]		) * d(matrix[2][0]		))
										)
										lowercase						     =						(d(matrix[0][1]		) * d(matrix[1][2]		)) - (
										    d(matrix[0][2]		) * d(matrix[1][1]		)
										)
										lowercase						     =						-(
										    (d(matrix[0][0]		) * d(matrix[1][2]		)) - (d(matrix[0][2]		) * d(matrix[1][0]		))
										)
										lowercase						     =						(d(matrix[0][0]		) * d(matrix[1][1]		)) - (
										    d(matrix[0][1]		) * d(matrix[1][0]		)
										)

										# Transpose the cofactor matrix (Adjoint matrix)
										lowercase						     =						array(lowerCAmelCase__		)
										for i in range(3		):
															for j in range(3		):
																				lowercase						     =						cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
										lowercase						     =						array(lowerCAmelCase__		)
										for i in range(3		):
															for j in range(3		):
																				inverse_matrix[i][j] /= d(lowerCAmelCase__		)

        # Calculate the inverse of the matrix
										return [[float(d(lowerCAmelCase__		)		) or 0.0 for n in row] for row in inverse_matrix]
					raise ValueError('''Please provide a matrix of size 2x2 or 3x3.'''		)




