
'''simple docstring'''





from typing import Any

import numpy as np


class 	UpperCamelCase__					:






 def __init__(     self					:Optional[Any]		,			_A					:np.ndarray		,			_A					:int     )			->     None:







       '''simple docstring'''



       if np.any(tableau[:, -1]		,			where=tableau[:, -1] < 0     ):
             raise ValueError('RHS must be > 0'     )

       __A    		=     tableau
       __A		, __A    		=     tableau.shape

       # Number of decision variables x1, x2, x3...
       __A    		=     n_vars

       # Number of artificial variables to be minimised
       __A    		=     len(np.where(tableau[self.n_vars : -1] == -1     )[0]     )

       # 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
       __A    		=     (self.n_art_vars > 0) + 1

       # Number of slack variables added to make inequalities into equalities
       __A    		=     self.n_rows - self.n_stages

       # Objectives for each stage
       __A    		=     ['max']

       # In two stage simplex, first minimise then maximise
       if self.n_art_vars:
             self.objectives.append('min'     )

       __A    		=     ['']

       # Index of current pivot row and column
       __A    		=     None
       __A    		=     None

       # Does objective row only contain (non)-negative values?
       __A    		=     False






 @staticmethod
 def 		lowercase_  (     *_A					:int     )			->     list[str]:







       '''simple docstring'''



       if len(_A     ) != 3:
             raise ValueError('Must provide n_vars, n_slack, and n_art_vars'     )

       if not all(x >= 0 and isinstance(_A		,			_A     ) for x in args     ):
             raise ValueError('All arguments must be non-negative integers'     )

       # decision | slack | artificial
       __A    		=     ['x', 's', 'a']
       __A    		=     []
       for i in range(3     ):
             for j in range(args[i]     ):
                   titles.append(string_starts[i] + str(j + 1     )     )
       titles.append('RHS'     )
       return titles






 def 		lowercase_  (     self					:Optional[Any]		,			_A					:np.ndarray     )			->     tuple[Any, Any]:







       '''simple docstring'''



       __A    		=     self.objectives[-1]

       # Find entries of highest magnitude in objective rows
       __A    		=     (objective == 'min') - (objective == 'max')
       __A    		=     np.argmax(sign * tableau[0, : self.n_vars]     )

       # Choice is only valid if below 0 for maximise, and above for minimise
       if sign * self.tableau[0, col_idx] <= 0:
             __A    		=     True
             return 0, 0

       # Pivot row is chosen as having the lowest quotient when elements of
       # the pivot column divide the right-hand side

       # Slice excluding the objective rows
       __A    		=     slice(self.n_stages		,			self.n_rows     )

       # RHS
       __A    		=     tableau[s, -1]

       # Elements of pivot column within slice
       __A    		=     tableau[s, col_idx]

       # Array filled with nans
       __A    		=     np.full(self.n_rows - self.n_stages		,			np.nan     )

       # If element in pivot column is greater than zeron_stages, return
       # quotient or nan otherwise
       __A    		=     np.divide(_A		,			_A		,			out=_A		,			where=divisor > 0     )

       # Arg of minimum quotient excluding the nan values. n_stages is added
       # to compensate for earlier exclusion of objective columns
       __A    		=     np.nanargmin(_A     ) + self.n_stages
       return row_idx, col_idx






 def 		lowercase_  (     self					:List[Any]		,			_A					:np.ndarray		,			_A					:int		,			_A					:int     )			->     np.ndarray:







       '''simple docstring'''



       __A    		=     tableau[row_idx].copy()

       __A    		=     piv_row[col_idx]

       # Entry becomes 1
       piv_row *= 1 / piv_val

       # Variable in pivot column becomes basic, ie the only non-zero entry
       for idx, coeff in enumerate(tableau[:, col_idx]     ):
             tableau[idx] += -coeff * piv_row
       __A    		=     piv_row
       return tableau






 def 		lowercase_  (     self					:List[Any]		,			_A					:np.ndarray     )			->     np.ndarray:







       '''simple docstring'''



       self.objectives.pop()

       if not self.objectives:
             return tableau

       # Slice containing ids for artificial columns
       __A    		=     slice(-self.n_art_vars - 1		,			-1     )

       # Delete the artificial variable columns
       __A    		=     np.delete(_A		,			_A		,			axis=1     )

       # Delete the objective row of the first stage
       __A    		=     np.delete(_A		,			0		,			axis=0     )

       __A    		=     1
       self.n_rows -= 1
       __A    		=     0
       __A    		=     False
       return tableau






 def 		lowercase_  (     self					:List[str]     )			->     dict[Any, Any]:







       '''simple docstring'''



       for _ in range(100     ):
             # Completion of each stage removes an objective. If both stages
             # are complete, then no objectives are left
             if not self.objectives:
                   __A    		=     self.generate_col_titles(
                       self.n_vars		,			self.n_slack		,			self.n_art_vars     )

                   # Find the values of each variable at optimal solution
                   return self.interpret_tableau(self.tableau		,			self.col_titles     )

             __A		, __A    		=     self.find_pivot(self.tableau     )

             # If there are no more negative values in objective row
             if self.stop_iter:
                   # Delete artificial variable columns and rows. Update attributes
                   __A    		=     self.change_stage(self.tableau     )
             else:
                   __A    		=     self.pivot(self.tableau		,			_A		,			_A     )
       return {}






 def 		lowercase_  (     self					:Union[str, Any]		,			_A					:np.ndarray		,			_A					:list[str]     )			->     dict[str, float]:







       '''simple docstring'''



       __A    		=     {'P': abs(tableau[0, -1]     )}

       for i in range(self.n_vars     ):
             # Gives ids of nonzero entries in the ith column
             __A    		=     np.nonzero(tableau[:, i]     )
             __A    		=     len(nonzero[0]     )

             # First entry in the nonzero ids
             __A    		=     nonzero[0][0]
             __A    		=     tableau[nonzero_rowidx, i]

             # If there is only one nonzero value in column, which is one
             if n_nonzero == nonzero_val == 1:
                   __A    		=     tableau[nonzero_rowidx, -1]
                   __A    		=     rhs_val

        # Check for basic variables
       for title in col_titles:
             # Don't add RHS or slack variables to output dict
             if title[0] not in "R-s-a":
                   output_dict.setdefault(_A		,			0     )
       return output_dict


if __name__ == "__main__":
 import doctest

 doctest.testmod()








'''simple docstring'''





import math
import os

import cva
import numpy as np

a__						:				List[Any]           =    255.0





def     snake_case							(						UpperCAmelCase ,					UpperCAmelCase		)->     float:







      """simple docstring"""
      __A    		=     np.mean((original - contrast) ** 2		)
      if mse == 0:
            return 1_0_0

      return 2_0 * math.logaa(PIXEL_MAX / math.sqrt(UpperCAmelCase		)		)





def     snake_case							(						)->     None:







      """simple docstring"""
      __A    		=     os.path.dirname(os.path.realpath(UpperCAmelCase		)		)
      # Loading images (original image and compressed image)
      __A    		=     cva.imread(os.path.join(UpperCAmelCase ,					'image_data/original_image.png'		)		)
      __A    		=     cva.imread(os.path.join(UpperCAmelCase ,					'image_data/compressed_image.png'		) ,					1		)

      __A    		=     cva.imread(os.path.join(UpperCAmelCase ,					'image_data/PSNR-example-base.png'		)		)
      __A    		=     cva.imread(
          os.path.join(UpperCAmelCase ,					'image_data/PSNR-example-comp-10.jpg'		) ,					1		)

      # Value expected: 29.73dB
      print('-- First Test --'		)
      print(f'PSNR value is {peak_signal_to_noise_ratio(UpperCAmelCase ,					UpperCAmelCase		)} dB'		)

      # # Value expected: 31.53dB (Wikipedia Example)
      print('\n-- Second Test --'		)
      print(f'PSNR value is {peak_signal_to_noise_ratio(UpperCAmelCase ,					UpperCAmelCase		)} dB'		)


if __name__ == "__main__":
 main()






