





'''simple docstring'''

from typing import Any

import numpy as np
class        __lowerCAmelCase  :






       """simple docstring"""





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

            '''simple docstring'''




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

            _UpperCamelCase       					= tableau
            _UpperCamelCase					,       _UpperCamelCase       					= tableau.shape

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

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

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

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

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

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

            _UpperCamelCase       					= ['''''']

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

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





       @staticmethod
       def snake_case__		(							*lowerCAmelCase__     :	int  )					->  list[str]:

            '''simple docstring'''




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

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

            # decision | slack | artificial
            _UpperCamelCase       					= ['''x''', '''s''', '''a''']
            _UpperCamelCase       					= []
            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 snake_case__		(							self     :	int ,				lowerCAmelCase__     :	np.ndarray  )					->  tuple[Any, Any]:

            '''simple docstring'''




            _UpperCamelCase       					= self.objectives[-1]

            # Find entries of highest magnitude in objective rows
            _UpperCamelCase       					= (objective == '''min''') - (objective == '''max''')
            _UpperCamelCase       					= 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:
                 _UpperCamelCase       					= 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
            _UpperCamelCase       					= slice(self.n_stages ,				self.n_rows  )

            # RHS
            _UpperCamelCase       					= tableau[s, -1]

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

            # Array filled with nans
            _UpperCamelCase       					= 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
            _UpperCamelCase       					= np.divide(lowerCAmelCase__ ,				lowerCAmelCase__ ,				out=lowerCAmelCase__ ,				where=divisor > 0  )

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





       def snake_case__		(							self     :	Dict ,				lowerCAmelCase__     :	np.ndarray ,				lowerCAmelCase__     :	int ,				lowerCAmelCase__     :	int  )					->  np.ndarray:

            '''simple docstring'''




            _UpperCamelCase       					= tableau[row_idx].copy()

            _UpperCamelCase       					= 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
            _UpperCamelCase       					= piv_row
            return tableau





       def snake_case__		(							self     :	str ,				lowerCAmelCase__     :	np.ndarray  )					->  np.ndarray:

            '''simple docstring'''




            self.objectives.pop()

            if not self.objectives:
                 return tableau

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

            # Delete the artificial variable columns
            _UpperCamelCase       					= np.delete(lowerCAmelCase__ ,				lowerCAmelCase__ ,				axis=1  )

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

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





       def snake_case__		(							self     :	Optional[int]  )					->  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:
                      _UpperCamelCase       					= 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  )

                 _UpperCamelCase					,       _UpperCamelCase       					= 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
                      _UpperCamelCase       					= self.change_stage(self.tableau  )
                 else:
                      _UpperCamelCase       					= self.pivot(self.tableau ,				lowerCAmelCase__ ,				lowerCAmelCase__  )
            return {}







       def snake_case__		(							self     :	Tuple ,				lowerCAmelCase__     :	np.ndarray ,				lowerCAmelCase__     :	list[str]  )					->  dict[str, float]:

            '''simple docstring'''




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

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

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

                 # If there is only one nonzero value in column, which is one
                 if n_nonzero == nonzero_val == 1:
                      _UpperCamelCase       					= tableau[nonzero_rowidx, -1]
                      _UpperCamelCase       					= 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(lowerCAmelCase__ ,				0  )
            return output_dict


if __name__ == "__main__":
   import doctest

   doctest.testmod()










'''simple docstring'''

import unittest
from dataclasses import dataclass
from typing import List, Union

import numpy as np
import PIL.Image

from diffusers.utils.outputs import BaseOutput
@dataclass
class        __lowerCAmelCase  (					__magic_name__				):






       """simple docstring"""
       _snake_case			:  Union[List[PIL.Image.Image], np.ndarray]

class        __lowerCAmelCase  (					unittest.TestCase				):






       """simple docstring"""





       def snake_case__		(							self     :	Any  )					->  Any:

            '''simple docstring'''




            _UpperCamelCase       					= CustomOutput(images=np.random.rand(1 ,				3 ,				4 ,				4  )  )

            # check every way of getting the attribute
            assert isinstance(outputs.images ,				np.ndarray  )
            assert outputs.images.shape == (1, 3, 4, 4)
            assert isinstance(outputs['''images'''] ,				np.ndarray  )
            assert outputs["images"].shape == (1, 3, 4, 4)
            assert isinstance(outputs[0] ,				np.ndarray  )
            assert outputs[0].shape == (1, 3, 4, 4)

            # test with a non-tensor attribute
            _UpperCamelCase       					= CustomOutput(images=[PIL.Image.new('''RGB''' ,				(4, 4)  )]  )

            # check every way of getting the attribute
            assert isinstance(outputs.images ,				lowerCAmelCase__  )
            assert isinstance(outputs.images[0] ,				PIL.Image.Image  )
            assert isinstance(outputs['''images'''] ,				lowerCAmelCase__  )
            assert isinstance(outputs['''images'''][0] ,				PIL.Image.Image  )
            assert isinstance(outputs[0] ,				lowerCAmelCase__  )
            assert isinstance(outputs[0][0] ,				PIL.Image.Image  )







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

            '''simple docstring'''




            _UpperCamelCase       					= CustomOutput({'''images''': np.random.rand(1 ,				3 ,				4 ,				4  )}  )

            # check every way of getting the attribute
            assert isinstance(outputs.images ,				np.ndarray  )
            assert outputs.images.shape == (1, 3, 4, 4)
            assert isinstance(outputs['''images'''] ,				np.ndarray  )
            assert outputs["images"].shape == (1, 3, 4, 4)
            assert isinstance(outputs[0] ,				np.ndarray  )
            assert outputs[0].shape == (1, 3, 4, 4)

            # test with a non-tensor attribute
            _UpperCamelCase       					= CustomOutput({'''images''': [PIL.Image.new('''RGB''' ,				(4, 4)  )]}  )

            # check every way of getting the attribute
            assert isinstance(outputs.images ,				lowerCAmelCase__  )
            assert isinstance(outputs.images[0] ,				PIL.Image.Image  )
            assert isinstance(outputs['''images'''] ,				lowerCAmelCase__  )
            assert isinstance(outputs['''images'''][0] ,				PIL.Image.Image  )
            assert isinstance(outputs[0] ,				lowerCAmelCase__  )
            assert isinstance(outputs[0][0] ,				PIL.Image.Image  )



