






"""simple docstring"""



from typing import Any

import numpy as np






class 				__SCREAMING_SNAKE_CASE    :


							def __init__(      self   :    Any      ,     snake_case   :    np.ndarray      ,     snake_case   :    int				):
													'''simple docstring'''





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

													A__    :	List[Any]			=	tableau
													A__	,	A__    :	Any			=	tableau.shape

													# Number of decision variables x1, x2, x3...
													A__    :	List[Any]			=	n_vars

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

													# 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
													A__    :	Union[str, Any]			=	(self.n_art_vars > 0) + 1

													# Number of slack variables added to make inequalities into equalities
													A__    :	Optional[Any]			=	self.n_rows - self.n_stages

													# Objectives for each stage
													A__    :	Any			=	["""max"""]

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

													A__    :	Any			=	[""""""]

													# Index of current pivot row and column
													A__    :	Union[str, Any]			=	None
													A__    :	List[str]			=	None

													# Does objective row only contain (non)-negative values?
													A__    :	int			=	False


							@staticmethod
							def     _UpperCamelCase							(      *snake_case   :    int				):
													'''simple docstring'''





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

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

													# decision | slack | artificial
													A__    :	Optional[int]			=	["""x""", """s""", """a"""]
													A__    :	List[Any]			=	[]
													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     _UpperCamelCase							(      self   :    Optional[Any]      ,     snake_case   :    np.ndarray				):
													'''simple docstring'''





													A__    :	str			=	self.objectives[-1]

													# Find entries of highest magnitude in objective rows
													A__    :	int			=	(objective == """min""") - (objective == """max""")
													A__    :	List[Any]			=	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__    :	Dict			=	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__    :	Optional[Any]			=	slice(self.n_stages      ,     self.n_rows				)

													# RHS
													A__    :	List[str]			=	tableau[s, -1]

													# Elements of pivot column within slice
													A__    :	List[Any]			=	tableau[s, col_idx]

													# Array filled with nans
													A__    :	Optional[Any]			=	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__    :	List[Any]			=	np.divide(snake_case__      ,     snake_case__      ,     out=snake_case__      ,     where=divisor > 0				)

													# Arg of minimum quotient excluding the nan values. n_stages is added
													# to compensate for earlier exclusion of objective columns
													A__    :	Optional[Any]			=	np.nanargmin(snake_case__				) + self.n_stages
													return row_idx, col_idx


							def     _UpperCamelCase							(      self   :    Optional[Any]      ,     snake_case   :    np.ndarray      ,     snake_case   :    int      ,     snake_case   :    int				):
													'''simple docstring'''





													A__    :	Optional[int]			=	tableau[row_idx].copy()

													A__    :	Union[str, Any]			=	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__    :	str			=	piv_row
													return tableau


							def     _UpperCamelCase							(      self   :    List[str]      ,     snake_case   :    np.ndarray				):
													'''simple docstring'''





													self.objectives.pop()

													if not self.objectives:
																			return tableau

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

													# Delete the artificial variable columns
													A__    :	Any			=	np.delete(snake_case__      ,     snake_case__      ,     axis=1				)

													# Delete the objective row of the first stage
													A__    :	int			=	np.delete(snake_case__      ,     0      ,     axis=0				)

													A__    :	List[Any]			=	1
													self.n_rows -= 1
													A__    :	Dict			=	0
													A__    :	List[Any]			=	False
													return tableau


							def     _UpperCamelCase							(      self   :    Tuple				):
													'''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__    :	Union[str, Any]			=	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__    :	str			=	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__    :	Tuple			=	self.change_stage(self.tableau				)
																			else:
																									A__    :	Optional[Any]			=	self.pivot(self.tableau      ,     snake_case__      ,     snake_case__				)
													return {}


							def     _UpperCamelCase							(      self   :    Dict      ,     snake_case   :    np.ndarray      ,     snake_case   :    list[str]				):
													'''simple docstring'''





													A__    :	Optional[int]			=	{"""P""": abs(tableau[0, -1]				)}

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

																			# First entry in the nonzero ids
																			A__    :	List[Any]			=	nonzero[0][0]
																			A__    :	List[str]			=	tableau[nonzero_rowidx, i]

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()












import torch
import torch.nn.functional as F

from diffusers import VQDiffusionScheduler

from .test_schedulers import SchedulerCommonTest






class        __lowerCAmelCase					(			UpperCAmelCase__					):
			snake_case_ :					List[str]						=	(VQDiffusionScheduler,)







			def UpperCamelCase     (			self       :     Dict       ,       **snake_case__       :     int ):




									"""simple docstring"""


									_UpperCAmelCase						=	{
									    "num_vec_classes": 4_097,
									    "num_train_timesteps": 100,
									}

									config.update(**snake_case__ )
									return config







			def UpperCamelCase     (			self       :     Optional[int]       ,       snake_case__       :     Any ):




									"""simple docstring"""


									_UpperCAmelCase						=	4
									_UpperCAmelCase						=	8
									_UpperCAmelCase						=	8

									_UpperCAmelCase						=	torch.randint(0       ,       snake_case__       ,       (batch_size, height * width) )

									return sample







			@property
			def UpperCamelCase     (			self       :     str ):




									"""simple docstring"""


									assert False







			def UpperCamelCase     (			self       :     List[str]       ,       snake_case__       :     Optional[Any] ):




									"""simple docstring"""


									def model(snake_case__       :     Dict       ,       snake_case__       :     Tuple       ,       *snake_case__       :     str ):
															_UpperCAmelCase				,					_UpperCAmelCase						=	sample.shape
															_UpperCAmelCase						=	torch.rand((batch_size, num_vec_classes - 1, num_latent_pixels) )
															_UpperCAmelCase						=	F.log_softmax(logits.double()       ,       dim=1 ).float()
															return return_value

									return model







			def UpperCamelCase     (			self       :     Optional[int] ):




									"""simple docstring"""


									for timesteps in [2, 5, 100, 1_000]:
															self.check_over_configs(num_train_timesteps=snake_case__ )







			def UpperCamelCase     (			self       :     Optional[int] ):




									"""simple docstring"""


									for num_vec_classes in [5, 100, 1_000, 4_000]:
															self.check_over_configs(num_vec_classes=snake_case__ )







			def UpperCamelCase     (			self       :     Optional[Any] ):




									"""simple docstring"""


									for t in [0, 50, 99]:
															self.check_over_forward(time_step=snake_case__ )







			def UpperCamelCase     (			self       :     Tuple ):




									"""simple docstring"""


									pass




