code: 
  
  
  '''simple docstring'''
  
  from typing import Any
  
  import numpy as np
  class _lowerCamelCase :
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		def __init__(      self	:		Any						,  _A	:		np.ndarray						,  _A	:		int    )						->				None:
  			# Check if RHS is negative
  			if np.any(tableau[:, -1]						,  where=tableau[:, -1] < 0    ):
  				raise ValueError('RHS must be > 0'    )
  
  			__magic_name__ :					List[Any]  			=  tableau
  			__magic_name__			,       __magic_name__ :					List[str]  			=  tableau.shape
  
  			# Number of decision variables x1, x2, x3...
  			__magic_name__ :					Optional[Any]  			=  n_vars
  
  			# Number of artificial variables to be minimised
  			__magic_name__ :					Dict  			=  len(np.where(tableau[self.n_vars : -1] == -1    )[0]    )
  
  			# 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
  			__magic_name__ :					List[str]  			=  (self.n_art_vars > 0) + 1
  
  			# Number of slack variables added to make inequalities into equalities
  			__magic_name__ :					Any  			=  self.n_rows - self.n_stages
  
  			# Objectives for each stage
  			__magic_name__ :					List[Any]  			=  ['max']
  
  			# In two stage simplex, first minimise then maximise
  			if self.n_art_vars:
  				self.objectives.append('min'    )
  
  			__magic_name__ :					List[Any]  			=  ['']
  
  			# Index of current pivot row and column
  			__magic_name__ :					Dict  			=  None
  			__magic_name__ :					List[str]  			=  None
  
  			# Does objective row only contain (non)-negative values?
  			__magic_name__ :					Optional[int]  			=  False
  
  
  
  
  
  
  
  		@staticmethod
  		def      __lowerCAmelCase	(      *_A	:		int    )						->				list[str]:
  			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
  			__magic_name__ :					Union[str, Any]  			=  ['x', 's', 'a']
  			__magic_name__ :					List[str]  			=  []
  			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      __lowerCAmelCase	(      self	:		Optional[Any]						,  _A	:		np.ndarray    )						->				tuple[Any, Any]:
  			__magic_name__ :					int  			=  self.objectives[-1]
  
  			# Find entries of highest magnitude in objective rows
  			__magic_name__ :					Optional[int]  			=  (objective == 'min') - (objective == 'max')
  			__magic_name__ :					Tuple  			=  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:
  				__magic_name__ :					List[str]  			=  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
  			__magic_name__ :					Optional[Any]  			=  slice(self.n_stages						,  self.n_rows    )
  
  			# RHS
  			__magic_name__ :					int  			=  tableau[s, -1]
  
  			# Elements of pivot column within slice
  			__magic_name__ :					Dict  			=  tableau[s, col_idx]
  
  			# Array filled with nans
  			__magic_name__ :					Tuple  			=  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
  			__magic_name__ :					Tuple  			=  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
  			__magic_name__ :					Tuple  			=  np.nanargmin(_A    ) + self.n_stages
  			return row_idx, col_idx
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Tuple						,  _A	:		np.ndarray						,  _A	:		int						,  _A	:		int    )						->				np.ndarray:
  			__magic_name__ :					Optional[int]  			=  tableau[row_idx].copy()
  
  			__magic_name__ :					Tuple  			=  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
  			__magic_name__ :					List[Any]  			=  piv_row
  			return tableau
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Optional[int]						,  _A	:		np.ndarray    )						->				np.ndarray:
  			self.objectives.pop()
  
  			if not self.objectives:
  				return tableau
  
  			# Slice containing ids for artificial columns
  			__magic_name__ :					List[str]  			=  slice(-self.n_art_vars - 1						,  -1    )
  
  			# Delete the artificial variable columns
  			__magic_name__ :					Union[str, Any]  			=  np.delete(_A						,  _A						,  axis=1    )
  
  			# Delete the objective row of the first stage
  			__magic_name__ :					Any  			=  np.delete(_A						,  0						,  axis=0    )
  
  			__magic_name__ :					int  			=  1
  			self.n_rows -= 1
  			__magic_name__ :					Tuple  			=  0
  			__magic_name__ :					str  			=  False
  			return tableau
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Dict    )						->				dict[Any, Any]:
  			# Stop simplex algorithm from cycling.
  			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:
  					__magic_name__ :					Optional[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    )
  
  				__magic_name__			,       __magic_name__ :					int  			=  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
  					__magic_name__ :					Optional[int]  			=  self.change_stage(self.tableau    )
  				else:
  					__magic_name__ :					int  			=  self.pivot(self.tableau						,  _A						,  _A    )
  			return {}
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Tuple						,  _A	:		np.ndarray						,  _A	:		list[str]    )						->				dict[str, float]:
  			__magic_name__ :					Optional[int]  			=  {'P': abs(tableau[0, -1]    )}
  
  			for i in range(self.n_vars    ):
  				# Gives ids of nonzero entries in the ith column
  				__magic_name__ :					List[str]  			=  np.nonzero(tableau[:, i]    )
  				__magic_name__ :					Dict  			=  len(nonzero[0]    )
  
  				# First entry in the nonzero ids
  				__magic_name__ :					Tuple  			=  nonzero[0][0]
  				__magic_name__ :					Union[str, Any]  			=  tableau[nonzero_rowidx, i]
  
  				# If there is only one nonzero value in column, which is one
  				if n_nonzero == nonzero_val == 1:
  					__magic_name__ :					List[Any]  			=  tableau[nonzero_rowidx, -1]
  					__magic_name__ :					Dict  			=  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()
style_context: 
  
  
  '''simple docstring'''
  
  import random
  import unittest
  
  import numpy as np
  import torch
  
  from diffusers import DDIMScheduler, LDMSuperResolutionPipeline, UNetaDModel, VQModel
  from diffusers.utils import PIL_INTERPOLATION, floats_tensor, load_image, slow, torch_device
  from diffusers.utils.testing_utils import enable_full_determinism, require_torch
  
  
  enable_full_determinism()
  class _lowerCamelCase (		unittest.TestCase							):
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		@property
  		def      __lowerCAmelCase	(      self	:		Union[str, Any]    )						->				List[Any]:
  			__magic_name__ :					Union[str, Any]  			=  1
  			__magic_name__ :					str  			=  3
  			__magic_name__ :					Optional[Any]  			=  (32, 32)
  
  			__magic_name__ :					Dict  			=  floats_tensor((batch_size, num_channels) + sizes						,  rng=random.Random(0    )    ).to(_A    )
  			return image
  
  
  
  
  
  
  
  		@property
  		def      __lowerCAmelCase	(      self	:		Optional[Any]    )						->				List[str]:
  			torch.manual_seed(0    )
  			__magic_name__ :					Dict  			=  UNetaDModel(
  			    block_out_channels=(32, 64)						,  layers_per_block=2						,  sample_size=32						,  in_channels=6						,  out_channels=3						,  down_block_types=('DownBlock2D', 'AttnDownBlock2D')						,  up_block_types=('AttnUpBlock2D', 'UpBlock2D')						,  )
  			return model
  
  
  
  
  
  
  
  		@property
  		def      __lowerCAmelCase	(      self	:		Any    )						->				Optional[int]:
  			torch.manual_seed(0    )
  			__magic_name__ :					Union[str, Any]  			=  VQModel(
  			    block_out_channels=[32, 64]						,  in_channels=3						,  out_channels=3						,  down_block_types=['DownEncoderBlock2D', 'DownEncoderBlock2D']						,  up_block_types=['UpDecoderBlock2D', 'UpDecoderBlock2D']						,  latent_channels=3						,  )
  			return model
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Optional[int]    )						->				int:
  			__magic_name__ :					Dict  			=  'cpu'
  			__magic_name__ :					str  			=  self.dummy_uncond_unet
  			__magic_name__ :					Optional[int]  			=  DDIMScheduler()
  			__magic_name__ :					Optional[Any]  			=  self.dummy_vq_model
  
  			__magic_name__ :					Tuple  			=  LDMSuperResolutionPipeline(unet=_A						,  vqvae=_A						,  scheduler=_A    )
  			ldm.to(_A    )
  			ldm.set_progress_bar_config(disable=_A    )
  
  			__magic_name__ :					Optional[int]  			=  self.dummy_image.to(_A    )
  
  			__magic_name__ :					List[Any]  			=  torch.Generator(device=_A    ).manual_seed(0    )
  			__magic_name__ :					str  			=  ldm(image=_A						,  generator=_A						,  num_inference_steps=2						,  output_type='numpy'    ).images
  
  			__magic_name__ :					List[Any]  			=  image[0, -3:, -3:, -1]
  
  			assert image.shape == (1, 64, 64, 3)
  			__magic_name__ :					Optional[Any]  			=  np.array([0.8678, 0.8245, 0.6381, 0.6830, 0.4385, 0.5599, 0.4641, 0.6201, 0.5150]    )
  
  			assert np.abs(image_slice.flatten() - expected_slice    ).max() < 1E-2
  
  
  
  
  
  
  
  		@unittest.skipIf(torch_device != 'cuda'						,  'This test requires a GPU'    )
  		def      __lowerCAmelCase	(      self	:		List[Any]    )						->				List[Any]:
  			__magic_name__ :					Union[str, Any]  			=  self.dummy_uncond_unet
  			__magic_name__ :					Tuple  			=  DDIMScheduler()
  			__magic_name__ :					Union[str, Any]  			=  self.dummy_vq_model
  
  			# put models in fp16
  			__magic_name__ :					Optional[int]  			=  unet.half()
  			__magic_name__ :					int  			=  vqvae.half()
  
  			__magic_name__ :					Optional[Any]  			=  LDMSuperResolutionPipeline(unet=_A						,  vqvae=_A						,  scheduler=_A    )
  			ldm.to(_A    )
  			ldm.set_progress_bar_config(disable=_A    )
  
  			__magic_name__ :					str  			=  self.dummy_image.to(_A    )
  
  			__magic_name__ :					Union[str, Any]  			=  ldm(_A						,  num_inference_steps=2						,  output_type='numpy'    ).images
  
  			assert image.shape == (1, 64, 64, 3)
  
  
  
  
  
  
  
  @slow
  @require_torch
  class _lowerCamelCase (		unittest.TestCase							):
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		str    )						->				Dict:
  			__magic_name__ :					Tuple  			=  load_image(
  			    'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'
  			    '/vq_diffusion/teddy_bear_pool.png'    )
  			__magic_name__ :					Dict  			=  init_image.resize((64, 64)						,  resample=PIL_INTERPOLATION['lanczos']    )
  
  			__magic_name__ :					List[Any]  			=  LDMSuperResolutionPipeline.from_pretrained('duongna/ldm-super-resolution'						,  device_map='auto'    )
  			ldm.set_progress_bar_config(disable=_A    )
  
  			__magic_name__ :					int  			=  torch.manual_seed(0    )
  			__magic_name__ :					Optional[Any]  			=  ldm(image=_A						,  generator=_A						,  num_inference_steps=20						,  output_type='numpy'    ).images
  
  			__magic_name__ :					List[str]  			=  image[0, -3:, -3:, -1]
  
  			assert image.shape == (1, 256, 256, 3)
  			__magic_name__ :					int  			=  np.array([0.7644, 0.7679, 0.7642, 0.7633, 0.7666, 0.7560, 0.7425, 0.7257, 0.6907]    )
  
  			assert np.abs(image_slice.flatten() - expected_slice    ).max() < 1E-2