






"""simple docstring"""


from typing import Any

import numpy as np






class 						snake_case  :





    def __init__(							self	:					Tuple				,		A	:					np.ndarray				,		A	:					int			):


      '''simple docstring'''




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

      a     :			Dict				=   tableau
      a,     a     :			List[str]				=   tableau.shape

      # Number of decision variables x1, x2, x3...
      a     :			int				=   n_vars

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

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

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

      # Objectives for each stage
      a     :			Union[str, Any]				=   ['max']

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

      a     :			Optional[int]				=   ['']

      # Index of current pivot row and column
      a     :			Optional[Any]				=   None
      a     :			List[Any]				=   None

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





    @staticmethod
    def 				lowerCamelCase__      (							*A	:					int			):


      '''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     :			Optional[Any]				=   ['x', 's', 'a']
      a     :			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	:					Any				,		A	:					np.ndarray			):


      '''simple docstring'''




      a     :			Optional[Any]				=   self.objectives[-1]

      # Find entries of highest magnitude in objective rows
      a     :			List[Any]				=   (objective == 'min') - (objective == 'max')
      a     :			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:
        a     :			Optional[Any]				=   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     :			Any				=   slice(self.n_stages				,		self.n_rows			)

      # RHS
      a     :			Any				=   tableau[s, -1]

      # Elements of pivot column within slice
      a     :			Tuple				=   tableau[s, col_idx]

      # Array filled with nans
      a     :			Dict				=   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(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     :			Union[str, Any]				=   np.nanargmin(A			) + self.n_stages
      return row_idx, col_idx





    def 				lowerCamelCase__      (							self	:					List[Any]				,		A	:					np.ndarray				,		A	:					int				,		A	:					int			):


      '''simple docstring'''




      a     :			List[str]				=   tableau[row_idx].copy()

      a     :			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     :			List[str]				=   piv_row
      return tableau





    def 				lowerCamelCase__      (							self	:					Optional[int]				,		A	:					np.ndarray			):


      '''simple docstring'''




      self.objectives.pop()

      if not self.objectives:
        return tableau

      # Slice containing ids for artificial columns
      a     :			Union[str, Any]				=   slice(-self.n_art_vars - 1				,		-1			)

      # Delete the artificial variable columns
      a     :			Dict				=   np.delete(A				,		A				,		axis=1			)

      # Delete the objective row of the first stage
      a     :			List[str]				=   np.delete(A				,		0				,		axis=0			)

      a     :			Optional[Any]				=   1
      self.n_rows -= 1
      a     :			List[Any]				=   0
      a     :			Any				=   False
      return tableau





    def 				lowerCamelCase__      (							self	:					Union[str, Any]			):


      '''simple docstring'''




      for _ in range(1_0_0			):
        # Completion of each stage removes an objective. If both stages
        # are complete, then no objectives are left
        if not self.objectives:
          a     :			List[str]				=   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     :			int				=   self.change_stage(self.tableau			)
        else:
          a     :			Dict				=   self.pivot(self.tableau				,		A				,		A			)
      return {}





    def 				lowerCamelCase__      (							self	:					Optional[Any]				,		A	:					np.ndarray				,		A	:					list[str]			):


      '''simple docstring'''




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

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

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

        # If there is only one nonzero value in column, which is one
        if n_nonzero == nonzero_val == 1:
          a     :			Union[str, Any]				=   tableau[nonzero_rowidx, -1]
          a     :			List[Any]				=   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 torch

from diffusers import LMSDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest






class 						snake_case  (  UpperCAmelCase       ):
    __magic_name__         =     (LMSDiscreteScheduler,)
    __magic_name__         =     10





    def 				lowerCamelCase__      (							self	:					Any				,		**A	:					Dict			):


      '''simple docstring'''




      a     :			Optional[Any]				=   {
          'num_train_timesteps': 1_1_0_0,
          'beta_start': 0.00_01,
          'beta_end': 0.02,
          'beta_schedule': 'linear',
      }

      config.update(**A			)
      return config





    def 				lowerCamelCase__      (							self	:					Optional[int]			):


      '''simple docstring'''




      for timesteps in [1_0, 5_0, 1_0_0, 1_0_0_0]:
        self.check_over_configs(num_train_timesteps=A			)





    def 				lowerCamelCase__      (							self	:					List[str]			):


      '''simple docstring'''




      for beta_start, beta_end in zip([0.0_00_01, 0.00_01, 0.0_01]				,		[0.00_02, 0.0_02, 0.02]			):
        self.check_over_configs(beta_start=A				,		beta_end=A			)





    def 				lowerCamelCase__      (							self	:					List[Any]			):


      '''simple docstring'''




      for schedule in ["linear", "scaled_linear"]:
        self.check_over_configs(beta_schedule=A			)





    def 				lowerCamelCase__      (							self	:					Any			):


      '''simple docstring'''




      for prediction_type in ["epsilon", "v_prediction"]:
        self.check_over_configs(prediction_type=A			)





    def 				lowerCamelCase__      (							self	:					Dict			):


      '''simple docstring'''




      for t in [0, 5_0_0, 8_0_0]:
        self.check_over_forward(time_step=A			)





    def 				lowerCamelCase__      (							self	:					Any			):


      '''simple docstring'''




      a     :			Any				=   self.scheduler_classes[0]
      a     :			Dict				=   self.get_scheduler_config()
      a     :			str				=   scheduler_class(**A			)

      scheduler.set_timesteps(self.num_inference_steps			)

      a     :			List[Any]				=   self.dummy_model()
      a     :			str				=   self.dummy_sample_deter * scheduler.init_noise_sigma

      for i, t in enumerate(scheduler.timesteps			):
        a     :			int				=   scheduler.scale_model_input(A				,		A			)

        a     :			int				=   model(A				,		A			)

        a     :			Optional[int]				=   scheduler.step(A				,		A				,		A			)
        a     :			Union[str, Any]				=   output.prev_sample

      a     :			Any				=   torch.sum(torch.abs(A			)			)
      a     :			List[str]				=   torch.mean(torch.abs(A			)			)

      assert abs(result_sum.item() - 10_06.3_88			) < 1E-2
      assert abs(result_mean.item() - 1.31			) < 1E-3





    def 				lowerCamelCase__      (							self	:					Optional[int]			):


      '''simple docstring'''




      a     :			List[str]				=   self.scheduler_classes[0]
      a     :			Any				=   self.get_scheduler_config(prediction_type='v_prediction'			)
      a     :			str				=   scheduler_class(**A			)

      scheduler.set_timesteps(self.num_inference_steps			)

      a     :			Tuple				=   self.dummy_model()
      a     :			Tuple				=   self.dummy_sample_deter * scheduler.init_noise_sigma

      for i, t in enumerate(scheduler.timesteps			):
        a     :			Any				=   scheduler.scale_model_input(A				,		A			)

        a     :			List[str]				=   model(A				,		A			)

        a     :			Optional[int]				=   scheduler.step(A				,		A				,		A			)
        a     :			Tuple				=   output.prev_sample

      a     :			Optional[Any]				=   torch.sum(torch.abs(A			)			)
      a     :			Optional[int]				=   torch.mean(torch.abs(A			)			)

      assert abs(result_sum.item() - 0.00_17			) < 1E-2
      assert abs(result_mean.item() - 2.2676E-06			) < 1E-3





    def 				lowerCamelCase__      (							self	:					Tuple			):


      '''simple docstring'''




      a     :			Optional[Any]				=   self.scheduler_classes[0]
      a     :			Union[str, Any]				=   self.get_scheduler_config()
      a     :			Union[str, Any]				=   scheduler_class(**A			)

      scheduler.set_timesteps(self.num_inference_steps				,		device=A			)

      a     :			Optional[Any]				=   self.dummy_model()
      a     :			Dict				=   self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
      a     :			Union[str, Any]				=   sample.to(A			)

      for i, t in enumerate(scheduler.timesteps			):
        a     :			Optional[int]				=   scheduler.scale_model_input(A				,		A			)

        a     :			List[str]				=   model(A				,		A			)

        a     :			Optional[Any]				=   scheduler.step(A				,		A				,		A			)
        a     :			str				=   output.prev_sample

      a     :			Dict				=   torch.sum(torch.abs(A			)			)
      a     :			Tuple				=   torch.mean(torch.abs(A			)			)

      assert abs(result_sum.item() - 10_06.3_88			) < 1E-2
      assert abs(result_mean.item() - 1.31			) < 1E-3





    def 				lowerCamelCase__      (							self	:					Dict			):


      '''simple docstring'''




      a     :			Tuple				=   self.scheduler_classes[0]
      a     :			Dict				=   self.get_scheduler_config()
      a     :			Optional[Any]				=   scheduler_class(**A				,		use_karras_sigmas=A			)

      scheduler.set_timesteps(self.num_inference_steps				,		device=A			)

      a     :			Any				=   self.dummy_model()
      a     :			Union[str, Any]				=   self.dummy_sample_deter.to(A			) * scheduler.init_noise_sigma
      a     :			Any				=   sample.to(A			)

      for t in scheduler.timesteps:
        a     :			int				=   scheduler.scale_model_input(A				,		A			)

        a     :			Tuple				=   model(A				,		A			)

        a     :			List[Any]				=   scheduler.step(A				,		A				,		A			)
        a     :			int				=   output.prev_sample

      a     :			Tuple				=   torch.sum(torch.abs(A			)			)
      a     :			Any				=   torch.mean(torch.abs(A			)			)

      assert abs(result_sum.item() - 38_12.99_27			) < 2E-2
      assert abs(result_mean.item() - 4.96_48			) < 1E-3




