


from typing import Any

import numpy as np



class 							a       :





     def __init__(     self       :					Union[str, Any]     ,						SCREAMING_SNAKE_CASE_       :					np.ndarray     ,						SCREAMING_SNAKE_CASE_       :					int				):





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

        __lowerCamelCase:					int	 =						tableau
        __lowerCamelCase ,  __lowerCamelCase:					Optional[int]	 =						tableau.shape

        # Number of decision variables x1, x2, x3...
        __lowerCamelCase:					Optional[int]	 =						n_vars

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

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

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

        # Objectives for each stage
        __lowerCamelCase:					Dict	 =						["""max"""]

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

        __lowerCamelCase:					List[Any]	 =						[""""""]

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

        # Does objective row only contain (non)-negative values?
        __lowerCamelCase:					List[Any]	 =						False





     @staticmethod
     def 			SCREAMING_SNAKE_CASE__							(     *SCREAMING_SNAKE_CASE_       :					int				):





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

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

        # decision | slack | artificial
        __lowerCamelCase:					Optional[int]	 =						["""x""", """s""", """a"""]
        __lowerCamelCase:					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 			SCREAMING_SNAKE_CASE__							(     self       :					Optional[Any]     ,						SCREAMING_SNAKE_CASE_       :					np.ndarray				):
        __lowerCamelCase:					int	 =						self.objectives[-1]

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

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

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

        # Array filled with nans
        __lowerCamelCase:					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
        __lowerCamelCase:					Dict	 =						np.divide(__UpperCamelCase     ,						__UpperCamelCase     ,						out=__UpperCamelCase     ,						where=divisor > 0				)

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





     def 			SCREAMING_SNAKE_CASE__							(     self       :					Tuple     ,						SCREAMING_SNAKE_CASE_       :					np.ndarray     ,						SCREAMING_SNAKE_CASE_       :					int     ,						SCREAMING_SNAKE_CASE_       :					int				):
        __lowerCamelCase:					Optional[Any]	 =						tableau[row_idx].copy()

        __lowerCamelCase:					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
        __lowerCamelCase:					int	 =						piv_row
        return tableau





     def 			SCREAMING_SNAKE_CASE__							(     self       :					int     ,						SCREAMING_SNAKE_CASE_       :					np.ndarray				):
        self.objectives.pop()

        if not self.objectives:
           return tableau

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

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

        # Delete the objective row of the first stage
        __lowerCamelCase:					str	 =						np.delete(__UpperCamelCase     ,						0     ,						axis=0				)

        __lowerCamelCase:					List[str]	 =						1
        self.n_rows -= 1
        __lowerCamelCase:					Any	 =						0
        __lowerCamelCase:					str	 =						False
        return tableau





     def 			SCREAMING_SNAKE_CASE__							(     self       :					Tuple				):





        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:
              __lowerCamelCase:					Tuple	 =						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				)

           __lowerCamelCase ,  __lowerCamelCase:					List[Any]	 =						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
              __lowerCamelCase:					int	 =						self.change_stage(self.tableau				)
           else:
              __lowerCamelCase:					Optional[Any]	 =						self.pivot(self.tableau     ,						__UpperCamelCase     ,						__UpperCamelCase				)
        return {}







     def 			SCREAMING_SNAKE_CASE__							(     self       :					Tuple     ,						SCREAMING_SNAKE_CASE_       :					np.ndarray     ,						SCREAMING_SNAKE_CASE_       :					list[str]				):
        __lowerCamelCase:					int	 =						{"""P""": abs(tableau[0, -1]				)}

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

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

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


if __name__ == "__main__":
   import doctest

   doctest.testmod()





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


A__							=				{"configuration_pegasus": ["PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP", "PegasusConfig"]}

try:
						if not is_sentencepiece_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A__							=				["PegasusTokenizer"]

try:
						if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A__							=				["PegasusTokenizerFast"]

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A__							=				[
						    "PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST",
						    "PegasusForCausalLM",
						    "PegasusForConditionalGeneration",
						    "PegasusModel",
						    "PegasusPreTrainedModel",
						]

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A__							=				[
						    "TFPegasusForConditionalGeneration",
						    "TFPegasusModel",
						    "TFPegasusPreTrainedModel",
						]

try:
						if not is_flax_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A__							=				[
						    "FlaxPegasusForConditionalGeneration",
						    "FlaxPegasusModel",
						    "FlaxPegasusPreTrainedModel",
						]


if TYPE_CHECKING:
						from .configuration_pegasus import PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP, PegasusConfig

						try:
												if not is_sentencepiece_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_pegasus import PegasusTokenizer

						try:
												if not is_tokenizers_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_pegasus_fast import PegasusTokenizerFast

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_pegasus import (
												    PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST,
												    PegasusForCausalLM,
												    PegasusForConditionalGeneration,
												    PegasusModel,
												    PegasusPreTrainedModel,
												)

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_pegasus import TFPegasusForConditionalGeneration, TFPegasusModel, TFPegasusPreTrainedModel

						try:
												if not is_flax_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_flax_pegasus import (
												    FlaxPegasusForConditionalGeneration,
												    FlaxPegasusModel,
												    FlaxPegasusPreTrainedModel,
												)

else:
						import sys

						A__							=				_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)




