

from typing import Any

import numpy as np
class 	_A						:

  def __init__(			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE   ):





        """simple docstring"""







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

        SCREAMING_SNAKE_CASE_			:					Dict          =       tableau
        SCREAMING_SNAKE_CASE_    ,  SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       tableau.shape

        # Number of decision variables x1, x2, x3...
        SCREAMING_SNAKE_CASE_			:					Tuple          =       n_vars

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

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

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

        # Objectives for each stage
        SCREAMING_SNAKE_CASE_			:					Any          =       ['max']

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

        SCREAMING_SNAKE_CASE_			:					int          =       ['']

        # Index of current pivot row and column
        SCREAMING_SNAKE_CASE_			:					List[str]          =       None
        SCREAMING_SNAKE_CASE_			:					List[str]          =       None

        # Does objective row only contain (non)-negative values?
        SCREAMING_SNAKE_CASE_			:					Optional[int]          =       False

  @staticmethod
  def 	UpperCAmelCase      (			*_SCREAMING_SNAKE_CASE   ):





        """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
        SCREAMING_SNAKE_CASE_			:					Any          =       ['x', 's', 'a']
        SCREAMING_SNAKE_CASE_			:					int          =       []
        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	,   _SCREAMING_SNAKE_CASE   ):





        """simple docstring"""







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

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

        # RHS
        SCREAMING_SNAKE_CASE_			:					int          =       tableau[s, -1]

        # Elements of pivot column within slice
        SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       tableau[s, col_idx]

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

  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE   ):





        """simple docstring"""







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

        SCREAMING_SNAKE_CASE_			:					List[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
        SCREAMING_SNAKE_CASE_			:					Any          =       piv_row
        return tableau

  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE   ):





        """simple docstring"""







        self.objectives.pop()

        if not self.objectives:
              return tableau

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

        # Delete the artificial variable columns
        SCREAMING_SNAKE_CASE_			:					str          =       np.delete(lowerCamelCase__	,   lowerCamelCase__	,   axis=1   )

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

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

  def 	UpperCAmelCase      (			self   ):





        """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:
                    SCREAMING_SNAKE_CASE_			:					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   )

              SCREAMING_SNAKE_CASE_    ,  SCREAMING_SNAKE_CASE_			:					Optional[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
                    SCREAMING_SNAKE_CASE_			:					Dict          =       self.change_stage(self.tableau   )
              else:
                    SCREAMING_SNAKE_CASE_			:					Dict          =       self.pivot(self.tableau	,   lowerCamelCase__	,   lowerCamelCase__   )
        return {}



  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE   ):





        """simple docstring"""







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

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

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

              # If there is only one nonzero value in column, which is one
              if n_nonzero == nonzero_val == 1:
                    SCREAMING_SNAKE_CASE_			:					Dict          =       tableau[nonzero_rowidx, -1]
                    SCREAMING_SNAKE_CASE_			:					List[str]          =       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()









from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import center_crop, normalize, rescale, resize, to_channel_dimension_format
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
    import PIL


lowerCAmelCase       :				Dict         =					logging.get_logger(__name__)
class 	_A						(					__magic_name__):
  SCREAMING_SNAKE_CASE      : Any    =					['''pixel_values''']

  def __init__(			self	,   _SCREAMING_SNAKE_CASE = True	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = PIL.Image.NEAREST	,   _SCREAMING_SNAKE_CASE = False	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = 1 / 255	,   _SCREAMING_SNAKE_CASE = False	,   _SCREAMING_SNAKE_CASE = True	,   _SCREAMING_SNAKE_CASE = True	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = True	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        super().__init__(**_SCREAMING_SNAKE_CASE   )
        SCREAMING_SNAKE_CASE_			:					str          =       size if size is not None else {'height': 346, 'width': 346}
        SCREAMING_SNAKE_CASE_			:					str          =       get_size_dict(_SCREAMING_SNAKE_CASE   )
        SCREAMING_SNAKE_CASE_			:					int          =       crop_size if crop_size is not None else {'height': 289, 'width': 289}
        SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       get_size_dict(_SCREAMING_SNAKE_CASE	,   param_name='crop_size'   )

        SCREAMING_SNAKE_CASE_			:					List[str]          =       do_resize
        SCREAMING_SNAKE_CASE_			:					int          =       size
        SCREAMING_SNAKE_CASE_			:					Tuple          =       resample
        SCREAMING_SNAKE_CASE_			:					int          =       do_center_crop
        SCREAMING_SNAKE_CASE_			:					List[str]          =       crop_size
        SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       do_rescale
        SCREAMING_SNAKE_CASE_			:					Optional[int]          =       rescale_factor
        SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       rescale_offset
        SCREAMING_SNAKE_CASE_			:					Dict          =       do_normalize
        SCREAMING_SNAKE_CASE_			:					str          =       image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
        SCREAMING_SNAKE_CASE_			:					List[str]          =       image_std if image_std is not None else IMAGENET_STANDARD_STD
        SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       include_top

  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE = PIL.Image.NEAREST	,   _SCREAMING_SNAKE_CASE = None	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        SCREAMING_SNAKE_CASE_			:					str          =       get_size_dict(_SCREAMING_SNAKE_CASE   )
        if "height" not in size or "width" not in size:
              raise ValueError(f"The size dictionary must have keys 'height' and 'width'. Got {size.keys()}"   )
        return resize(
            _SCREAMING_SNAKE_CASE	,   size=(size['height'], size['width'])	,   resample=_SCREAMING_SNAKE_CASE	,   data_format=_SCREAMING_SNAKE_CASE	,   **_SCREAMING_SNAKE_CASE   )

  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE = None	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        SCREAMING_SNAKE_CASE_			:					Tuple          =       get_size_dict(_SCREAMING_SNAKE_CASE   )
        if "height" not in size or "width" not in size:
              raise ValueError(f"The size dictionary must have keys 'height' and 'width'. Got {size.keys()}"   )
        return center_crop(_SCREAMING_SNAKE_CASE	,   size=(size['height'], size['width'])	,   data_format=_SCREAMING_SNAKE_CASE	,   **_SCREAMING_SNAKE_CASE   )

  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE = True	,   _SCREAMING_SNAKE_CASE = None	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        if offset:
              SCREAMING_SNAKE_CASE_			:					Dict          =       (image - 127.5) * scale
              if data_format is not None:
                    SCREAMING_SNAKE_CASE_			:					Tuple          =       to_channel_dimension_format(_SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE   )
              SCREAMING_SNAKE_CASE_			:					int          =       rescaled_image.astype(np.floataa   )
        else:
              SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       rescale(_SCREAMING_SNAKE_CASE	,   scale=_SCREAMING_SNAKE_CASE	,   data_format=_SCREAMING_SNAKE_CASE	,   **_SCREAMING_SNAKE_CASE   )
        return rescaled_image

  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE = None	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        return normalize(_SCREAMING_SNAKE_CASE	,   mean=_SCREAMING_SNAKE_CASE	,   std=_SCREAMING_SNAKE_CASE	,   data_format=_SCREAMING_SNAKE_CASE	,   **_SCREAMING_SNAKE_CASE   )



  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE=None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = ChannelDimension.FIRST	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        SCREAMING_SNAKE_CASE_			:					List[Any]          =       do_resize if do_resize is not None else self.do_resize
        SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       resample if resample is not None else self.resample
        SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       do_center_crop if do_center_crop is not None else self.do_center_crop
        SCREAMING_SNAKE_CASE_			:					Optional[int]          =       do_rescale if do_rescale is not None else self.do_rescale
        SCREAMING_SNAKE_CASE_			:					int          =       rescale_factor if rescale_factor is not None else self.rescale_factor
        SCREAMING_SNAKE_CASE_			:					Tuple          =       rescale_offset if rescale_offset is not None else self.rescale_offset
        SCREAMING_SNAKE_CASE_			:					Dict          =       do_normalize if do_normalize is not None else self.do_normalize
        SCREAMING_SNAKE_CASE_			:					str          =       image_mean if image_mean is not None else self.image_mean
        SCREAMING_SNAKE_CASE_			:					List[Any]          =       image_std if image_std is not None else self.image_std
        SCREAMING_SNAKE_CASE_			:					List[Any]          =       include_top if include_top is not None else self.include_top

        SCREAMING_SNAKE_CASE_			:					Optional[int]          =       size if size is not None else self.size
        SCREAMING_SNAKE_CASE_			:					Tuple          =       get_size_dict(_SCREAMING_SNAKE_CASE   )
        SCREAMING_SNAKE_CASE_			:					Any          =       crop_size if crop_size is not None else self.crop_size
        SCREAMING_SNAKE_CASE_			:					Optional[int]          =       get_size_dict(_SCREAMING_SNAKE_CASE	,   param_name='crop_size'   )

        SCREAMING_SNAKE_CASE_			:					List[str]          =       make_list_of_images(_SCREAMING_SNAKE_CASE   )

        if not valid_images(_SCREAMING_SNAKE_CASE   ):
              raise ValueError(
                  'Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, '
                  'torch.Tensor, tf.Tensor or jax.ndarray.'   )

        if do_resize and size is None or resample is None:
              raise ValueError('Size and resample must be specified if do_resize is True.'   )

        if do_center_crop and crop_size is None:
              raise ValueError('Crop size must be specified if do_center_crop is True.'   )

        if do_rescale and rescale_factor is None:
              raise ValueError('Rescale factor must be specified if do_rescale is True.'   )

        if do_normalize and (image_mean is None or image_std is None):
              raise ValueError('Image mean and std must be specified if do_normalize is True.'   )

        # All transformations expect numpy arrays.
        SCREAMING_SNAKE_CASE_			:					int          =       [to_numpy_array(_SCREAMING_SNAKE_CASE   ) for image in images]

        if do_resize:
              SCREAMING_SNAKE_CASE_			:					Dict          =       [self.resize(image=_SCREAMING_SNAKE_CASE	,   size=_SCREAMING_SNAKE_CASE	,   resample=_SCREAMING_SNAKE_CASE   ) for image in images]

        if do_center_crop:
              SCREAMING_SNAKE_CASE_			:					str          =       [self.center_crop(image=_SCREAMING_SNAKE_CASE	,   size=_SCREAMING_SNAKE_CASE   ) for image in images]

        if do_rescale:
              SCREAMING_SNAKE_CASE_			:					Tuple          =       [self.rescale(image=_SCREAMING_SNAKE_CASE	,   scale=_SCREAMING_SNAKE_CASE	,   offset=_SCREAMING_SNAKE_CASE   ) for image in images]

        if do_normalize:
              SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       [self.normalize(image=_SCREAMING_SNAKE_CASE	,   mean=_SCREAMING_SNAKE_CASE	,   std=_SCREAMING_SNAKE_CASE   ) for image in images]

        if include_top:
              SCREAMING_SNAKE_CASE_			:					Dict          =       [self.normalize(image=_SCREAMING_SNAKE_CASE	,   mean=[0, 0, 0]	,   std=_SCREAMING_SNAKE_CASE   ) for image in images]

        SCREAMING_SNAKE_CASE_			:					Dict          =       [to_channel_dimension_format(_SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE   ) for image in images]

        SCREAMING_SNAKE_CASE_			:					Any          =       {'pixel_values': images}
        return BatchFeature(data=_SCREAMING_SNAKE_CASE	,   tensor_type=_SCREAMING_SNAKE_CASE   )






