




from typing import Any

import numpy as np

class 			_lowerCamelCase    :

      """simple docstring"""

      def __init__(  self       :			Optional[Any]			,							snake_case       :			np.ndarray			,							snake_case       :			int					):
          # Check if RHS is negative
          if np.any(tableau[:, -1]			,							where=tableau[:, -1] < 0					):
              raise ValueError('''RHS must be > 0'''					)

          __UpperCamelCase			=    tableau
          __UpperCamelCase		,   __UpperCamelCase			=    tableau.shape

          # Number of decision variables x1, x2, x3...
          __UpperCamelCase			=    n_vars

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

          # 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
          __UpperCamelCase			=    (self.n_art_vars > 0) + 1

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

          # Objectives for each stage
          __UpperCamelCase			=    ['''max''']

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

          __UpperCamelCase			=    ['''''']

          # Index of current pivot row and column
          __UpperCamelCase			=    None
          __UpperCamelCase			=    None

          # Does objective row only contain (non)-negative values?
          __UpperCamelCase			=    False







      @staticmethod
      def    snake_case						(  *snake_case       :			int					):
          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
          __UpperCamelCase			=    ['''x''', '''s''', '''a''']
          __UpperCamelCase			=    []
          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    snake_case						(  self       :			Any			,							snake_case       :			np.ndarray					):
          __UpperCamelCase			=    self.objectives[-1]

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

          # RHS
          __UpperCamelCase			=    tableau[s, -1]

          # Elements of pivot column within slice
          __UpperCamelCase			=    tableau[s, col_idx]

          # Array filled with nans
          __UpperCamelCase			=    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
          __UpperCamelCase			=    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
          __UpperCamelCase			=    np.nanargmin(lowerCamelCase__					) + self.n_stages
          return row_idx, col_idx







      def    snake_case						(  self       :			List[str]			,							snake_case       :			np.ndarray			,							snake_case       :			int			,							snake_case       :			int					):
          __UpperCamelCase			=    tableau[row_idx].copy()

          __UpperCamelCase			=    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
          __UpperCamelCase			=    piv_row
          return tableau







      def    snake_case						(  self       :			Optional[int]			,							snake_case       :			np.ndarray					):
          self.objectives.pop()

          if not self.objectives:
              return tableau

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

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

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

          __UpperCamelCase			=    1
          self.n_rows -= 1
          __UpperCamelCase			=    0
          __UpperCamelCase			=    False
          return tableau







      def    snake_case						(  self       :			Optional[int]					):
          # 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:
                  __UpperCamelCase			=    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					)

              __UpperCamelCase		,   __UpperCamelCase			=    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
                  __UpperCamelCase			=    self.change_stage(self.tableau					)
              else:
                  __UpperCamelCase			=    self.pivot(self.tableau			,							lowerCamelCase__			,							lowerCamelCase__					)
          return {}







      def    snake_case						(  self       :			List[str]			,							snake_case       :			np.ndarray			,							snake_case       :			list[str]					):
          __UpperCamelCase			=    {'''P''': abs(tableau[0, -1]					)}

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

              # First entry in the nonzero ids
              __UpperCamelCase			=    nonzero[0][0]
              __UpperCamelCase			=    tableau[nonzero_rowidx, i]

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







"""simple docstring"""






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_DEFAULT_MEAN,
    IMAGENET_DEFAULT_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    get_image_size,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
						import PIL


lowerCAmelCase__    :    Tuple			=      logging.get_logger(__name__)
class 							snake_case			(					__UpperCAmelCase							):




					"""simple docstring"""

					snake_case__							       =					["pixel_values"]







					def __init__(							self  :      str       ,lowerCamelCase__  :      bool = True       ,lowerCamelCase__  :      Dict[str, int] = None       ,lowerCamelCase__  :      bool = True       ,lowerCamelCase__  :      Dict[str, int] = None       ,lowerCamelCase__  :      PILImageResampling = PILImageResampling.BICUBIC       ,lowerCamelCase__  :      bool = True       ,lowerCamelCase__  :      Union[int, float] = 1 / 255       ,lowerCamelCase__  :      bool = True       ,lowerCamelCase__  :      Optional[Union[float, List[float]]] = None       ,lowerCamelCase__  :      Optional[Union[float, List[float]]] = None       ,**lowerCamelCase__  :      List[Any]       ,):
									super().__init__(**lowerCamelCase__     )
									UpperCAmelCase__			 =				crop_size if crop_size is not None else {'height': 256, 'width': 256}
									UpperCAmelCase__			 =				get_size_dict(lowerCamelCase__       ,param_name='crop_size'     )
									UpperCAmelCase__			 =				size if size is not None else {'height': 224, 'width': 224}
									UpperCAmelCase__			 =				get_size_dict(lowerCamelCase__     )

									UpperCAmelCase__			 =				do_center_crop
									UpperCAmelCase__			 =				crop_size
									UpperCAmelCase__			 =				do_resize
									UpperCAmelCase__			 =				size
									UpperCAmelCase__			 =				resample
									UpperCAmelCase__			 =				do_rescale
									UpperCAmelCase__			 =				rescale_factor
									UpperCAmelCase__			 =				do_normalize
									UpperCAmelCase__			 =				image_mean if image_mean is not None else IMAGENET_DEFAULT_MEAN
									UpperCAmelCase__			 =				image_std if image_std is not None else IMAGENET_DEFAULT_STD







					def 						__lowerCAmelCase		(							self  :      Optional[int]       ,lowerCamelCase__  :      np.ndarray       ,lowerCamelCase__  :      Dict[str, int]       ,lowerCamelCase__  :      Optional[int] = None       ,lowerCamelCase__  :      Optional[Union[str, ChannelDimension]] = None       ,**lowerCamelCase__  :      List[str]       ,):
									UpperCAmelCase__			 =				self.size if size is None else size
									UpperCAmelCase__			 =				get_size_dict(lowerCamelCase__     )
									UpperCAmelCase__			 =				get_size_dict(lowerCamelCase__       ,param_name='crop_size'     )

									UpperCAmelCase__ ,      UpperCAmelCase__			 =				get_image_size(lowerCamelCase__     )
									UpperCAmelCase__			 =				min(lowerCamelCase__       ,lowerCamelCase__     )
									UpperCAmelCase__			 =				(size['height'] / crop_size['height']) * min_dim
									UpperCAmelCase__			 =				(size['width'] / crop_size['width']) * min_dim
									return center_crop(lowerCamelCase__       ,size=(cropped_height, cropped_width)       ,data_format=lowerCamelCase__       ,**lowerCamelCase__     )







					def 						__lowerCAmelCase		(							self  :      Any       ,lowerCamelCase__  :      np.ndarray       ,lowerCamelCase__  :      Dict[str, int]       ,lowerCamelCase__  :      PILImageResampling = PIL.Image.BICUBIC       ,lowerCamelCase__  :      Optional[Union[str, ChannelDimension]] = None       ,**lowerCamelCase__  :      Any       ,):
									UpperCAmelCase__			 =				get_size_dict(lowerCamelCase__     )
									if "height" not in size or "width" not in size:
													raise ValueError(f'''The size dictionary must contain the keys \'height\' and \'width\'. Got {size.keys()}'''     )
									return resize(
									    lowerCamelCase__       ,size=(size['height'], size['width'])       ,resample=lowerCamelCase__       ,data_format=lowerCamelCase__       ,**lowerCamelCase__     )







					def 						__lowerCAmelCase		(							self  :      Optional[int]       ,lowerCamelCase__  :      np.ndarray       ,lowerCamelCase__  :      Union[int, float]       ,lowerCamelCase__  :      Optional[Union[str, ChannelDimension]] = None       ,**lowerCamelCase__  :      int       ,):
									return rescale(lowerCamelCase__       ,scale=lowerCamelCase__       ,data_format=lowerCamelCase__       ,**lowerCamelCase__     )







					def 						__lowerCAmelCase		(							self  :      int       ,lowerCamelCase__  :      np.ndarray       ,lowerCamelCase__  :      Union[float, List[float]]       ,lowerCamelCase__  :      Union[float, List[float]]       ,lowerCamelCase__  :      Optional[Union[str, ChannelDimension]] = None       ,**lowerCamelCase__  :      List[Any]       ,):
									return normalize(lowerCamelCase__       ,mean=lowerCamelCase__       ,std=lowerCamelCase__       ,data_format=lowerCamelCase__       ,**lowerCamelCase__     )







					def 						__lowerCAmelCase		(							self  :      Optional[Any]       ,lowerCamelCase__  :      ImageInput       ,lowerCamelCase__  :      Optional[bool] = None       ,lowerCamelCase__  :      Optional[Dict[str, int]] = None       ,lowerCamelCase__  :      Optional[bool] = None       ,lowerCamelCase__  :      Optional[Dict[str, int]] = None       ,lowerCamelCase__  :      PILImageResampling = None       ,lowerCamelCase__  :      Optional[bool] = None       ,lowerCamelCase__  :      Optional[float] = None       ,lowerCamelCase__  :      Optional[bool] = None       ,lowerCamelCase__  :      Optional[Union[float, List[float]]] = None       ,lowerCamelCase__  :      Optional[Union[float, List[float]]] = None       ,lowerCamelCase__  :      Optional[Union[str, TensorType]] = None       ,lowerCamelCase__  :      ChannelDimension = ChannelDimension.FIRST       ,**lowerCamelCase__  :      Optional[int]       ,):
									UpperCAmelCase__			 =				do_center_crop if do_center_crop is not None else self.do_center_crop
									UpperCAmelCase__			 =				crop_size if crop_size is not None else self.crop_size
									UpperCAmelCase__			 =				get_size_dict(lowerCamelCase__       ,param_name='crop_size'     )
									UpperCAmelCase__			 =				do_resize if do_resize is not None else self.do_resize
									UpperCAmelCase__			 =				size if size is not None else self.size
									UpperCAmelCase__			 =				get_size_dict(lowerCamelCase__     )
									UpperCAmelCase__			 =				resample if resample is not None else self.resample
									UpperCAmelCase__			 =				do_rescale if do_rescale is not None else self.do_rescale
									UpperCAmelCase__			 =				rescale_factor if rescale_factor is not None else self.rescale_factor
									UpperCAmelCase__			 =				do_normalize if do_normalize is not None else self.do_normalize
									UpperCAmelCase__			 =				image_mean if image_mean is not None else self.image_mean
									UpperCAmelCase__			 =				image_std if image_std is not None else self.image_std

									UpperCAmelCase__			 =				make_list_of_images(lowerCamelCase__     )

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

									if do_center_crop and crop_size is None:
													raise ValueError('If `do_center_crop` is set to `True`, `crop_size` must be provided.'     )

									if do_resize and size is None:
													raise ValueError('Size must be specified if do_resize 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 image standard deviation must be specified if do_normalize is True.'     )

									# All transformations expect numpy arrays.
									UpperCAmelCase__			 =				[to_numpy_array(lowerCamelCase__     ) for image in images]

									if do_center_crop:
													UpperCAmelCase__			 =				[self.center_crop(lowerCamelCase__       ,lowerCamelCase__       ,size=lowerCamelCase__     ) for image in images]

									if do_resize:
													UpperCAmelCase__			 =				[self.resize(image=lowerCamelCase__       ,size=lowerCamelCase__       ,resample=lowerCamelCase__     ) for image in images]

									if do_rescale:
													UpperCAmelCase__			 =				[self.rescale(image=lowerCamelCase__       ,scale=lowerCamelCase__     ) for image in images]

									if do_normalize:
													UpperCAmelCase__			 =				[self.normalize(image=lowerCamelCase__       ,mean=lowerCamelCase__       ,std=lowerCamelCase__     ) for image in images]

									UpperCAmelCase__			 =				[to_channel_dimension_format(lowerCamelCase__       ,lowerCamelCase__     ) for image in images]

									UpperCAmelCase__			 =				{'pixel_values': images}
									return BatchFeature(data=lowerCamelCase__       ,tensor_type=lowerCamelCase__     )



