


from math import cos, sin



def 			_a      (    __UpperCamelCase			):
     a_     :  Tuple				      =     float(__UpperCamelCase			)
     return [[scaling_factor * int(x == y			) for x in range(2			)] for y in range(2			)]



def 			_a      (    __UpperCamelCase			):
     a_      ,      a_     :  List[Any]				      =     cos(__UpperCamelCase			), sin(__UpperCamelCase			)
     return [[c, -s], [s, c]]



def 			_a      (    __UpperCamelCase			):
     a_      ,      a_     :  Dict				      =     cos(__UpperCamelCase			), sin(__UpperCamelCase			)
     a_     :  List[Any]				      =     c * s
     return [[c * c, cs], [cs, s * s]]



def 			_a      (    __UpperCamelCase			):
     a_      ,      a_     :  Any				      =     cos(__UpperCamelCase			), sin(__UpperCamelCase			)
     a_     :  Optional[int]				      =     c * s
     return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(f'''    {scaling(5) = }''')
print(f'''  {rotation(45) = }''')
print(f'''{projection(45) = }''')
print(f'''{reflection(45) = }''')







import bisect
import copy
from collections import defaultdict

import numpy as np
from torch.utils.data import BatchSampler, Sampler

from utils import logger



def 			_a      (    __UpperCamelCase	,	__UpperCamelCase			):
     a_     :  Optional[Any]				      =     copy.deepcopy(__UpperCamelCase			)
     a_     :  Dict				      =     sorted(__UpperCamelCase			)
     a_     :  Dict				      =     [bisect.bisect_right(__UpperCamelCase	,	__UpperCamelCase			) for y in x]
     return quantized



def 			_a      (    __UpperCamelCase	,	__UpperCamelCase=0			):
     a_     :  str				      =     np.arange(start=3	,	stop=__UpperCamelCase	,	step=4			).tolist() if k > 0 else [1_0]
     a_     :  Any				      =     _quantize(__UpperCamelCase	,	__UpperCamelCase			)
     # count number of elements per group
     a_     :  Optional[int]				      =     np.unique(__UpperCamelCase	,	return_counts=__UpperCamelCase			)[1]
     a_     :  List[str]				      =     [0] + bins + [np.inf]
     logger.info("""Using {} as bins for aspect lengths quantization""".format(__UpperCamelCase			)			)
     logger.info("""Count of instances per bin: {}""".format(__UpperCamelCase			)			)
     return groups


class 	a__						(    lowerCAmelCase_     ):

       def __init__( self   :  int   ,				lowerCamelCase_   :  str   ,				lowerCamelCase_   :  int   ,				lowerCamelCase_   :  str     ):
            if not isinstance(lowerCamelCase_   ,				lowerCamelCase_     ):
                 raise ValueError(
                     """sampler should be an instance of torch.utils.data.Sampler, but got sampler={}""".format(lowerCamelCase_     )     )
            a_     :  Optional[Any]				      =     sampler
            a_     :  List[Any]				      =     group_ids
            a_     :  Tuple				      =     batch_size

       def __iter__( self   :  Dict     ):
            a_     :  Tuple				      =     defaultdict(lowerCamelCase_     )
            a_     :  Any				      =     defaultdict(lowerCamelCase_     )

            a_     :  Any				      =     0
            for idx in self.sampler:
                 a_     :  str				      =     self.group_ids[idx]
                 buffer_per_group[group_id].append(lowerCamelCase_     )
                 samples_per_group[group_id].append(lowerCamelCase_     )
                 if len(buffer_per_group[group_id]     ) == self.batch_size:
                      yield buffer_per_group[group_id]  # TODO
                      num_batches += 1
                      del buffer_per_group[group_id]
                 assert len(buffer_per_group[group_id]     ) < self.batch_size

            # now we have run out of elements that satisfy
            # the group criteria, let's return the remaining
            # elements so that the size of the sampler is
            # deterministic
            a_     :  Optional[Any]				      =     len(self     )
            a_     :  Any				      =     expected_num_batches - num_batches
            if num_remaining > 0:
                 # for the remaining batches, group the batches by similar lengths
                 a_     :  str				      =     []
                 for group_id, idxs in sorted(buffer_per_group.items()   ,				key=lambda lowerCamelCase_     : x[0]     ):
                      batch_idx.extend(lowerCamelCase_     )
                      if len(lowerCamelCase_     ) >= self.batch_size:
                           yield batch_idx[: self.batch_size]
                           a_     :  Union[str, Any]				      =     batch_idx[self.batch_size :]
                           num_remaining -= 1
                 if len(lowerCamelCase_     ) > 0:
                      yield batch_idx
                      num_remaining -= 1
            assert num_remaining == 0

       def __len__( self   :  List[Any]     ):
            return (len(self.sampler     ) + self.batch_size - 1) // self.batch_size



