

"""simple docstring"""




from math import isclose, sqrt

def 						A							(  snake_case__		,					snake_case__		,					snake_case__     ):




			'''simple docstring'''


			SCREAMING_SNAKE_CASE__										=   point_y / 4 / point_x
			SCREAMING_SNAKE_CASE__										=   2 * normal_gradient / (1 + normal_gradient * normal_gradient)
			SCREAMING_SNAKE_CASE__										=   (1 - normal_gradient * normal_gradient) / (
			    1 + normal_gradient * normal_gradient
			)
			SCREAMING_SNAKE_CASE__										=   (sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

			# to find the next point, solve the simultaeneous equations:
			# y^2 + 4x^2 = 100
			# y - b = m * (x - a)
			# ==> A x^2 + B x + C = 0
			SCREAMING_SNAKE_CASE__										=   outgoing_gradient**2 + 4
			SCREAMING_SNAKE_CASE__										=   2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
			SCREAMING_SNAKE_CASE__										=   (point_y - outgoing_gradient * point_x) ** 2 - 1_00

			SCREAMING_SNAKE_CASE__										=   (
			    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term     )
			) / (2 * quadratic_term)
			SCREAMING_SNAKE_CASE__										=   (
			    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term     )
			) / (2 * quadratic_term)

			# two solutions, one of which is our input point
			SCREAMING_SNAKE_CASE__										=   x_minus if isclose(snake_case__		,					snake_case__     ) else x_plus
			SCREAMING_SNAKE_CASE__										=   point_y + outgoing_gradient * (next_x - point_x)

			return next_x, next_y, outgoing_gradient

def 						A							(  snake_case__ = 1.4		,					snake_case__ = -9.6     ):




			'''simple docstring'''


			SCREAMING_SNAKE_CASE__										=   0
			SCREAMING_SNAKE_CASE__										=   first_x_coord
			SCREAMING_SNAKE_CASE__										=   first_y_coord
			SCREAMING_SNAKE_CASE__										=   (10.1 - point_y) / (0.0 - point_x)

			while not (-0.01 <= point_x <= 0.01 and point_y > 0):
						SCREAMING_SNAKE_CASE__				,		SCREAMING_SNAKE_CASE__				,		SCREAMING_SNAKE_CASE__										=   next_point(snake_case__		,					snake_case__		,					snake_case__     )
						num_reflections += 1

			return num_reflections


if __name__ == "__main__":
						print(F'{solution() = }')





"""simple docstring"""




import inspect
import unittest
import warnings

from transformers import DeiTConfig
from transformers.models.auto import get_values
from transformers.testing_utils import (
    require_accelerate,
    require_torch,
    require_torch_gpu,
    require_vision,
    slow,
    torch_device,
)
from transformers.utils import cached_property, is_torch_available, is_vision_available

from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, floats_tensor, ids_tensor
from ...test_pipeline_mixin import PipelineTesterMixin


if is_torch_available():
						import torch
						from torch import nn

						from transformers import (
						    MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING,
						    MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING,
						    MODEL_MAPPING,
						    DeiTForImageClassification,
						    DeiTForImageClassificationWithTeacher,
						    DeiTForMaskedImageModeling,
						    DeiTModel,
						)
						from transformers.models.deit.modeling_deit import DEIT_PRETRAINED_MODEL_ARCHIVE_LIST


if is_vision_available():
						from PIL import Image

						from transformers import DeiTImageProcessor





class  lowerCamelCase    :

			def __init__(       self					:    Tuple     ,					__UpperCAmelCase					:    Union[str, Any]     ,					__UpperCAmelCase					:    Any=1_3     ,					__UpperCAmelCase					:    Optional[Any]=3_0     ,					__UpperCAmelCase					:    List[Any]=2     ,					__UpperCAmelCase					:    Tuple=3     ,					__UpperCAmelCase					:    List[str]=True     ,					__UpperCAmelCase					:    List[Any]=True     ,					__UpperCAmelCase					:    Optional[int]=3_2     ,					__UpperCAmelCase					:    Any=5     ,					__UpperCAmelCase					:    str=4     ,					__UpperCAmelCase					:    Any=3_7     ,					__UpperCAmelCase					:    Dict="gelu"     ,					__UpperCAmelCase					:    Union[str, Any]=0.1     ,					__UpperCAmelCase					:    Optional[int]=0.1     ,					__UpperCAmelCase					:    Dict=1_0     ,					__UpperCAmelCase					:    int=0.02     ,					__UpperCAmelCase					:    Optional[Any]=3     ,					__UpperCAmelCase					:    List[str]=None     ,					__UpperCAmelCase					:    List[Any]=2     ,					) ->     Any:
						SCREAMING_SNAKE_CASE__										=   parent
						SCREAMING_SNAKE_CASE__										=   batch_size
						SCREAMING_SNAKE_CASE__										=   image_size
						SCREAMING_SNAKE_CASE__										=   patch_size
						SCREAMING_SNAKE_CASE__										=   num_channels
						SCREAMING_SNAKE_CASE__										=   is_training
						SCREAMING_SNAKE_CASE__										=   use_labels
						SCREAMING_SNAKE_CASE__										=   hidden_size
						SCREAMING_SNAKE_CASE__										=   num_hidden_layers
						SCREAMING_SNAKE_CASE__										=   num_attention_heads
						SCREAMING_SNAKE_CASE__										=   intermediate_size
						SCREAMING_SNAKE_CASE__										=   hidden_act
						SCREAMING_SNAKE_CASE__										=   hidden_dropout_prob
						SCREAMING_SNAKE_CASE__										=   attention_probs_dropout_prob
						SCREAMING_SNAKE_CASE__										=   type_sequence_label_size
						SCREAMING_SNAKE_CASE__										=   initializer_range
						SCREAMING_SNAKE_CASE__										=   scope
						SCREAMING_SNAKE_CASE__										=   encoder_stride

						# in DeiT, the seq length equals the number of patches + 2 (we add 2 for the [CLS] and distilation tokens)
						SCREAMING_SNAKE_CASE__										=   (image_size // patch_size) ** 2
						SCREAMING_SNAKE_CASE__										=   num_patches + 2

			def        SCREAMING_SNAKE_CASE					(       self					:    str							) ->     Optional[int]:
						SCREAMING_SNAKE_CASE__										=   floats_tensor([self.batch_size, self.num_channels, self.image_size, self.image_size]							)

						SCREAMING_SNAKE_CASE__										=   None
						if self.use_labels:
									SCREAMING_SNAKE_CASE__										=   ids_tensor([self.batch_size]     ,					self.type_sequence_label_size							)

						SCREAMING_SNAKE_CASE__										=   self.get_config()

						return config, pixel_values, labels

			def        SCREAMING_SNAKE_CASE					(       self					:    List[str]							) ->     Optional[int]:
						return DeiTConfig(
						    image_size=self.image_size     ,					patch_size=self.patch_size     ,					num_channels=self.num_channels     ,					hidden_size=self.hidden_size     ,					num_hidden_layers=self.num_hidden_layers     ,					num_attention_heads=self.num_attention_heads     ,					intermediate_size=self.intermediate_size     ,					hidden_act=self.hidden_act     ,					hidden_dropout_prob=self.hidden_dropout_prob     ,					attention_probs_dropout_prob=self.attention_probs_dropout_prob     ,					is_decoder=__UpperCAmelCase     ,					initializer_range=self.initializer_range     ,					encoder_stride=self.encoder_stride     ,					)

			def        SCREAMING_SNAKE_CASE					(       self					:    int     ,					__UpperCAmelCase					:    Optional[Any]     ,					__UpperCAmelCase					:    Union[str, Any]     ,					__UpperCAmelCase					:    Any							) ->     Union[str, Any]:
						SCREAMING_SNAKE_CASE__										=   DeiTModel(config=__UpperCAmelCase							)
						model.to(__UpperCAmelCase							)
						model.eval()
						SCREAMING_SNAKE_CASE__										=   model(__UpperCAmelCase							)
						self.parent.assertEqual(result.last_hidden_state.shape     ,					(self.batch_size, self.seq_length, self.hidden_size)							)

			def        SCREAMING_SNAKE_CASE					(       self					:    List[str]     ,					__UpperCAmelCase					:    Any     ,					__UpperCAmelCase					:    Optional[Any]     ,					__UpperCAmelCase					:    str							) ->     Optional[Any]:
						SCREAMING_SNAKE_CASE__										=   DeiTForMaskedImageModeling(config=__UpperCAmelCase							)
						model.to(__UpperCAmelCase							)
						model.eval()
						SCREAMING_SNAKE_CASE__										=   model(__UpperCAmelCase							)
						self.parent.assertEqual(
						    result.reconstruction.shape     ,					(self.batch_size, self.num_channels, self.image_size, self.image_size)							)

						# test greyscale images
						SCREAMING_SNAKE_CASE__										=   1
						SCREAMING_SNAKE_CASE__										=   DeiTForMaskedImageModeling(__UpperCAmelCase							)
						model.to(__UpperCAmelCase							)
						model.eval()

						SCREAMING_SNAKE_CASE__										=   floats_tensor([self.batch_size, 1, self.image_size, self.image_size]							)
						SCREAMING_SNAKE_CASE__										=   model(__UpperCAmelCase							)
						self.parent.assertEqual(result.reconstruction.shape     ,					(self.batch_size, 1, self.image_size, self.image_size)							)

			def        SCREAMING_SNAKE_CASE					(       self					:    Dict     ,					__UpperCAmelCase					:    List[Any]     ,					__UpperCAmelCase					:    Any     ,					__UpperCAmelCase					:    Optional[int]							) ->     List[Any]:
						SCREAMING_SNAKE_CASE__										=   self.type_sequence_label_size
						SCREAMING_SNAKE_CASE__										=   DeiTForImageClassification(__UpperCAmelCase							)
						model.to(__UpperCAmelCase							)
						model.eval()
						SCREAMING_SNAKE_CASE__										=   model(__UpperCAmelCase     ,					labels=__UpperCAmelCase							)
						self.parent.assertEqual(result.logits.shape     ,					(self.batch_size, self.type_sequence_label_size)							)

						# test greyscale images
						SCREAMING_SNAKE_CASE__										=   1
						SCREAMING_SNAKE_CASE__										=   DeiTForImageClassification(__UpperCAmelCase							)
						model.to(__UpperCAmelCase							)
						model.eval()

						SCREAMING_SNAKE_CASE__										=   floats_tensor([self.batch_size, 1, self.image_size, self.image_size]							)
						SCREAMING_SNAKE_CASE__										=   model(__UpperCAmelCase     ,					labels=__UpperCAmelCase							)
						self.parent.assertEqual(result.logits.shape     ,					(self.batch_size, self.type_sequence_label_size)							)





			def        SCREAMING_SNAKE_CASE					(       self					:    Optional[int]							) ->     Dict:
						SCREAMING_SNAKE_CASE__										=   self.prepare_config_and_inputs()
						(
						    (
						    SCREAMING_SNAKE_CASE__
						)				,		(
						    SCREAMING_SNAKE_CASE__
						)				,		(
						    SCREAMING_SNAKE_CASE__
						)				,		
						)										=   config_and_inputs
						SCREAMING_SNAKE_CASE__										=   {"""pixel_values""": pixel_values}
						return config, inputs_dict





@require_torch
class  lowerCamelCase    (A__      ,A__      ,unittest.TestCase      ):
			lowerCamelCase__ :		Any       		=				(
			    (
			        DeiTModel,
			        DeiTForImageClassification,
			        DeiTForImageClassificationWithTeacher,
			        DeiTForMaskedImageModeling,
			    )
			    if is_torch_available()
			    else ()
			)
			lowerCamelCase__ :		Tuple       		=				(
			    {
			        'feature-extraction': DeiTModel,
			        'image-classification': (DeiTForImageClassification, DeiTForImageClassificationWithTeacher),
			    }
			    if is_torch_available()
			    else {}
			)

			lowerCamelCase__ :		List[str]       		=				False
			lowerCamelCase__ :		Optional[Any]       		=				False
			lowerCamelCase__ :		Optional[int]       		=				False

			def        SCREAMING_SNAKE_CASE					(       self					:    Optional[Any]							) ->     int:
						SCREAMING_SNAKE_CASE__										=   DeiTModelTester(self							)
						SCREAMING_SNAKE_CASE__										=   ConfigTester(self     ,					config_class=__UpperCAmelCase     ,					has_text_modality=__UpperCAmelCase     ,					hidden_size=3_7							)

			def        SCREAMING_SNAKE_CASE					(       self					:    Tuple							) ->     Optional[int]:
						self.config_tester.run_common_tests()

			@unittest.skip(reason="""DeiT does not use inputs_embeds"""							)
			def        SCREAMING_SNAKE_CASE					(       self					:    int							) ->     Tuple:
						pass

			def        SCREAMING_SNAKE_CASE					(       self					:    Optional[int]							) ->     str:
						SCREAMING_SNAKE_CASE__				,		SCREAMING_SNAKE_CASE__										=   self.model_tester.prepare_config_and_inputs_for_common()

						for model_class in self.all_model_classes:
									SCREAMING_SNAKE_CASE__										=   model_class(__UpperCAmelCase							)
									self.assertIsInstance(model.get_input_embeddings()     ,					(nn.Module)							)
									SCREAMING_SNAKE_CASE__										=   model.get_output_embeddings()
									self.assertTrue(x is None or isinstance(__UpperCAmelCase     ,					nn.Linear							)							)

			def        SCREAMING_SNAKE_CASE					(       self					:    int							) ->     int:
						SCREAMING_SNAKE_CASE__				,		SCREAMING_SNAKE_CASE__										=   self.model_tester.prepare_config_and_inputs_for_common()

						for model_class in self.all_model_classes:
									SCREAMING_SNAKE_CASE__										=   model_class(__UpperCAmelCase							)
									SCREAMING_SNAKE_CASE__										=   inspect.signature(model.forward							)
									# signature.parameters is an OrderedDict => so arg_names order is deterministic
									SCREAMING_SNAKE_CASE__										=   [*signature.parameters.keys()]

									SCREAMING_SNAKE_CASE__										=   ["""pixel_values"""]
									self.assertListEqual(arg_names[:1]     ,					__UpperCAmelCase							)

			def        SCREAMING_SNAKE_CASE					(       self					:    List[Any]							) ->     Dict:
						SCREAMING_SNAKE_CASE__										=   self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_model(*__UpperCAmelCase							)

			def        SCREAMING_SNAKE_CASE					(       self					:    Optional[int]							) ->     int:
						SCREAMING_SNAKE_CASE__										=   self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_for_masked_image_modeling(*__UpperCAmelCase							)

			def        SCREAMING_SNAKE_CASE					(       self					:    str							) ->     Dict:
						SCREAMING_SNAKE_CASE__										=   self.model_tester.prepare_config_and_inputs()
						self.model_tester.create_and_check_for_image_classification(*__UpperCAmelCase							)

			def        SCREAMING_SNAKE_CASE					(       self					:    List[Any]     ,					__UpperCAmelCase					:    Dict     ,					__UpperCAmelCase					:    Optional[int]     ,					__UpperCAmelCase					:    List[Any]=False							) ->     str:
						SCREAMING_SNAKE_CASE__										=   super()._prepare_for_class(__UpperCAmelCase     ,					__UpperCAmelCase     ,					return_labels=__UpperCAmelCase							)

						if return_labels:
									if model_class.__name__ == "DeiTForImageClassificationWithTeacher":
												del inputs_dict["labels"]

						return inputs_dict

			def        SCREAMING_SNAKE_CASE					(       self					:    Union[str, Any]							) ->     Union[str, Any]:
						if not self.model_tester.is_training:
									return

						SCREAMING_SNAKE_CASE__				,		SCREAMING_SNAKE_CASE__										=   self.model_tester.prepare_config_and_inputs_for_common()
						SCREAMING_SNAKE_CASE__										=   True

						for model_class in self.all_model_classes:
									# DeiTForImageClassificationWithTeacher supports inference-only
									if (
									    model_class in get_values(__UpperCAmelCase							)
									    or model_class.__name__ == "DeiTForImageClassificationWithTeacher"
									):
												continue
									SCREAMING_SNAKE_CASE__										=   model_class(__UpperCAmelCase							)
									model.to(__UpperCAmelCase							)
									model.train()
									SCREAMING_SNAKE_CASE__										=   self._prepare_for_class(__UpperCAmelCase     ,					__UpperCAmelCase     ,					return_labels=__UpperCAmelCase							)
									SCREAMING_SNAKE_CASE__										=   model(**__UpperCAmelCase							).loss
									loss.backward()

			def        SCREAMING_SNAKE_CASE					(       self					:    int							) ->     Dict:
						SCREAMING_SNAKE_CASE__				,		SCREAMING_SNAKE_CASE__										=   self.model_tester.prepare_config_and_inputs_for_common()
						if not self.model_tester.is_training:
									return

						SCREAMING_SNAKE_CASE__										=   False
						SCREAMING_SNAKE_CASE__										=   True

						for model_class in self.all_model_classes:
									if model_class in get_values(__UpperCAmelCase							) or not model_class.supports_gradient_checkpointing:
												continue
									# DeiTForImageClassificationWithTeacher supports inference-only
									if model_class.__name__ == "DeiTForImageClassificationWithTeacher":
												continue
									SCREAMING_SNAKE_CASE__										=   model_class(__UpperCAmelCase							)
									model.gradient_checkpointing_enable()
									model.to(__UpperCAmelCase							)
									model.train()
									SCREAMING_SNAKE_CASE__										=   self._prepare_for_class(__UpperCAmelCase     ,					__UpperCAmelCase     ,					return_labels=__UpperCAmelCase							)
									SCREAMING_SNAKE_CASE__										=   model(**__UpperCAmelCase							).loss
									loss.backward()

			def        SCREAMING_SNAKE_CASE					(       self					:    Union[str, Any]							) ->     Any:
						SCREAMING_SNAKE_CASE__				,		SCREAMING_SNAKE_CASE__										=   self.model_tester.prepare_config_and_inputs_for_common()

						SCREAMING_SNAKE_CASE__										=   [
						    {"""title""": """multi_label_classification""", """num_labels""": 2, """dtype""": torch.float},
						    {"""title""": """single_label_classification""", """num_labels""": 1, """dtype""": torch.long},
						    {"""title""": """regression""", """num_labels""": 1, """dtype""": torch.float},
						]

						for model_class in self.all_model_classes:
									if (
									    model_class
									    not in [
									        *get_values(__UpperCAmelCase							),
									        *get_values(__UpperCAmelCase							),
									    ]
									    or model_class.__name__ == "DeiTForImageClassificationWithTeacher"
									):
												continue

									for problem_type in problem_types:
												with self.subTest(msg=F"""Testing {model_class} with {problem_type["title"]}"""							):
															SCREAMING_SNAKE_CASE__										=   problem_type["""title"""]
															SCREAMING_SNAKE_CASE__										=   problem_type["""num_labels"""]

															SCREAMING_SNAKE_CASE__										=   model_class(__UpperCAmelCase							)
															model.to(__UpperCAmelCase							)
															model.train()

															SCREAMING_SNAKE_CASE__										=   self._prepare_for_class(__UpperCAmelCase     ,					__UpperCAmelCase     ,					return_labels=__UpperCAmelCase							)

															if problem_type["num_labels"] > 1:
																		SCREAMING_SNAKE_CASE__										=   inputs["""labels"""].unsqueeze(1							).repeat(1     ,					problem_type["""num_labels"""]							)

															SCREAMING_SNAKE_CASE__										=   inputs["""labels"""].to(problem_type["""dtype"""]							)

															# This tests that we do not trigger the warning form PyTorch "Using a target size that is different
															# to the input size. This will likely lead to incorrect results due to broadcasting. Please ensure
															# they have the same size." which is a symptom something in wrong for the regression problem.
															# See https://github.com/huggingface/transformers/issues/11780
															with warnings.catch_warnings(record=__UpperCAmelCase							) as warning_list:
																		SCREAMING_SNAKE_CASE__										=   model(**__UpperCAmelCase							).loss
															for w in warning_list:
																		if "Using a target size that is different to the input size" in str(w.message							):
																					raise ValueError(
																					    F"""Something is going wrong in the regression problem: intercepted {w.message}"""							)

															loss.backward()





			@slow
			def        SCREAMING_SNAKE_CASE					(       self					:    Dict							) ->     Union[str, Any]:
						for model_name in DEIT_PRETRAINED_MODEL_ARCHIVE_LIST[:1]:
									SCREAMING_SNAKE_CASE__										=   DeiTModel.from_pretrained(__UpperCAmelCase							)
									self.assertIsNotNone(__UpperCAmelCase							)

def 						A							(  ):




			'''simple docstring'''


			SCREAMING_SNAKE_CASE__										=   Image.open("""./tests/fixtures/tests_samples/COCO/000000039769.png"""     )
			return image





@require_torch
@require_vision
class  lowerCamelCase    (unittest.TestCase      ):

			@cached_property
			def        SCREAMING_SNAKE_CASE					(       self					:    str							) ->     List[str]:
						return (
						    DeiTImageProcessor.from_pretrained("""facebook/deit-base-distilled-patch16-224"""							)
						    if is_vision_available()
						    else None
						)

			@slow
			def        SCREAMING_SNAKE_CASE					(       self					:    Union[str, Any]							) ->     Dict:
						SCREAMING_SNAKE_CASE__										=   DeiTForImageClassificationWithTeacher.from_pretrained("""facebook/deit-base-distilled-patch16-224"""							).to(
						    __UpperCAmelCase							)

						SCREAMING_SNAKE_CASE__										=   self.default_image_processor
						SCREAMING_SNAKE_CASE__										=   prepare_img()
						SCREAMING_SNAKE_CASE__										=   image_processor(images=__UpperCAmelCase     ,					return_tensors="""pt"""							).to(__UpperCAmelCase							)

						# forward pass
						with torch.no_grad():
									SCREAMING_SNAKE_CASE__										=   model(**__UpperCAmelCase							)

						# verify the logits
						SCREAMING_SNAKE_CASE__										=   torch.Size((1, 1_0_0_0)							)
						self.assertEqual(outputs.logits.shape     ,					__UpperCAmelCase							)

						SCREAMING_SNAKE_CASE__										=   torch.tensor([-1.0_266, 0.1_912, -1.2_861]							).to(__UpperCAmelCase							)

						self.assertTrue(torch.allclose(outputs.logits[0, :3]     ,					__UpperCAmelCase     ,					atol=1e-4							)							)





			@slow
			@require_accelerate
			@require_torch_gpu
			def        SCREAMING_SNAKE_CASE					(       self					:    Union[str, Any]							) ->     List[str]:
						SCREAMING_SNAKE_CASE__										=   DeiTModel.from_pretrained(
						    """facebook/deit-base-distilled-patch16-224"""     ,					torch_dtype=torch.floataa     ,					device_map="""auto"""							)
						SCREAMING_SNAKE_CASE__										=   self.default_image_processor

						SCREAMING_SNAKE_CASE__										=   prepare_img()
						SCREAMING_SNAKE_CASE__										=   image_processor(images=__UpperCAmelCase     ,					return_tensors="""pt"""							)
						SCREAMING_SNAKE_CASE__										=   inputs.pixel_values.to(__UpperCAmelCase							)

						# forward pass to make sure inference works in fp16
						with torch.no_grad():
									SCREAMING_SNAKE_CASE__										=   model(__UpperCAmelCase							)


