
"""simple docstring"""




from math import isclose, sqrt




def 			_lowerCAmelCase		(		_UpperCamelCase			,					_UpperCamelCase			,					_UpperCamelCase    ):






  """simple docstring"""



  _lowercase:      List[str]   			=  point_y / 4 / point_x
  _lowercase:      Optional[Any]   			=  2 * normal_gradient / (1 + normal_gradient * normal_gradient)
  _lowercase:      List[str]   			=  (1 - normal_gradient * normal_gradient) / (
      1 + normal_gradient * normal_gradient
  )
  _lowercase:      int   			=  (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
  _lowercase:      Optional[int]   			=  outgoing_gradient**2 + 4
  _lowercase:      int   			=  2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
  _lowercase:      Optional[Any]   			=  (point_y - outgoing_gradient * point_x) ** 2 - 100

  _lowercase:      Dict   			=  (
      -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term    )
  ) / (2 * quadratic_term)
  _lowercase:      Optional[Any]   			=  (
      -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term    )
  ) / (2 * quadratic_term)

  # two solutions, one of which is our input point
  _lowercase:      List[Any]   			=  x_minus if isclose(_UpperCamelCase			,					_UpperCamelCase    ) else x_plus
  _lowercase:      str   			=  point_y + outgoing_gradient * (next_x - point_x)

  return next_x, next_y, outgoing_gradient




def 			_lowerCAmelCase		(		_UpperCamelCase = 1.4			,					_UpperCamelCase = -9.6    ):






  """simple docstring"""



  _lowercase:      int   			=  0
  _lowercase:      float   			=  first_x_coord
  _lowercase:      float   			=  first_y_coord
  _lowercase:      float   			=  (10.1 - point_y) / (0.0 - point_x)

  while not (-0.01 <= point_x <= 0.01 and point_y > 0):
    _lowercase			,					_lowercase			,					_lowercase:      int   			=  next_point(_UpperCamelCase			,					_UpperCamelCase			,					_UpperCamelCase    )
    num_reflections += 1

  return num_reflections


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


"""simple docstring"""




import unittest

from transformers import is_vision_available
from transformers.pipelines import pipeline
from transformers.testing_utils import (
    is_pipeline_test,
    nested_simplify,
    require_tf,
    require_torch,
    require_vision,
    slow,
)

from .test_pipelines_common import ANY


if is_vision_available():
  from PIL import Image
else:


  class       __magic_name__							:
         @staticmethod
         def 				lowercase_				(  *A_			,					**A_							)  ->						Optional[int]:





           """simple docstring"""




           pass


@is_pipeline_test
@require_vision
class       __magic_name__							(							unittest.TestCase			):
       @require_torch
       def 				lowercase_				(  self							)  ->						int:





         """simple docstring"""




         _lowercase:      Optional[Any]   			=  pipeline(
             model='''hf-internal-testing/tiny-random-clip-zero-shot-image-classification'''			,					)
         _lowercase:      List[Any]   			=  Image.open('''./tests/fixtures/tests_samples/COCO/000000039769.png'''							)
         _lowercase:      str   			=  image_classifier(A_			,					candidate_labels=['''a''', '''b''', '''c''']							)

         # The floating scores are so close, we enter floating error approximation and the order is not guaranteed across
         # python and torch versions.
         self.assertIn(
             nested_simplify(A_							)			,					[
                 [{'''score''': 0.3_33, '''label''': '''a'''}, {'''score''': 0.3_33, '''label''': '''b'''}, {'''score''': 0.3_33, '''label''': '''c'''}],
                 [{'''score''': 0.3_33, '''label''': '''a'''}, {'''score''': 0.3_33, '''label''': '''c'''}, {'''score''': 0.3_33, '''label''': '''b'''}],
             ]			,					)

         _lowercase:      Any   			=  image_classifier([image] * 5			,					candidate_labels=['''A''', '''B''', '''C''']			,					batch_size=2							)
         self.assertEqual(
             nested_simplify(A_							)			,					[
                 [
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                 ],
                 [
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                 ],
                 [
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                 ],
                 [
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                 ],
                 [
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                 ],
             ]			,					)
       @require_tf
       def 				lowercase_				(  self							)  ->						int:





         """simple docstring"""




         _lowercase:      Union[str, Any]   			=  pipeline(
             model='''hf-internal-testing/tiny-random-clip-zero-shot-image-classification'''			,					framework='''tf'''							)
         _lowercase:      List[str]   			=  Image.open('''./tests/fixtures/tests_samples/COCO/000000039769.png'''							)
         _lowercase:      Union[str, Any]   			=  image_classifier(A_			,					candidate_labels=['''a''', '''b''', '''c''']							)

         self.assertEqual(
             nested_simplify(A_							)			,					[{'''score''': 0.3_33, '''label''': '''a'''}, {'''score''': 0.3_33, '''label''': '''b'''}, {'''score''': 0.3_33, '''label''': '''c'''}]			,					)

         _lowercase:      List[str]   			=  image_classifier([image] * 5			,					candidate_labels=['''A''', '''B''', '''C''']			,					batch_size=2							)
         self.assertEqual(
             nested_simplify(A_							)			,					[
                 [
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                 ],
                 [
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                 ],
                 [
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                 ],
                 [
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                 ],
                 [
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                     {'''score''': 0.3_33, '''label''': ANY(A_							)},
                 ],
             ]			,					)
       @slow
       @require_torch
       def 				lowercase_				(  self							)  ->						Any:





         """simple docstring"""




         _lowercase:      Tuple   			=  pipeline(
             task='''zero-shot-image-classification'''			,					model='''openai/clip-vit-base-patch32'''			,					)
         # This is an image of 2 cats with remotes and no planes
         _lowercase:      str   			=  Image.open('''./tests/fixtures/tests_samples/COCO/000000039769.png'''							)
         _lowercase:      Optional[Any]   			=  image_classifier(A_			,					candidate_labels=['''cat''', '''plane''', '''remote''']							)

         self.assertEqual(
             nested_simplify(A_							)			,					[
                 {'''score''': 0.5_11, '''label''': '''remote'''},
                 {'''score''': 0.4_85, '''label''': '''cat'''},
                 {'''score''': 0.0_04, '''label''': '''plane'''},
             ]			,					)

         _lowercase:      Optional[Any]   			=  image_classifier([image] * 5			,					candidate_labels=['''cat''', '''plane''', '''remote''']			,					batch_size=2							)
         self.assertEqual(
             nested_simplify(A_							)			,					[
                 [
                     {'''score''': 0.5_11, '''label''': '''remote'''},
                     {'''score''': 0.4_85, '''label''': '''cat'''},
                     {'''score''': 0.0_04, '''label''': '''plane'''},
                 ],
             ]
             * 5			,					)



       @slow
       @require_tf
       def 				lowercase_				(  self							)  ->						Optional[Any]:





         """simple docstring"""




         _lowercase:      Tuple   			=  pipeline(
             task='''zero-shot-image-classification'''			,					model='''openai/clip-vit-base-patch32'''			,					framework='''tf'''							)
         # This is an image of 2 cats with remotes and no planes
         _lowercase:      str   			=  Image.open('''./tests/fixtures/tests_samples/COCO/000000039769.png'''							)
         _lowercase:      Optional[int]   			=  image_classifier(A_			,					candidate_labels=['''cat''', '''plane''', '''remote''']							)
         self.assertEqual(
             nested_simplify(A_							)			,					[
                 {'''score''': 0.5_11, '''label''': '''remote'''},
                 {'''score''': 0.4_85, '''label''': '''cat'''},
                 {'''score''': 0.0_04, '''label''': '''plane'''},
             ]			,					)

         _lowercase:      Optional[Any]   			=  image_classifier([image] * 5			,					candidate_labels=['''cat''', '''plane''', '''remote''']			,					batch_size=2							)
         self.assertEqual(
             nested_simplify(A_							)			,					[
                 [
                     {'''score''': 0.5_11, '''label''': '''remote'''},
                     {'''score''': 0.4_85, '''label''': '''cat'''},
                     {'''score''': 0.0_04, '''label''': '''plane'''},
                 ],
             ]
             * 5			,					)
