


from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE = False )->  list[float]:




     """simple docstring"""

     if radian_mode:
          return [magnitude * cos(lowercase__ ), magnitude * sin(lowercase__ )]
     return [magnitude * cos(radians(lowercase__ ) ), magnitude * sin(radians(lowercase__ ) )]






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE = 10**-1 )->  bool:




     """simple docstring"""

     snake_case_	=				cross(lowercase__ , lowercase__ )
     snake_case_	=				sum(lowercase__ )
     return abs(lowercase__ ) < eps


if __name__ == "__main__":
   # Test to check if it works
   UpperCAmelCase      =   array(
       [
           polar_force(718.4, 180 - 30),
           polar_force(879.54, 45),
           polar_force(100, -90),
       ]
   )

   UpperCAmelCase      =   array([[0, 0], [0, 0], [0, 0]])

   assert in_static_equilibrium(forces, location)

   # Problem 1 in image_data/2D_problems.jpg
   UpperCAmelCase      =   array(
       [
           polar_force(30 * 9.81, 15),
           polar_force(215, 180 - 45),
           polar_force(264, 90 - 30),
       ]
   )

   UpperCAmelCase      =   array([[0, 0], [0, 0], [0, 0]])

   assert in_static_equilibrium(forces, location)

   # Problem in image_data/2D_problems_1.jpg
   UpperCAmelCase      =   array([[0, -2000], [0, -1200], [0, 1_5600], [0, -1_2400]])

   UpperCAmelCase      =   array([[0, 0], [6, 0], [10, 0], [12, 0]])

   assert in_static_equilibrium(forces, location)

   import doctest

   doctest.testmod()



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCAmelCase      =   {"""configuration_xglm""": ["""XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP""", """XGLMConfig"""]}

try:
   if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase      =   ["""XGLMTokenizer"""]

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase      =   ["""XGLMTokenizerFast"""]

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase      =   [
       """XGLM_PRETRAINED_MODEL_ARCHIVE_LIST""",
       """XGLMForCausalLM""",
       """XGLMModel""",
       """XGLMPreTrainedModel""",
   ]


try:
   if not is_flax_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase      =   [
       """FlaxXGLMForCausalLM""",
       """FlaxXGLMModel""",
       """FlaxXGLMPreTrainedModel""",
   ]


try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase      =   [
       """TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST""",
       """TFXGLMForCausalLM""",
       """TFXGLMModel""",
       """TFXGLMPreTrainedModel""",
   ]


if TYPE_CHECKING:
   from .configuration_xglm import XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP, XGLMConfig

   try:
      if not is_sentencepiece_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_xglm import XGLMTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_xglm_fast import XGLMTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_xglm import XGLM_PRETRAINED_MODEL_ARCHIVE_LIST, XGLMForCausalLM, XGLMModel, XGLMPreTrainedModel

   try:
      if not is_flax_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_flax_xglm import FlaxXGLMForCausalLM, FlaxXGLMModel, FlaxXGLMPreTrainedModel

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_xglm import (
          TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST,
          TFXGLMForCausalLM,
          TFXGLMModel,
          TFXGLMPreTrainedModel,
      )


else:
   import sys

   UpperCAmelCase      =   _LazyModule(__name__, globals()["""__file__"""], _import_structure)