



'''simple docstring'''





def 	a_					(							_lowerCAmelCase	,_lowerCAmelCase	,_lowerCAmelCase	)				->				float:
  if common_ratio == 1:
    # Formula for sum if common ratio is 1
    return num_of_terms * first_term

  # Formula for finding sum of n terms of a GeometricProgression
  return (first_term / (1 - common_ratio)) * (1 - common_ratio**num_of_terms)











'''simple docstring'''





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


_UpperCamelCase							    =						{
    'configuration_imagegpt': ['IMAGEGPT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'ImageGPTConfig', 'ImageGPTOnnxConfig']
}

try:
   if not is_vision_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _UpperCamelCase							    =						['ImageGPTFeatureExtractor']
   _UpperCamelCase							    =						['ImageGPTImageProcessor']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _UpperCamelCase							    =						[
       'IMAGEGPT_PRETRAINED_MODEL_ARCHIVE_LIST',
       'ImageGPTForCausalImageModeling',
       'ImageGPTForImageClassification',
       'ImageGPTModel',
       'ImageGPTPreTrainedModel',
       'load_tf_weights_in_imagegpt',
   ]


if TYPE_CHECKING:
   from .configuration_imagegpt import IMAGEGPT_PRETRAINED_CONFIG_ARCHIVE_MAP, ImageGPTConfig, ImageGPTOnnxConfig

   try:
      if not is_vision_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .feature_extraction_imagegpt import ImageGPTFeatureExtractor
      from .image_processing_imagegpt import ImageGPTImageProcessor

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_imagegpt import (
          IMAGEGPT_PRETRAINED_MODEL_ARCHIVE_LIST,
          ImageGPTForCausalImageModeling,
          ImageGPTForImageClassification,
          ImageGPTModel,
          ImageGPTPreTrainedModel,
          load_tf_weights_in_imagegpt,
      )

else:
   import sys

   _UpperCamelCase							    =						_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)






