
from math import isclose, sqrt





def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase    ,		__lowerCAmelCase    ,		__lowerCAmelCase							):
    snake_case__						=				point_y / 4 / point_x
    snake_case__						=				2 * normal_gradient / (1 + normal_gradient * normal_gradient)
    snake_case__						=				(1 - normal_gradient * normal_gradient) / (
        1 + normal_gradient * normal_gradient
    )
    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
    snake_case__						=				outgoing_gradient**2 + 4
    snake_case__						=				2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
    snake_case__						=				(point_y - outgoing_gradient * point_x) ** 2 - 100

    snake_case__						=				(
        -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term							)
    ) / (2 * quadratic_term)
    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
    snake_case__						=				x_minus if isclose(__lowerCAmelCase    ,		__lowerCAmelCase							) else x_plus
    snake_case__						=				point_y + outgoing_gradient * (next_x - point_x)

    return next_x, next_y, outgoing_gradient





def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase = 1.4    ,		__lowerCAmelCase = -9.6							):
    snake_case__						=				0
    snake_case__						=				first_x_coord
    snake_case__						=				first_y_coord
    snake_case__						=				(10.1 - point_y) / (0.0 - point_x)

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

    return num_reflections


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





import argparse

from diffusers.pipelines.stable_diffusion.convert_from_ckpt import download_controlnet_from_original_ckpt


if __name__ == "__main__":
     __magic_name__            =  argparse.ArgumentParser()

     parser.add_argument(
         '''--checkpoint_path''', default=None, type=str, required=True, help='''Path to the checkpoint to convert.'''
     )
     parser.add_argument(
         '''--original_config_file''',
         type=str,
         required=True,
         help='''The YAML config file corresponding to the original architecture.''',
     )
     parser.add_argument(
         '''--num_in_channels''',
         default=None,
         type=int,
         help='''The number of input channels. If `None` number of input channels will be automatically inferred.''',
     )
     parser.add_argument(
         '''--image_size''',
         default=512,
         type=int,
         help=(
             '''The image size that the model was trained on. Use 512 for Stable Diffusion v1.X and Stable Siffusion v2'''
             ''' Base. Use 768 for Stable Diffusion v2.'''
         ),
     )
     parser.add_argument(
         '''--extract_ema''',
         action='''store_true''',
         help=(
             '''Only relevant for checkpoints that have both EMA and non-EMA weights. Whether to extract the EMA weights'''
             ''' or not. Defaults to `False`. Add `--extract_ema` to extract the EMA weights. EMA weights usually yield'''
             ''' higher quality images for inference. Non-EMA weights are usually better to continue fine-tuning.'''
         ),
     )
     parser.add_argument(
         '''--upcast_attention''',
         action='''store_true''',
         help=(
             '''Whether the attention computation should always be upcasted. This is necessary when running stable'''
             ''' diffusion 2.1.'''
         ),
     )
     parser.add_argument(
         '''--from_safetensors''',
         action='''store_true''',
         help='''If `--checkpoint_path` is in `safetensors` format, load checkpoint with safetensors instead of PyTorch.''',
     )
     parser.add_argument(
         '''--to_safetensors''',
         action='''store_true''',
         help='''Whether to store pipeline in safetensors format or not.''',
     )
     parser.add_argument('''--dump_path''', default=None, type=str, required=True, help='''Path to the output model.''')
     parser.add_argument('''--device''', type=str, help='''Device to use (e.g. cpu, cuda:0, cuda:1, etc.)''')





     def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase							):
         if string == "True":
             return True
         elif string == "False":
             return False
         else:
             raise ValueError(F"""could not parse string as bool {string}"""							)

     parser.add_argument(
         '''--use_linear_projection''', help='''Override for use linear projection''', required=False, type=parse_bool
     )

     parser.add_argument('''--cross_attention_dim''', help='''Override for cross attention_dim''', required=False, type=int)

     __magic_name__            =  parser.parse_args()

     __magic_name__            =  download_controlnet_from_original_ckpt(
         checkpoint_path=args.checkpoint_path,
         original_config_file=args.original_config_file,
         image_size=args.image_size,
         extract_ema=args.extract_ema,
         num_in_channels=args.num_in_channels,
         upcast_attention=args.upcast_attention,
         from_safetensors=args.from_safetensors,
         device=args.device,
         use_linear_projection=args.use_linear_projection,
         cross_attention_dim=args.cross_attention_dim,
     )





     controlnet.save_pretrained(args.dump_path, safe_serialization=args.to_safetensors)



