import mpmath  # for roots of unity
import numpy as np





class      A							:


   def __init__(self     :						Union[str, Any]       ,  __UpperCAmelCase     :						Any=None       ,  __UpperCAmelCase     :						Optional[int]=None		)						->				Dict:
         """simple docstring"""



         UpperCAmelCase__								=  list(poly_a or [0]		)[:]
         UpperCAmelCase__								=  list(poly_b or [0]		)[:]

         # Remove leading zero coefficients
         while self.polyA[-1] == 0:
               self.polyA.pop()
         UpperCAmelCase__								=  len(self.polyA		)

         while self.polyB[-1] == 0:
               self.polyB.pop()
         UpperCAmelCase__								=  len(self.polyB		)

         # Add 0 to make lengths equal a power of 2
         UpperCAmelCase__								=  int(
             2 ** np.ceil(np.loga(len(self.polyA		) + len(self.polyB		) - 1		)		)		)

         while len(self.polyA		) < self.c_max_length:
               self.polyA.append(0		)
         while len(self.polyB		) < self.c_max_length:
               self.polyB.append(0		)
         # A complex root used for the fourier transform
         UpperCAmelCase__								=  complex(mpmath.root(x=1       ,  n=self.c_max_length       ,  k=1		)		)

         # The product
         UpperCAmelCase__								=  self.__multiply()


   def 			lowercase_      (self     :						Dict       ,  __UpperCAmelCase     :						str		)						->				Optional[Any]:
         """simple docstring"""



         UpperCAmelCase__								=  [[x] for x in self.polyA] if which == "A" else [[x] for x in self.polyB]
         # Corner case
         if len(__UpperCAmelCase		) <= 1:
               return dft[0]
         #
         UpperCAmelCase__								=  self.c_max_length // 2
         while next_ncol > 0:
               UpperCAmelCase__								=  [[] for i in range(__UpperCAmelCase		)]
               UpperCAmelCase__								=  self.root**next_ncol

               # First half of next step
               UpperCAmelCase__								=  1
               for j in range(self.c_max_length // (next_ncol * 2)		):
                     for i in range(__UpperCAmelCase		):
                           new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]		)
                     current_root *= root
               # Second half of next step
               UpperCAmelCase__								=  1
               for j in range(self.c_max_length // (next_ncol * 2)		):
                     for i in range(__UpperCAmelCase		):
                           new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]		)
                     current_root *= root
               # Update
               UpperCAmelCase__								=  new_dft
               UpperCAmelCase__								=  next_ncol // 2
         return dft[0]


   def 			lowercase_      (self     :						str		)						->				int:
         """simple docstring"""



         UpperCAmelCase__								=  self.__dft("A"		)
         UpperCAmelCase__								=  self.__dft("B"		)
         UpperCAmelCase__								=  [[dft_a[i] * dft_b[i] for i in range(self.c_max_length		)]]
         del dft_a
         del dft_b

         # Corner Case
         if len(inverce_c[0]		) <= 1:
               return inverce_c[0]
         # Inverse DFT
         UpperCAmelCase__								=  2
         while next_ncol <= self.c_max_length:
               UpperCAmelCase__								=  [[] for i in range(__UpperCAmelCase		)]
               UpperCAmelCase__								=  self.root ** (next_ncol // 2)
               UpperCAmelCase__								=  1
               # First half of next step
               for j in range(self.c_max_length // next_ncol		):
                     for i in range(next_ncol // 2		):
                           # Even positions
                           new_inverse_c[i].append(
                               (
                                   inverce_c[i][j]
                                   + inverce_c[i][j + self.c_max_length // next_ncol]
                               )
                               / 2		)
                           # Odd positions
                           new_inverse_c[i + next_ncol // 2].append(
                               (
                                   inverce_c[i][j]
                                   - inverce_c[i][j + self.c_max_length // next_ncol]
                               )
                               / (2 * current_root)		)
                     current_root *= root
               # Update
               UpperCAmelCase__								=  new_inverse_c
               next_ncol *= 2
         # Unpack
         UpperCAmelCase__								=  [round(x[0].real       ,  8		) + round(x[0].imag       ,  8		) * 1j for x in inverce_c]

         # Remove leading 0's
         while inverce_c[-1] == 0:
               inverce_c.pop()
         return inverce_c





   def __str__(self     :						Tuple		)						->				Tuple:
         """simple docstring"""



         UpperCAmelCase__								=  "A = " + " + ".join(
             f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]		)		)
         UpperCAmelCase__								=  "B = " + " + ".join(
             f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]		)		)
         UpperCAmelCase__								=  "A*B = " + " + ".join(
             f"""{coef}*x^{i}""" for coef, i in enumerate(self.product		)		)

         return f"""{a}\n{b}\n{c}"""


# Unit tests
if __name__ == "__main__":
      import doctest

      doctest.testmod()







'''simple docstring'''

import gc
import random
import unittest

import numpy as np
import torch
from transformers import CLIPImageProcessor, CLIPVisionConfig, CLIPVisionModel

from diffusers import HeunDiscreteScheduler, PriorTransformer, ShapEImgaImgPipeline
from diffusers.pipelines.shap_e import ShapERenderer
from diffusers.utils import floats_tensor, load_image, load_numpy, slow
from diffusers.utils.testing_utils import require_torch_gpu, torch_device

from ..test_pipelines_common import PipelineTesterMixin, assert_mean_pixel_difference
class   __lowerCAmelCase						(lowercase_  ,     unittest.TestCase     ):





      '''simple docstring'''






      lowerCAmelCase__					:     Dict  					=							ShapEImgaImgPipeline
      lowerCAmelCase__					:     List[str]  					=							["""image"""]
      lowerCAmelCase__					:     Any  					=							["""image"""]
      lowerCAmelCase__					:     Any  					=							[
          """num_images_per_prompt""",
          """num_inference_steps""",
          """generator""",
          """latents""",
          """guidance_scale""",
          """frame_size""",
          """output_type""",
          """return_dict""",
      ]
      lowerCAmelCase__					:     Tuple  					=							False



      @property
      def       UpperCamelCase__		(self    :    List[Any] ):

             '''simple docstring'''







             return 32



      @property
      def       UpperCamelCase__		(self    :    str ):

             '''simple docstring'''







             return 32



      @property
      def       UpperCamelCase__		(self    :    Union[str, Any] ):

             '''simple docstring'''







             return self.time_input_dim * 4



      @property
      def       UpperCamelCase__		(self    :    int ):

             '''simple docstring'''







             return 8



      @property
      def       UpperCamelCase__		(self    :    Any ):

             '''simple docstring'''







             torch.manual_seed(0 )
             lowercase__      			= CLIPVisionConfig(
                 hidden_size=self.text_embedder_hidden_size   ,						image_size=64   ,						projection_dim=self.text_embedder_hidden_size   ,						intermediate_size=37   ,						num_attention_heads=4   ,						num_channels=3   ,						num_hidden_layers=5   ,						patch_size=1   ,						)

             lowercase__      			= CLIPVisionModel(UpperCamelCase )
             return model



      @property
      def       UpperCamelCase__		(self    :    List[Any] ):

             '''simple docstring'''







             lowercase__      			= CLIPImageProcessor(
                 crop_size=224   ,						do_center_crop=UpperCamelCase   ,						do_normalize=UpperCamelCase   ,						do_resize=UpperCamelCase   ,						image_mean=[0.48_14_54_66, 0.4_57_82_75, 0.40_82_10_73]   ,						image_std=[0.26_86_29_54, 0.26_13_02_58, 0.27_57_77_11]   ,						resample=3   ,						size=224   ,						)

             return image_processor



      @property
      def       UpperCamelCase__		(self    :    str ):

             '''simple docstring'''







             torch.manual_seed(0 )

             lowercase__      			= {
                 '''num_attention_heads''': 2,
                 '''attention_head_dim''': 16,
                 '''embedding_dim''': self.time_input_dim,
                 '''num_embeddings''': 32,
                 '''embedding_proj_dim''': self.text_embedder_hidden_size,
                 '''time_embed_dim''': self.time_embed_dim,
                 '''num_layers''': 1,
                 '''clip_embed_dim''': self.time_input_dim * 2,
                 '''additional_embeddings''': 0,
                 '''time_embed_act_fn''': '''gelu''',
                 '''norm_in_type''': '''layer''',
                 '''embedding_proj_norm_type''': '''layer''',
                 '''encoder_hid_proj_type''': None,
                 '''added_emb_type''': None,
             }

             lowercase__      			= PriorTransformer(**UpperCamelCase )
             return model



      @property
      def       UpperCamelCase__		(self    :    int ):

             '''simple docstring'''







             torch.manual_seed(0 )

             lowercase__      			= {
                 '''param_shapes''': (
                     (self.renderer_dim, 93),
                     (self.renderer_dim, 8),
                     (self.renderer_dim, 8),
                     (self.renderer_dim, 8),
                 ),
                 '''d_latent''': self.time_input_dim,
                 '''d_hidden''': self.renderer_dim,
                 '''n_output''': 12,
                 '''background''': (
                     0.1,
                     0.1,
                     0.1,
                 ),
             }
             lowercase__      			= ShapERenderer(**UpperCamelCase )
             return model



      def       UpperCamelCase__		(self    :    Union[str, Any] ):

             '''simple docstring'''







             lowercase__      			= self.dummy_prior
             lowercase__      			= self.dummy_image_encoder
             lowercase__      			= self.dummy_image_processor
             lowercase__      			= self.dummy_renderer

             lowercase__      			= HeunDiscreteScheduler(
                 beta_schedule='''exp'''   ,						num_train_timesteps=1024   ,						prediction_type='''sample'''   ,						use_karras_sigmas=UpperCamelCase   ,						clip_sample=UpperCamelCase   ,						clip_sample_range=1.0   ,						)
             lowercase__      			= {
                 '''prior''': prior,
                 '''image_encoder''': image_encoder,
                 '''image_processor''': image_processor,
                 '''renderer''': renderer,
                 '''scheduler''': scheduler,
             }

             return components



      def       UpperCamelCase__		(self    :    Optional[int]   ,						UpperCamelCase    :    Optional[int]   ,						UpperCamelCase    :    str=0 ):

             '''simple docstring'''







             lowercase__      			= floats_tensor((1, 3, 64, 64)   ,						rng=random.Random(UpperCamelCase ) ).to(UpperCamelCase )

             if str(UpperCamelCase ).startswith('''mps''' ):
                    lowercase__      			= torch.manual_seed(UpperCamelCase )
             else:
                    lowercase__      			= torch.Generator(device=UpperCamelCase ).manual_seed(UpperCamelCase )
             lowercase__      			= {
                 '''image''': input_image,
                 '''generator''': generator,
                 '''num_inference_steps''': 1,
                 '''frame_size''': 32,
                 '''output_type''': '''np''',
             }
             return inputs



      def       UpperCamelCase__		(self    :    Tuple ):

             '''simple docstring'''







             lowercase__      			= '''cpu'''

             lowercase__      			= self.get_dummy_components()

             lowercase__      			= self.pipeline_class(**UpperCamelCase )
             lowercase__      			= pipe.to(UpperCamelCase )

             pipe.set_progress_bar_config(disable=UpperCamelCase )

             lowercase__      			= pipe(**self.get_dummy_inputs(UpperCamelCase ) )
             lowercase__      			= output.images[0]
             lowercase__      			= image[0, -3:, -3:, -1]

             assert image.shape == (20, 32, 32, 3)

             lowercase__      			= np.array(
                 [
                     0.00_03_92_16,
                     0.00_03_92_16,
                     0.00_03_92_16,
                     0.00_03_92_16,
                     0.00_03_92_16,
                     0.00_03_92_16,
                     0.00_03_92_16,
                     0.00_03_92_16,
                     0.00_03_92_16,
                 ] )

             assert np.abs(image_slice.flatten() - expected_slice ).max() < 1E-2



      def       UpperCamelCase__		(self    :    Optional[Any] ):

             '''simple docstring'''







             self._test_inference_batch_consistent(batch_sizes=[1, 2] )



      def       UpperCamelCase__		(self    :    int ):

             '''simple docstring'''







             lowercase__      			= torch_device == '''cpu'''
             lowercase__      			= True
             self._test_inference_batch_single_identical(
                 batch_size=2   ,						test_max_difference=UpperCamelCase   ,						relax_max_difference=UpperCamelCase   ,						)






      def       UpperCamelCase__		(self    :    int ):

             '''simple docstring'''







             lowercase__      			= self.get_dummy_components()
             lowercase__      			= self.pipeline_class(**UpperCamelCase )
             lowercase__      			= pipe.to(UpperCamelCase )
             pipe.set_progress_bar_config(disable=UpperCamelCase )

             lowercase__      			= 1
             lowercase__      			= 2

             lowercase__      			= self.get_dummy_inputs(UpperCamelCase )

             for key in inputs.keys():
                    if key in self.batch_params:
                           lowercase__      			= batch_size * [inputs[key]]

             lowercase__      			= pipe(**UpperCamelCase   ,						num_images_per_prompt=UpperCamelCase )[0]

             assert images.shape[0] == batch_size * num_images_per_prompt






@slow
@require_torch_gpu
class   __lowerCAmelCase						(unittest.TestCase     ):





      '''simple docstring'''






      def       UpperCamelCase__		(self    :    Optional[Any] ):

             '''simple docstring'''







             super().tearDown()
             gc.collect()
             torch.cuda.empty_cache()






      def       UpperCamelCase__		(self    :    Union[str, Any] ):

             '''simple docstring'''







             lowercase__      			= load_image(
                 '''https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main''' '''/shap_e/corgi.png''' )
             lowercase__      			= load_numpy(
                 '''https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'''
                 '''/shap_e/test_shap_e_img2img_out.npy''' )
             lowercase__      			= ShapEImgaImgPipeline.from_pretrained('''openai/shap-e-img2img''' )
             lowercase__      			= pipe.to(UpperCamelCase )
             pipe.set_progress_bar_config(disable=UpperCamelCase )

             lowercase__      			= torch.Generator(device=UpperCamelCase ).manual_seed(0 )

             lowercase__      			= pipe(
                 UpperCamelCase   ,						generator=UpperCamelCase   ,						guidance_scale=3.0   ,						num_inference_steps=64   ,						frame_size=64   ,						output_type='''np'''   ,						).images[0]

             assert images.shape == (20, 64, 64, 3)

             assert_mean_pixel_difference(UpperCamelCase   ,						UpperCamelCase )




