'''simple docstring'''





import mpmath  # for roots of unity
import numpy as np






class 				UpperCAmelCase :




				'''simple docstring'''







				def __init__(       self    ,							lowercase__=None    ,							lowercase__=None )							-> Dict:
									SCREAMING_SNAKE_CASE					:			Optional[int]    	=       list(poly_a or [0] )[:]
									SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       list(poly_b or [0] )[:]

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

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

									# Add 0 to make lengths equal a power of 2
									SCREAMING_SNAKE_CASE					:			int    	=       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
									SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       complex(mpmath.root(x=1    ,							n=self.c_max_length    ,							k=1 ) )

									# The product
									SCREAMING_SNAKE_CASE					:			Tuple    	=       self.__multiply()






				def       _UpperCamelCase    (       self    ,							lowercase__ )							-> Union[str, Any]:
									SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       [[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]
									#
									SCREAMING_SNAKE_CASE					:			Any    	=       self.c_max_length // 2
									while next_ncol > 0:
														SCREAMING_SNAKE_CASE					:			Optional[int]    	=       [[] for i in range(UpperCAmelCase__ )]
														SCREAMING_SNAKE_CASE					:			Tuple    	=       self.root**next_ncol

														# First half of next step
														SCREAMING_SNAKE_CASE					:			str    	=       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
														SCREAMING_SNAKE_CASE					:			int    	=       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
														SCREAMING_SNAKE_CASE					:			Dict    	=       new_dft
														SCREAMING_SNAKE_CASE					:			Tuple    	=       next_ncol // 2
									return dft[0]






				def       _UpperCamelCase    (       self )							-> int:
									SCREAMING_SNAKE_CASE					:			Any    	=       self.__dft('A' )
									SCREAMING_SNAKE_CASE					:			Any    	=       self.__dft('B' )
									SCREAMING_SNAKE_CASE					:			Optional[int]    	=       [[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
									SCREAMING_SNAKE_CASE					:			Optional[int]    	=       2
									while next_ncol <= self.c_max_length:
														SCREAMING_SNAKE_CASE					:			Optional[int]    	=       [[] for i in range(UpperCAmelCase__ )]
														SCREAMING_SNAKE_CASE					:			List[str]    	=       self.root ** (next_ncol // 2)
														SCREAMING_SNAKE_CASE					:			Optional[int]    	=       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
														SCREAMING_SNAKE_CASE					:			List[Any]    	=       new_inverse_c
														next_ncol *= 2
									# Unpack
									SCREAMING_SNAKE_CASE					:			Tuple    	=       [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:
									SCREAMING_SNAKE_CASE					:			Any    	=       '''A = ''' + ''' + '''.join(
									    F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A] ) )
									SCREAMING_SNAKE_CASE					:			Tuple    	=       '''B = ''' + ''' + '''.join(
									    F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B] ) )
									SCREAMING_SNAKE_CASE					:			List[str]    	=       '''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 tempfile
import unittest

import numpy as np
import torch

from diffusers import VersatileDiffusionTextToImagePipeline
from diffusers.utils.testing_utils import nightly, require_torch_gpu, torch_device


_lowerCAmelCase  :List[Any]  				=    False






class 				UpperCAmelCase (       unittest.TestCase ):




    '''simple docstring'''







    pass






@nightly
@require_torch_gpu
class 				UpperCAmelCase (       unittest.TestCase ):




    '''simple docstring'''







    def       _UpperCamelCase    (       self )							-> Any:
         # clean up the VRAM after each test
         super().tearDown()
         gc.collect()
         torch.cuda.empty_cache()






    def       _UpperCamelCase    (       self )							-> Tuple:
         SCREAMING_SNAKE_CASE					:			Dict    	=       VersatileDiffusionTextToImagePipeline.from_pretrained('shi-labs/versatile-diffusion' )
         # remove text_unet
         pipe.remove_unused_weights()
         pipe.to(lowercase__ )
         pipe.set_progress_bar_config(disable=lowercase__ )

         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       'A painting of a squirrel eating a burger '
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       torch.manual_seed(0 )
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       pipe(
             prompt=lowercase__    ,							generator=lowercase__    ,							guidance_scale=7.5    ,							num_inference_steps=2    ,							output_type='numpy' ).images

         with tempfile.TemporaryDirectory() as tmpdirname:
              pipe.save_pretrained(lowercase__ )
              SCREAMING_SNAKE_CASE					:			int    	=       VersatileDiffusionTextToImagePipeline.from_pretrained(lowercase__ )
         pipe.to(lowercase__ )
         pipe.set_progress_bar_config(disable=lowercase__ )

         SCREAMING_SNAKE_CASE					:			List[str]    	=       generator.manual_seed(0 )
         SCREAMING_SNAKE_CASE					:			List[str]    	=       pipe(
             prompt=lowercase__    ,							generator=lowercase__    ,							guidance_scale=7.5    ,							num_inference_steps=2    ,							output_type='numpy' ).images

         assert np.abs(image - new_image ).sum() < 1E-5, "Models don't have the same forward pass"






    def       _UpperCamelCase    (       self )							-> Any:
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       VersatileDiffusionTextToImagePipeline.from_pretrained(
             'shi-labs/versatile-diffusion'    ,							torch_dtype=torch.floataa )
         pipe.to(lowercase__ )
         pipe.set_progress_bar_config(disable=lowercase__ )

         SCREAMING_SNAKE_CASE					:			int    	=       'A painting of a squirrel eating a burger '
         SCREAMING_SNAKE_CASE					:			Tuple    	=       torch.manual_seed(0 )
         SCREAMING_SNAKE_CASE					:			Tuple    	=       pipe(
             prompt=lowercase__    ,							generator=lowercase__    ,							guidance_scale=7.5    ,							num_inference_steps=50    ,							output_type='numpy' ).images

         SCREAMING_SNAKE_CASE					:			Dict    	=       image[0, 253:256, 253:256, -1]

         assert image.shape == (1, 512, 512, 3)
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       np.array([0.3_3_6_7, 0.3_1_6_9, 0.2_6_5_6, 0.3_8_7_0, 0.4_7_9_0, 0.3_7_9_6, 0.4_0_0_9, 0.4_8_7_8, 0.4_7_7_8] )

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



