


def 	_snake_case		(    SCREAMING_SNAKE_CASE				)       ->      Any:

     """simple docstring"""







     _lowerCAmelCase   :					List[Any]        =    current_set.copy()
     for row_index, row in enumerate(snake_case_				):
          _lowerCAmelCase   :					str        =    row[0]
          for column_index, column in enumerate(snake_case_				):
               if magnitude == 0:
                    _lowerCAmelCase   :					Any        =    column
                    continue
               _lowerCAmelCase   :					Dict        =    column / magnitude
                # Subtract to cancel term
     _lowerCAmelCase   :					Optional[Any]        =    current_set[0]
     _lowerCAmelCase   :					Any        =    [first_row]
     _lowerCAmelCase   :					str        =    current_set[1::]
     for row in current_set:
          _lowerCAmelCase   :					Dict        =    []
          # If first term is 0, it is already in form we want, so we preserve it
          if row[0] == 0:
               final_set.append(snake_case_				)
               continue
          for column_index in range(len(snake_case_				)				):
               temp_row.append(first_row[column_index] - row[column_index]				)
          final_set.append(snake_case_				)
     # Create next recursion iteration set
     if len(final_set[0]				) != 3:
          _lowerCAmelCase   :					Tuple        =    final_set[0]
          _lowerCAmelCase   :					Dict        =    []
          _lowerCAmelCase   :					List[str]        =    []
          for row in final_set[1::]:
               current_first_column.append(row[0]				)
               next_iteration.append(row[1::]				)
          _lowerCAmelCase   :					List[Any]        =    simplify(snake_case_				)
          for i in range(len(snake_case_				)				):
               resultant[i].insert(0		,							current_first_column[i]				)
          resultant.insert(0		,							snake_case_				)
          _lowerCAmelCase   :					Optional[Any]        =    resultant
     return final_set







def 	_snake_case		(    SCREAMING_SNAKE_CASE				)       ->      List[Any]:

     """simple docstring"""







     if len(snake_case_				) == 0:
          raise IndexError("solve_simultaneous() requires n lists of length n+1"				)
     _lowerCAmelCase   :					Dict        =    len(snake_case_				) + 1
     if any(len(snake_case_				) != _length for item in equations				):
          raise IndexError("solve_simultaneous() requires n lists of length n+1"				)
     for row in equations:
          if any(not isinstance(snake_case_		,							(int, float)				) for column in row				):
               raise ValueError("solve_simultaneous() requires lists of integers"				)
     if len(snake_case_				) == 1:
          return [equations[0][-1] / equations[0][0]]
     _lowerCAmelCase   :					str        =    equations.copy()
     if any(0 in row for row in data_set				):
          _lowerCAmelCase   :					Dict        =    data_set.copy()
          _lowerCAmelCase   :					Union[str, Any]        =    []
          for row_index, row in enumerate(snake_case_				):
               if 0 not in row:
                    _lowerCAmelCase   :					List[Any]        =    data_set.pop(snake_case_				)
                    break
          if not full_row:
               raise ValueError("solve_simultaneous() requires at least 1 full equation"				)
          data_set.insert(0		,							snake_case_				)
     _lowerCAmelCase   :					int        =    data_set.copy()
     _lowerCAmelCase   :					int        =    simplify(snake_case_				)
     _lowerCAmelCase   :					List[Any]        =    simplified[::-1]
     _lowerCAmelCase   :					list        =    []
     for row in simplified:
          _lowerCAmelCase   :					Optional[int]        =    row[-1]
          if not solutions:
               if row[-2] == 0:
                    solutions.append(0				)
                    continue
               solutions.append(current_solution / row[-2]				)
               continue
          _lowerCAmelCase   :					Tuple        =    row.copy()[: len(snake_case_				) - 1 :]
          while temp_row[0] == 0:
               temp_row.pop(0				)
          if len(snake_case_				) == 0:
               solutions.append(0				)
               continue
          _lowerCAmelCase   :					List[Any]        =    temp_row[1::]
          _lowerCAmelCase   :					List[Any]        =    temp_row[::-1]
          for column_index, column in enumerate(snake_case_				):
               current_solution -= column * solutions[column_index]
          solutions.append(snake_case_				)
     _lowerCAmelCase   :					List[Any]        =    []
     for item in solutions:
          final.append(float(round(snake_case_		,							5				)				)				)
     return final[::-1]


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  __UpperCAmelCase    				=     [
      [2, 1, 1, 1, 1, 4],
      [1, 2, 1, 1, 1, 5],
      [1, 1, 2, 1, 1, 6],
      [1, 1, 1, 2, 1, 7],
      [1, 1, 1, 1, 2, 8],
  ]
  print(solve_simultaneous(eq))
  print(solve_simultaneous([[4, 2]]))









import gc
import random
import unittest

import numpy as np
import torch
from PIL import Image
from transformers import CLIPTextConfig, CLIPTextModel, CLIPTokenizer

from diffusers import AutoencoderKL, DDIMScheduler, DDPMScheduler, StableDiffusionUpscalePipeline, UNetaDConditionModel
from diffusers.utils import floats_tensor, load_image, load_numpy, slow, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu


enable_full_determinism()





class A__    ( unittest.TestCase ):



 """simple docstring"""







 def    __magic_name__       (		self :	Any       ):






      '''simple docstring'''




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

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






      '''simple docstring'''




      _lowerCAmelCase   :					Optional[int]        =    1
      _lowerCAmelCase   :					List[str]        =    3
      _lowerCAmelCase   :					int        =    (3_2, 3_2)

      _lowerCAmelCase   :					Dict        =    floats_tensor((batch_size, num_channels) + sizes     ,						rng=random.Random(0       )       ).to(A_       )
      return image

 @property
 def    __magic_name__       (		self :	List[str]       ):






      '''simple docstring'''




      torch.manual_seed(0       )
      _lowerCAmelCase   :					Dict        =    UNetaDConditionModel(
          block_out_channels=(3_2, 3_2, 6_4)     ,						layers_per_block=2     ,						sample_size=3_2     ,						in_channels=7     ,						out_channels=4     ,						down_block_types=("DownBlock2D", "CrossAttnDownBlock2D", "CrossAttnDownBlock2D")     ,						up_block_types=("CrossAttnUpBlock2D", "CrossAttnUpBlock2D", "UpBlock2D")     ,						cross_attention_dim=3_2     ,						attention_head_dim=8     ,						use_linear_projection=A_     ,						only_cross_attention=(True, True, False)     ,						num_class_embeds=1_0_0     ,						)
      return model

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






      '''simple docstring'''




      torch.manual_seed(0       )
      _lowerCAmelCase   :					Union[str, Any]        =    AutoencoderKL(
          block_out_channels=[3_2, 3_2, 6_4]     ,						in_channels=3     ,						out_channels=3     ,						down_block_types=["DownEncoderBlock2D", "DownEncoderBlock2D", "DownEncoderBlock2D"]     ,						up_block_types=["UpDecoderBlock2D", "UpDecoderBlock2D", "UpDecoderBlock2D"]     ,						latent_channels=4     ,						)
      return model

 @property
 def    __magic_name__       (		self :	Tuple       ):






      '''simple docstring'''




      torch.manual_seed(0       )
      _lowerCAmelCase   :					Optional[Any]        =    CLIPTextConfig(
          bos_token_id=0     ,						eos_token_id=2     ,						hidden_size=3_2     ,						intermediate_size=3_7     ,						layer_norm_eps=1E-05     ,						num_attention_heads=4     ,						num_hidden_layers=5     ,						pad_token_id=1     ,						vocab_size=1_0_0_0     ,						hidden_act="gelu"     ,						projection_dim=5_1_2     ,						)
      return CLIPTextModel(A_       )

 def    __magic_name__       (		self :	str       ):






      '''simple docstring'''




      _lowerCAmelCase   :					List[str]        =    "cpu"  # ensure determinism for the device-dependent torch.Generator
      _lowerCAmelCase   :					Tuple        =    self.dummy_cond_unet_upscale
      _lowerCAmelCase   :					Optional[int]        =    DDPMScheduler()
      _lowerCAmelCase   :					Optional[Any]        =    DDIMScheduler(prediction_type="v_prediction"       )
      _lowerCAmelCase   :					str        =    self.dummy_vae
      _lowerCAmelCase   :					Any        =    self.dummy_text_encoder
      _lowerCAmelCase   :					Dict        =    CLIPTokenizer.from_pretrained("hf-internal-testing/tiny-random-clip"       )

      _lowerCAmelCase   :					List[Any]        =    self.dummy_image.cpu().permute(0     ,						2     ,						3     ,						1       )[0]
      _lowerCAmelCase   :					List[Any]        =    Image.fromarray(np.uinta(A_       )       ).convert("RGB"       ).resize((6_4, 6_4)       )

      # make sure here that pndm scheduler skips prk
      _lowerCAmelCase   :					List[Any]        =    StableDiffusionUpscalePipeline(
          unet=A_     ,						low_res_scheduler=A_     ,						scheduler=A_     ,						vae=A_     ,						text_encoder=A_     ,						tokenizer=A_     ,						max_noise_level=3_5_0     ,						)
      _lowerCAmelCase   :					Optional[int]        =    sd_pipe.to(A_       )
      sd_pipe.set_progress_bar_config(disable=A_       )

      _lowerCAmelCase   :					List[str]        =    "A painting of a squirrel eating a burger"
      _lowerCAmelCase   :					Tuple        =    torch.Generator(device=A_       ).manual_seed(0       )
      _lowerCAmelCase   :					Optional[int]        =    sd_pipe(
          [prompt]     ,						image=A_     ,						generator=A_     ,						guidance_scale=6.0     ,						noise_level=2_0     ,						num_inference_steps=2     ,						output_type="np"     ,						)

      _lowerCAmelCase   :					Tuple        =    output.images

      _lowerCAmelCase   :					Optional[int]        =    torch.Generator(device=A_       ).manual_seed(0       )
      _lowerCAmelCase   :					Union[str, Any]        =    sd_pipe(
          [prompt]     ,						image=A_     ,						generator=A_     ,						guidance_scale=6.0     ,						noise_level=2_0     ,						num_inference_steps=2     ,						output_type="np"     ,						return_dict=A_     ,						)[0]

      _lowerCAmelCase   :					List[Any]        =    image[0, -3:, -3:, -1]
      _lowerCAmelCase   :					List[str]        =    image_from_tuple[0, -3:, -3:, -1]

      _lowerCAmelCase   :					Optional[int]        =    low_res_image.size[0] * 4
      assert image.shape == (1, expected_height_width, expected_height_width, 3)
      _lowerCAmelCase   :					str        =    np.array([0.3113, 0.3910, 0.4272, 0.4859, 0.5061, 0.4652, 0.5362, 0.5715, 0.5661]       )

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

 def    __magic_name__       (		self :	int       ):






      '''simple docstring'''




      _lowerCAmelCase   :					List[str]        =    "cpu"  # ensure determinism for the device-dependent torch.Generator
      _lowerCAmelCase   :					List[str]        =    self.dummy_cond_unet_upscale
      _lowerCAmelCase   :					str        =    DDPMScheduler()
      _lowerCAmelCase   :					Union[str, Any]        =    DDIMScheduler(prediction_type="v_prediction"       )
      _lowerCAmelCase   :					Tuple        =    self.dummy_vae
      _lowerCAmelCase   :					Union[str, Any]        =    self.dummy_text_encoder
      _lowerCAmelCase   :					List[Any]        =    CLIPTokenizer.from_pretrained("hf-internal-testing/tiny-random-clip"       )

      _lowerCAmelCase   :					Dict        =    self.dummy_image.cpu().permute(0     ,						2     ,						3     ,						1       )[0]
      _lowerCAmelCase   :					Tuple        =    Image.fromarray(np.uinta(A_       )       ).convert("RGB"       ).resize((6_4, 6_4)       )

      # make sure here that pndm scheduler skips prk
      _lowerCAmelCase   :					Optional[Any]        =    StableDiffusionUpscalePipeline(
          unet=A_     ,						low_res_scheduler=A_     ,						scheduler=A_     ,						vae=A_     ,						text_encoder=A_     ,						tokenizer=A_     ,						max_noise_level=3_5_0     ,						)
      _lowerCAmelCase   :					Dict        =    sd_pipe.to(A_       )
      sd_pipe.set_progress_bar_config(disable=A_       )

      _lowerCAmelCase   :					Union[str, Any]        =    "A painting of a squirrel eating a burger"
      _lowerCAmelCase   :					Tuple        =    sd_pipe(
          2 * [prompt]     ,						image=2 * [low_res_image]     ,						guidance_scale=6.0     ,						noise_level=2_0     ,						num_inference_steps=2     ,						output_type="np"     ,						)
      _lowerCAmelCase   :					List[str]        =    output.images
      assert image.shape[0] == 2

      _lowerCAmelCase   :					str        =    torch.Generator(device=A_       ).manual_seed(0       )
      _lowerCAmelCase   :					List[Any]        =    sd_pipe(
          [prompt]     ,						image=A_     ,						generator=A_     ,						num_images_per_prompt=2     ,						guidance_scale=6.0     ,						noise_level=2_0     ,						num_inference_steps=2     ,						output_type="np"     ,						)
      _lowerCAmelCase   :					int        =    output.images
      assert image.shape[0] == 2


 @unittest.skipIf(torch_device != "cuda"     ,						"This test requires a GPU"       )
 def    __magic_name__       (		self :	Tuple       ):






      '''simple docstring'''




      _lowerCAmelCase   :					Any        =    self.dummy_cond_unet_upscale
      _lowerCAmelCase   :					List[str]        =    DDPMScheduler()
      _lowerCAmelCase   :					Optional[int]        =    DDIMScheduler(prediction_type="v_prediction"       )
      _lowerCAmelCase   :					Optional[Any]        =    self.dummy_vae
      _lowerCAmelCase   :					List[str]        =    self.dummy_text_encoder
      _lowerCAmelCase   :					Union[str, Any]        =    CLIPTokenizer.from_pretrained("hf-internal-testing/tiny-random-clip"       )

      _lowerCAmelCase   :					Any        =    self.dummy_image.cpu().permute(0     ,						2     ,						3     ,						1       )[0]
      _lowerCAmelCase   :					Any        =    Image.fromarray(np.uinta(A_       )       ).convert("RGB"       ).resize((6_4, 6_4)       )

      # put models in fp16, except vae as it overflows in fp16
      _lowerCAmelCase   :					Tuple        =    unet.half()
      _lowerCAmelCase   :					Optional[Any]        =    text_encoder.half()

      # make sure here that pndm scheduler skips prk
      _lowerCAmelCase   :					List[str]        =    StableDiffusionUpscalePipeline(
          unet=A_     ,						low_res_scheduler=A_     ,						scheduler=A_     ,						vae=A_     ,						text_encoder=A_     ,						tokenizer=A_     ,						max_noise_level=3_5_0     ,						)
      _lowerCAmelCase   :					Optional[Any]        =    sd_pipe.to(A_       )
      sd_pipe.set_progress_bar_config(disable=A_       )

      _lowerCAmelCase   :					str        =    "A painting of a squirrel eating a burger"
      _lowerCAmelCase   :					Any        =    torch.manual_seed(0       )
      _lowerCAmelCase   :					Optional[Any]        =    sd_pipe(
          [prompt]     ,						image=A_     ,						generator=A_     ,						num_inference_steps=2     ,						output_type="np"     ,						).images

      _lowerCAmelCase   :					List[str]        =    low_res_image.size[0] * 4
      assert image.shape == (1, expected_height_width, expected_height_width, 3)





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



 """simple docstring"""







 def    __magic_name__       (		self :	Any       ):






      '''simple docstring'''




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

 def    __magic_name__       (		self :	List[str]       ):






      '''simple docstring'''




      _lowerCAmelCase   :					List[Any]        =    load_image(
          "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main"
          "/sd2-upscale/low_res_cat.png"       )
      _lowerCAmelCase   :					Dict        =    load_numpy(
          "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/sd2-upscale"
          "/upsampled_cat.npy"       )

      _lowerCAmelCase   :					Union[str, Any]        =    "stabilityai/stable-diffusion-x4-upscaler"
      _lowerCAmelCase   :					Optional[int]        =    StableDiffusionUpscalePipeline.from_pretrained(A_       )
      pipe.to(A_       )
      pipe.set_progress_bar_config(disable=A_       )
      pipe.enable_attention_slicing()

      _lowerCAmelCase   :					str        =    "a cat sitting on a park bench"

      _lowerCAmelCase   :					str        =    torch.manual_seed(0       )
      _lowerCAmelCase   :					Optional[int]        =    pipe(
          prompt=A_     ,						image=A_     ,						generator=A_     ,						output_type="np"     ,						)
      _lowerCAmelCase   :					int        =    output.images[0]

      assert image.shape == (5_1_2, 5_1_2, 3)
      assert np.abs(expected_image - image       ).max() < 1E-3

 def    __magic_name__       (		self :	Tuple       ):






      '''simple docstring'''




      _lowerCAmelCase   :					Optional[int]        =    load_image(
          "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main"
          "/sd2-upscale/low_res_cat.png"       )
      _lowerCAmelCase   :					Dict        =    load_numpy(
          "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/sd2-upscale"
          "/upsampled_cat_fp16.npy"       )

      _lowerCAmelCase   :					Union[str, Any]        =    "stabilityai/stable-diffusion-x4-upscaler"
      _lowerCAmelCase   :					Any        =    StableDiffusionUpscalePipeline.from_pretrained(
          A_     ,						torch_dtype=torch.floataa     ,						)
      pipe.to(A_       )
      pipe.set_progress_bar_config(disable=A_       )
      pipe.enable_attention_slicing()

      _lowerCAmelCase   :					Optional[Any]        =    "a cat sitting on a park bench"

      _lowerCAmelCase   :					Any        =    torch.manual_seed(0       )
      _lowerCAmelCase   :					int        =    pipe(
          prompt=A_     ,						image=A_     ,						generator=A_     ,						output_type="np"     ,						)
      _lowerCAmelCase   :					Union[str, Any]        =    output.images[0]

      assert image.shape == (5_1_2, 5_1_2, 3)
      assert np.abs(expected_image - image       ).max() < 5E-1


 def    __magic_name__       (		self :	List[Any]       ):






      '''simple docstring'''




      torch.cuda.empty_cache()
      torch.cuda.reset_max_memory_allocated()
      torch.cuda.reset_peak_memory_stats()

      _lowerCAmelCase   :					int        =    load_image(
          "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main"
          "/sd2-upscale/low_res_cat.png"       )

      _lowerCAmelCase   :					Tuple        =    "stabilityai/stable-diffusion-x4-upscaler"
      _lowerCAmelCase   :					Any        =    StableDiffusionUpscalePipeline.from_pretrained(
          A_     ,						torch_dtype=torch.floataa     ,						)
      pipe.to(A_       )
      pipe.set_progress_bar_config(disable=A_       )
      pipe.enable_attention_slicing(1       )
      pipe.enable_sequential_cpu_offload()

      _lowerCAmelCase   :					List[Any]        =    "a cat sitting on a park bench"

      _lowerCAmelCase   :					Union[str, Any]        =    torch.manual_seed(0       )
      _lowerCAmelCase   :					List[Any]        =    pipe(
          prompt=A_     ,						image=A_     ,						generator=A_     ,						num_inference_steps=5     ,						output_type="np"     ,						)

      _lowerCAmelCase   :					Optional[Any]        =    torch.cuda.max_memory_allocated()
      # make sure that less than 2.9 GB is allocated
      assert mem_bytes < 2.9 * 1_0**9






