
from typing import List, Optional, Union

import torch

from ...models import UNetaDConditionModel, VQModel
from ...pipelines import DiffusionPipeline
from ...pipelines.pipeline_utils import ImagePipelineOutput
from ...schedulers import DDPMScheduler
from ...utils import (
    is_accelerate_available,
    is_accelerate_version,
    logging,
    randn_tensor,
    replace_example_docstring,
)


lowerCamelCase__    :		Tuple          =   logging.get_logger(__name__)  # pylint: disable=invalid-name

lowerCamelCase__    :		Any          =   """
    Examples:
        ```py
        >>> import torch
        >>> import numpy as np

        >>> from diffusers import KandinskyV22PriorPipeline, KandinskyV22ControlnetPipeline
        >>> from transformers import pipeline
        >>> from diffusers.utils import load_image


        >>> def make_hint(image, depth_estimator):
        ...     image = depth_estimator(image)[\"depth\"]
        ...     image = np.array(image)
        ...     image = image[:, :, None]
        ...     image = np.concatenate([image, image, image], axis=2)
        ...     detected_map = torch.from_numpy(image).float() / 255.0
        ...     hint = detected_map.permute(2, 0, 1)
        ...     return hint


        >>> depth_estimator = pipeline(\"depth-estimation\")

        >>> pipe_prior = KandinskyV22PriorPipeline.from_pretrained(
        ...     \"kandinsky-community/kandinsky-2-2-prior\", torch_dtype=torch.float16
        ... )
        >>> pipe_prior = pipe_prior.to(\"cuda\")

        >>> pipe = KandinskyV22ControlnetPipeline.from_pretrained(
        ...     \"kandinsky-community/kandinsky-2-2-controlnet-depth\", torch_dtype=torch.float16
        ... )
        >>> pipe = pipe.to(\"cuda\")


        >>> img = load_image(
        ...     \"https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main\"
        ...     \"/kandinsky/cat.png\"
        ... ).resize((768, 768))

        >>> hint = make_hint(img, depth_estimator).unsqueeze(0).half().to(\"cuda\")

        >>> prompt = \"A robot, 4k photo\"
        >>> negative_prior_prompt = \"lowres, text, error, cropped, worst quality, low quality, jpeg artifacts, ugly, duplicate, morbid, mutilated, out of frame, extra fingers, mutated hands, poorly drawn hands, poorly drawn face, mutation, deformed, blurry, dehydrated, bad anatomy, bad proportions, extra limbs, cloned face, disfigured, gross proportions, malformed limbs, missing arms, missing legs, extra arms, extra legs, fused fingers, too many fingers, long neck, username, watermark, signature\"

        >>> generator = torch.Generator(device=\"cuda\").manual_seed(43)

        >>> image_emb, zero_image_emb = pipe_prior(
        ...     prompt=prompt, negative_prompt=negative_prior_prompt, generator=generator
        ... ).to_tuple()

        >>> images = pipe(
        ...     image_embeds=image_emb,
        ...     negative_image_embeds=zero_image_emb,
        ...     hint=hint,
        ...     num_inference_steps=50,
        ...     generator=generator,
        ...     height=768,
        ...     width=768,
        ... ).images

        >>> images[0].save(\"robot_cat.png\")
        ```
"""

def 		UpperCamelCase	(      lowercase_ , lowercase_ , lowercase_=8   )		->	Dict:


  '''simple docstring'''






  lowercase__  :   List[str]    		=      height // scale_factor**2
  if height % scale_factor**2 != 0:
    new_height += 1
  lowercase__  :   Tuple    		=      width // scale_factor**2
  if width % scale_factor**2 != 0:
    new_width += 1
  return new_height * scale_factor, new_width * scale_factor



class       _snake_case   (	UpperCAmelCase_							):


 def __init__(					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  ):


   '''simple docstring'''




   super().__init__()

   self.register_modules(
       unet=SCREAMING_SNAKE_CASE_					,  scheduler=SCREAMING_SNAKE_CASE_					,  movq=SCREAMING_SNAKE_CASE_					,  )
   lowercase__  :   str    		=      2 ** (len(self.movq.config.block_out_channels) - 1)


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if latents is None:
     lowercase__  :   List[str]    		=      randn_tensor(SCREAMING_SNAKE_CASE_					,  generator=SCREAMING_SNAKE_CASE_					,  device=SCREAMING_SNAKE_CASE_					,  dtype=SCREAMING_SNAKE_CASE_)
   else:
     if latents.shape != shape:
       raise ValueError(f'Unexpected latents shape, got {latents.shape}, expected {shape}')
     lowercase__  :   List[str]    		=      latents.to(SCREAMING_SNAKE_CASE_)

   lowercase__  :   Tuple    		=      latents * scheduler.init_noise_sigma
   return latents


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_=0):


   '''simple docstring'''




   if is_accelerate_available():
     from accelerate import cpu_offload
   else:
     raise ImportError("""Please install accelerate via `pip install accelerate`""")

   lowercase__  :   Tuple    		=      torch.device(f'cuda:{gpu_id}')

   lowercase__  :   Union[str, Any]    		=      [
       self.unet,
       self.movq,
   ]
   for cpu_offloaded_model in models:
     if cpu_offloaded_model is not None:
       cpu_offload(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_)


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_=0):


   '''simple docstring'''




   if is_accelerate_available() and is_accelerate_version(""">="""					,  """0.17.0.dev0"""):
     from accelerate import cpu_offload_with_hook
   else:
     raise ImportError("""`enable_model_cpu_offload` requires `accelerate v0.17.0` or higher.""")

   lowercase__  :   int    		=      torch.device(f'cuda:{gpu_id}')

   if self.device.type != "cpu":
     self.to("""cpu"""					,  silence_dtype_warnings=SCREAMING_SNAKE_CASE_)
     torch.cuda.empty_cache()  # otherwise we don't see the memory savings (but they probably exist)

   lowercase__  :   Union[str, Any]    		=      None
   for cpu_offloaded_model in [self.unet, self.movq]:
     lowercase__		,    lowercase__  :   List[str]    		=      cpu_offload_with_hook(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  prev_module_hook=SCREAMING_SNAKE_CASE_)

   # We'll offload the last model manually.
   lowercase__  :   Tuple    		=      hook


 @property
 # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline._execution_device
 def      lowercase__     (					self):


   '''simple docstring'''




   if not hasattr(self.unet					,  """_hf_hook"""):
     return self.device
   for module in self.unet.modules():
     if (
         hasattr(SCREAMING_SNAKE_CASE_					,  """_hf_hook""")
         and hasattr(module._hf_hook					,  """execution_device""")
         and module._hf_hook.execution_device is not None
     ):
       return torch.device(module._hf_hook.execution_device)
   return self.device



 @torch.no_grad()
 @replace_example_docstring(SCREAMING_SNAKE_CASE_)
 def __call__(					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_ = 5_12					,  SCREAMING_SNAKE_CASE_ = 5_12					,  SCREAMING_SNAKE_CASE_ = 1_00					,  SCREAMING_SNAKE_CASE_ = 4.0					,  SCREAMING_SNAKE_CASE_ = 1					,  SCREAMING_SNAKE_CASE_ = None					,  SCREAMING_SNAKE_CASE_ = None					,  SCREAMING_SNAKE_CASE_ = "pil"					,  SCREAMING_SNAKE_CASE_ = True					,  ):


   '''simple docstring'''




   lowercase__  :   List[str]    		=      self._execution_device

   lowercase__  :   Dict    		=      guidance_scale > 1.0

   if isinstance(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):
     lowercase__  :   List[Any]    		=      torch.cat(SCREAMING_SNAKE_CASE_					,  dim=0)
   if isinstance(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):
     lowercase__  :   int    		=      torch.cat(SCREAMING_SNAKE_CASE_					,  dim=0)
   if isinstance(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):
     lowercase__  :   Dict    		=      torch.cat(SCREAMING_SNAKE_CASE_					,  dim=0)

   lowercase__  :   Tuple    		=      image_embeds.shape[0] * num_images_per_prompt

   if do_classifier_free_guidance:
     lowercase__  :   Tuple    		=      image_embeds.repeat_interleave(SCREAMING_SNAKE_CASE_					,  dim=0)
     lowercase__  :   str    		=      negative_image_embeds.repeat_interleave(SCREAMING_SNAKE_CASE_					,  dim=0)
     lowercase__  :   Tuple    		=      hint.repeat_interleave(SCREAMING_SNAKE_CASE_					,  dim=0)

   lowercase__  :   Optional[Any]    		=      torch.cat([negative_image_embeds, image_embeds]					,  dim=0).to(dtype=self.unet.dtype					,  device=SCREAMING_SNAKE_CASE_)
   lowercase__  :   Any    		=      torch.cat([hint, hint]					,  dim=0).to(dtype=self.unet.dtype					,  device=SCREAMING_SNAKE_CASE_)
   self.scheduler.set_timesteps(SCREAMING_SNAKE_CASE_					,  device=SCREAMING_SNAKE_CASE_)
   lowercase__  :   Dict    		=      self.scheduler.timesteps

   lowercase__  :   int    		=      self.movq.config.latent_channels

   lowercase__		,    lowercase__  :   Optional[Any]    		=      downscale_height_and_width(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  self.movq_scale_factor)

   # create initial latent
   lowercase__  :   int    		=      self.prepare_latents(
       (batch_size, num_channels_latents, height, width)					,  image_embeds.dtype					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  self.scheduler					,  )

   for i, t in enumerate(self.progress_bar(SCREAMING_SNAKE_CASE_)):
     # expand the latents if we are doing classifier free guidance
     lowercase__  :   List[Any]    		=      torch.cat([latents] * 2) if do_classifier_free_guidance else latents

     lowercase__  :   List[Any]    		=      {"""image_embeds""": image_embeds, """hint""": hint}
     lowercase__  :   Optional[int]    		=      self.unet(
         sample=SCREAMING_SNAKE_CASE_					,  timestep=SCREAMING_SNAKE_CASE_					,  encoder_hidden_states=SCREAMING_SNAKE_CASE_					,  added_cond_kwargs=SCREAMING_SNAKE_CASE_					,  return_dict=SCREAMING_SNAKE_CASE_					,  )[0]

     if do_classifier_free_guidance:
       lowercase__		,    lowercase__  :   Union[str, Any]    		=      noise_pred.split(latents.shape[1]					,  dim=1)
       lowercase__		,    lowercase__  :   Any    		=      noise_pred.chunk(2)
       lowercase__		,    lowercase__  :   int    		=      variance_pred.chunk(2)
       lowercase__  :   Optional[Any]    		=      noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
       lowercase__  :   str    		=      torch.cat([noise_pred, variance_pred_text]					,  dim=1)

     if not (
         hasattr(self.scheduler.config					,  """variance_type""")
         and self.scheduler.config.variance_type in ["learned", "learned_range"]
     ):
       lowercase__		,    lowercase__  :   Optional[int]    		=      noise_pred.split(latents.shape[1]					,  dim=1)

     # compute the previous noisy sample x_t -> x_t-1
     lowercase__  :   List[Any]    		=      self.scheduler.step(
         SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  generator=SCREAMING_SNAKE_CASE_					,  )[0]
   # post-processing
   lowercase__  :   Tuple    		=      self.movq.decode(SCREAMING_SNAKE_CASE_					,  force_not_quantize=SCREAMING_SNAKE_CASE_)["""sample"""]

   if output_type not in ["pt", "np", "pil"]:
     raise ValueError(f'Only the output types `pt`, `pil` and `np` are supported not output_type={output_type}')

   if output_type in ["np", "pil"]:
     lowercase__  :   List[str]    		=      image * 0.5 + 0.5
     lowercase__  :   List[Any]    		=      image.clamp(0					,  1)
     lowercase__  :   int    		=      image.cpu().permute(0					,  2					,  3					,  1).float().numpy()

   if output_type == "pil":
     lowercase__  :   Optional[int]    		=      self.numpy_to_pil(SCREAMING_SNAKE_CASE_)

   if not return_dict:
     return (image,)

   return ImagePipelineOutput(images=SCREAMING_SNAKE_CASE_)








from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload



class       _snake_case   :


 def __init__(					self					,  SCREAMING_SNAKE_CASE_ = None):


   '''simple docstring'''




   if components is None:
     lowercase__  :   List[str]    		=      []
   lowercase__  :   Dict    		=      list(SCREAMING_SNAKE_CASE_)


 def __len__(					self):


   '''simple docstring'''




   return len(self.__components)


 def __str__(					self):


   '''simple docstring'''




   return "(" + ",".join(map(SCREAMING_SNAKE_CASE_					,  self.__components)) + ")"


 def __add__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   lowercase__  :   Optional[Any]    		=      len(self)
   if size == len(SCREAMING_SNAKE_CASE_):
     lowercase__  :   List[str]    		=      [self.__components[i] + other.component(SCREAMING_SNAKE_CASE_) for i in range(SCREAMING_SNAKE_CASE_)]
     return Vector(SCREAMING_SNAKE_CASE_)
   else:
     raise Exception("""must have the same size""")


 def __sub__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   lowercase__  :   List[Any]    		=      len(self)
   if size == len(SCREAMING_SNAKE_CASE_):
     lowercase__  :   Optional[Any]    		=      [self.__components[i] - other.component(SCREAMING_SNAKE_CASE_) for i in range(SCREAMING_SNAKE_CASE_)]
     return Vector(SCREAMING_SNAKE_CASE_)
   else:  # error case
     raise Exception("""must have the same size""")


 @overload
 def __mul__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   ...


 @overload
 def __mul__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   ...


 def __mul__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if isinstance(SCREAMING_SNAKE_CASE_					,  (float, int)):
     lowercase__  :   Optional[int]    		=      [c * other for c in self.__components]
     return Vector(SCREAMING_SNAKE_CASE_)
   elif isinstance(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_) and len(self) == len(SCREAMING_SNAKE_CASE_):
     lowercase__  :   Dict    		=      len(self)
     lowercase__  :   Optional[Any]    		=      [self.__components[i] * other.component(SCREAMING_SNAKE_CASE_) for i in range(SCREAMING_SNAKE_CASE_)]
     return sum(SCREAMING_SNAKE_CASE_)
   else:  # error case
     raise Exception("""invalid operand!""")


 def      lowercase__     (					self):


   '''simple docstring'''




   return Vector(self.__components)


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if isinstance(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_) and -len(self.__components) <= i < len(self.__components):
     return self.__components[i]
   else:
     raise Exception("""index out of range""")


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   assert -len(self.__components) <= pos < len(self.__components)
   lowercase__  :   List[Any]    		=      value


 def      lowercase__     (					self):


   '''simple docstring'''




   if len(self.__components) == 0:
     raise Exception("""Vector is empty""")
   lowercase__  :   Union[str, Any]    		=      [c**2 for c in self.__components]
   return math.sqrt(sum(SCREAMING_SNAKE_CASE_))



 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_ = False):


   '''simple docstring'''




   lowercase__  :   Union[str, Any]    		=      self * other
   lowercase__  :   Optional[Any]    		=      self.euclidean_length() * other.euclidean_length()
   if deg:
     return math.degrees(math.acos(num / den))
   else:
     return math.acos(num / den)

def 		UpperCamelCase	(      lowercase_   )		->	Vector:


  '''simple docstring'''






  assert isinstance(lowercase_ , lowercase_   )
  return Vector([0] * dimension   )

def 		UpperCamelCase	(      lowercase_ , lowercase_   )		->	Vector:


  '''simple docstring'''






  assert isinstance(lowercase_ , lowercase_   ) and (isinstance(lowercase_ , lowercase_   ))
  lowercase__  :   Union[str, Any]    		=      [0] * dimension
  lowercase__  :   Any    		=      1
  return Vector(lowercase_   )

def 		UpperCamelCase	(      lowercase_ , lowercase_ , lowercase_   )		->	Vector:


  '''simple docstring'''






  assert (
      isinstance(lowercase_ , lowercase_   )
      and isinstance(lowercase_ , lowercase_   )
      and (isinstance(lowercase_ , (int, float)   ))
  )
  return x * scalar + y

def 		UpperCamelCase	(      lowercase_ , lowercase_ , lowercase_   )		->	Vector:


  '''simple docstring'''






  random.seed(lowercase_   )
  lowercase__  :   int    		=      [random.randint(lowercase_ , lowercase_   ) for _ in range(lowercase_   )]
  return Vector(lowercase_   )



class       _snake_case   :


 def __init__(					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   lowercase__  :   List[Any]    		=      matrix
   lowercase__  :   Any    		=      w
   lowercase__  :   Any    		=      h


 def __str__(					self):


   '''simple docstring'''




   lowercase__  :   str    		=      """"""
   for i in range(self.__height):
     ans += "|"
     for j in range(self.__width):
       if j < self.__width - 1:
         ans += str(self.__matrix[i][j]) + ","
       else:
         ans += str(self.__matrix[i][j]) + "|\n"
   return ans


 def __add__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if self.__width == other.width() and self.__height == other.height():
     lowercase__  :   Tuple    		=      []
     for i in range(self.__height):
       lowercase__  :   Tuple    		=      [
           self.__matrix[i][j] + other.component(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_)
           for j in range(self.__width)
       ]
       matrix.append(SCREAMING_SNAKE_CASE_)
     return Matrix(SCREAMING_SNAKE_CASE_					,  self.__width					,  self.__height)
   else:
     raise Exception("""matrix must have the same dimension!""")


 def __sub__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if self.__width == other.width() and self.__height == other.height():
     lowercase__  :   Optional[int]    		=      []
     for i in range(self.__height):
       lowercase__  :   List[str]    		=      [
           self.__matrix[i][j] - other.component(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_)
           for j in range(self.__width)
       ]
       matrix.append(SCREAMING_SNAKE_CASE_)
     return Matrix(SCREAMING_SNAKE_CASE_					,  self.__width					,  self.__height)
   else:
     raise Exception("""matrices must have the same dimension!""")


 @overload
 def __mul__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   ...


 @overload
 def __mul__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   ...


 def __mul__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if isinstance(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):  # matrix-vector
     if len(SCREAMING_SNAKE_CASE_) == self.__width:
       lowercase__  :   List[Any]    		=      zero_vector(self.__height)
       for i in range(self.__height):
         lowercase__  :   Union[str, Any]    		=      [
             self.__matrix[i][j] * other.component(SCREAMING_SNAKE_CASE_)
             for j in range(self.__width)
         ]
         ans.change_component(SCREAMING_SNAKE_CASE_					,  sum(SCREAMING_SNAKE_CASE_))
       return ans
     else:
       raise Exception(
           """vector must have the same size as the """
           """number of columns of the matrix!""")
   elif isinstance(SCREAMING_SNAKE_CASE_					,  (int, float)):  # matrix-scalar
     lowercase__  :   Tuple    		=      [
         [self.__matrix[i][j] * other for j in range(self.__width)]
         for i in range(self.__height)
     ]
     return Matrix(SCREAMING_SNAKE_CASE_					,  self.__width					,  self.__height)
   return None


 def      lowercase__     (					self):


   '''simple docstring'''




   return self.__height


 def      lowercase__     (					self):


   '''simple docstring'''




   return self.__width


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if 0 <= x < self.__height and 0 <= y < self.__width:
     return self.__matrix[x][y]
   else:
     raise Exception("""change_component: indices out of bounds""")


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if 0 <= x < self.__height and 0 <= y < self.__width:
     lowercase__  :   Tuple    		=      value
   else:
     raise Exception("""change_component: indices out of bounds""")


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if self.__height != self.__width:
     raise Exception("""Matrix is not square""")
   lowercase__  :   List[Any]    		=      self.__matrix[:x] + self.__matrix[x + 1 :]
   for i in range(len(SCREAMING_SNAKE_CASE_)):
     lowercase__  :   List[str]    		=      minor[i][:y] + minor[i][y + 1 :]
   return Matrix(SCREAMING_SNAKE_CASE_					,  self.__width - 1					,  self.__height - 1).determinant()


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if self.__height != self.__width:
     raise Exception("""Matrix is not square""")
   if 0 <= x < self.__height and 0 <= y < self.__width:
     return (-1) ** (x + y) * self.minor(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_)
   else:
     raise Exception("""Indices out of bounds""")



 def      lowercase__     (					self):


   '''simple docstring'''




   if self.__height != self.__width:
     raise Exception("""Matrix is not square""")
   if self.__height < 1:
     raise Exception("""Matrix has no element""")
   elif self.__height == 1:
     return self.__matrix[0][0]
   elif self.__height == 2:
     return (
         self.__matrix[0][0] * self.__matrix[1][1]
         - self.__matrix[0][1] * self.__matrix[1][0]
     )
   else:
     lowercase__  :   Optional[int]    		=      [
         self.__matrix[0][y] * self.cofactor(0					,  SCREAMING_SNAKE_CASE_) for y in range(self.__width)
     ]
     return sum(SCREAMING_SNAKE_CASE_)

def 		UpperCamelCase	(      lowercase_   )		->	Matrix:


  '''simple docstring'''






  lowercase__  :   list[list[float]]    		=      [[0] * n for _ in range(lowercase_   )]
  return Matrix(lowercase_ , lowercase_ , lowercase_   )



def 		UpperCamelCase	(      lowercase_ , lowercase_ , lowercase_ , lowercase_   )		->	Matrix:


  '''simple docstring'''






  random.seed(lowercase_   )
  lowercase__  :   list[list[float]]    		=      [
      [random.randint(lowercase_ , lowercase_   ) for _ in range(lowercase_   )] for _ in range(lowercase_   )
  ]
  return Matrix(lowercase_ , lowercase_ , lowercase_   )






