
import numpy as np

def 		UpperCamelCase						(   lowercase_			,			lowercase_			,			lowercase_ = 1E-12			,			lowercase_ = 1_00			,			)		->						tuple[float, np.ndarray]:


  '''simple docstring'''






  assert np.shape(lowercase_ )[0] == np.shape(lowercase_ )[1]
  # Ensure proper dimensionality.
  assert np.shape(lowercase_ )[0] == np.shape(lowercase_ )[0]
  # Ensure inputs are either both complex or both real
  assert np.iscomplexobj(lowercase_ ) == np.iscomplexobj(lowercase_ )
  lowercase__	: Dict     		=   np.iscomplexobj(lowercase_ )
  if is_complex:
    # Ensure complex input_matrix is Hermitian
    assert np.array_equal(lowercase_			,			input_matrix.conj().T )

  # Set convergence to False. Will define convergence when we exceed max_iterations
  # or when we have small changes from one iteration to next.

  lowercase__	: Optional[Any]     		=   False
  lowercase__	: Union[str, Any]     		=   0
  lowercase__	: Tuple     		=   0
  lowercase__	: Dict     		=   1E12

  while not convergence:
    # Multiple matrix by the vector.
    lowercase__	: Tuple     		=   np.dot(lowercase_			,			lowercase_ )
    # Normalize the resulting output vector.
    lowercase__	: int     		=   w / np.linalg.norm(lowercase_ )
    # Find rayleigh quotient
    # (faster than usual b/c we know vector is normalized already)
    lowercase__	: List[Any]     		=   vector.conj().T if is_complex else vector.T
    lowercase__	: Optional[Any]     		=   np.dot(lowercase_			,			np.dot(lowercase_			,			lowercase_ ) )

    # Check convergence.
    lowercase__	: Union[str, Any]     		=   np.abs(lambda_ - lambda_previous ) / lambda_
    iterations += 1

    if error <= error_tol or iterations >= max_iterations:
      lowercase__	: Any     		=   True

    lowercase__	: List[str]     		=   lambda_

  if is_complex:
    lowercase__	: Tuple     		=   np.real(lambda_ )

  return lambda_, vector

def 		UpperCamelCase						(   )		->						None:


  '''simple docstring'''






  lowercase__	: Dict     		=   np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]] )
  lowercase__	: Any     		=   np.array([41, 4, 20] )
  lowercase__	: Optional[int]     		=   real_input_matrix.astype(np.complexaaa )
  lowercase__	: Tuple     		=   np.triu(1J * complex_input_matrix			,			1 )
  complex_input_matrix += imag_matrix
  complex_input_matrix += -1 * imag_matrix.T
  lowercase__	: Any     		=   np.array([41, 4, 20] ).astype(np.complexaaa )

  for problem_type in ["real", "complex"]:
    if problem_type == "real":
      lowercase__	: Tuple     		=   real_input_matrix
      lowercase__	: Optional[Any]     		=   real_vector
    elif problem_type == "complex":
      lowercase__	: Optional[int]     		=   complex_input_matrix
      lowercase__	: int     		=   complex_vector

    # Our implementation.
    lowercase__		,     lowercase__	: Tuple     		=   power_iteration(lowercase_			,			lowercase_ )

    # Numpy implementation.

    # Get eigenvalues and eigenvectors using built-in numpy
    # eigh (eigh used for symmetric or hermetian matrices).
    lowercase__		,     lowercase__	: Dict     		=   np.linalg.eigh(lowercase_ )
    # Last eigenvalue is the maximum one.
    lowercase__	: List[Any]     		=   eigen_values[-1]
    # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
    lowercase__	: Any     		=   eigen_vectors[:, -1]

    # Check our implementation and numpy gives close answers.
    assert np.abs(eigen_value - eigen_value_max ) <= 1E-6
    # Take absolute values element wise of each eigenvector.
    # as they are only unique to a minus sign.
    assert np.linalg.norm(np.abs(lowercase_ ) - np.abs(lowercase_ ) ) <= 1E-6


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     test_power_iteration()













from dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import PIL
from PIL import Image

from ...utils import (
    BaseOutput,
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_k_diffusion_available,
    is_k_diffusion_version,
    is_onnx_available,
    is_torch_available,
    is_transformers_available,
    is_transformers_version,
)







@dataclass
class 	__lowerCAmelCase      (       _UpperCamelCase	):
   _UpperCamelCase			:    Union[List[PIL.Image.Image], np.ndarray]
   _UpperCamelCase			:    Optional[List[bool]]


try:
  if not (is_transformers_available() and is_torch_available()):
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
  from .pipeline_cycle_diffusion import CycleDiffusionPipeline
  from .pipeline_stable_diffusion import StableDiffusionPipeline
  from .pipeline_stable_diffusion_attend_and_excite import StableDiffusionAttendAndExcitePipeline
  from .pipeline_stable_diffusion_imgaimg import StableDiffusionImgaImgPipeline
  from .pipeline_stable_diffusion_inpaint import StableDiffusionInpaintPipeline
  from .pipeline_stable_diffusion_inpaint_legacy import StableDiffusionInpaintPipelineLegacy
  from .pipeline_stable_diffusion_instruct_pixapix import StableDiffusionInstructPixaPixPipeline
  from .pipeline_stable_diffusion_latent_upscale import StableDiffusionLatentUpscalePipeline
  from .pipeline_stable_diffusion_ldmad import StableDiffusionLDMaDPipeline
  from .pipeline_stable_diffusion_model_editing import StableDiffusionModelEditingPipeline
  from .pipeline_stable_diffusion_panorama import StableDiffusionPanoramaPipeline
  from .pipeline_stable_diffusion_paradigms import StableDiffusionParadigmsPipeline
  from .pipeline_stable_diffusion_sag import StableDiffusionSAGPipeline
  from .pipeline_stable_diffusion_upscale import StableDiffusionUpscalePipeline
  from .pipeline_stable_unclip import StableUnCLIPPipeline
  from .pipeline_stable_unclip_imgaimg import StableUnCLIPImgaImgPipeline
  from .safety_checker import StableDiffusionSafetyChecker
  from .stable_unclip_image_normalizer import StableUnCLIPImageNormalizer

try:
  if not (is_transformers_available() and is_torch_available() and is_transformers_version(""">=""", """4.25.0""")):
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  from ...utils.dummy_torch_and_transformers_objects import StableDiffusionImageVariationPipeline
else:
  from .pipeline_stable_diffusion_image_variation import StableDiffusionImageVariationPipeline


try:
  if not (is_transformers_available() and is_torch_available() and is_transformers_version(""">=""", """4.26.0""")):
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  from ...utils.dummy_torch_and_transformers_objects import (
      StableDiffusionDepthaImgPipeline,
      StableDiffusionDiffEditPipeline,
      StableDiffusionPixaPixZeroPipeline,
  )
else:
  from .pipeline_stable_diffusion_depthaimg import StableDiffusionDepthaImgPipeline
  from .pipeline_stable_diffusion_diffedit import StableDiffusionDiffEditPipeline
  from .pipeline_stable_diffusion_pixapix_zero import StableDiffusionPixaPixZeroPipeline


try:
  if not (
      is_torch_available()
      and is_transformers_available()
      and is_k_diffusion_available()
      and is_k_diffusion_version(""">=""", """0.0.12""")
  ):
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  from ...utils.dummy_torch_and_transformers_and_k_diffusion_objects import *  # noqa F403
else:
  from .pipeline_stable_diffusion_k_diffusion import StableDiffusionKDiffusionPipeline

try:
  if not (is_transformers_available() and is_onnx_available()):
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  from ...utils.dummy_onnx_objects import *  # noqa F403
else:
  from .pipeline_onnx_stable_diffusion import OnnxStableDiffusionPipeline, StableDiffusionOnnxPipeline
  from .pipeline_onnx_stable_diffusion_imgaimg import OnnxStableDiffusionImgaImgPipeline
  from .pipeline_onnx_stable_diffusion_inpaint import OnnxStableDiffusionInpaintPipeline
  from .pipeline_onnx_stable_diffusion_inpaint_legacy import OnnxStableDiffusionInpaintPipelineLegacy
  from .pipeline_onnx_stable_diffusion_upscale import OnnxStableDiffusionUpscalePipeline

if is_transformers_available() and is_flax_available():
  import flax







  @flax.struct.dataclass
  class 	__lowerCAmelCase      (       _UpperCamelCase	):
     _UpperCamelCase			:    np.ndarray
     _UpperCamelCase			:    List[bool]







  from ...schedulers.scheduling_pndm_flax import PNDMSchedulerState
  from .pipeline_flax_stable_diffusion import FlaxStableDiffusionPipeline
  from .pipeline_flax_stable_diffusion_imgaimg import FlaxStableDiffusionImgaImgPipeline
  from .pipeline_flax_stable_diffusion_inpaint import FlaxStableDiffusionInpaintPipeline
  from .safety_checker_flax import FlaxStableDiffusionSafetyChecker

