



import inspect
from typing import Optional, Union

import numpy as np
import PIL
import torch
from torch.nn import functional as F
from torchvision import transforms
from transformers import CLIPFeatureExtractor, CLIPModel, CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
    DPMSolverMultistepScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
    UNetaDConditionModel,
)
from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion import StableDiffusionPipelineOutput
from diffusers.utils import (
    PIL_INTERPOLATION,
    randn_tensor,
)






def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							if isinstance(_lowerCamelCase       ,				torch.Tensor						):
														return image
							elif isinstance(_lowerCamelCase       ,				PIL.Image.Image						):
														_lowerCAmelCase  :							str				     =					[image]

							if isinstance(image[0]       ,				PIL.Image.Image						):
														_lowerCAmelCase  :							Any				     =					[np.array(i.resize((w, h)       ,				resample=PIL_INTERPOLATION["lanczos"]						)						)[None, :] for i in image]
														_lowerCAmelCase  :							Dict				     =					np.concatenate(_lowerCamelCase       ,				axis=0						)
														_lowerCAmelCase  :							Tuple				     =					np.array(_lowerCamelCase						).astype(np.floataa						) / 255.0
														_lowerCAmelCase  :							Optional[Any]				     =					image.transpose(0       ,				3       ,				1       ,				2						)
														_lowerCAmelCase  :							Any				     =					2.0 * image - 1.0
														_lowerCAmelCase  :							str				     =					torch.from_numpy(_lowerCamelCase						)
							elif isinstance(image[0]       ,				torch.Tensor						):
														_lowerCAmelCase  :							Optional[Any]				     =					torch.cat(_lowerCamelCase       ,				dim=0						)
							return image






def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase=0.99_95						):





							'''simple docstring'''




							if not isinstance(_lowerCamelCase       ,				np.ndarray						):
														_lowerCAmelCase  :							List[Any]				     =					True
														_lowerCAmelCase  :							Optional[Any]				     =					va.device
														_lowerCAmelCase  :							Dict				     =					va.cpu().numpy()
														_lowerCAmelCase  :							str				     =					va.cpu().numpy()

							_lowerCAmelCase  :							Dict				     =					np.sum(va * va / (np.linalg.norm(_lowerCamelCase						) * np.linalg.norm(_lowerCamelCase						))						)
							if np.abs(_lowerCamelCase						) > DOT_THRESHOLD:
														_lowerCAmelCase  :							Dict				     =					(1 - t) * va + t * va
							else:
														_lowerCAmelCase  :							str				     =					np.arccos(_lowerCamelCase						)
														_lowerCAmelCase  :							Optional[int]				     =					np.sin(_lowerCamelCase						)
														_lowerCAmelCase  :							Optional[Any]				     =					theta_a * t
														_lowerCAmelCase  :							Tuple				     =					np.sin(_lowerCamelCase						)
														_lowerCAmelCase  :							Optional[int]				     =					np.sin(theta_a - theta_t						) / sin_theta_a
														_lowerCAmelCase  :							Optional[int]				     =					sin_theta_t / sin_theta_a
														_lowerCAmelCase  :							Optional[int]				     =					sa * va + sa * va

							if inputs_are_torch:
														_lowerCAmelCase  :							List[Any]				     =					torch.from_numpy(_lowerCamelCase						).to(_lowerCamelCase						)

							return va






def        A       (      _lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							_lowerCAmelCase  :							Optional[Any]				     =					F.normalize(_lowerCamelCase       ,				dim=-1						)
							_lowerCAmelCase  :							Tuple				     =					F.normalize(_lowerCamelCase       ,				dim=-1						)
							return (x - y).norm(dim=-1						).div(2						).arcsin().pow(2						).mul(2						)






def        A       (      _lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							for param in model.parameters():
														_lowerCAmelCase  :							Any				     =					value



class 						UpperCAmelCase_					( a):







							def __init__(     self,    __a,    __a,    __a,    __a,    __a,    __a,    __a,    __a=None,    __a=None,    __a=None,    ):

														'''simple docstring'''

														super().__init__()
														self.register_modules(
														    vae=__a,    text_encoder=__a,    clip_model=__a,    tokenizer=__a,    unet=__a,    scheduler=__a,    feature_extractor=__a,    coca_model=__a,    coca_tokenizer=__a,    coca_transform=__a,    )
														_lowerCAmelCase  :							Optional[Any]				     =					(
														    feature_extractor.size
														    if isinstance(feature_extractor.size,    __a)
														    else feature_extractor.size["shortest_edge"]
														)
														_lowerCAmelCase  :							List[Any]				     =					transforms.Normalize(mean=feature_extractor.image_mean,    std=feature_extractor.image_std)
														set_requires_grad(self.text_encoder,    __a)
														set_requires_grad(self.clip_model,    __a)







							def      snake_case__   (     self,    __a = "auto"):

														'''simple docstring'''

														if slice_size == "auto":
																					# half the attention head size is usually a good trade-off between
																					# speed and memory
																					_lowerCAmelCase  :							str				     =					self.unet.config.attention_head_dim // 2
														self.unet.set_attention_slice(__a)







							def      snake_case__   (     self):

														'''simple docstring'''

														self.enable_attention_slicing(__a)







							def      snake_case__   (     self):

														'''simple docstring'''

														set_requires_grad(self.vae,    __a)







							def      snake_case__   (     self):

														'''simple docstring'''

														set_requires_grad(self.vae,    __a)







							def      snake_case__   (     self):

														'''simple docstring'''

														set_requires_grad(self.unet,    __a)







							def      snake_case__   (     self):

														'''simple docstring'''

														set_requires_grad(self.unet,    __a)







							def      snake_case__   (     self,    __a,    __a,    __a):

														'''simple docstring'''

														_lowerCAmelCase  :							List[str]				     =					min(int(num_inference_steps * strength),    __a)

														_lowerCAmelCase  :							List[str]				     =					max(num_inference_steps - init_timestep,    0)
														_lowerCAmelCase  :							str				     =					self.scheduler.timesteps[t_start:]

														return timesteps, num_inference_steps - t_start







							def      snake_case__   (     self,    __a,    __a,    __a,    __a,    __a,    __a=None):

														'''simple docstring'''

														if not isinstance(__a,    torch.Tensor):
																					raise ValueError(f"`image` has to be of type `torch.Tensor` but is {type(__a)}")

														_lowerCAmelCase  :							List[str]				     =					image.to(device=__a,    dtype=__a)

														if isinstance(__a,    __a):
																					_lowerCAmelCase  :							Any				     =					[
																					    self.vae.encode(image[i : i + 1]).latent_dist.sample(generator[i]) for i in range(__a)
																					]
																					_lowerCAmelCase  :							Optional[Any]				     =					torch.cat(__a,    dim=0)
														else:
																					_lowerCAmelCase  :							Any				     =					self.vae.encode(__a).latent_dist.sample(__a)

														# Hardcode 0.18215 because stable-diffusion-2-base has not self.vae.config.scaling_factor
														_lowerCAmelCase  :							List[str]				     =					0.18_215 * init_latents
														_lowerCAmelCase  :							List[Any]				     =					init_latents.repeat_interleave(__a,    dim=0)

														_lowerCAmelCase  :							Union[str, Any]				     =					randn_tensor(init_latents.shape,    generator=__a,    device=__a,    dtype=__a)

														# get latents
														_lowerCAmelCase  :							Union[str, Any]				     =					self.scheduler.add_noise(__a,    __a,    __a)
														_lowerCAmelCase  :							Optional[int]				     =					init_latents

														return latents







							def      snake_case__   (     self,    __a):

														'''simple docstring'''

														_lowerCAmelCase  :							str				     =					self.coca_transform(__a).unsqueeze(0)
														with torch.no_grad(), torch.cuda.amp.autocast():
																					_lowerCAmelCase  :							Optional[int]				     =					self.coca_model.generate(transformed_image.to(device=self.device,    dtype=self.coca_model.dtype))
														_lowerCAmelCase  :							Tuple				     =					self.coca_tokenizer.decode(generated[0].cpu().numpy())
														return generated.split("<end_of_text>")[0].replace("<start_of_text>",    "").rstrip(" .,")







							def      snake_case__   (     self,    __a,    __a):

														'''simple docstring'''

														_lowerCAmelCase  :							Optional[int]				     =					self.feature_extractor.preprocess(__a)
														_lowerCAmelCase  :							Tuple				     =					torch.from_numpy(clip_image_input["pixel_values"][0]).unsqueeze(0).to(self.device).half()
														_lowerCAmelCase  :							int				     =					self.clip_model.get_image_features(__a)
														_lowerCAmelCase  :							str				     =					image_embeddings_clip / image_embeddings_clip.norm(p=2,    dim=-1,    keepdim=__a)
														_lowerCAmelCase  :							Union[str, Any]				     =					image_embeddings_clip.repeat_interleave(__a,    dim=0)
														return image_embeddings_clip







							@torch.enable_grad()
							def      snake_case__   (     self,    __a,    __a,    __a,    __a,    __a,    __a,    __a,    ):

														'''simple docstring'''

														_lowerCAmelCase  :							Optional[Any]				     =					latents.detach().requires_grad_()

														_lowerCAmelCase  :							Any				     =					self.scheduler.scale_model_input(__a,    __a)

														# predict the noise residual
														_lowerCAmelCase  :							Union[str, Any]				     =					self.unet(__a,    __a,    encoder_hidden_states=__a).sample

														if isinstance(self.scheduler,    (PNDMScheduler, DDIMScheduler, DPMSolverMultistepScheduler)):
																					_lowerCAmelCase  :							int				     =					self.scheduler.alphas_cumprod[timestep]
																					_lowerCAmelCase  :							str				     =					1 - alpha_prod_t
																					# compute predicted original sample from predicted noise also called
																					# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
																					_lowerCAmelCase  :							str				     =					(latents - beta_prod_t ** 0.5 * noise_pred) / alpha_prod_t ** 0.5

																					_lowerCAmelCase  :							Optional[int]				     =					torch.sqrt(__a)
																					_lowerCAmelCase  :							Union[str, Any]				     =					pred_original_sample * (fac) + latents * (1 - fac)
														elif isinstance(self.scheduler,    __a):
																					_lowerCAmelCase  :							List[Any]				     =					self.scheduler.sigmas[index]
																					_lowerCAmelCase  :							int				     =					latents - sigma * noise_pred
														else:
																					raise ValueError(f"scheduler type {type(self.scheduler)} not supported")

														# Hardcode 0.18215 because stable-diffusion-2-base has not self.vae.config.scaling_factor
														_lowerCAmelCase  :							Any				     =					1 / 0.18_215 * sample
														_lowerCAmelCase  :							Optional[Any]				     =					self.vae.decode(__a).sample
														_lowerCAmelCase  :							Tuple				     =					(image / 2 + 0.5).clamp(0,    1)

														_lowerCAmelCase  :							str				     =					transforms.Resize(self.feature_extractor_size)(__a)
														_lowerCAmelCase  :							Any				     =					self.normalize(__a).to(latents.dtype)

														_lowerCAmelCase  :							Tuple				     =					self.clip_model.get_image_features(__a)
														_lowerCAmelCase  :							Dict				     =					image_embeddings_clip / image_embeddings_clip.norm(p=2,    dim=-1,    keepdim=__a)

														_lowerCAmelCase  :							Any				     =					spherical_dist_loss(__a,    __a).mean() * clip_guidance_scale

														_lowerCAmelCase  :							str				     =					-torch.autograd.grad(__a,    __a)[0]

														if isinstance(self.scheduler,    __a):
																					_lowerCAmelCase  :							Tuple				     =					latents.detach() + grads * (sigma**2)
																					_lowerCAmelCase  :							List[Any]				     =					noise_pred_original
														else:
																					_lowerCAmelCase  :							Optional[int]				     =					noise_pred_original - torch.sqrt(__a) * grads
														return noise_pred, latents







							@torch.no_grad()
							def __call__(     self,    __a,    __a,    __a = None,    __a = None,    __a = 512,    __a = 512,    __a = 0.6,    __a = 50,    __a = 7.5,    __a = 1,    __a = 0.0,    __a = 100,    __a = None,    __a = "pil",    __a = True,    __a = 0.8,    __a = 0.1,    __a = 0.1,    ):

														'''simple docstring'''

														if isinstance(__a,    __a) and len(__a) != batch_size:
																					raise ValueError(f"You have passed {batch_size} batch_size, but only {len(__a)} generators.")

														if height % 8 != 0 or width % 8 != 0:
																					raise ValueError(f"`height` and `width` have to be divisible by 8 but are {height} and {width}.")

														if isinstance(__a,    torch.Generator) and batch_size > 1:
																					_lowerCAmelCase  :							Dict				     =					[generator] + [None] * (batch_size - 1)

														_lowerCAmelCase  :							Dict				     =					[
														    ("model", self.coca_model is None),
														    ("tokenizer", self.coca_tokenizer is None),
														    ("transform", self.coca_transform is None),
														]
														_lowerCAmelCase  :							Optional[Any]				     =					[x[0] for x in coca_is_none if x[1]]
														_lowerCAmelCase  :							Optional[int]				     =					", ".join(__a)
														# generate prompts with coca model if prompt is None
														if content_prompt is None:
																					if len(__a):
																												raise ValueError(
																												    f"Content prompt is None and CoCa [{coca_is_none_str}] is None."
																												    f"Set prompt or pass Coca [{coca_is_none_str}] to DiffusionPipeline.")
																					_lowerCAmelCase  :							List[str]				     =					self.get_image_description(__a)
														if style_prompt is None:
																					if len(__a):
																												raise ValueError(
																												    f"Style prompt is None and CoCa [{coca_is_none_str}] is None."
																												    f" Set prompt or pass Coca [{coca_is_none_str}] to DiffusionPipeline.")
																					_lowerCAmelCase  :							List[str]				     =					self.get_image_description(__a)

														# get prompt text embeddings for content and style
														_lowerCAmelCase  :							Optional[Any]				     =					self.tokenizer(
														    __a,    padding="max_length",    max_length=self.tokenizer.model_max_length,    truncation=__a,    return_tensors="pt",    )
														_lowerCAmelCase  :							List[Any]				     =					self.text_encoder(content_text_input.input_ids.to(self.device))[0]

														_lowerCAmelCase  :							int				     =					self.tokenizer(
														    __a,    padding="max_length",    max_length=self.tokenizer.model_max_length,    truncation=__a,    return_tensors="pt",    )
														_lowerCAmelCase  :							List[str]				     =					self.text_encoder(style_text_input.input_ids.to(self.device))[0]

														_lowerCAmelCase  :							str				     =					slerp(__a,    __a,    __a)

														# duplicate text embeddings for each generation per prompt
														_lowerCAmelCase  :							Union[str, Any]				     =					text_embeddings.repeat_interleave(__a,    dim=0)

														# set timesteps
														_lowerCAmelCase  :							Tuple				     =					"offset" in set(inspect.signature(self.scheduler.set_timesteps).parameters.keys())
														_lowerCAmelCase  :							List[str]				     =					{}
														if accepts_offset:
																					_lowerCAmelCase  :							Optional[int]				     =					1

														self.scheduler.set_timesteps(__a,    **__a)
														# Some schedulers like PNDM have timesteps as arrays
														# It's more optimized to move all timesteps to correct device beforehand
														self.scheduler.timesteps.to(self.device)

														_lowerCAmelCase  :							Union[str, Any]				     =					self.get_timesteps(__a,    __a,    self.device)
														_lowerCAmelCase  :							Dict				     =					timesteps[:1].repeat(__a)

														# Preprocess image
														_lowerCAmelCase  :							Optional[int]				     =					preprocess(__a,    __a,    __a)
														_lowerCAmelCase  :							Any				     =					self.prepare_latents(
														    __a,    __a,    __a,    text_embeddings.dtype,    self.device,    __a)

														_lowerCAmelCase  :							List[Any]				     =					preprocess(__a,    __a,    __a)
														_lowerCAmelCase  :							str				     =					self.prepare_latents(
														    __a,    __a,    __a,    text_embeddings.dtype,    self.device,    __a)

														_lowerCAmelCase  :							Tuple				     =					slerp(__a,    __a,    __a)

														if clip_guidance_scale > 0:
																					_lowerCAmelCase  :							List[str]				     =					self.get_clip_image_embeddings(__a,    __a)
																					_lowerCAmelCase  :							Optional[Any]				     =					self.get_clip_image_embeddings(__a,    __a)
																					_lowerCAmelCase  :							Optional[int]				     =					slerp(
																					    __a,    __a,    __a)

														# here `guidance_scale` is defined analog to the guidance weight `w` of equation (2)
														# of the Imagen paper: https://arxiv.org/pdf/2205.11487.pdf . `guidance_scale = 1`
														# corresponds to doing no classifier free guidance.
														_lowerCAmelCase  :							Union[str, Any]				     =					guidance_scale > 1.0
														# get unconditional embeddings for classifier free guidance
														if do_classifier_free_guidance:
																					_lowerCAmelCase  :							str				     =					content_text_input.input_ids.shape[-1]
																					_lowerCAmelCase  :							Union[str, Any]				     =					self.tokenizer([""],    padding="max_length",    max_length=__a,    return_tensors="pt")
																					_lowerCAmelCase  :							str				     =					self.text_encoder(uncond_input.input_ids.to(self.device))[0]
																					# duplicate unconditional embeddings for each generation per prompt
																					_lowerCAmelCase  :							Optional[int]				     =					uncond_embeddings.repeat_interleave(__a,    dim=0)

																					# For classifier free guidance, we need to do two forward passes.
																					# Here we concatenate the unconditional and text embeddings into a single batch
																					# to avoid doing two forward passes
																					_lowerCAmelCase  :							Optional[int]				     =					torch.cat([uncond_embeddings, text_embeddings])

														# get the initial random noise unless the user supplied it

														# Unlike in other pipelines, latents need to be generated in the target device
														# for 1-to-1 results reproducibility with the CompVis implementation.
														# However this currently doesn't work in `mps`.
														_lowerCAmelCase  :							str				     =					(batch_size, self.unet.config.in_channels, height // 8, width // 8)
														_lowerCAmelCase  :							Union[str, Any]				     =					text_embeddings.dtype
														if latents is None:
																					if self.device.type == "mps":
																												# randn does not work reproducibly on mps
																												_lowerCAmelCase  :							List[str]				     =					torch.randn(__a,    generator=__a,    device="cpu",    dtype=__a).to(
																												    self.device)
																					else:
																												_lowerCAmelCase  :							Optional[Any]				     =					torch.randn(__a,    generator=__a,    device=self.device,    dtype=__a)
														else:
																					if latents.shape != latents_shape:
																												raise ValueError(f"Unexpected latents shape, got {latents.shape}, expected {latents_shape}")
																					_lowerCAmelCase  :							Dict				     =					latents.to(self.device)

														# scale the initial noise by the standard deviation required by the scheduler
														_lowerCAmelCase  :							Tuple				     =					latents * self.scheduler.init_noise_sigma

														# prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
														# eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
														# eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
														# and should be between [0, 1]
														_lowerCAmelCase  :							List[Any]				     =					"eta" in set(inspect.signature(self.scheduler.step).parameters.keys())
														_lowerCAmelCase  :							Optional[int]				     =					{}
														if accepts_eta:
																					_lowerCAmelCase  :							List[Any]				     =					eta

														# check if the scheduler accepts generator
														_lowerCAmelCase  :							Optional[int]				     =					"generator" in set(inspect.signature(self.scheduler.step).parameters.keys())
														if accepts_generator:
																					_lowerCAmelCase  :							Optional[int]				     =					generator

														with self.progress_bar(total=__a):
																					for i, t in enumerate(__a):
																												# expand the latents if we are doing classifier free guidance
																												_lowerCAmelCase  :							List[Any]				     =					torch.cat([latents] * 2) if do_classifier_free_guidance else latents
																												_lowerCAmelCase  :							List[str]				     =					self.scheduler.scale_model_input(__a,    __a)

																												# predict the noise residual
																												_lowerCAmelCase  :							List[Any]				     =					self.unet(__a,    __a,    encoder_hidden_states=__a).sample

																												# perform classifier free guidance
																												if do_classifier_free_guidance:
																																			_lowerCAmelCase  :							List[Any]				     =					noise_pred.chunk(2)
																																			_lowerCAmelCase  :							List[Any]				     =					noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

																												# perform clip guidance
																												if clip_guidance_scale > 0:
																																			_lowerCAmelCase  :							str				     =					(
																																			    text_embeddings.chunk(2)[1] if do_classifier_free_guidance else text_embeddings
																																			)
																																			_lowerCAmelCase  :							str				     =					self.cond_fn(
																																			    __a,    __a,    __a,    __a,    __a,    __a,    __a,    )

																												# compute the previous noisy sample x_t -> x_t-1
																												_lowerCAmelCase  :							Union[str, Any]				     =					self.scheduler.step(__a,    __a,    __a,    **__a).prev_sample

        # Hardcode 0.18215 because stable-diffusion-2-base has not self.vae.config.scaling_factor
														_lowerCAmelCase  :							Tuple				     =					1 / 0.18_215 * latents
														_lowerCAmelCase  :							Optional[Any]				     =					self.vae.decode(__a).sample

														_lowerCAmelCase  :							List[Any]				     =					(image / 2 + 0.5).clamp(0,    1)
														_lowerCAmelCase  :							List[Any]				     =					image.cpu().permute(0,    2,    3,    1).numpy()

														if output_type == "pil":
																					_lowerCAmelCase  :							str				     =					self.numpy_to_pil(__a)

														if not return_dict:
																					return (image, None)

														return StableDiffusionPipelineOutput(images=__a,    nsfw_content_detected=__a)





import logging

import numpy as np
import pytest
from scipy.linalg import eigh

logging.basicConfig(level=logging.INFO, format="%(message)s")






def        A       (      _lowerCamelCase						):





							'''simple docstring'''




							return input_array.reshape((input_array.size, 1)						)






def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							_lowerCAmelCase  :							Any				     =					np.nan
							for i in range(_lowerCamelCase						):
														_lowerCAmelCase  :							Tuple				     =					features[:, labels == i]
														_lowerCAmelCase  :							Dict				     =					data.mean(1						)
														# Centralize the data of class i
														_lowerCAmelCase  :							Union[str, Any]				     =					data - column_reshape(_lowerCamelCase						)
														if i > 0:
																					# If covariance_sum is not None
																					covariance_sum += np.dot(_lowerCamelCase       ,				centered_data.T						)
														else:
																					# If covariance_sum is np.nan (i.e. first loop)
																					_lowerCAmelCase  :							int				     =					np.dot(_lowerCamelCase       ,				centered_data.T						)

							return covariance_sum / features.shape[1]






def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							_lowerCAmelCase  :							Optional[Any]				     =					features.mean(1						)
							_lowerCAmelCase  :							List[str]				     =					np.nan
							for i in range(_lowerCamelCase						):
														_lowerCAmelCase  :							str				     =					features[:, labels == i]
														_lowerCAmelCase  :							Optional[Any]				     =					data.shape[1]
														_lowerCAmelCase  :							Optional[Any]				     =					data.mean(1						)
														if i > 0:
																					# If covariance_sum is not None
																					covariance_sum += device_data * np.dot(
																					    column_reshape(_lowerCamelCase						) - column_reshape(_lowerCamelCase						)       ,				(column_reshape(_lowerCamelCase						) - column_reshape(_lowerCamelCase						)).T       ,				)
														else:
																					# If covariance_sum is np.nan (i.e. first loop)
																					_lowerCAmelCase  :							Optional[Any]				     =					device_data * np.dot(
																					    column_reshape(_lowerCamelCase						) - column_reshape(_lowerCamelCase						)       ,				(column_reshape(_lowerCamelCase						) - column_reshape(_lowerCamelCase						)).T       ,				)

							return covariance_sum / features.shape[1]






def        A       (      _lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							if features.any():
														_lowerCAmelCase  :							List[Any]				     =					features.mean(1						)
														# Center the dataset
														_lowerCAmelCase  :							List[Any]				     =					features - np.reshape(_lowerCamelCase       ,				(data_mean.size, 1)						)
														_lowerCAmelCase  :							Optional[Any]				     =					np.dot(_lowerCamelCase       ,				centered_data.T						) / features.shape[1]
														_lowerCAmelCase     ,					_lowerCAmelCase  :							List[Any]				     =					np.linalg.eigh(_lowerCamelCase						)
														# Take all the columns in the reverse order (-1), and then takes only the first
														_lowerCAmelCase  :							Union[str, Any]				     =					eigenvectors[:, ::-1][:, 0:dimensions]
														# Project the database on the new space
														_lowerCAmelCase  :							List[Any]				     =					np.dot(filtered_eigenvectors.T       ,				_lowerCamelCase						)
														logging.info("Principal Component Analysis computed"						)

														return projected_data
							else:
														logging.basicConfig(level=logging.ERROR       ,				format="%(message)s"       ,				force=_lowerCamelCase						)
														logging.error("Dataset empty"						)
														raise AssertionError






def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							assert classes > dimensions

							# Check if features have been already loaded
							if features.any:
														_lowerCAmelCase     ,					_lowerCAmelCase  :							List[str]				     =					eigh(
														    covariance_between_classes(_lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						)       ,				covariance_within_classes(_lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						)       ,				)
														_lowerCAmelCase  :							List[str]				     =					eigenvectors[:, ::-1][:, :dimensions]
														_lowerCAmelCase     ,					_lowerCAmelCase     ,					_lowerCAmelCase  :							Any				     =					np.linalg.svd(_lowerCamelCase						)
														_lowerCAmelCase  :							Optional[Any]				     =					svd_matrix[:, 0:dimensions]
														_lowerCAmelCase  :							str				     =					np.dot(filtered_svd_matrix.T       ,				_lowerCamelCase						)
														logging.info("Linear Discriminant Analysis computed"						)

														return projected_data
							else:
														logging.basicConfig(level=logging.ERROR       ,				format="%(message)s"       ,				force=_lowerCamelCase						)
														logging.error("Dataset empty"						)
														raise AssertionError






def        A       (      ):





							'''simple docstring'''




							_lowerCAmelCase  :							Optional[int]				     =					np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]						)
							_lowerCAmelCase  :							List[Any]				     =					np.array([0, 0, 0, 1, 1]						)
							_lowerCAmelCase  :							List[Any]				     =					2
							_lowerCAmelCase  :							Union[str, Any]				     =					2

							# Assert that the function raises an AssertionError if dimensions > classes
							with pytest.raises(_lowerCamelCase						) as error_info:
														_lowerCAmelCase  :							Union[str, Any]				     =					linear_discriminant_analysis(
														    _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						)
														if isinstance(_lowerCamelCase       ,				np.ndarray						):
																					raise AssertionError(
																					    "Did not raise AssertionError for dimensions > classes"						)
														assert error_info.type is AssertionError






def        A       (      ):





							'''simple docstring'''




							_lowerCAmelCase  :							Optional[Any]				     =					np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]						)
							_lowerCAmelCase  :							List[str]				     =					2
							_lowerCAmelCase  :							List[Any]				     =					np.array([[6.92_82_03_23, 8.66_02_54_04, 10.39_23_04_85], [3.0, 3.0, 3.0]]						)

							with pytest.raises(_lowerCamelCase						) as error_info:
														_lowerCAmelCase  :							Tuple				     =					principal_component_analysis(_lowerCamelCase       ,				_lowerCamelCase						)
														if not np.allclose(_lowerCamelCase       ,				_lowerCamelCase						):
																					raise AssertionError
														assert error_info.type is AssertionError


if __name__ == "__main__":
						import doctest

						doctest.testmod()
