




from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch



@dataclass
class    lowercase_		:
						lowerCAmelCase__			      =42  # [batch_size x 3]
						lowerCAmelCase__			      =42  # [batch_size x 3]
						lowerCAmelCase__			      =42  # [batch_size x 3]
						lowerCAmelCase__			      =42  # [batch_size x 3]
						lowerCAmelCase__			      =42
						lowerCAmelCase__			      =42
						lowerCAmelCase__			      =42
						lowerCAmelCase__			      =42
						lowerCAmelCase__			      =42



						def 	__a					(			self	:   Optional[Any]  ):

								"""simple docstring"""

								assert self.x.shape[0] == self.y.shape[0] == self.z.shape[0] == self.origin.shape[0]
								assert self.x.shape[1] == self.y.shape[1] == self.z.shape[1] == self.origin.shape[1] == 3
								assert len(self.x.shape  ) == len(self.y.shape  ) == len(self.z.shape  ) == len(self.origin.shape  ) == 2



						def 	__a					(			self	:   Union[str, Any]  ):

								"""simple docstring"""

								return torch.from_numpy(np.array([self.width, self.height]					,							dtype=np.floataa  )  )



						def 	__a					(			self	:   Optional[int]  ):

								"""simple docstring"""

								return torch.from_numpy(np.array([self.x_fov, self.y_fov]					,							dtype=np.floataa  )  )



						def 	__a					(			self	:   int  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							torch.arange(self.height * self.width  )
								SCREAMING_SNAKE_CASE_					      =							torch.stack(
								    [
								        pixel_indices % self.width,
								        torch.div(snake_case__					,							self.width					,							rounding_mode='trunc'  ),
								    ]					,							axis=1					,							)
								return coords



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

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_      ,				*SCREAMING_SNAKE_CASE_					      =							self.shape
								SCREAMING_SNAKE_CASE_					      =							int(np.prod(snake_case__  )  )

								SCREAMING_SNAKE_CASE_					      =							self.get_image_coords()
								SCREAMING_SNAKE_CASE_					      =							torch.broadcast_to(coords.unsqueeze(0  )					,							[batch_size * inner_batch_size, *coords.shape]  )
								SCREAMING_SNAKE_CASE_					      =							self.get_camera_rays(snake_case__  )

								SCREAMING_SNAKE_CASE_					      =							rays.view(snake_case__					,							inner_batch_size * self.height * self.width					,							2					,							3  )

								return rays



						def 	__a					(			self	:   Optional[Any]					,							snake_case__	:   torch.Tensor  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_      ,				*SCREAMING_SNAKE_CASE_      ,				SCREAMING_SNAKE_CASE_					      =							coords.shape
								assert n_coords == 2
								assert batch_size == self.origin.shape[0]

								SCREAMING_SNAKE_CASE_					      =							coords.view(snake_case__					,							-1					,							2  )

								SCREAMING_SNAKE_CASE_					      =							self.resolution()
								SCREAMING_SNAKE_CASE_					      =							self.fov()

								SCREAMING_SNAKE_CASE_					      =							(flat.float() / (res - 1)) * 2 - 1
								SCREAMING_SNAKE_CASE_					      =							fracs * torch.tan(fov / 2  )

								SCREAMING_SNAKE_CASE_					      =							fracs.view(snake_case__					,							-1					,							2  )
								SCREAMING_SNAKE_CASE_					      =							(
								    self.z.view(snake_case__					,							1					,							3  )
								    + self.x.view(snake_case__					,							1					,							3  ) * fracs[:, :, :1]
								    + self.y.view(snake_case__					,							1					,							3  ) * fracs[:, :, 1:]
								)
								SCREAMING_SNAKE_CASE_					      =							directions / directions.norm(dim=-1					,							keepdim=snake_case__  )
								SCREAMING_SNAKE_CASE_					      =							torch.stack(
								    [
								        torch.broadcast_to(self.origin.view(snake_case__					,							1					,							3  )					,							[batch_size, directions.shape[1], 3]  ),
								        directions,
								    ]					,							dim=2					,							)
								return rays.view(snake_case__					,							*snake_case__					,							2					,							3  )






						def 	__a					(			self	:   Optional[int]					,							snake_case__	:   int					,							snake_case__	:   int  ):

								"""simple docstring"""

								assert width * self.height == height * self.width, "The aspect ratio should not change."
								return DifferentiableProjectiveCamera(
								    origin=self.origin					,							x=self.x					,							y=self.y					,							z=self.z					,							width=snake_case__					,							height=snake_case__					,							x_fov=self.x_fov					,							y_fov=self.y_fov					,							)


def 					_a							(					lowerCAmelCase )->	DifferentiableProjectiveCamera:
		SCREAMING_SNAKE_CASE_					      =							[]
		SCREAMING_SNAKE_CASE_					      =							[]
		SCREAMING_SNAKE_CASE_					      =							[]
		SCREAMING_SNAKE_CASE_					      =							[]
		for theta in np.linspace(0    ,						2 * np.pi    ,						num=20 ):
				SCREAMING_SNAKE_CASE_					      =							np.array([np.sin(lowerCAmelCase ), np.cos(lowerCAmelCase ), -0.5] )
				z /= np.sqrt(np.sum(z**2 ) )
				SCREAMING_SNAKE_CASE_					      =							-z * 4
				SCREAMING_SNAKE_CASE_					      =							np.array([np.cos(lowerCAmelCase ), -np.sin(lowerCAmelCase ), 0.0] )
				SCREAMING_SNAKE_CASE_					      =							np.cross(lowerCAmelCase    ,						lowerCAmelCase )
				origins.append(lowerCAmelCase )
				xs.append(lowerCAmelCase )
				ys.append(lowerCAmelCase )
				zs.append(lowerCAmelCase )
		return DifferentiableProjectiveCamera(
		    origin=torch.from_numpy(np.stack(lowerCAmelCase    ,						axis=0 ) ).float()    ,						x=torch.from_numpy(np.stack(lowerCAmelCase    ,						axis=0 ) ).float()    ,						y=torch.from_numpy(np.stack(lowerCAmelCase    ,						axis=0 ) ).float()    ,						z=torch.from_numpy(np.stack(lowerCAmelCase    ,						axis=0 ) ).float()    ,						width=lowerCAmelCase    ,						height=lowerCAmelCase    ,						x_fov=0.7    ,						y_fov=0.7    ,						shape=(1, len(lowerCAmelCase ))    ,						)





import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize


def 					_a							(					lowerCAmelCase )->	float:
		return np.dot(lowerCAmelCase    ,						lowerCAmelCase )



class    lowercase_		:



						def __init__(			self	:   int					,							*,
						    snake_case__	:   float = np.inf					,							snake_case__	:   str = "linear"					,							snake_case__	:   float = 0.0					,							):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							regularization
								SCREAMING_SNAKE_CASE_					      =							gamma
								if kernel == "linear":
										SCREAMING_SNAKE_CASE_					      =							self.__linear
								elif kernel == "rbf":
										if self.gamma == 0:
												raise ValueError('rbf kernel requires gamma'  )
										if not isinstance(self.gamma					,							(float, int)  ):
												raise ValueError('gamma must be float or int'  )
										if not self.gamma > 0:
												raise ValueError('gamma must be > 0'  )
										SCREAMING_SNAKE_CASE_					      =							self.__rbf
										# in the future, there could be a default value like in sklearn
										# sklear: def_gamma = 1/(n_features * X.var()) (wiki)
										# previously it was 1/(n_features)
								else:
										SCREAMING_SNAKE_CASE_					      =							f'''Unknown kernel: {kernel}'''
										raise ValueError(snake_case__  )



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

								"""simple docstring"""

								return np.dot(snake_case__					,							snake_case__  )



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

								"""simple docstring"""

								return np.exp(-(self.gamma * norm_squared(vectora - vectora  ))  )



						def 	__a					(			self	:   int					,							snake_case__	:   list[ndarray]					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							observations
								SCREAMING_SNAKE_CASE_					      =							classes

								# using Wolfe's Dual to calculate w.
								# Primal problem: minimize 1/2*norm_squared(w)
								#   constraint: yn(w . xn + b) >= 1
								#
								# With l a vector
								# Dual problem: maximize sum_n(ln) -
								#       1/2 * sum_n(sum_m(ln*lm*yn*ym*xn . xm))
								#   constraint: self.C >= ln >= 0
								#           and sum_n(ln*yn) = 0
								# Then we get w using w = sum_n(ln*yn*xn)
								# At the end we can get b ~= mean(yn - w . xn)
								#
								# Since we use kernels, we only need l_star to calculate b
								# and to classify observations

								((SCREAMING_SNAKE_CASE_)      ,				)					      =							np.shape(snake_case__  )

								def to_minimize(snake_case__	:   ndarray  ) -> float:
										SCREAMING_SNAKE_CASE_					      =							0
										((SCREAMING_SNAKE_CASE_)      ,				)					      =							np.shape(snake_case__  )
										for i in range(snake_case__  ):
												for j in range(snake_case__  ):
														s += (
														    candidate[i]
														    * candidate[j]
														    * classes[i]
														    * classes[j]
														    * self.kernel(observations[i]					,							observations[j]  )
														)
										return 1 / 2 * s - sum(snake_case__  )

								SCREAMING_SNAKE_CASE_					      =							LinearConstraint(snake_case__					,							0					,							0  )
								SCREAMING_SNAKE_CASE_					      =							Bounds(0					,							self.regularization  )

								SCREAMING_SNAKE_CASE_					      =							minimize(
								    snake_case__					,							np.ones(snake_case__  )					,							bounds=snake_case__					,							constraints=[ly_contraint]  ).x
								SCREAMING_SNAKE_CASE_					      =							l_star

								# calculating mean offset of separation plane to points
								SCREAMING_SNAKE_CASE_					      =							0
								for i in range(snake_case__  ):
										for j in range(snake_case__  ):
												s += classes[i] - classes[i] * self.optimum[i] * self.kernel(
												    observations[i]					,							observations[j]  )
								SCREAMING_SNAKE_CASE_					      =							s / n






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

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							sum(
								    self.optimum[n]
								    * self.classes[n]
								    * self.kernel(self.observations[n]					,							snake_case__  )
								    for n in range(len(self.classes  )  )  )
								return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
						import doctest

						doctest.testmod()