




from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch



@dataclass
class       a_       :
	A    							= 42  # [batch_size x 3]
	A    							= 42  # [batch_size x 3]
	A    							= 42  # [batch_size x 3]
	A    							= 42  # [batch_size x 3]
	A    							= 42
	A    							= 42
	A    							= 42
	A    							= 42
	A    							= 42





	def 						A_(							self      )  ->					Union[str, 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      )  ->					Optional[int]:




				"""simple docstring"""



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





	def 						A_(							self      )  ->					str:




				"""simple docstring"""



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





	def 						A_(							self      )  ->					torch.Tensor:




				"""simple docstring"""



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





	@property
	def 						A_(							self      )  ->					Optional[int]:




				"""simple docstring"""



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

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

				return rays





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





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      )  ->					"DifferentiableProjectiveCamera":




				"""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=SCREAMING_SNAKE_CASE      ,     height=SCREAMING_SNAKE_CASE      ,     x_fov=self.x_fov      ,     y_fov=self.y_fov      ,     )




def lowercase    (  SCREAMING_SNAKE_CASE )			->							DifferentiableProjectiveCamera:


			'''simple docstring'''







			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(SCREAMING_SNAKE_CASE ), np.cos(SCREAMING_SNAKE_CASE ), -0.5] )
						z /= np.sqrt(np.sum(z**2 ) )
						SCREAMING_SNAKE_CASE_								=						-z * 4
						SCREAMING_SNAKE_CASE_								=						np.array([np.cos(SCREAMING_SNAKE_CASE ), -np.sin(SCREAMING_SNAKE_CASE ), 0.0] )
						SCREAMING_SNAKE_CASE_								=						np.cross(SCREAMING_SNAKE_CASE       ,    SCREAMING_SNAKE_CASE )
						origins.append(SCREAMING_SNAKE_CASE )
						xs.append(SCREAMING_SNAKE_CASE )
						ys.append(SCREAMING_SNAKE_CASE )
						zs.append(SCREAMING_SNAKE_CASE )
			return DifferentiableProjectiveCamera(
			    origin=torch.from_numpy(np.stack(SCREAMING_SNAKE_CASE       ,    axis=0 ) ).float()       ,    x=torch.from_numpy(np.stack(SCREAMING_SNAKE_CASE       ,    axis=0 ) ).float()       ,    y=torch.from_numpy(np.stack(SCREAMING_SNAKE_CASE       ,    axis=0 ) ).float()       ,    z=torch.from_numpy(np.stack(SCREAMING_SNAKE_CASE       ,    axis=0 ) ).float()       ,    width=SCREAMING_SNAKE_CASE       ,    height=SCREAMING_SNAKE_CASE       ,    x_fov=0.7       ,    y_fov=0.7       ,    shape=(1, len(SCREAMING_SNAKE_CASE ))       ,    )






from __future__ import annotations

from decimal import Decimal

from numpy import array

def lowercase    (  SCREAMING_SNAKE_CASE )			->							list[list[float]]:


			'''simple docstring'''







			SCREAMING_SNAKE_CASE_								=						Decimal

			# Check if the provided matrix has 2 rows and 2 columns
			# since this implementation only works for 2x2 matrices
			if len(SCREAMING_SNAKE_CASE ) == 2 and len(matrix[0] ) == 2 and len(matrix[1] ) == 2:
						# Calculate the determinant of the matrix
						SCREAMING_SNAKE_CASE_								=						float(
						    d(matrix[0][0] ) * d(matrix[1][1] ) - d(matrix[1][0] ) * d(matrix[0][1] ) )
						if determinant == 0:
									raise ValueError('This matrix has no inverse.' )

						# Creates a copy of the matrix with swapped positions of the elements
						SCREAMING_SNAKE_CASE_								=						[[0.0, 0.0], [0.0, 0.0]]
						SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						matrix[1][1], matrix[0][0]
						SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						-matrix[1][0], -matrix[0][1]

						# Calculate the inverse of the matrix
						return [
						    [(float(d(SCREAMING_SNAKE_CASE ) ) / determinant) or 0.0 for n in row] for row in swapped_matrix
						]
			elif (
			    len(SCREAMING_SNAKE_CASE ) == 3
			    and len(matrix[0] ) == 3
			    and len(matrix[1] ) == 3
			    and len(matrix[2] ) == 3
			):
						# Calculate the determinant of the matrix using Sarrus rule
						SCREAMING_SNAKE_CASE_								=						float(
						    (
						        (d(matrix[0][0] ) * d(matrix[1][1] ) * d(matrix[2][2] ))
						        + (d(matrix[0][1] ) * d(matrix[1][2] ) * d(matrix[2][0] ))
						        + (d(matrix[0][2] ) * d(matrix[1][0] ) * d(matrix[2][1] ))
						    )
						    - (
						        (d(matrix[0][2] ) * d(matrix[1][1] ) * d(matrix[2][0] ))
						        + (d(matrix[0][1] ) * d(matrix[1][0] ) * d(matrix[2][2] ))
						        + (d(matrix[0][0] ) * d(matrix[1][2] ) * d(matrix[2][1] ))
						    ) )
						if determinant == 0:
									raise ValueError('This matrix has no inverse.' )

						# Creating cofactor matrix
						SCREAMING_SNAKE_CASE_								=						[
						    [d(0.0 ), d(0.0 ), d(0.0 )],
						    [d(0.0 ), d(0.0 ), d(0.0 )],
						    [d(0.0 ), d(0.0 ), d(0.0 )],
						]
						SCREAMING_SNAKE_CASE_								=						(d(matrix[1][1] ) * d(matrix[2][2] )) - (
						    d(matrix[1][2] ) * d(matrix[2][1] )
						)
						SCREAMING_SNAKE_CASE_								=						-(
						    (d(matrix[1][0] ) * d(matrix[2][2] )) - (d(matrix[1][2] ) * d(matrix[2][0] ))
						)
						SCREAMING_SNAKE_CASE_								=						(d(matrix[1][0] ) * d(matrix[2][1] )) - (
						    d(matrix[1][1] ) * d(matrix[2][0] )
						)
						SCREAMING_SNAKE_CASE_								=						-(
						    (d(matrix[0][1] ) * d(matrix[2][2] )) - (d(matrix[0][2] ) * d(matrix[2][1] ))
						)
						SCREAMING_SNAKE_CASE_								=						(d(matrix[0][0] ) * d(matrix[2][2] )) - (
						    d(matrix[0][2] ) * d(matrix[2][0] )
						)
						SCREAMING_SNAKE_CASE_								=						-(
						    (d(matrix[0][0] ) * d(matrix[2][1] )) - (d(matrix[0][1] ) * d(matrix[2][0] ))
						)
						SCREAMING_SNAKE_CASE_								=						(d(matrix[0][1] ) * d(matrix[1][2] )) - (
						    d(matrix[0][2] ) * d(matrix[1][1] )
						)
						SCREAMING_SNAKE_CASE_								=						-(
						    (d(matrix[0][0] ) * d(matrix[1][2] )) - (d(matrix[0][2] ) * d(matrix[1][0] ))
						)
						SCREAMING_SNAKE_CASE_								=						(d(matrix[0][0] ) * d(matrix[1][1] )) - (
						    d(matrix[0][1] ) * d(matrix[1][0] )
						)

						# Transpose the cofactor matrix (Adjoint matrix)
						SCREAMING_SNAKE_CASE_								=						array(SCREAMING_SNAKE_CASE )
						for i in range(3 ):
									for j in range(3 ):
												SCREAMING_SNAKE_CASE_								=						cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
						SCREAMING_SNAKE_CASE_								=						array(SCREAMING_SNAKE_CASE )
						for i in range(3 ):
									for j in range(3 ):
												inverse_matrix[i][j] /= d(SCREAMING_SNAKE_CASE )

        # Calculate the inverse of the matrix
						return [[float(d(SCREAMING_SNAKE_CASE ) ) or 0.0 for n in row] for row in inverse_matrix]
			raise ValueError('Please provide a matrix of size 2x2 or 3x3.' )
