



"""simple docstring"""


from __future__ import annotations

from decimal import Decimal

from numpy import array

def 			_lowerCAmelCase				(       lowercase_						):
						UpperCAmelCase					=			Decimal

						# Check if the provided matrix has 2 rows and 2 columns
						# since this implementation only works for 2x2 matrices
						if len(lowercase_						) == 2 and len(matrix[0]						) == 2 and len(matrix[1]						) == 2:
												# Calculate the determinant of the matrix
												UpperCAmelCase					=			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
												UpperCAmelCase					=			[[0.0, 0.0], [0.0, 0.0]]
												UpperCAmelCase				,   UpperCAmelCase					=			matrix[1][1], matrix[0][0]
												UpperCAmelCase				,   UpperCAmelCase					=			-matrix[1][0], -matrix[0][1]

												# Calculate the inverse of the matrix
												return [
												    [(float(d(lowercase_						)						) / determinant) or 0.0 for n in row] for row in swapped_matrix
												]
						elif (
						    len(lowercase_						) == 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
												UpperCAmelCase					=			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
												UpperCAmelCase					=			[
												    [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						)],
												]
												UpperCAmelCase					=			(d(matrix[1][1]						) * d(matrix[2][2]						)) - (
												    d(matrix[1][2]						) * d(matrix[2][1]						)
												)
												UpperCAmelCase					=			-(
												    (d(matrix[1][0]						) * d(matrix[2][2]						)) - (d(matrix[1][2]						) * d(matrix[2][0]						))
												)
												UpperCAmelCase					=			(d(matrix[1][0]						) * d(matrix[2][1]						)) - (
												    d(matrix[1][1]						) * d(matrix[2][0]						)
												)
												UpperCAmelCase					=			-(
												    (d(matrix[0][1]						) * d(matrix[2][2]						)) - (d(matrix[0][2]						) * d(matrix[2][1]						))
												)
												UpperCAmelCase					=			(d(matrix[0][0]						) * d(matrix[2][2]						)) - (
												    d(matrix[0][2]						) * d(matrix[2][0]						)
												)
												UpperCAmelCase					=			-(
												    (d(matrix[0][0]						) * d(matrix[2][1]						)) - (d(matrix[0][1]						) * d(matrix[2][0]						))
												)
												UpperCAmelCase					=			(d(matrix[0][1]						) * d(matrix[1][2]						)) - (
												    d(matrix[0][2]						) * d(matrix[1][1]						)
												)
												UpperCAmelCase					=			-(
												    (d(matrix[0][0]						) * d(matrix[1][2]						)) - (d(matrix[0][2]						) * d(matrix[1][0]						))
												)
												UpperCAmelCase					=			(d(matrix[0][0]						) * d(matrix[1][1]						)) - (
												    d(matrix[0][1]						) * d(matrix[1][0]						)
												)

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

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

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










"""simple docstring"""


import math

import flax.linen as nn
import jax.numpy as jnp

def 			_lowerCAmelCase				(       lowercase_		,     lowercase_		,     lowercase_ = 1		,     lowercase_ = 1		,     lowercase_ = 1.0e4		,     lowercase_ = False		,     lowercase_ = 1.0		,     ):
						assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
						assert embedding_dim % 2 == 0, F"""Embedding dimension {embedding_dim} should be even"""
						UpperCAmelCase					=			float(embedding_dim // 2						)
						UpperCAmelCase					=			math.log(max_timescale / min_timescale						) / (num_timescales - freq_shift)
						UpperCAmelCase					=			min_timescale * jnp.exp(jnp.arange(lowercase_		,     dtype=jnp.floataa						) * -log_timescale_increment						)
						UpperCAmelCase					=			jnp.expand_dims(lowercase_		,     1						) * jnp.expand_dims(lowercase_		,     0						)

						# scale embeddings
						UpperCAmelCase					=			scale * emb

						if flip_sin_to_cos:
												UpperCAmelCase					=			jnp.concatenate([jnp.cos(lowercase_						), jnp.sin(lowercase_						)]		,     axis=1						)
						else:
												UpperCAmelCase					=			jnp.concatenate([jnp.sin(lowercase_						), jnp.cos(lowercase_						)]		,     axis=1						)
						UpperCAmelCase					=			jnp.reshape(lowercase_		,     [jnp.shape(lowercase_						)[0], embedding_dim]						)
						return signal







class 				A_      (					nn.Module    ):



						"""simple docstring"""
						__UpperCamelCase		    =							32
						__UpperCamelCase		    =							jnp.floataa






						@nn.compact
						def __call__( self			:Union[str, Any]       ,  lowercase_			:Tuple )    ->      str:
												UpperCAmelCase					=			nn.Dense(self.time_embed_dim       ,  dtype=self.dtype       ,  name='linear_1' )(lowercase_ )
												UpperCAmelCase					=			nn.silu(lowercase_ )
												UpperCAmelCase					=			nn.Dense(self.time_embed_dim       ,  dtype=self.dtype       ,  name='linear_2' )(lowercase_ )
												return temb







class 				A_      (					nn.Module    ):



						"""simple docstring"""
						__UpperCamelCase		    =							32
						__UpperCamelCase		    =							False
						__UpperCamelCase		    =							1






						@nn.compact
						def __call__( self			:Any       ,  lowercase_			:int )    ->      Union[str, Any]:
												return get_sinusoidal_embeddings(
												    lowercase_       ,  embedding_dim=self.dim       ,  flip_sin_to_cos=self.flip_sin_to_cos       ,  freq_shift=self.freq_shift )





