
import functools
import math

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




def 		A						(  SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE = 4096							):




			"""simple docstring"""


			UpperCAmelCase__		,       UpperCAmelCase__		,       UpperCAmelCase__		:List[str] 		=    key.shape[-3:]
			UpperCAmelCase__		:List[str] 		=    value.shape[-1]
			UpperCAmelCase__		:str 		=    min(SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE							)
			UpperCAmelCase__		:Union[str, Any] 		=    query / jnp.sqrt(SCREAMING_SNAKE_CASE							)

			@functools.partial(jax.checkpoint     ,						prevent_cse=SCREAMING_SNAKE_CASE							)
			def summarize_chunk(SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE							):
						UpperCAmelCase__		:Optional[Any] 		=    jnp.einsum('...qhd,...khd->...qhk'     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						precision=SCREAMING_SNAKE_CASE							)

						UpperCAmelCase__		:Any 		=    jnp.max(SCREAMING_SNAKE_CASE     ,						axis=-1     ,						keepdims=SCREAMING_SNAKE_CASE							)
						UpperCAmelCase__		:Union[str, Any] 		=    jax.lax.stop_gradient(SCREAMING_SNAKE_CASE							)
						UpperCAmelCase__		:str 		=    jnp.exp(attn_weights - max_score							)

						UpperCAmelCase__		:Any 		=    jnp.einsum('...vhf,...qhv->...qhf'     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						precision=SCREAMING_SNAKE_CASE							)
						UpperCAmelCase__		:Any 		=    jnp.einsum('...qhk->...qh'     ,						SCREAMING_SNAKE_CASE							)

						return (exp_values, exp_weights.sum(axis=-1							), max_score)

			def chunk_scanner(SCREAMING_SNAKE_CASE							):
						# julienne key array
						UpperCAmelCase__		:Dict 		=    jax.lax.dynamic_slice(
						    operand=SCREAMING_SNAKE_CASE     ,						start_indices=[0] * (key.ndim - 3) + [chunk_idx, 0, 0]     ,						slice_sizes=list(key.shape[:-3]							) + [key_chunk_size, num_heads, k_features]     ,						)

						# julienne value array
						UpperCAmelCase__		:Union[str, Any] 		=    jax.lax.dynamic_slice(
						    operand=SCREAMING_SNAKE_CASE     ,						start_indices=[0] * (value.ndim - 3) + [chunk_idx, 0, 0]     ,						slice_sizes=list(value.shape[:-3]							) + [key_chunk_size, num_heads, v_features]     ,						)

						return summarize_chunk(SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE							)

			UpperCAmelCase__		,       UpperCAmelCase__		,       UpperCAmelCase__		:str 		=    jax.lax.map(f=SCREAMING_SNAKE_CASE     ,						xs=jnp.arange(0     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE							)							)

			UpperCAmelCase__		:Union[str, Any] 		=    jnp.max(SCREAMING_SNAKE_CASE     ,						axis=0     ,						keepdims=SCREAMING_SNAKE_CASE							)
			UpperCAmelCase__		:Union[str, Any] 		=    jnp.exp(chunk_max - global_max							)

			chunk_values *= jnp.expand_dims(SCREAMING_SNAKE_CASE     ,						axis=-1							)
			chunk_weights *= max_diffs

			UpperCAmelCase__		:Union[str, Any] 		=    chunk_values.sum(axis=0							)
			UpperCAmelCase__		:Dict 		=    jnp.expand_dims(SCREAMING_SNAKE_CASE     ,						-1							).sum(axis=0							)

			return all_values / all_weights




def 		A						(  SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE=jax.lax.Precision.HIGHEST     ,						SCREAMING_SNAKE_CASE = 1024     ,						SCREAMING_SNAKE_CASE = 4096							):




			"""simple docstring"""


			UpperCAmelCase__		,       UpperCAmelCase__		,       UpperCAmelCase__		:Union[str, Any] 		=    query.shape[-3:]

			def chunk_scanner(SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE							):
						# julienne query array
						UpperCAmelCase__		:Dict 		=    jax.lax.dynamic_slice(
						    operand=SCREAMING_SNAKE_CASE     ,						start_indices=([0] * (query.ndim - 3)) + [chunk_idx, 0, 0]     ,						slice_sizes=list(query.shape[:-3]							) + [min(SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE							), num_heads, q_features]     ,						)

						return (
						    chunk_idx + query_chunk_size,  # unused ignore it
						    _query_chunk_attention(
						        query=SCREAMING_SNAKE_CASE     ,						key=SCREAMING_SNAKE_CASE     ,						value=SCREAMING_SNAKE_CASE     ,						precision=SCREAMING_SNAKE_CASE     ,						key_chunk_size=SCREAMING_SNAKE_CASE							),
						)

			UpperCAmelCase__		,       UpperCAmelCase__		:Optional[Any] 		=    jax.lax.scan(
			    f=SCREAMING_SNAKE_CASE     ,						init=0     ,						xs=SCREAMING_SNAKE_CASE     ,						length=math.ceil(num_q / query_chunk_size							)							)

			return jnp.concatenate(SCREAMING_SNAKE_CASE     ,						axis=-3							)  # fuse the chunked result back


class 	UpperCamelCase__       (  nn.Module):

						'''simple docstring'''



						__a     :    int
						__a     :    int												=			8
						__a     :    int												=			6_4
						__a     :    float												=			0.0
						__a     :    bool												=			False
						__a     :    jnp.dtype												=			jnp.floataa


						def    A__       (  self	)  ->List[Any]:
									UpperCAmelCase__		:Tuple 		=    self.dim_head * self.heads
									UpperCAmelCase__		:Optional[Any] 		=    self.dim_head**-0.5

									# Weights were exported with old names {to_q, to_k, to_v, to_out}
									UpperCAmelCase__		:Union[str, Any] 		=    nn.Dense(A  , use_bias=A  , dtype=self.dtype  , name='to_q'	)
									UpperCAmelCase__		:Optional[Any] 		=    nn.Dense(A  , use_bias=A  , dtype=self.dtype  , name='to_k'	)
									UpperCAmelCase__		:Union[str, Any] 		=    nn.Dense(A  , use_bias=A  , dtype=self.dtype  , name='to_v'	)

									UpperCAmelCase__		:List[str] 		=    nn.Dense(self.query_dim  , dtype=self.dtype  , name='to_out_0'	)
									UpperCAmelCase__		:Tuple 		=    nn.Dropout(rate=self.dropout	)


						def    A__       (  self  , A	)  ->str:
									UpperCAmelCase__		,       UpperCAmelCase__		,       UpperCAmelCase__		:Any 		=    tensor.shape
									UpperCAmelCase__		:Dict 		=    self.heads
									UpperCAmelCase__		:Dict 		=    tensor.reshape(A  , A  , A  , dim // head_size	)
									UpperCAmelCase__		:Optional[Any] 		=    jnp.transpose(A  , (0, 2, 1, 3)	)
									UpperCAmelCase__		:Optional[int] 		=    tensor.reshape(batch_size * head_size  , A  , dim // head_size	)
									return tensor


						def    A__       (  self  , A	)  ->int:
									UpperCAmelCase__		,       UpperCAmelCase__		,       UpperCAmelCase__		:Optional[Any] 		=    tensor.shape
									UpperCAmelCase__		:List[Any] 		=    self.heads
									UpperCAmelCase__		:List[Any] 		=    tensor.reshape(batch_size // head_size  , A  , A  , A	)
									UpperCAmelCase__		:Any 		=    jnp.transpose(A  , (0, 2, 1, 3)	)
									UpperCAmelCase__		:int 		=    tensor.reshape(batch_size // head_size  , A  , dim * head_size	)
									return tensor


						def __call__(  self  , A  , A=None  , A=True	)  ->Optional[int]:
									UpperCAmelCase__		:Any 		=    hidden_states if context is None else context

									UpperCAmelCase__		:Union[str, Any] 		=    self.query(A	)
									UpperCAmelCase__		:Tuple 		=    self.key(A	)
									UpperCAmelCase__		:Optional[int] 		=    self.value(A	)

									UpperCAmelCase__		:Tuple 		=    self.reshape_heads_to_batch_dim(A	)
									UpperCAmelCase__		:Dict 		=    self.reshape_heads_to_batch_dim(A	)
									UpperCAmelCase__		:Dict 		=    self.reshape_heads_to_batch_dim(A	)

									if self.use_memory_efficient_attention:
												UpperCAmelCase__		:Dict 		=    query_states.transpose(1  , 0  , 2	)
												UpperCAmelCase__		:int 		=    key_states.transpose(1  , 0  , 2	)
												UpperCAmelCase__		:List[str] 		=    value_states.transpose(1  , 0  , 2	)

												# this if statement create a chunk size for each layer of the unet
												# the chunk size is equal to the query_length dimension of the deepest layer of the unet

												UpperCAmelCase__		:Dict 		=    query_states.shape[-3]
												if flatten_latent_dim % 64 == 0:
															UpperCAmelCase__		:str 		=    int(flatten_latent_dim / 64	)
												elif flatten_latent_dim % 16 == 0:
															UpperCAmelCase__		:List[Any] 		=    int(flatten_latent_dim / 16	)
												elif flatten_latent_dim % 4 == 0:
															UpperCAmelCase__		:Union[str, Any] 		=    int(flatten_latent_dim / 4	)
												else:
															UpperCAmelCase__		:Optional[int] 		=    int(A	)

												UpperCAmelCase__		:List[Any] 		=    jax_memory_efficient_attention(
												    A  , A  , A  , query_chunk_size=A  , key_chunk_size=40_96 * 4	)

												UpperCAmelCase__		:int 		=    hidden_states.transpose(1  , 0  , 2	)
									else:
												# compute attentions
												UpperCAmelCase__		:Optional[int] 		=    jnp.einsum('b i d, b j d->b i j'  , A  , A	)
												UpperCAmelCase__		:Optional[Any] 		=    attention_scores * self.scale
												UpperCAmelCase__		:Optional[int] 		=    nn.softmax(A  , axis=2	)

												# attend to values
												UpperCAmelCase__		:Any 		=    jnp.einsum('b i j, b j d -> b i d'  , A  , A	)

									UpperCAmelCase__		:Dict 		=    self.reshape_batch_dim_to_heads(A	)
									UpperCAmelCase__		:List[str] 		=    self.proj_attn(A	)
									return self.dropout_layer(A  , deterministic=A	)


class 	UpperCamelCase__       (  nn.Module):

						'''simple docstring'''



						__a     :    int
						__a     :    int
						__a     :    int
						__a     :    float												=			0.0
						__a     :    bool												=			False
						__a     :    jnp.dtype												=			jnp.floataa
						__a     :    bool												=			False


						def    A__       (  self	)  ->Optional[Any]:
									# self attention (or cross_attention if only_cross_attention is True)
									UpperCAmelCase__		:List[Any] 		=    FlaxAttention(
									    self.dim  , self.n_heads  , self.d_head  , self.dropout  , self.use_memory_efficient_attention  , dtype=self.dtype	)
									# cross attention
									UpperCAmelCase__		:int 		=    FlaxAttention(
									    self.dim  , self.n_heads  , self.d_head  , self.dropout  , self.use_memory_efficient_attention  , dtype=self.dtype	)
									UpperCAmelCase__		:str 		=    FlaxFeedForward(dim=self.dim  , dropout=self.dropout  , dtype=self.dtype	)
									UpperCAmelCase__		:Tuple 		=    nn.LayerNorm(epsilon=1e-5  , dtype=self.dtype	)
									UpperCAmelCase__		:Any 		=    nn.LayerNorm(epsilon=1e-5  , dtype=self.dtype	)
									UpperCAmelCase__		:Union[str, Any] 		=    nn.LayerNorm(epsilon=1e-5  , dtype=self.dtype	)
									UpperCAmelCase__		:Optional[int] 		=    nn.Dropout(rate=self.dropout	)


						def __call__(  self  , A  , A  , A=True	)  ->Dict:
									# self attention
									UpperCAmelCase__		:Dict 		=    hidden_states
									if self.only_cross_attention:
												UpperCAmelCase__		:List[Any] 		=    self.attna(self.norma(A	)  , A  , deterministic=A	)
									else:
												UpperCAmelCase__		:Union[str, Any] 		=    self.attna(self.norma(A	)  , deterministic=A	)
									UpperCAmelCase__		:List[Any] 		=    hidden_states + residual

									# cross attention
									UpperCAmelCase__		:Optional[int] 		=    hidden_states
									UpperCAmelCase__		:Optional[Any] 		=    self.attna(self.norma(A	)  , A  , deterministic=A	)
									UpperCAmelCase__		:Optional[int] 		=    hidden_states + residual

									# feed forward
									UpperCAmelCase__		:List[str] 		=    hidden_states
									UpperCAmelCase__		:Optional[Any] 		=    self.ff(self.norma(A	)  , deterministic=A	)
									UpperCAmelCase__		:Optional[Any] 		=    hidden_states + residual

									return self.dropout_layer(A  , deterministic=A	)


class 	UpperCamelCase__       (  nn.Module):

						'''simple docstring'''



						__a     :    int
						__a     :    int
						__a     :    int
						__a     :    int												=			1
						__a     :    float												=			0.0
						__a     :    bool												=			False
						__a     :    bool												=			False
						__a     :    jnp.dtype												=			jnp.floataa
						__a     :    bool												=			False


						def    A__       (  self	)  ->List[str]:
									UpperCAmelCase__		:Dict 		=    nn.GroupNorm(num_groups=32  , epsilon=1e-5	)

									UpperCAmelCase__		:List[Any] 		=    self.n_heads * self.d_head
									if self.use_linear_projection:
												UpperCAmelCase__		:str 		=    nn.Dense(A  , dtype=self.dtype	)
									else:
												UpperCAmelCase__		:Optional[Any] 		=    nn.Conv(
												    A  , kernel_size=(1, 1)  , strides=(1, 1)  , padding='VALID'  , dtype=self.dtype  , )

									UpperCAmelCase__		:Tuple 		=    [
									    FlaxBasicTransformerBlock(
									        A  , self.n_heads  , self.d_head  , dropout=self.dropout  , only_cross_attention=self.only_cross_attention  , dtype=self.dtype  , use_memory_efficient_attention=self.use_memory_efficient_attention  , )
									    for _ in range(self.depth	)
									]

									if self.use_linear_projection:
												UpperCAmelCase__		:Any 		=    nn.Dense(A  , dtype=self.dtype	)
									else:
												UpperCAmelCase__		:Dict 		=    nn.Conv(
												    A  , kernel_size=(1, 1)  , strides=(1, 1)  , padding='VALID'  , dtype=self.dtype  , )

									UpperCAmelCase__		:List[str] 		=    nn.Dropout(rate=self.dropout	)


						def __call__(  self  , A  , A  , A=True	)  ->int:
									UpperCAmelCase__		,       UpperCAmelCase__		,       UpperCAmelCase__		,       UpperCAmelCase__		:List[Any] 		=    hidden_states.shape
									UpperCAmelCase__		:Any 		=    hidden_states
									UpperCAmelCase__		:Any 		=    self.norm(A	)
									if self.use_linear_projection:
												UpperCAmelCase__		:Any 		=    hidden_states.reshape(A  , height * width  , A	)
												UpperCAmelCase__		:Tuple 		=    self.proj_in(A	)
									else:
												UpperCAmelCase__		:Optional[int] 		=    self.proj_in(A	)
												UpperCAmelCase__		:int 		=    hidden_states.reshape(A  , height * width  , A	)

									for transformer_block in self.transformer_blocks:
												UpperCAmelCase__		:Optional[Any] 		=    transformer_block(A  , A  , deterministic=A	)

									if self.use_linear_projection:
												UpperCAmelCase__		:Optional[int] 		=    self.proj_out(A	)
												UpperCAmelCase__		:int 		=    hidden_states.reshape(A  , A  , A  , A	)
									else:
												UpperCAmelCase__		:Dict 		=    hidden_states.reshape(A  , A  , A  , A	)
												UpperCAmelCase__		:List[Any] 		=    self.proj_out(A	)

									UpperCAmelCase__		:int 		=    hidden_states + residual
									return self.dropout_layer(A  , deterministic=A	)


class 	UpperCamelCase__       (  nn.Module):

						'''simple docstring'''



						__a     :    int
						__a     :    float												=			0.0
						__a     :    jnp.dtype												=			jnp.floataa


						def    A__       (  self	)  ->List[str]:
									# The second linear layer needs to be called
									# net_2 for now to match the index of the Sequential layer
									UpperCAmelCase__		:Optional[Any] 		=    FlaxGEGLU(self.dim  , self.dropout  , self.dtype	)
									UpperCAmelCase__		:str 		=    nn.Dense(self.dim  , dtype=self.dtype	)


						def __call__(  self  , A  , A=True	)  ->List[Any]:
									UpperCAmelCase__		:Dict 		=    self.net_a(A  , deterministic=A	)
									UpperCAmelCase__		:Tuple 		=    self.net_a(A	)
									return hidden_states


class 	UpperCamelCase__       (  nn.Module):

						'''simple docstring'''



						__a     :    int
						__a     :    float												=			0.0
						__a     :    jnp.dtype												=			jnp.floataa


						def    A__       (  self	)  ->Tuple:
									UpperCAmelCase__		:Tuple 		=    self.dim * 4
									UpperCAmelCase__		:Optional[int] 		=    nn.Dense(inner_dim * 2  , dtype=self.dtype	)
									UpperCAmelCase__		:Tuple 		=    nn.Dropout(rate=self.dropout	)


						def __call__(  self  , A  , A=True	)  ->List[str]:
									UpperCAmelCase__		:Optional[int] 		=    self.proj(A	)
									UpperCAmelCase__		,       UpperCAmelCase__		:Dict 		=    jnp.split(A  , 2  , axis=2	)
									return self.dropout_layer(hidden_linear * nn.gelu(A	)  , deterministic=A	)







from __future__ import annotations




def 		A						(  SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						SCREAMING_SNAKE_CASE     ,						):




			"""simple docstring"""


			if not all((nth_term, start_term_a, common_ratio_r)							):
						return []
			UpperCAmelCase__		:list[float | int] 		=    []
			UpperCAmelCase__		:str 		=    1
			UpperCAmelCase__		:Any 		=    common_ratio_r
			for _ in range(int(SCREAMING_SNAKE_CASE							)							):
						if not series:
									series.append(SCREAMING_SNAKE_CASE							)
						else:
									power += 1
									series.append(float(start_term_a * multiple							)							)
									UpperCAmelCase__		:str 		=    pow(float(SCREAMING_SNAKE_CASE							)     ,						SCREAMING_SNAKE_CASE							)
			return series


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						__snake_case					:							Optional[int]           =							float(input('Enter the last number (n term) of the Geometric Series'))
						__snake_case					:							List[str]           =							float(input('Enter the starting term (a) of the Geometric Series'))
						__snake_case					:							Optional[int]           =							float(
						    input('Enter the common ratio between two terms (r) of the Geometric Series')
						)
						print('Formula of Geometric Series => a + ar + ar^2 ... +ar^n')
						print(geometric_series(nth_term, start_term_a, common_ratio_r))





