




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   )     ->			str:
       lowerCamelCase       :				Dict      			= key.shape[-3:]
       lowerCamelCase       :				Union[str, Any]      			= value.shape[-1]
       lowerCamelCase       :				Tuple      			= min(_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE   )
       lowerCamelCase       :				List[str]      			= 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   ):
              lowerCamelCase       :				Optional[int]      			= jnp.einsum("...qhd,...khd->...qhk"			,_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE			,precision=_SCREAMING_SNAKE_CASE   )

              lowerCamelCase       :				int      			= jnp.max(_SCREAMING_SNAKE_CASE			,axis=-1			,keepdims=_SCREAMING_SNAKE_CASE   )
              lowerCamelCase       :				List[Any]      			= jax.lax.stop_gradient(_SCREAMING_SNAKE_CASE   )
              lowerCamelCase       :				int      			= jnp.exp(attn_weights - max_score   )

              lowerCamelCase       :				Optional[Any]      			= jnp.einsum("...vhf,...qhv->...qhf"			,_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE			,precision=_SCREAMING_SNAKE_CASE   )
              lowerCamelCase       :				int      			= 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
              lowerCamelCase       :				Optional[int]      			= 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
              lowerCamelCase       :				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   )

       lowerCamelCase       :				Tuple      			= jax.lax.map(f=_SCREAMING_SNAKE_CASE			,xs=jnp.arange(0			,_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE   )   )

       lowerCamelCase       :				Tuple      			= jnp.max(_SCREAMING_SNAKE_CASE			,axis=0			,keepdims=_SCREAMING_SNAKE_CASE   )
       lowerCamelCase       :				Any      			= jnp.exp(chunk_max - global_max   )

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

       lowerCamelCase       :				Optional[Any]      			= chunk_values.sum(axis=0   )
       lowerCamelCase       :				Any      			= 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   )     ->			str:
       lowerCamelCase       :				int      			= query.shape[-3:]

       def chunk_scanner(_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE   ):
              # julienne query array
              lowerCamelCase       :				Union[str, Any]      			= 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   ),
              )

       lowerCamelCase       :				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'''



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







    def 	_lowercase					(   self					)					->				str:
           lowerCamelCase       :				List[str]      			= self.dim_head * self.heads
           lowerCamelCase       :				Any      			= self.dim_head**-0.5

           # Weights were exported with old names {to_q, to_k, to_v, to_out}
           lowerCamelCase       :				Optional[Any]      			= nn.Dense(UpperCamelCase__					,  use_bias=UpperCamelCase__					,  dtype=self.dtype					,  name="to_q"					)
           lowerCamelCase       :				List[Any]      			= nn.Dense(UpperCamelCase__					,  use_bias=UpperCamelCase__					,  dtype=self.dtype					,  name="to_k"					)
           lowerCamelCase       :				Any      			= nn.Dense(UpperCamelCase__					,  use_bias=UpperCamelCase__					,  dtype=self.dtype					,  name="to_v"					)

           lowerCamelCase       :				List[Any]      			= nn.Dense(self.query_dim					,  dtype=self.dtype					,  name="to_out_0"					)
           lowerCamelCase       :				Union[str, Any]      			= nn.Dropout(rate=self.dropout					)







    def 	_lowercase					(   self					,  UpperCamelCase__					)					->				Optional[Any]:
           lowerCamelCase       :				Union[str, Any]      			= tensor.shape
           lowerCamelCase       :				Union[str, Any]      			= self.heads
           lowerCamelCase       :				Tuple      			= tensor.reshape(UpperCamelCase__					,  UpperCamelCase__					,  UpperCamelCase__					,  dim // head_size					)
           lowerCamelCase       :				Dict      			= jnp.transpose(UpperCamelCase__					,  (0, 2, 1, 3)					)
           lowerCamelCase       :				Tuple      			= tensor.reshape(batch_size * head_size					,  UpperCamelCase__					,  dim // head_size					)
           return tensor







    def 	_lowercase					(   self					,  UpperCamelCase__					)					->				str:
           lowerCamelCase       :				List[Any]      			= tensor.shape
           lowerCamelCase       :				Tuple      			= self.heads
           lowerCamelCase       :				Optional[Any]      			= tensor.reshape(batch_size // head_size					,  UpperCamelCase__					,  UpperCamelCase__					,  UpperCamelCase__					)
           lowerCamelCase       :				str      			= jnp.transpose(UpperCamelCase__					,  (0, 2, 1, 3)					)
           lowerCamelCase       :				List[str]      			= tensor.reshape(batch_size // head_size					,  UpperCamelCase__					,  dim * head_size					)
           return tensor







    def __call__(   self					,  UpperCamelCase__					,  UpperCamelCase__=None					,  UpperCamelCase__=True					)					->				Tuple:
           lowerCamelCase       :				int      			= hidden_states if context is None else context

           lowerCamelCase       :				Optional[Any]      			= self.query(UpperCamelCase__					)
           lowerCamelCase       :				Optional[Any]      			= self.key(UpperCamelCase__					)
           lowerCamelCase       :				Tuple      			= self.value(UpperCamelCase__					)

           lowerCamelCase       :				Optional[int]      			= self.reshape_heads_to_batch_dim(UpperCamelCase__					)
           lowerCamelCase       :				List[str]      			= self.reshape_heads_to_batch_dim(UpperCamelCase__					)
           lowerCamelCase       :				Any      			= self.reshape_heads_to_batch_dim(UpperCamelCase__					)

           if self.use_memory_efficient_attention:
                  lowerCamelCase       :				List[str]      			= query_states.transpose(1					,  0					,  2					)
                  lowerCamelCase       :				Tuple      			= key_states.transpose(1					,  0					,  2					)
                  lowerCamelCase       :				Optional[Any]      			= 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

                  lowerCamelCase       :				Tuple      			= query_states.shape[-3]
                  if flatten_latent_dim % 64 == 0:
                         lowerCamelCase       :				str      			= int(flatten_latent_dim / 64					)
                  elif flatten_latent_dim % 16 == 0:
                         lowerCamelCase       :				Tuple      			= int(flatten_latent_dim / 16					)
                  elif flatten_latent_dim % 4 == 0:
                         lowerCamelCase       :				Tuple      			= int(flatten_latent_dim / 4					)
                  else:
                         lowerCamelCase       :				List[Any]      			= int(UpperCamelCase__					)

                  lowerCamelCase       :				List[Any]      			= jax_memory_efficient_attention(
                      UpperCamelCase__					,  UpperCamelCase__					,  UpperCamelCase__					,  query_chunk_size=UpperCamelCase__					,  key_chunk_size=4096 * 4					)

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

                  # attend to values
                  lowerCamelCase       :				Optional[Any]      			= jnp.einsum("b i j, b j d -> b i d"					,  UpperCamelCase__					,  UpperCamelCase__					)

           lowerCamelCase       :				Tuple      			= self.reshape_batch_dim_to_heads(UpperCamelCase__					)
           lowerCamelCase       :				Union[str, Any]      			= self.proj_attn(UpperCamelCase__					)
           return self.dropout_layer(UpperCamelCase__					,  deterministic=UpperCamelCase__					)




class 		UpperCamelCase__     (nn.Module					):

    '''simple docstring'''



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







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







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

           # cross attention
           lowerCamelCase       :				Union[str, Any]      			= hidden_states
           lowerCamelCase       :				Optional[Any]      			= self.attna(self.norma(UpperCamelCase__					)					,  UpperCamelCase__					,  deterministic=UpperCamelCase__					)
           lowerCamelCase       :				Tuple      			= hidden_states + residual

           # feed forward
           lowerCamelCase       :				Union[str, Any]      			= hidden_states
           lowerCamelCase       :				List[str]      			= self.ff(self.norma(UpperCamelCase__					)					,  deterministic=UpperCamelCase__					)
           lowerCamelCase       :				Dict      			= hidden_states + residual

           return self.dropout_layer(UpperCamelCase__					,  deterministic=UpperCamelCase__					)




class 		UpperCamelCase__     (nn.Module					):

    '''simple docstring'''



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







    def 	_lowercase					(   self					)					->				List[str]:
           lowerCamelCase       :				Optional[int]      			= nn.GroupNorm(num_groups=32					,  epsilon=1e-5					)

           lowerCamelCase       :				Optional[Any]      			= self.n_heads * self.d_head
           if self.use_linear_projection:
                  lowerCamelCase       :				Any      			= nn.Dense(UpperCamelCase__					,  dtype=self.dtype					)
           else:
                  lowerCamelCase       :				Dict      			= nn.Conv(
                      UpperCamelCase__					,  kernel_size=(1, 1)					,  strides=(1, 1)					,  padding="VALID"					,  dtype=self.dtype					,  )

           lowerCamelCase       :				Union[str, Any]      			= [
               FlaxBasicTransformerBlock(
                   UpperCamelCase__					,  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:
                  lowerCamelCase       :				List[str]      			= nn.Dense(UpperCamelCase__					,  dtype=self.dtype					)
           else:
                  lowerCamelCase       :				Union[str, Any]      			= nn.Conv(
                      UpperCamelCase__					,  kernel_size=(1, 1)					,  strides=(1, 1)					,  padding="VALID"					,  dtype=self.dtype					,  )

           lowerCamelCase       :				Union[str, Any]      			= nn.Dropout(rate=self.dropout					)







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

           for transformer_block in self.transformer_blocks:
                  lowerCamelCase       :				Optional[int]      			= transformer_block(UpperCamelCase__					,  UpperCamelCase__					,  deterministic=UpperCamelCase__					)

           if self.use_linear_projection:
                  lowerCamelCase       :				List[Any]      			= self.proj_out(UpperCamelCase__					)
                  lowerCamelCase       :				Any      			= hidden_states.reshape(UpperCamelCase__					,  UpperCamelCase__					,  UpperCamelCase__					,  UpperCamelCase__					)
           else:
                  lowerCamelCase       :				Optional[int]      			= hidden_states.reshape(UpperCamelCase__					,  UpperCamelCase__					,  UpperCamelCase__					,  UpperCamelCase__					)
                  lowerCamelCase       :				str      			= self.proj_out(UpperCamelCase__					)

           lowerCamelCase       :				Tuple      			= hidden_states + residual
           return self.dropout_layer(UpperCamelCase__					,  deterministic=UpperCamelCase__					)




class 		UpperCamelCase__     (nn.Module					):

    '''simple docstring'''



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







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







    def __call__(   self					,  UpperCamelCase__					,  UpperCamelCase__=True					)					->				Any:
           lowerCamelCase       :				List[str]      			= self.net_a(UpperCamelCase__					,  deterministic=UpperCamelCase__					)
           lowerCamelCase       :				str      			= self.net_a(UpperCamelCase__					)
           return hidden_states




class 		UpperCamelCase__     (nn.Module					):

    '''simple docstring'''



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







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







    def __call__(   self					,  UpperCamelCase__					,  UpperCamelCase__=True					)					->				List[str]:
           lowerCamelCase       :				Any      			= self.proj(UpperCamelCase__					)
           lowerCamelCase       :				Tuple      			= jnp.split(UpperCamelCase__					,  2					,  axis=2					)
           return self.dropout_layer(hidden_linear * nn.gelu(UpperCamelCase__					)					,  deterministic=UpperCamelCase__					)












import numpy as np

def 					A				(				_SCREAMING_SNAKE_CASE   )     ->			str:
       lowerCamelCase			,				lowerCamelCase       :				Dict      			= a.shape
       lowerCamelCase       :				Union[str, Any]      			= min(_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE   )
       lowerCamelCase       :				Union[str, Any]      			= np.eye(_SCREAMING_SNAKE_CASE   )
       lowerCamelCase       :				List[Any]      			= a.copy()

       for k in range(t - 1   ):
              # select a column of modified matrix A':
              lowerCamelCase       :				Optional[Any]      			= r[k:, [k]]
              # construct first basis vector
              lowerCamelCase       :				Union[str, Any]      			= np.zeros_like(_SCREAMING_SNAKE_CASE   )
              lowerCamelCase       :				int      			= 1.0
              # determine scaling factor
              lowerCamelCase       :				Any      			= np.linalg.norm(_SCREAMING_SNAKE_CASE   )
              # construct vector v for Householder reflection
              lowerCamelCase       :				List[str]      			= x + np.sign(x[0]   ) * alpha * ea
              v /= np.linalg.norm(_SCREAMING_SNAKE_CASE   )

              # construct the Householder matrix
              lowerCamelCase       :				List[Any]      			= np.eye(m - k   ) - 2.0 * v @ v.T
              # pad with ones and zeros as necessary
              lowerCamelCase       :				Union[str, Any]      			= np.block([[np.eye(_SCREAMING_SNAKE_CASE   ), np.zeros((k, m - k)   )], [np.zeros((m - k, k)   ), q_k]]   )

              lowerCamelCase       :				Any      			= q @ q_k.T
              lowerCamelCase       :				List[Any]      			= q_k @ r

       return q, r


if __name__ == "__main__":
       import doctest

       doctest.testmod()






