



"""simple docstring"""


import functools
import math

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

def 				_lowerCAmelCase   (     lowercase_	,			lowercase_	,			lowercase_	,			lowercase_	,			lowercase_ = 4096		):
						UpperCAmelCase    =				key.shape[-3:]
						UpperCAmelCase    =				value.shape[-1]
						UpperCAmelCase    =				min(_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE		)
						UpperCAmelCase    =				query / jnp.sqrt(_SCREAMING_SNAKE_CASE		)

						@functools.partial(jax.checkpoint	,			prevent_cse=_SCREAMING_SNAKE_CASE		)
						def summarize_chunk(lowercase_	,			lowercase_	,			lowercase_		):
												UpperCAmelCase    =				jnp.einsum('...qhd,...khd->...qhk'	,			_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE	,			precision=_SCREAMING_SNAKE_CASE		)

												UpperCAmelCase    =				jnp.max(_SCREAMING_SNAKE_CASE	,			axis=-1	,			keepdims=_SCREAMING_SNAKE_CASE		)
												UpperCAmelCase    =				jax.lax.stop_gradient(_SCREAMING_SNAKE_CASE		)
												UpperCAmelCase    =				jnp.exp(attn_weights - max_score		)

												UpperCAmelCase    =				jnp.einsum('...vhf,...qhv->...qhf'	,			_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE	,			precision=_SCREAMING_SNAKE_CASE		)
												UpperCAmelCase    =				jnp.einsum('...qhk->...qh'	,			_SCREAMING_SNAKE_CASE		)

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

						def chunk_scanner(lowercase_		):
												# julienne key array
												UpperCAmelCase    =				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    =				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    =				jax.lax.map(f=_SCREAMING_SNAKE_CASE	,			xs=jnp.arange(0	,			_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE		)		)

						UpperCAmelCase    =				jnp.max(_SCREAMING_SNAKE_CASE	,			axis=0	,			keepdims=_SCREAMING_SNAKE_CASE		)
						UpperCAmelCase    =				jnp.exp(chunk_max - global_max		)

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

						UpperCAmelCase    =				chunk_values.sum(axis=0		)
						UpperCAmelCase    =				jnp.expand_dims(_SCREAMING_SNAKE_CASE	,			-1		).sum(axis=0		)

						return all_values / all_weights

def 				_lowerCAmelCase   (     lowercase_	,			lowercase_	,			lowercase_	,			lowercase_=jax.lax.Precision.HIGHEST	,			lowercase_ = 1024	,			lowercase_ = 4096		):
						UpperCAmelCase    =				query.shape[-3:]

						def chunk_scanner(lowercase_	,			lowercase_		):
												# julienne query array
												UpperCAmelCase    =				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    =				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    A_    (  nn.Module       ):



						"""simple docstring"""
						__UpperCamelCase	       =							42
						__UpperCamelCase	       =							8
						__UpperCamelCase	       =							64
						__UpperCamelCase	       =							0.0
						__UpperCamelCase	       =							False
						__UpperCamelCase	       =							jnp.floataa






						def 			UpperCAmelCase__  (      self				:Tuple      )       ->    List[str]:
												UpperCAmelCase    =				self.dim_head * self.heads
												UpperCAmelCase    =				self.dim_head**-0.5

												# Weights were exported with old names {to_q, to_k, to_v, to_out}
												UpperCAmelCase    =				nn.Dense(__a     ,						use_bias=__a     ,						dtype=self.dtype     ,						name='to_q'      )
												UpperCAmelCase    =				nn.Dense(__a     ,						use_bias=__a     ,						dtype=self.dtype     ,						name='to_k'      )
												UpperCAmelCase    =				nn.Dense(__a     ,						use_bias=__a     ,						dtype=self.dtype     ,						name='to_v'      )

												UpperCAmelCase    =				nn.Dense(self.query_dim     ,						dtype=self.dtype     ,						name='to_out_0'      )
												UpperCAmelCase    =				nn.Dropout(rate=self.dropout      )






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






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






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

												UpperCAmelCase    =				self.query(__a      )
												UpperCAmelCase    =				self.key(__a      )
												UpperCAmelCase    =				self.value(__a      )

												UpperCAmelCase    =				self.reshape_heads_to_batch_dim(__a      )
												UpperCAmelCase    =				self.reshape_heads_to_batch_dim(__a      )
												UpperCAmelCase    =				self.reshape_heads_to_batch_dim(__a      )

												if self.use_memory_efficient_attention:
																		UpperCAmelCase    =				query_states.transpose(1     ,						0     ,						2      )
																		UpperCAmelCase    =				key_states.transpose(1     ,						0     ,						2      )
																		UpperCAmelCase    =				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    =				query_states.shape[-3]
																		if flatten_latent_dim % 64 == 0:
																								UpperCAmelCase    =				int(flatten_latent_dim / 64      )
																		elif flatten_latent_dim % 16 == 0:
																								UpperCAmelCase    =				int(flatten_latent_dim / 16      )
																		elif flatten_latent_dim % 4 == 0:
																								UpperCAmelCase    =				int(flatten_latent_dim / 4      )
																		else:
																								UpperCAmelCase    =				int(__a      )

																		UpperCAmelCase    =				jax_memory_efficient_attention(
																		    __a     ,						__a     ,						__a     ,						query_chunk_size=__a     ,						key_chunk_size=40_96 * 4      )

																		UpperCAmelCase    =				hidden_states.transpose(1     ,						0     ,						2      )
												else:
																		# compute attentions
																		UpperCAmelCase    =				jnp.einsum('b i d, b j d->b i j'     ,						__a     ,						__a      )
																		UpperCAmelCase    =				attention_scores * self.scale
																		UpperCAmelCase    =				nn.softmax(__a     ,						axis=2      )

																		# attend to values
																		UpperCAmelCase    =				jnp.einsum('b i j, b j d -> b i d'     ,						__a     ,						__a      )

												UpperCAmelCase    =				self.reshape_batch_dim_to_heads(__a      )
												UpperCAmelCase    =				self.proj_attn(__a      )
												return self.dropout_layer(__a     ,						deterministic=__a      )







class    A_    (  nn.Module       ):



						"""simple docstring"""
						__UpperCamelCase	       =							42
						__UpperCamelCase	       =							42
						__UpperCamelCase	       =							42
						__UpperCamelCase	       =							0.0
						__UpperCamelCase	       =							False
						__UpperCamelCase	       =							jnp.floataa
						__UpperCamelCase	       =							False






						def 			UpperCAmelCase__  (      self				:Dict      )       ->    Optional[Any]:
												UpperCAmelCase    =				FlaxAttention(
												    self.dim     ,						self.n_heads     ,						self.d_head     ,						self.dropout     ,						self.use_memory_efficient_attention     ,						dtype=self.dtype      )
												# cross attention
												UpperCAmelCase    =				FlaxAttention(
												    self.dim     ,						self.n_heads     ,						self.d_head     ,						self.dropout     ,						self.use_memory_efficient_attention     ,						dtype=self.dtype      )
												UpperCAmelCase    =				FlaxFeedForward(dim=self.dim     ,						dropout=self.dropout     ,						dtype=self.dtype      )
												UpperCAmelCase    =				nn.LayerNorm(epsilon=1E-5     ,						dtype=self.dtype      )
												UpperCAmelCase    =				nn.LayerNorm(epsilon=1E-5     ,						dtype=self.dtype      )
												UpperCAmelCase    =				nn.LayerNorm(epsilon=1E-5     ,						dtype=self.dtype      )
												UpperCAmelCase    =				nn.Dropout(rate=self.dropout      )






						def __call__(      self				:Dict     ,						lowercase_				:Optional[Any]     ,						lowercase_				:Union[str, Any]     ,						lowercase_				:Optional[Any]=True      )       ->    List[Any]:
												UpperCAmelCase    =				hidden_states
												if self.only_cross_attention:
																		UpperCAmelCase    =				self.attna(self.norma(__a      )     ,						__a     ,						deterministic=__a      )
												else:
																		UpperCAmelCase    =				self.attna(self.norma(__a      )     ,						deterministic=__a      )
												UpperCAmelCase    =				hidden_states + residual

												# cross attention
												UpperCAmelCase    =				hidden_states
												UpperCAmelCase    =				self.attna(self.norma(__a      )     ,						__a     ,						deterministic=__a      )
												UpperCAmelCase    =				hidden_states + residual

												# feed forward
												UpperCAmelCase    =				hidden_states
												UpperCAmelCase    =				self.ff(self.norma(__a      )     ,						deterministic=__a      )
												UpperCAmelCase    =				hidden_states + residual

												return self.dropout_layer(__a     ,						deterministic=__a      )







class    A_    (  nn.Module       ):



						"""simple docstring"""
						__UpperCamelCase	       =							42
						__UpperCamelCase	       =							42
						__UpperCamelCase	       =							42
						__UpperCamelCase	       =							1
						__UpperCamelCase	       =							0.0
						__UpperCamelCase	       =							False
						__UpperCamelCase	       =							False
						__UpperCamelCase	       =							jnp.floataa
						__UpperCamelCase	       =							False






						def 			UpperCAmelCase__  (      self				:int      )       ->    Any:
												UpperCAmelCase    =				nn.GroupNorm(num_groups=32     ,						epsilon=1E-5      )

												UpperCAmelCase    =				self.n_heads * self.d_head
												if self.use_linear_projection:
																		UpperCAmelCase    =				nn.Dense(__a     ,						dtype=self.dtype      )
												else:
																		UpperCAmelCase    =				nn.Conv(
																		    __a     ,						kernel_size=(1, 1)     ,						strides=(1, 1)     ,						padding='VALID'     ,						dtype=self.dtype     ,						)

												UpperCAmelCase    =				[
												    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    =				nn.Dense(__a     ,						dtype=self.dtype      )
												else:
																		UpperCAmelCase    =				nn.Conv(
																		    __a     ,						kernel_size=(1, 1)     ,						strides=(1, 1)     ,						padding='VALID'     ,						dtype=self.dtype     ,						)

												UpperCAmelCase    =				nn.Dropout(rate=self.dropout      )






						def __call__(      self				:List[str]     ,						lowercase_				:List[Any]     ,						lowercase_				:Dict     ,						lowercase_				:Any=True      )       ->    List[str]:
												UpperCAmelCase    =				hidden_states.shape
												UpperCAmelCase    =				hidden_states
												UpperCAmelCase    =				self.norm(__a      )
												if self.use_linear_projection:
																		UpperCAmelCase    =				hidden_states.reshape(__a     ,						height * width     ,						__a      )
																		UpperCAmelCase    =				self.proj_in(__a      )
												else:
																		UpperCAmelCase    =				self.proj_in(__a      )
																		UpperCAmelCase    =				hidden_states.reshape(__a     ,						height * width     ,						__a      )

												for transformer_block in self.transformer_blocks:
																		UpperCAmelCase    =				transformer_block(__a     ,						__a     ,						deterministic=__a      )

												if self.use_linear_projection:
																		UpperCAmelCase    =				self.proj_out(__a      )
																		UpperCAmelCase    =				hidden_states.reshape(__a     ,						__a     ,						__a     ,						__a      )
												else:
																		UpperCAmelCase    =				hidden_states.reshape(__a     ,						__a     ,						__a     ,						__a      )
																		UpperCAmelCase    =				self.proj_out(__a      )

												UpperCAmelCase    =				hidden_states + residual
												return self.dropout_layer(__a     ,						deterministic=__a      )







class    A_    (  nn.Module       ):



						"""simple docstring"""
						__UpperCamelCase	       =							42
						__UpperCamelCase	       =							0.0
						__UpperCamelCase	       =							jnp.floataa






						def 			UpperCAmelCase__  (      self				:Any      )       ->    List[str]:
												UpperCAmelCase    =				FlaxGEGLU(self.dim     ,						self.dropout     ,						self.dtype      )
												UpperCAmelCase    =				nn.Dense(self.dim     ,						dtype=self.dtype      )






						def __call__(      self				:List[Any]     ,						lowercase_				:Tuple     ,						lowercase_				:Any=True      )       ->    Any:
												UpperCAmelCase    =				self.net_a(__a     ,						deterministic=__a      )
												UpperCAmelCase    =				self.net_a(__a      )
												return hidden_states







class    A_    (  nn.Module       ):



						"""simple docstring"""
						__UpperCamelCase	       =							42
						__UpperCamelCase	       =							0.0
						__UpperCamelCase	       =							jnp.floataa






						def 			UpperCAmelCase__  (      self				:List[str]      )       ->    Any:
												UpperCAmelCase    =				self.dim * 4
												UpperCAmelCase    =				nn.Dense(inner_dim * 2     ,						dtype=self.dtype      )
												UpperCAmelCase    =				nn.Dropout(rate=self.dropout      )






						def __call__(      self				:Tuple     ,						lowercase_				:str     ,						lowercase_				:str=True      )       ->    str:
												UpperCAmelCase    =				self.proj(__a      )
												UpperCAmelCase    =				jnp.split(__a     ,						2     ,						axis=2      )
												return self.dropout_layer(hidden_linear * nn.gelu(__a      )     ,						deterministic=__a      )










"""simple docstring"""


from typing import Any

import numpy as np







class    A_    :



						"""simple docstring"""






						def __init__(      self				:List[str]     ,						lowercase_				:np.ndarray     ,						lowercase_				:int      )       ->    None:
												# Check if RHS is negative
												if np.any(tableau[:, -1]     ,						where=tableau[:, -1] < 0      ):
																		raise ValueError('RHS must be > 0'      )

												UpperCAmelCase    =				tableau
												UpperCAmelCase   ,					UpperCAmelCase    =				tableau.shape

												# Number of decision variables x1, x2, x3...
												UpperCAmelCase    =				n_vars

												# Number of artificial variables to be minimised
												UpperCAmelCase    =				len(np.where(tableau[self.n_vars : -1] == -1      )[0]      )

												# 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
												UpperCAmelCase    =				(self.n_art_vars > 0) + 1

												# Number of slack variables added to make inequalities into equalities
												UpperCAmelCase    =				self.n_rows - self.n_stages

												# Objectives for each stage
												UpperCAmelCase    =				['max']

												# In two stage simplex, first minimise then maximise
												if self.n_art_vars:
																		self.objectives.append('min'      )

												UpperCAmelCase    =				['']

												# Index of current pivot row and column
												UpperCAmelCase    =				None
												UpperCAmelCase    =				None

												# Does objective row only contain (non)-negative values?
												UpperCAmelCase    =				False






						@staticmethod
						def 			UpperCAmelCase__  (      *lowercase_				:int      )       ->    list[str]:
												if len(lowercase_      ) != 3:
																		raise ValueError('Must provide n_vars, n_slack, and n_art_vars'      )

												if not all(x >= 0 and isinstance(lowercase_     ,						lowercase_      ) for x in args      ):
																		raise ValueError('All arguments must be non-negative integers'      )

												# decision | slack | artificial
												UpperCAmelCase    =				['x', 's', 'a']
												UpperCAmelCase    =				[]
												for i in range(3      ):
																		for j in range(args[i]      ):
																								titles.append(string_starts[i] + str(j + 1      )      )
												titles.append('RHS'      )
												return titles






						def 			UpperCAmelCase__  (      self				:List[str]     ,						lowercase_				:np.ndarray      )       ->    tuple[Any, Any]:
												UpperCAmelCase    =				self.objectives[-1]

												# Find entries of highest magnitude in objective rows
												UpperCAmelCase    =				(objective == 'min') - (objective == 'max')
												UpperCAmelCase    =				np.argmax(sign * tableau[0, : self.n_vars]      )

												# Choice is only valid if below 0 for maximise, and above for minimise
												if sign * self.tableau[0, col_idx] <= 0:
																		UpperCAmelCase    =				True
																		return 0, 0

												# Pivot row is chosen as having the lowest quotient when elements of
												# the pivot column divide the right-hand side

												# Slice excluding the objective rows
												UpperCAmelCase    =				slice(self.n_stages     ,						self.n_rows      )

												# RHS
												UpperCAmelCase    =				tableau[s, -1]

												# Elements of pivot column within slice
												UpperCAmelCase    =				tableau[s, col_idx]

												# Array filled with nans
												UpperCAmelCase    =				np.full(self.n_rows - self.n_stages     ,						np.nan      )

												# If element in pivot column is greater than zeron_stages, return
												# quotient or nan otherwise
												UpperCAmelCase    =				np.divide(lowercase_     ,						lowercase_     ,						out=lowercase_     ,						where=divisor > 0      )

												# Arg of minimum quotient excluding the nan values. n_stages is added
												# to compensate for earlier exclusion of objective columns
												UpperCAmelCase    =				np.nanargmin(lowercase_      ) + self.n_stages
												return row_idx, col_idx






						def 			UpperCAmelCase__  (      self				:Union[str, Any]     ,						lowercase_				:np.ndarray     ,						lowercase_				:int     ,						lowercase_				:int      )       ->    np.ndarray:
												UpperCAmelCase    =				tableau[row_idx].copy()

												UpperCAmelCase    =				piv_row[col_idx]

												# Entry becomes 1
												piv_row *= 1 / piv_val

												# Variable in pivot column becomes basic, ie the only non-zero entry
												for idx, coeff in enumerate(tableau[:, col_idx]      ):
																		tableau[idx] += -coeff * piv_row
												UpperCAmelCase    =				piv_row
												return tableau






						def 			UpperCAmelCase__  (      self				:Optional[Any]     ,						lowercase_				:np.ndarray      )       ->    np.ndarray:
												self.objectives.pop()

												if not self.objectives:
																		return tableau

												# Slice containing ids for artificial columns
												UpperCAmelCase    =				slice(-self.n_art_vars - 1     ,						-1      )

												# Delete the artificial variable columns
												UpperCAmelCase    =				np.delete(lowercase_     ,						lowercase_     ,						axis=1      )

												# Delete the objective row of the first stage
												UpperCAmelCase    =				np.delete(lowercase_     ,						0     ,						axis=0      )

												UpperCAmelCase    =				1
												self.n_rows -= 1
												UpperCAmelCase    =				0
												UpperCAmelCase    =				False
												return tableau






						def 			UpperCAmelCase__  (      self				:List[Any]      )       ->    dict[Any, Any]:
												# Stop simplex algorithm from cycling.
												for _ in range(1_00      ):
																		# Completion of each stage removes an objective. If both stages
																		# are complete, then no objectives are left
																		if not self.objectives:
																								UpperCAmelCase    =				self.generate_col_titles(
																								    self.n_vars     ,						self.n_slack     ,						self.n_art_vars      )

																								# Find the values of each variable at optimal solution
																								return self.interpret_tableau(self.tableau     ,						self.col_titles      )

																		UpperCAmelCase   ,					UpperCAmelCase    =				self.find_pivot(self.tableau      )

																		# If there are no more negative values in objective row
																		if self.stop_iter:
																								# Delete artificial variable columns and rows. Update attributes
																								UpperCAmelCase    =				self.change_stage(self.tableau      )
																		else:
																								UpperCAmelCase    =				self.pivot(self.tableau     ,						lowercase_     ,						lowercase_      )
												return {}






						def 			UpperCAmelCase__  (      self				:Union[str, Any]     ,						lowercase_				:np.ndarray     ,						lowercase_				:list[str]      )       ->    dict[str, float]:
												UpperCAmelCase    =				{'P': abs(tableau[0, -1]      )}

												for i in range(self.n_vars      ):
																		# Gives ids of nonzero entries in the ith column
																		UpperCAmelCase    =				np.nonzero(tableau[:, i]      )
																		UpperCAmelCase    =				len(nonzero[0]      )

																		# First entry in the nonzero ids
																		UpperCAmelCase    =				nonzero[0][0]
																		UpperCAmelCase    =				tableau[nonzero_rowidx, i]

																		# If there is only one nonzero value in column, which is one
																		if n_nonzero == nonzero_val == 1:
																								UpperCAmelCase    =				tableau[nonzero_rowidx, -1]
																								UpperCAmelCase    =				rhs_val

        # Check for basic variables
												for title in col_titles:
																		# Don't add RHS or slack variables to output dict
																		if title[0] not in "R-s-a":
																								output_dict.setdefault(lowercase_     ,						0      )
												return output_dict


if __name__ == "__main__":
				import doctest

				doctest.testmod()





