
"""simple docstring"""





import functools
from math import sqrt
from time import time







def       __a	(						__lowerCamelCase,						*__lowerCamelCase,						**__lowerCamelCase    ):
   UpperCAmelCase_   :   Union[str, Any]     	=       time()
   UpperCAmelCase_   :   Dict     	=       func(*__lowerCamelCase,						**__lowerCamelCase    )
   UpperCAmelCase_   :   str     	=       time()
   if int(end - start    ) > 0:
      print(f"""{func.__name__} runtime: {(end - start):0.4f} s"""    )
   else:
      print(f"""{func.__name__} runtime: {(end - start) * 1000:0.4f} ms"""    )
   return output







def       __a	(						__lowerCamelCase    ):
   if n < 0:
      raise Exception("n is negative"    )
   if n == 0:
      return [0]
   UpperCAmelCase_   :   Optional[int]     	=       [0, 1]
   for _ in range(n - 1    ):
      fib.append(fib[-1] + fib[-2]    )
   return fib







def       __a	(						__lowerCamelCase    ):

   def fib_recursive_term(__lowerCamelCase    ) -> int:
      if i < 0:
         raise Exception("n is negative"    )
      if i < 2:
         return i
      return fib_recursive_term(i - 1    ) + fib_recursive_term(i - 2    )

   if n < 0:
      raise Exception("n is negative"    )
   return [fib_recursive_term(__lowerCamelCase    ) for i in range(n + 1    )]







def       __a	(						__lowerCamelCase    ):

   @functools.cache
   def fib_recursive_term(__lowerCamelCase    ) -> int:
      if i < 0:
         raise Exception("n is negative"    )
      if i < 2:
         return i
      return fib_recursive_term(i - 1    ) + fib_recursive_term(i - 2    )

   if n < 0:
      raise Exception("n is negative"    )
   return [fib_recursive_term(__lowerCamelCase    ) for i in range(n + 1    )]







def       __a	(						__lowerCamelCase    ):
   if n < 0:
      raise Exception("n is negative"    )
   # Cache must be outside recursuive function
   # other it will reset every time it calls itself.
   UpperCAmelCase_   :   dict[int, int]     	=       {0: 0, 1: 1, 2: 1}  # Prefilled cache

   def rec_fn_memoized(__lowerCamelCase    ) -> int:
      if num in cache:
         return cache[num]

      UpperCAmelCase_   :   List[Any]     	=       rec_fn_memoized(num - 1    ) + rec_fn_memoized(num - 2    )
      UpperCAmelCase_   :   List[Any]     	=       value
      return value

   return [rec_fn_memoized(__lowerCamelCase    ) for i in range(n + 1    )]







def       __a	(						__lowerCamelCase    ):
   if n < 0:
      raise Exception("n is negative"    )
   if n >= 1475:
      raise Exception("n is too large"    )
   UpperCAmelCase_   :   Any     	=       sqrt(5    )
   UpperCAmelCase_   :   Any     	=       (1 + sqrt_a) / 2
   return [round(phi**i / sqrt_a    ) for i in range(n + 1    )]


if __name__ == "__main__":
    _a									=				30
    time_func(fib_iterative, num)
    time_func(fib_recursive, num)  # Around 3s runtime
    time_func(fib_recursive_cached, num)  # Around 0ms runtime
    time_func(fib_memoization, num)
    time_func(fib_binet, num)







from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    broadcast_to_shape_from_left,
)





@flax.struct.dataclass
class 							lowerCAmelCase_		:
		SCREAMING_SNAKE_CASE_       :			CommonSchedulerState

		# setable values
		SCREAMING_SNAKE_CASE_       :			jnp.ndarray
		SCREAMING_SNAKE_CASE_       :			jnp.ndarray
		SCREAMING_SNAKE_CASE_       :			jnp.ndarray
		SCREAMING_SNAKE_CASE_       :			Optional[int]					       =	None

		# running values
		SCREAMING_SNAKE_CASE_       :			Optional[jnp.ndarray]					       =	None







		@classmethod
		def 					a_  (    cls  :   List[Any]       ,		UpperCAmelCase_  :   CommonSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray					)       ->		Optional[Any]:


						'''simple docstring'''







						return cls(common=UpperCAmelCase_       ,		init_noise_sigma=UpperCAmelCase_       ,		timesteps=UpperCAmelCase_       ,		sigmas=UpperCAmelCase_					)





@dataclass
class 							lowerCAmelCase_		(		lowercase_     ):
		SCREAMING_SNAKE_CASE_       :			LMSDiscreteSchedulerState





class 							lowerCAmelCase_		(		lowercase_							,		lowercase_     ):
		SCREAMING_SNAKE_CASE_       :			Union[str, Any]					       =	[e.name for e in FlaxKarrasDiffusionSchedulers]

		SCREAMING_SNAKE_CASE_       :			jnp.dtype







		@property
		def 					a_  (    self  :   Union[str, Any]					)       ->		List[Any]:


						'''simple docstring'''







						return True







		@register_to_config
		def __init__(    self  :   Optional[Any]       ,		UpperCAmelCase_  :   int = 1000       ,		UpperCAmelCase_  :   float = 0.0_001       ,		UpperCAmelCase_  :   float = 0.02       ,		UpperCAmelCase_  :   str = "linear"       ,		UpperCAmelCase_  :   Optional[jnp.ndarray] = None       ,		UpperCAmelCase_  :   str = "epsilon"       ,		UpperCAmelCase_  :   jnp.dtype = jnp.floataa       ,		)       ->		List[str]:


						'''simple docstring'''







						_UpperCAmelCase						:  str     					=	dtype







		def 					a_  (    self  :   Tuple       ,		UpperCAmelCase_  :   Optional[CommonSchedulerState] = None					)       ->		LMSDiscreteSchedulerState:


						'''simple docstring'''







						if common is None:
										_UpperCAmelCase						:  int     					=	CommonSchedulerState.create(self					)

						_UpperCAmelCase						:  Any     					=	jnp.arange(0       ,		self.config.num_train_timesteps					).round()[::-1]
						_UpperCAmelCase						:  Any     					=	((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

						# standard deviation of the initial noise distribution
						_UpperCAmelCase						:  Dict     					=	sigmas.max()

						return LMSDiscreteSchedulerState.create(
						    common=UpperCAmelCase_       ,		init_noise_sigma=UpperCAmelCase_       ,		timesteps=UpperCAmelCase_       ,		sigmas=UpperCAmelCase_       ,		)







		def 					a_  (    self  :   Optional[Any]       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   int					)       ->		jnp.ndarray:


						'''simple docstring'''







						((_UpperCAmelCase)					, )						:  Optional[Any]     					=	jnp.where(state.timesteps == timestep       ,		size=1					)
						_UpperCAmelCase						:  List[str]     					=	step_index[0]

						_UpperCAmelCase						:  List[Any]     					=	state.sigmas[step_index]
						_UpperCAmelCase						:  Union[str, Any]     					=	sample / ((sigma**2 + 1) ** 0.5)
						return sample







		def 					a_  (    self  :   List[Any]       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   int       ,		UpperCAmelCase_  :   str       ,		UpperCAmelCase_  :   Union[str, Any]					)       ->		Union[str, Any]:


						'''simple docstring'''







						def lms_derivative(UpperCAmelCase_  :   Optional[int]					):
										_UpperCAmelCase						:  Optional[Any]     					=	1.0
										for k in range(UpperCAmelCase_					):
														if current_order == k:
																		continue
														prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
										return prod

						_UpperCAmelCase						:  Optional[Any]     					=	integrate.quad(UpperCAmelCase_       ,		state.sigmas[t]       ,		state.sigmas[t + 1]       ,		epsrel=1E-4					)[0]

						return integrated_coeff







		def 					a_  (    self  :   Dict       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   int       ,		UpperCAmelCase_  :   Tuple = ()					)       ->		LMSDiscreteSchedulerState:


						'''simple docstring'''







						_UpperCAmelCase						:  List[str]     					=	jnp.linspace(self.config.num_train_timesteps - 1       ,		0       ,		UpperCAmelCase_       ,		dtype=self.dtype					)

						_UpperCAmelCase						:  Any     					=	jnp.floor(UpperCAmelCase_					).astype(jnp.intaa					)
						_UpperCAmelCase						:  Optional[Any]     					=	jnp.ceil(UpperCAmelCase_					).astype(jnp.intaa					)

						_UpperCAmelCase						:  str     					=	jnp.mod(UpperCAmelCase_       ,		1.0					)

						_UpperCAmelCase						:  Optional[Any]     					=	((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
						_UpperCAmelCase						:  Any     					=	(1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
						_UpperCAmelCase						:  Tuple     					=	jnp.concatenate([sigmas, jnp.array([0.0]       ,		dtype=self.dtype					)]					)

						_UpperCAmelCase						:  int     					=	timesteps.astype(jnp.intaa					)

						# initial running values
						_UpperCAmelCase						:  List[str]     					=	jnp.zeros((0,) + shape       ,		dtype=self.dtype					)

						return state.replace(
						    timesteps=UpperCAmelCase_       ,		sigmas=UpperCAmelCase_       ,		num_inference_steps=UpperCAmelCase_       ,		derivatives=UpperCAmelCase_       ,		)







		def 					a_  (    self  :   Tuple       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   int       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   int = 4       ,		UpperCAmelCase_  :   bool = True       ,		)       ->		Union[FlaxLMSSchedulerOutput, Tuple]:


						'''simple docstring'''







						if state.num_inference_steps is None:
										raise ValueError(
										    '''Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'''					)

						_UpperCAmelCase						:  List[Any]     					=	state.sigmas[timestep]

						# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
						if self.config.prediction_type == "epsilon":
										_UpperCAmelCase						:  Optional[int]     					=	sample - sigma * model_output
						elif self.config.prediction_type == "v_prediction":
										# * c_out + input * c_skip
										_UpperCAmelCase						:  Tuple     					=	model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
						else:
										raise ValueError(
										    F'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''					)

						# 2. Convert to an ODE derivative
						_UpperCAmelCase						:  Tuple     					=	(sample - pred_original_sample) / sigma
						_UpperCAmelCase						:  Tuple     					=	state.replace(derivatives=jnp.append(state.derivatives       ,		UpperCAmelCase_					)					)
						if len(state.derivatives					) > order:
										_UpperCAmelCase						:  Union[str, Any]     					=	state.replace(derivatives=jnp.delete(state.derivatives       ,		0					)					)

						# 3. Compute linear multistep coefficients
						_UpperCAmelCase						:  int     					=	min(timestep + 1       ,		UpperCAmelCase_					)
						_UpperCAmelCase						:  Optional[int]     					=	[self.get_lms_coefficient(UpperCAmelCase_       ,		UpperCAmelCase_       ,		UpperCAmelCase_       ,		UpperCAmelCase_					) for curr_order in range(UpperCAmelCase_					)]

						# 4. Compute previous sample based on the derivatives path
						_UpperCAmelCase						:  int     					=	sample + sum(
						    coeff * derivative for coeff, derivative in zip(UpperCAmelCase_       ,		reversed(state.derivatives					)					)					)

						if not return_dict:
										return (prev_sample, state)

						return FlaxLMSSchedulerOutput(prev_sample=UpperCAmelCase_       ,		state=UpperCAmelCase_					)







		def 					a_  (    self  :   Union[str, Any]       ,		UpperCAmelCase_  :   LMSDiscreteSchedulerState       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray       ,		UpperCAmelCase_  :   jnp.ndarray       ,		)       ->		jnp.ndarray:


						'''simple docstring'''







						_UpperCAmelCase						:  Union[str, Any]     					=	state.sigmas[timesteps].flatten()
						_UpperCAmelCase						:  Union[str, Any]     					=	broadcast_to_shape_from_left(UpperCAmelCase_       ,		noise.shape					)

						_UpperCAmelCase						:  Any     					=	original_samples + noise * sigma

						return noisy_samples







		def __len__(    self  :   Dict					)       ->		Tuple:


						'''simple docstring'''







						return self.config.num_train_timesteps
