




'''simple docstring'''


import random
import unittest

import numpy as np

import transformers
from transformers import is_flax_available, is_torch_available
from transformers.testing_utils import is_pt_flax_cross_test, require_flax


if is_flax_available():
	import os

	import jax.numpy as jnp
	from jax import jit

	from transformers import AutoTokenizer, FlaxAutoModelForCausalLM
	from transformers.modeling_flax_pytorch_utils import load_flax_weights_in_pytorch_model

	_lowercase  =			"""0.12"""  # assumed parallelism: 8


if is_torch_available():
	import torch
def 						lowerCamelCase__   (				a    ,	a    ,	a=None							):
						if rng is None:
												__snake_case						 =   random.Random()

						__snake_case						 =   1
						for dim in shape:
												total_dims *= dim

						__snake_case						 =   []
						for _ in range(a							):
												values.append(rng.randint(0    ,	vocab_size - 1							)							)

						__snake_case						 =   np.array(a    ,	dtype=jnp.intaa							).reshape(a							)

						return output
def 						lowerCamelCase__   (				a    ,	a=None							):
						__snake_case						 =   ids_tensor(a    ,	vocab_size=2    ,	rng=a							)
						# make sure that at least one token is attended to for each batch
						__snake_case						 =   1
						return attn_mask
@require_flax
class 						a_				:
	lowercase_       :     Tuple			  =      None
	lowercase_       :     List[Any]			  =      ()




	def   lowercase__   (       self     :  str      ):
							__snake_case ,       __snake_case						 =   self.model_tester.prepare_config_and_inputs_for_common()

							# cut to half length & take max batch_size 3
							__snake_case						 =   2
							__snake_case						 =   inputs['input_ids'].shape[-1] // 2
							__snake_case						 =   inputs['input_ids'][:max_batch_size, :sequence_length]

							__snake_case						 =   jnp.ones_like(__lowerCAmelCase      )
							__snake_case						 =   attention_mask[:max_batch_size, :sequence_length]

							# generate max 5 tokens
							__snake_case						 =   input_ids.shape[-1] + 5
							if config.eos_token_id is not None and config.pad_token_id is None:
													# hack to allow generate for models such as GPT2 as is done in `generate()`
													__snake_case						 =   config.eos_token_id
							return config, input_ids, attention_mask, max_length




	@is_pt_flax_cross_test
	def   lowercase__   (       self     :  Optional[int]      ):
							__snake_case ,       __snake_case ,       __snake_case ,       __snake_case						 =   self._get_input_ids_and_config()
							__snake_case						 =   False
							__snake_case						 =   max_length
							__snake_case						 =   0

							for model_class in self.all_generative_model_classes:
													__snake_case						 =   model_class(__lowerCAmelCase      )

													__snake_case						 =   model_class.__name__[4:]  # Skip the "Flax" at the beginning
													__snake_case						 =   getattr(__lowerCAmelCase       ,		__lowerCAmelCase      )
													__snake_case						 =   pt_model_class(__lowerCAmelCase      ).eval()
													__snake_case						 =   load_flax_weights_in_pytorch_model(__lowerCAmelCase       ,		flax_model.params      )

													__snake_case						 =   flax_model.generate(__lowerCAmelCase      ).sequences
													__snake_case						 =   pt_model.generate(torch.tensor(__lowerCAmelCase       ,		dtype=torch.long      )      )

													if flax_generation_outputs.shape[-1] > pt_generation_outputs.shape[-1]:
																			__snake_case						 =   flax_generation_outputs[:, : pt_generation_outputs.shape[-1]]

													self.assertListEqual(pt_generation_outputs.numpy().tolist()       ,		flax_generation_outputs.tolist()      )




	def   lowercase__   (       self     :  Optional[int]      ):
							__snake_case ,       __snake_case ,       __snake_case ,       __snake_case						 =   self._get_input_ids_and_config()
							__snake_case						 =   False
							__snake_case						 =   max_length

							for model_class in self.all_generative_model_classes:
													__snake_case						 =   model_class(__lowerCAmelCase      )

													__snake_case						 =   model.generate(__lowerCAmelCase      ).sequences
													self.assertEqual(generation_outputs.shape[-1]       ,		__lowerCAmelCase      )

													__snake_case						 =   jit(model.generate      )
													__snake_case						 =   jit_generate(__lowerCAmelCase      ).sequences

													self.assertListEqual(generation_outputs.tolist()       ,		jit_generation_outputs.tolist()      )




	def   lowercase__   (       self     :  List[str]      ):
							__snake_case ,       __snake_case ,       __snake_case ,       __snake_case						 =   self._get_input_ids_and_config()
							__snake_case						 =   True
							__snake_case						 =   max_length

							for model_class in self.all_generative_model_classes:
													__snake_case						 =   model_class(__lowerCAmelCase      )

													__snake_case						 =   model.generate(__lowerCAmelCase      ).sequences
													self.assertEqual(generation_outputs.shape[-1]       ,		__lowerCAmelCase      )

													__snake_case						 =   jit(model.generate      )
													__snake_case						 =   jit_generate(__lowerCAmelCase      ).sequences

													self.assertListEqual(generation_outputs.tolist()       ,		jit_generation_outputs.tolist()      )




	def   lowercase__   (       self     :  Optional[int]      ):
							__snake_case ,       __snake_case ,       __snake_case ,       __snake_case						 =   self._get_input_ids_and_config()
							__snake_case						 =   False
							__snake_case						 =   max_length
							__snake_case						 =   2

							for model_class in self.all_generative_model_classes:
													__snake_case						 =   model_class(__lowerCAmelCase      )

													__snake_case						 =   model.generate(__lowerCAmelCase      ).sequences
													self.assertEqual(generation_outputs.shape[-1]       ,		__lowerCAmelCase      )

													__snake_case						 =   jit(model.generate      )
													__snake_case						 =   jit_generate(__lowerCAmelCase      ).sequences

													self.assertListEqual(generation_outputs.tolist()       ,		jit_generation_outputs.tolist()      )




	def   lowercase__   (       self     :  List[Any]      ):
							__snake_case ,       __snake_case ,       __snake_case ,       __snake_case						 =   self._get_input_ids_and_config()
							__snake_case						 =   False
							__snake_case						 =   max_length
							__snake_case						 =   2
							__snake_case						 =   2

							for model_class in self.all_generative_model_classes:
													__snake_case						 =   model_class(__lowerCAmelCase      )

													__snake_case						 =   model.generate(__lowerCAmelCase      ).sequences
													self.assertEqual(generation_outputs.shape[0]       ,		input_ids.shape[0] * config.num_return_sequences      )




	def   lowercase__   (       self     :  List[str]      ):
							__snake_case ,       __snake_case ,       __snake_case ,       __snake_case						 =   self._get_input_ids_and_config()
							__snake_case						 =   True
							__snake_case						 =   max_length
							__snake_case						 =   0.8
							__snake_case						 =   1_0
							__snake_case						 =   0.3
							__snake_case						 =   1
							__snake_case						 =   8
							__snake_case						 =   9

							for model_class in self.all_generative_model_classes:
													__snake_case						 =   model_class(__lowerCAmelCase      )

													__snake_case						 =   model.generate(__lowerCAmelCase      ).sequences
													self.assertEqual(generation_outputs.shape[-1]       ,		__lowerCAmelCase      )

													__snake_case						 =   jit(model.generate      )
													__snake_case						 =   jit_generate(__lowerCAmelCase      ).sequences

													self.assertListEqual(generation_outputs.tolist()       ,		jit_generation_outputs.tolist()      )




	def   lowercase__   (       self     :  Tuple      ):
							__snake_case ,       __snake_case ,       __snake_case ,       __snake_case						 =   self._get_input_ids_and_config()
							__snake_case						 =   max_length
							__snake_case						 =   1
							__snake_case						 =   8
							__snake_case						 =   9

							for model_class in self.all_generative_model_classes:
													__snake_case						 =   model_class(__lowerCAmelCase      )

													__snake_case						 =   model.generate(__lowerCAmelCase      ).sequences
													self.assertEqual(generation_outputs.shape[-1]       ,		__lowerCAmelCase      )

													__snake_case						 =   jit(model.generate      )
													__snake_case						 =   jit_generate(__lowerCAmelCase      ).sequences

													self.assertListEqual(generation_outputs.tolist()       ,		jit_generation_outputs.tolist()      )




	def   lowercase__   (       self     :  Optional[int]      ):
							__snake_case ,       __snake_case ,       __snake_case ,       __snake_case						 =   self._get_input_ids_and_config()
							__snake_case						 =   max_length
							__snake_case						 =   2
							__snake_case						 =   1
							__snake_case						 =   8
							__snake_case						 =   9

							for model_class in self.all_generative_model_classes:
													__snake_case						 =   model_class(__lowerCAmelCase      )

													__snake_case						 =   model.generate(__lowerCAmelCase      ).sequences
													self.assertEqual(generation_outputs.shape[-1]       ,		__lowerCAmelCase      )

													__snake_case						 =   jit(model.generate      )
													__snake_case						 =   jit_generate(__lowerCAmelCase      ).sequences

													self.assertListEqual(generation_outputs.tolist()       ,		jit_generation_outputs.tolist()      )




	def   lowercase__   (       self     :  Optional[int]      ):
							__snake_case ,       __snake_case ,       __snake_case ,       __snake_case						 =   self._get_input_ids_and_config()

							# pad attention mask on the left
							__snake_case						 =   attention_mask.at[(0, 0)].set(0      )

							__snake_case						 =   False
							__snake_case						 =   max_length

							for model_class in self.all_generative_model_classes:
													__snake_case						 =   model_class(__lowerCAmelCase      )

													__snake_case						 =   model.generate(__lowerCAmelCase       ,		attention_mask=__lowerCAmelCase      ).sequences
													self.assertEqual(generation_outputs.shape[-1]       ,		__lowerCAmelCase      )

													__snake_case						 =   jit(model.generate      )
													__snake_case						 =   jit_generate(__lowerCAmelCase       ,		attention_mask=__lowerCAmelCase      ).sequences

													self.assertListEqual(generation_outputs.tolist()       ,		jit_generation_outputs.tolist()      )




	def   lowercase__   (       self     :  List[Any]      ):
							__snake_case ,       __snake_case ,       __snake_case ,       __snake_case						 =   self._get_input_ids_and_config()

							# pad attention mask on the left
							__snake_case						 =   attention_mask.at[(0, 0)].set(0      )

							__snake_case						 =   True
							__snake_case						 =   max_length

							for model_class in self.all_generative_model_classes:
													__snake_case						 =   model_class(__lowerCAmelCase      )

													__snake_case						 =   model.generate(__lowerCAmelCase       ,		attention_mask=__lowerCAmelCase      ).sequences
													self.assertEqual(generation_outputs.shape[-1]       ,		__lowerCAmelCase      )

													__snake_case						 =   jit(model.generate      )
													__snake_case						 =   jit_generate(__lowerCAmelCase       ,		attention_mask=__lowerCAmelCase      ).sequences

													self.assertListEqual(generation_outputs.tolist()       ,		jit_generation_outputs.tolist()      )




	def   lowercase__   (       self     :  List[str]      ):
							__snake_case ,       __snake_case ,       __snake_case ,       __snake_case						 =   self._get_input_ids_and_config()

							# pad attention mask on the left
							__snake_case						 =   attention_mask.at[(0, 0)].set(0      )

							__snake_case						 =   2
							__snake_case						 =   max_length

							for model_class in self.all_generative_model_classes:
													__snake_case						 =   model_class(__lowerCAmelCase      )

													__snake_case						 =   model.generate(__lowerCAmelCase       ,		attention_mask=__lowerCAmelCase      ).sequences
													self.assertEqual(generation_outputs.shape[-1]       ,		__lowerCAmelCase      )

													__snake_case						 =   jit(model.generate      )
													__snake_case						 =   jit_generate(__lowerCAmelCase       ,		attention_mask=__lowerCAmelCase      ).sequences

													self.assertListEqual(generation_outputs.tolist()       ,		jit_generation_outputs.tolist()      )





@require_flax
class 						a_				(			unittest.TestCase						):




	def   lowercase__   (       self     :  int      ):
							__snake_case						 =   AutoTokenizer.from_pretrained('hf-internal-testing/tiny-bert'      )
							__snake_case						 =   FlaxAutoModelForCausalLM.from_pretrained('hf-internal-testing/tiny-bert-flax-only'      )

							__snake_case						 =   'Hello world'
							__snake_case						 =   tokenizer(__lowerCAmelCase       ,		return_tensors='np'      ).input_ids

							# typos are quickly detected (the correct argument is `do_sample`)
							with self.assertRaisesRegex(__lowerCAmelCase       ,		'do_samples'      ):
													model.generate(__lowerCAmelCase       ,		do_samples=__lowerCAmelCase      )

							# arbitrary arguments that will not be used anywhere are also not accepted
							with self.assertRaisesRegex(__lowerCAmelCase       ,		'foo'      ):
													__snake_case						 =   {'foo': 'bar'}
													model.generate(__lowerCAmelCase       ,		**__lowerCAmelCase      )







'''simple docstring'''


from __future__ import annotations

import math
def 						lowerCamelCase__   (				a    ,	a							):
						__snake_case						 =   u
						for i in range(1    ,	a							):
												__snake_case						 =   temp * (u - i)
						return temp
def 						lowerCamelCase__   (				):
						__snake_case						 =   int(input('enter the numbers of values: '							)							)
						__snake_case						 =   []
						for _ in range(a							):
												y.append([]							)
						for i in range(a							):
												for j in range(a							):
																		y[i].append(a							)
																		__snake_case						 =   0

						print('enter the values of parameters in a list: '							)
						__snake_case						 =   list(map(a    ,	input().split()							)							)

						print('enter the values of corresponding parameters: '							)
						for i in range(a							):
												__snake_case						 =   float(input()							)

						__snake_case						 =   int(input('enter the value to interpolate: '							)							)
						__snake_case						 =   (value - x[0]) / (x[1] - x[0])

						# for calculating forward difference table

						for i in range(1    ,	a							):
												for j in range(n - i							):
																		__snake_case						 =   y[j + 1][i - 1] - y[j][i - 1]

						__snake_case						 =   y[0][0]
						for i in range(1    ,	a							):
												summ += (ucal(a    ,	a							) * y[0][i]) / math.factorial(a							)

						print(f'the value at {value} is {summ}'							)


if __name__ == "__main__":
	main()

