
'''simple docstring'''







import doctest
from collections import deque

import numpy as np


class 		__UpperCAmelCase :


							def __init__(			self    ):





								"""simple docstring"""






								_snake_case  		=						[2, 1, 2, -1]
								_snake_case  		=						[1, 2, 3, 4]




							def 					lowerCamelCase							(			self    ):





								"""simple docstring"""






								_snake_case  		=						len(self.first_signal    )
								_snake_case  		=						len(self.second_signal    )

								_snake_case  		=						max(lowerCAmelCase__       ,  lowerCAmelCase__    )

								# create a zero matrix of max_length x max_length
								_snake_case  		=						[[0] * max_length for i in range(lowerCAmelCase__    )]

								# fills the smaller signal with zeros to make both signals of same length
								if length_first_signal < length_second_signal:
									self.first_signal += [0] * (max_length - length_first_signal)
								elif length_first_signal > length_second_signal:
									self.second_signal += [0] * (max_length - length_second_signal)
								for i in range(lowerCAmelCase__    ):
									_snake_case  		=						deque(self.second_signal    )
									rotated_signal.rotate(lowerCAmelCase__    )
									for j, item in enumerate(lowerCAmelCase__    ):
										matrix[i][j] += item

        # multiply the matrix with the first signal
								_snake_case  		=						np.matmul(np.transpose(lowerCAmelCase__    )       ,  np.transpose(self.first_signal    )    )

								# rounding-off to two decimal places
								return [round(lowerCAmelCase__       ,  2    ) for i in final_signal]


if __name__ == "__main__":
					doctest.testmod()



import os
import tempfile
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch


if is_torch_available():
						import torch
						from torch import nn

						from transformers import (
						    Adafactor,
						    AdamW,
						    get_constant_schedule,
						    get_constant_schedule_with_warmup,
						    get_cosine_schedule_with_warmup,
						    get_cosine_with_hard_restarts_schedule_with_warmup,
						    get_inverse_sqrt_schedule,
						    get_linear_schedule_with_warmup,
						    get_polynomial_decay_schedule_with_warmup,
						)

def  __snake_case							(	__magic_name__		,    __magic_name__=10						):







				'''simple docstring'''


				lowercase         =      []
				for _ in range(__magic_name__						):
								lrs.append(scheduler.get_lr()[0]						)
								scheduler.step()
				return lrs

def  __snake_case							(	__magic_name__		,    __magic_name__=10						):







				'''simple docstring'''


				lowercase         =      []
				for step in range(__magic_name__						):
								lrs.append(scheduler.get_lr()[0]						)
								scheduler.step()
								if step == num_steps // 2:
												with tempfile.TemporaryDirectory() as tmpdirname:
																lowercase         =      os.path.join(__magic_name__		,    "schedule.bin"						)
																torch.save(scheduler.state_dict()		,    __magic_name__						)

																lowercase         =      torch.load(__magic_name__						)
																scheduler.load_state_dict(__magic_name__						)
				return lrs





@require_torch
class   UpperCamelCase_      (      unittest.TestCase		):







						'''simple docstring'''



						def        SCREAMING_SNAKE_CASE(			self							:Optional[Any]		,    lowerCAmelCase__							:List[str]		,    lowerCAmelCase__							:Tuple		,    lowerCAmelCase__							:Dict     )  ->Tuple:
										self.assertEqual(len(lowerCAmelCase__     )		,    len(lowerCAmelCase__     )     )
										for a, b in zip(lowerCAmelCase__		,    lowerCAmelCase__     ):
														self.assertAlmostEqual(lowerCAmelCase__		,    lowerCAmelCase__		,    delta=lowerCAmelCase__     )





						def        SCREAMING_SNAKE_CASE(			self							:Optional[int]     )  ->Dict:
										lowercase         =      torch.tensor([0.1, -0.2, -0.1]		,    requires_grad=lowerCAmelCase__     )
										lowercase         =      torch.tensor([0.4, 0.2, -0.5]     )
										lowercase         =      nn.MSELoss()
										# No warmup, constant schedule, no gradient clipping
										lowercase         =      AdamW(params=[w]		,    lr=2E-1		,    weight_decay=0.0     )
										for _ in range(100     ):
														lowercase         =      criterion(lowerCAmelCase__		,    lowerCAmelCase__     )
														loss.backward()
														optimizer.step()
														w.grad.detach_()  # No zero_grad() function on simple tensors. we do it ourselves.
														w.grad.zero_()
										self.assertListAlmostEqual(w.tolist()		,    [0.4, 0.2, -0.5]		,    tol=1E-2     )





						def        SCREAMING_SNAKE_CASE(			self							:int     )  ->List[Any]:
										lowercase         =      torch.tensor([0.1, -0.2, -0.1]		,    requires_grad=lowerCAmelCase__     )
										lowercase         =      torch.tensor([0.4, 0.2, -0.5]     )
										lowercase         =      nn.MSELoss()
										# No warmup, constant schedule, no gradient clipping
										lowercase         =      Adafactor(
										    params=[w]		,    lr=1E-2		,    eps=(1E-3_0, 1E-3)		,    clip_threshold=1.0		,    decay_rate=-0.8		,    betaa=lowerCAmelCase__		,    weight_decay=0.0		,    relative_step=lowerCAmelCase__		,    scale_parameter=lowerCAmelCase__		,    warmup_init=lowerCAmelCase__		,    )
										for _ in range(1000     ):
														lowercase         =      criterion(lowerCAmelCase__		,    lowerCAmelCase__     )
														loss.backward()
														optimizer.step()
														w.grad.detach_()  # No zero_grad() function on simple tensors. we do it ourselves.
														w.grad.zero_()
										self.assertListAlmostEqual(w.tolist()		,    [0.4, 0.2, -0.5]		,    tol=1E-2     )





@require_torch
class   UpperCamelCase_      (      unittest.TestCase		):







						'''simple docstring'''



						UpperCamelCase      :  Any				   =					nn.Linear(50		,    50		) if is_torch_available() else None
						UpperCamelCase      :  Union[str, Any]				   =					AdamW(m.parameters()		,    lr=10.0		) if is_torch_available() else None
						UpperCamelCase      :  int				   =					10





						def        SCREAMING_SNAKE_CASE(			self							:Any		,    lowerCAmelCase__							:Optional[Any]		,    lowerCAmelCase__							:Optional[Any]		,    lowerCAmelCase__							:Any		,    lowerCAmelCase__							:Any=None     )  ->Dict:
										self.assertEqual(len(lowerCAmelCase__     )		,    len(lowerCAmelCase__     )     )
										for a, b in zip(lowerCAmelCase__		,    lowerCAmelCase__     ):
														self.assertAlmostEqual(lowerCAmelCase__		,    lowerCAmelCase__		,    delta=lowerCAmelCase__		,    msg=lowerCAmelCase__     )





						def        SCREAMING_SNAKE_CASE(			self							:Any     )  ->str:
										lowercase         =      {"num_warmup_steps": 2, "num_training_steps": 10}
										# schedulers doct format
										# function: (sched_args_dict, expected_learning_rates)
										lowercase         =      {
										    get_constant_schedule: ({}, [10.0] * self.num_steps),
										    get_constant_schedule_with_warmup: (
										        {"num_warmup_steps": 4},
										        [0.0, 2.5, 5.0, 7.5, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0],
										    ),
										    get_linear_schedule_with_warmup: (
										        {**common_kwargs},
										        [0.0, 5.0, 10.0, 8.75, 7.5, 6.25, 5.0, 3.75, 2.5, 1.25],
										    ),
										    get_cosine_schedule_with_warmup: (
										        {**common_kwargs},
										        [0.0, 5.0, 10.0, 9.61, 8.53, 6.91, 5.0, 3.08, 1.46, 0.38],
										    ),
										    get_cosine_with_hard_restarts_schedule_with_warmup: (
										        {**common_kwargs, "num_cycles": 2},
										        [0.0, 5.0, 10.0, 8.53, 5.0, 1.46, 10.0, 8.53, 5.0, 1.46],
										    ),
										    get_polynomial_decay_schedule_with_warmup: (
										        {**common_kwargs, "power": 2.0, "lr_end": 1E-7},
										        [0.0, 5.0, 10.0, 7.6_56, 5.6_25, 3.9_06, 2.5, 1.4_06, 0.6_25, 0.1_56],
										    ),
										    get_inverse_sqrt_schedule: (
										        {"num_warmup_steps": 2},
										        [0.0, 5.0, 10.0, 8.1_65, 7.0_71, 6.3_25, 5.7_74, 5.3_45, 5.0, 4.7_14],
										    ),
										}

										for scheduler_func, data in scheds.items():
														lowercase     ,	lowercase         =      data

														lowercase         =      scheduler_func(self.optimizer		,    **lowerCAmelCase__     )
														self.assertEqual(len([scheduler.get_lr()[0]]     )		,    1     )
														lowercase         =      unwrap_schedule(lowerCAmelCase__		,    self.num_steps     )
														self.assertListAlmostEqual(
														    lowerCAmelCase__		,    lowerCAmelCase__		,    tol=1E-2		,    msg=F'''failed for {scheduler_func} in normal scheduler'''		,    )

														lowercase         =      scheduler_func(self.optimizer		,    **lowerCAmelCase__     )
														if scheduler_func.__name__ != "get_constant_schedule":
																		LambdaScheduleWrapper.wrap_scheduler(lowerCAmelCase__     )  # wrap to test picklability of the schedule
														lowercase         =      unwrap_and_save_reload_schedule(lowerCAmelCase__		,    self.num_steps     )
														self.assertListEqual(lowerCAmelCase__		,    lowerCAmelCase__		,    msg=F'''failed for {scheduler_func} in save and reload'''     )





class   UpperCamelCase_      :







						'''simple docstring'''



						def __init__(			self							:List[str]		,    lowerCAmelCase__							:int     )  ->Optional[int]:
										lowercase         =      fn





						def __call__(			self							:Optional[Any]		,    *lowerCAmelCase__							:int		,    **lowerCAmelCase__							:List[str]     )  ->List[str]:
										return self.fn(*lowerCAmelCase__		,    **lowerCAmelCase__     )





						@classmethod
						def        SCREAMING_SNAKE_CASE(			self							:List[Any]		,    lowerCAmelCase__							:Optional[Any]     )  ->str:
										lowercase         =      list(map(self		,    scheduler.lr_lambdas     )     )
