




'''simple docstring'''

from __future__ import annotations

import math


def 		__magic_name__    (	__UpperCAmelCase,      __UpperCAmelCase	)		->					list:

					'''simple docstring'''

					if len(__UpperCAmelCase	) != 2 or len(a[0]	) != 2 or len(__UpperCAmelCase	) != 2 or len(b[0]	) != 2:
										raise Exception('''Matrices are not 2x2'''	)
					snake_case_									=				[
					    [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
					    [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
					]
					return new_matrix


def 		__magic_name__    (	__UpperCAmelCase,      __UpperCAmelCase	)		->					Any:

					'''simple docstring'''

					return [
					    [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]	)	)]
					    for row in range(len(__UpperCAmelCase	)	)
					]


def 		__magic_name__    (	__UpperCAmelCase,      __UpperCAmelCase	)		->					int:

					'''simple docstring'''

					return [
					    [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]	)	)]
					    for row in range(len(__UpperCAmelCase	)	)
					]


def 		__magic_name__    (	__UpperCAmelCase	)		->					tuple[list, list, list, list]:

					'''simple docstring'''

					if len(__UpperCAmelCase	) % 2 != 0 or len(a[0]	) % 2 != 0:
										raise Exception('''Odd matrices are not supported!'''	)

					snake_case_									=				len(__UpperCAmelCase	)
					snake_case_									=				matrix_length // 2

					snake_case_									=				[[a[i][j] for j in range(__UpperCAmelCase,      __UpperCAmelCase	)] for i in range(__UpperCAmelCase	)]
					snake_case_									=				[
					    [a[i][j] for j in range(__UpperCAmelCase,      __UpperCAmelCase	)] for i in range(__UpperCAmelCase,      __UpperCAmelCase	)
					]

					snake_case_									=				[[a[i][j] for j in range(__UpperCAmelCase	)] for i in range(__UpperCAmelCase	)]
					snake_case_									=				[[a[i][j] for j in range(__UpperCAmelCase	)] for i in range(__UpperCAmelCase,      __UpperCAmelCase	)]

					return top_left, top_right, bot_left, bot_right


def 		__magic_name__    (	__UpperCAmelCase	)		->					tuple[int, int]:

					'''simple docstring'''

					return len(__UpperCAmelCase	), len(matrix[0]	)


def 		__magic_name__    (	__UpperCAmelCase	)		->					None:

					'''simple docstring'''

					print('''\n'''.join(str(__UpperCAmelCase	) for line in matrix	)	)


def 		__magic_name__    (	__UpperCAmelCase,      __UpperCAmelCase	)		->					list:

					'''simple docstring'''

					if matrix_dimensions(__UpperCAmelCase	) == (2, 2):
										return default_matrix_multiplication(__UpperCAmelCase,      __UpperCAmelCase	)

					snake_case_			,snake_case_			,snake_case_			,snake_case_									=				split_matrix(__UpperCAmelCase	)
					snake_case_			,snake_case_			,snake_case_			,snake_case_									=				split_matrix(__UpperCAmelCase	)

					snake_case_									=				actual_strassen(__UpperCAmelCase,      matrix_subtraction(__UpperCAmelCase,      __UpperCAmelCase	)	)
					snake_case_									=				actual_strassen(matrix_addition(__UpperCAmelCase,      __UpperCAmelCase	),      __UpperCAmelCase	)
					snake_case_									=				actual_strassen(matrix_addition(__UpperCAmelCase,      __UpperCAmelCase	),      __UpperCAmelCase	)
					snake_case_									=				actual_strassen(__UpperCAmelCase,      matrix_subtraction(__UpperCAmelCase,      __UpperCAmelCase	)	)
					snake_case_									=				actual_strassen(matrix_addition(__UpperCAmelCase,      __UpperCAmelCase	),      matrix_addition(__UpperCAmelCase,      __UpperCAmelCase	)	)
					snake_case_									=				actual_strassen(matrix_subtraction(__UpperCAmelCase,      __UpperCAmelCase	),      matrix_addition(__UpperCAmelCase,      __UpperCAmelCase	)	)
					snake_case_									=				actual_strassen(matrix_subtraction(__UpperCAmelCase,      __UpperCAmelCase	),      matrix_addition(__UpperCAmelCase,      __UpperCAmelCase	)	)

					snake_case_									=				matrix_addition(matrix_subtraction(matrix_addition(__UpperCAmelCase,      __UpperCAmelCase	),      __UpperCAmelCase	),      __UpperCAmelCase	)
					snake_case_									=				matrix_addition(__UpperCAmelCase,      __UpperCAmelCase	)
					snake_case_									=				matrix_addition(__UpperCAmelCase,      __UpperCAmelCase	)
					snake_case_									=				matrix_subtraction(matrix_subtraction(matrix_addition(__UpperCAmelCase,      __UpperCAmelCase	),      __UpperCAmelCase	),      __UpperCAmelCase	)

					# construct the new matrix from our 4 quadrants
					snake_case_									=				[]
					for i in range(len(__UpperCAmelCase	)	):
										new_matrix.append(top_left[i] + top_right[i]	)
					for i in range(len(__UpperCAmelCase	)	):
										new_matrix.append(bot_left[i] + bot_right[i]	)
					return new_matrix


def 		__magic_name__    (	__UpperCAmelCase,      __UpperCAmelCase	)		->					list:

					'''simple docstring'''

					if matrix_dimensions(__UpperCAmelCase	)[1] != matrix_dimensions(__UpperCAmelCase	)[0]:
										snake_case_									=				(
										    '''Unable to multiply these matrices, please check the dimensions.\n'''
										    F"Matrix A: {matrixa}\n"
										    F"Matrix B: {matrixa}"
										)
										raise Exception(__UpperCAmelCase	)
					snake_case_									=				matrix_dimensions(__UpperCAmelCase	)
					snake_case_									=				matrix_dimensions(__UpperCAmelCase	)

					if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
										return [matrixa, matrixa]

					snake_case_									=				max(*__UpperCAmelCase,      *__UpperCAmelCase	)
					snake_case_									=				int(math.pow(2,      math.ceil(math.loga(__UpperCAmelCase	)	)	)	)
					snake_case_									=				matrixa
					snake_case_									=				matrixa

					# Adding zeros to the matrices so that the arrays dimensions are the same and also
					# power of 2
					for i in range(0,      __UpperCAmelCase	):
										if i < dimensiona[0]:
															for _ in range(dimensiona[1],      __UpperCAmelCase	):
																				new_matrixa[i].append(0	)
										else:
															new_matrixa.append([0] * maxim	)
										if i < dimensiona[0]:
															for _ in range(dimensiona[1],      __UpperCAmelCase	):
																				new_matrixa[i].append(0	)
										else:
															new_matrixa.append([0] * maxim	)

					snake_case_									=				actual_strassen(__UpperCAmelCase,      __UpperCAmelCase	)

					# Removing the additional zeros
					for i in range(0,      __UpperCAmelCase	):
										if i < dimensiona[0]:
															for _ in range(dimensiona[1],      __UpperCAmelCase	):
																				final_matrix[i].pop()
										else:
															final_matrix.pop()
					return final_matrix


if __name__ == "__main__":
							a  :				List[Any]									=  [
							    [2, 3, 4, 5],
							    [6, 4, 3, 1],
							    [2, 3, 6, 7],
							    [3, 1, 2, 4],
							    [2, 3, 4, 5],
							    [6, 4, 3, 1],
							    [2, 3, 6, 7],
							    [3, 1, 2, 4],
							    [2, 3, 4, 5],
							    [6, 2, 3, 1],
							]
							a  :				Union[str, Any]									=  [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
							print(strassen(matrixa, matrixa))




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 			A_      (    _UpperCAmelCase				,	_UpperCAmelCase=10    ):
						SCREAMING_SNAKE_CASE_: Union[str, Any]  		=       []
						for _ in range(_UpperCAmelCase    ):
												lrs.append(scheduler.get_lr()[0]    )
												scheduler.step()
						return lrs







def 			A_      (    _UpperCAmelCase				,	_UpperCAmelCase=10    ):
						SCREAMING_SNAKE_CASE_: List[str]  		=       []
						for step in range(_UpperCAmelCase    ):
												lrs.append(scheduler.get_lr()[0]    )
												scheduler.step()
												if step == num_steps // 2:
																		with tempfile.TemporaryDirectory() as tmpdirname:
																								SCREAMING_SNAKE_CASE_: Optional[int]  		=       os.path.join(_UpperCAmelCase				,	"schedule.bin"    )
																								torch.save(scheduler.state_dict()				,	_UpperCAmelCase    )

																								SCREAMING_SNAKE_CASE_: Optional[Any]  		=       torch.load(_UpperCAmelCase    )
																								scheduler.load_state_dict(_UpperCAmelCase    )
						return lrs



@require_torch
class   __lowercase				( unittest.TestCase	):




			"""simple docstring"""







			def        _SCREAMING_SNAKE_CASE			( self  :     Dict   ,						lowerCAmelCase__  :     int   ,						lowerCAmelCase__  :     Dict   ,						lowerCAmelCase__  :     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  :     Dict):
									SCREAMING_SNAKE_CASE_: Union[str, Any]  		=       torch.tensor([0.1, -0.2, -0.1]   ,						requires_grad=lowerCAmelCase__)
									SCREAMING_SNAKE_CASE_: str  		=       torch.tensor([0.4, 0.2, -0.5])
									SCREAMING_SNAKE_CASE_: Optional[Any]  		=       nn.MSELoss()
									# No warmup, constant schedule, no gradient clipping
									SCREAMING_SNAKE_CASE_: int  		=       AdamW(params=[w]   ,						lr=2E-1   ,						weight_decay=0.0)
									for _ in range(100):
															SCREAMING_SNAKE_CASE_: Dict  		=       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  :     Dict):
									SCREAMING_SNAKE_CASE_: Union[str, Any]  		=       torch.tensor([0.1, -0.2, -0.1]   ,						requires_grad=lowerCAmelCase__)
									SCREAMING_SNAKE_CASE_: int  		=       torch.tensor([0.4, 0.2, -0.5])
									SCREAMING_SNAKE_CASE_: Any  		=       nn.MSELoss()
									# No warmup, constant schedule, no gradient clipping
									SCREAMING_SNAKE_CASE_: int  		=       Adafactor(
									    params=[w]   ,						lr=1E-2   ,						eps=(1E-30, 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):
															SCREAMING_SNAKE_CASE_: List[Any]  		=       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   __lowercase				( unittest.TestCase	):




			"""simple docstring"""







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



			def        _SCREAMING_SNAKE_CASE			( self  :     Optional[int]   ,						lowerCAmelCase__  :     List[Any]   ,						lowerCAmelCase__  :     int   ,						lowerCAmelCase__  :     int   ,						lowerCAmelCase__  :     Optional[Any]=None):
									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  :     int):
									SCREAMING_SNAKE_CASE_: Dict  		=       {"num_warmup_steps": 2, "num_training_steps": 10}
									# schedulers doct format
									# function: (sched_args_dict, expected_learning_rates)
									SCREAMING_SNAKE_CASE_: Dict  		=       {
									    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, 7.656, 5.625, 3.906, 2.5, 1.406, 0.625, 0.156],
									    ),
									    get_inverse_sqrt_schedule: (
									        {"num_warmup_steps": 2},
									        [0.0, 5.0, 10.0, 8.165, 7.071, 6.325, 5.774, 5.345, 5.0, 4.714],
									    ),
									}

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

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

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







class   __lowercase				:




			"""simple docstring"""







			def __init__( self  :     str   ,						lowerCAmelCase__  :     List[str]):
									SCREAMING_SNAKE_CASE_: List[Any]  		=       fn



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




			@classmethod
			def        _SCREAMING_SNAKE_CASE			( self  :     Optional[int]   ,						lowerCAmelCase__  :     str):
									SCREAMING_SNAKE_CASE_: str  		=       list(map(self   ,						scheduler.lr_lambdas))






