





from __future__ import annotations




class 	UpperCamelCase_							:


							def __init__(				self     :Tuple				,					__A     :list[list[int]]		) -> int:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								=   TypeError(
									    """Matrices must be formed from a list of zero or more lists containing at """
									    """least one and the same number of values, each of which must be of type """
									    """int or float."""		)
									if len(__A		) != 0:
											SCREAMING_SNAKE_CASE__								=   len(rows[0]		)
											if cols == 0:
													raise error
											for row in rows:
													if len(__A		) != cols:
															raise error
													for value in row:
															if not isinstance(__A				,					(int, float)		):
																	raise error
											SCREAMING_SNAKE_CASE__								=   rows
									else:
											SCREAMING_SNAKE_CASE__								=   []


							def   _snake_case	(				self     :int		) -> list[list[int]]:



									"""simple docstring"""



									return [[row[i] for row in self.rows] for i in range(len(self.rows[0]		)		)]


							@property
							def   _snake_case	(				self     :List[Any]		) -> int:



									"""simple docstring"""



									return len(self.rows		)


							@property
							def   _snake_case	(				self     :Optional[int]		) -> int:



									"""simple docstring"""



									return len(self.rows[0]		)


							@property
							def   _snake_case	(				self     :Dict		) -> tuple[int, int]:



									"""simple docstring"""



									return (self.num_rows, self.num_columns)


							@property
							def   _snake_case	(				self     :Any		) -> bool:



									"""simple docstring"""



									return self.order[0] == self.order[1]


							def   _snake_case	(				self     :int		) -> Matrix:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								=   [
									    [0 if column_num != row_num else 1 for column_num in range(self.num_rows		)]
									    for row_num in range(self.num_rows		)
									]
									return Matrix(__A		)


							def   _snake_case	(				self     :List[Any]		) -> int:



									"""simple docstring"""



									if not self.is_square:
											return 0
									if self.order == (0, 0):
											return 1
									if self.order == (1, 1):
											return int(self.rows[0][0]		)
									if self.order == (2, 2):
											return int(
											    (self.rows[0][0] * self.rows[1][1])
											    - (self.rows[0][1] * self.rows[1][0])		)
									else:
											return sum(
											    self.rows[0][column] * self.cofactors().rows[0][column]
											    for column in range(self.num_columns		)		)


							def   _snake_case	(				self     :Any		) -> bool:



									"""simple docstring"""



									return bool(self.determinant()		)


							def   _snake_case	(				self     :str				,					__A     :int				,					__A     :int		) -> int:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								=   [
									    [
									        self.rows[other_row][other_column]
									        for other_column in range(self.num_columns		)
									        if other_column != column
									    ]
									    for other_row in range(self.num_rows		)
									    if other_row != row
									]
									return Matrix(__A		).determinant()


							def   _snake_case	(				self     :List[str]				,					__A     :int				,					__A     :int		) -> int:



									"""simple docstring"""



									if (row + column) % 2 == 0:
											return self.get_minor(__A				,					__A		)
									return -1 * self.get_minor(__A				,					__A		)


							def   _snake_case	(				self     :Dict		) -> Matrix:



									"""simple docstring"""



									return Matrix(
									    [
									        [self.get_minor(__A				,					__A		) for column in range(self.num_columns		)]
									        for row in range(self.num_rows		)
									    ]		)


							def   _snake_case	(				self     :List[Any]		) -> Matrix:



									"""simple docstring"""



									return Matrix(
									    [
									        [
									            self.minors().rows[row][column]
									            if (row + column) % 2 == 0
									            else self.minors().rows[row][column] * -1
									            for column in range(self.minors().num_columns		)
									        ]
									        for row in range(self.minors().num_rows		)
									    ]		)


							def   _snake_case	(				self     :Tuple		) -> Matrix:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								=   [
									    [self.cofactors().rows[column][row] for column in range(self.num_columns		)]
									    for row in range(self.num_rows		)
									]
									return Matrix(__A		)


							def   _snake_case	(				self     :List[str]		) -> Matrix:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								=   self.determinant()
									if not determinant:
											raise TypeError("""Only matrices with a non-zero determinant have an inverse"""		)
									return self.adjugate() * (1 / determinant)


							def __repr__(				self     :Any		) -> str:



									"""simple docstring"""



									return str(self.rows		)


							def __str__(				self     :Optional[Any]		) -> str:



									"""simple docstring"""



									if self.num_rows == 0:
											return "[]"
									if self.num_rows == 1:
											return "[[" + ". ".join(str(self.rows[0]		)		) + "]]"
									return (
									    "["
									    + "\n ".join(
									        [
									            """[""" + """. """.join([str(__A		) for value in row]		) + """.]"""
									            for row in self.rows
									        ]		)
									    + "]"
									)


							def   _snake_case	(				self     :Optional[Any]				,					__A     :list[int]				,					__A     :int | None = None		) -> None:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								=   TypeError("""Row must be a list containing all ints and/or floats"""		)
									if not isinstance(__A				,					__A		):
											raise type_error
									for value in row:
											if not isinstance(__A				,					(int, float)		):
													raise type_error
									if len(__A		) != self.num_columns:
											raise ValueError(
											    """Row must be equal in length to the other rows in the matrix"""		)
									if position is None:
											self.rows.append(__A		)
									else:
											SCREAMING_SNAKE_CASE__								=   self.rows[0:position] + [row] + self.rows[position:]


							def   _snake_case	(				self     :List[str]				,					__A     :list[int]				,					__A     :int | None = None		) -> None:



									"""simple docstring"""



									SCREAMING_SNAKE_CASE__								=   TypeError(
									    """Column must be a list containing all ints and/or floats"""		)
									if not isinstance(__A				,					__A		):
											raise type_error
									for value in column:
											if not isinstance(__A				,					(int, float)		):
													raise type_error
									if len(__A		) != self.num_rows:
											raise ValueError(
											    """Column must be equal in length to the other columns in the matrix"""		)
									if position is None:
											SCREAMING_SNAKE_CASE__								=   [self.rows[i] + [column[i]] for i in range(self.num_rows		)]
									else:
											SCREAMING_SNAKE_CASE__								=   [
											    self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
											    for i in range(self.num_rows		)
											]


							def __eq__(				self     :Optional[int]				,					__A     :object		) -> bool:



									"""simple docstring"""



									if not isinstance(__A				,					__A		):
											return NotImplemented
									return self.rows == other.rows


							def __ne__(				self     :Dict				,					__A     :object		) -> bool:



									"""simple docstring"""



									return not self == other


							def __neg__(				self     :Optional[int]		) -> Matrix:



									"""simple docstring"""



									return self * -1


							def __add__(				self     :Dict				,					__A     :Matrix		) -> Matrix:



									"""simple docstring"""



									if self.order != other.order:
											raise ValueError("""Addition requires matrices of the same order"""		)
									return Matrix(
									    [
									        [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns		)]
									        for i in range(self.num_rows		)
									    ]		)


							def __sub__(				self     :str				,					__A     :Matrix		) -> Matrix:



									"""simple docstring"""



									if self.order != other.order:
											raise ValueError("""Subtraction requires matrices of the same order"""		)
									return Matrix(
									    [
									        [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns		)]
									        for i in range(self.num_rows		)
									    ]		)


							def __mul__(				self     :Optional[int]				,					__A     :Matrix | int | float		) -> Matrix:



									"""simple docstring"""



									if isinstance(__A				,					(int, float)		):
											return Matrix(
											    [[int(element * other		) for element in row] for row in self.rows]		)
									elif isinstance(__A				,					__A		):
											if self.num_columns != other.num_rows:
													raise ValueError(
													    """The number of columns in the first matrix must """
													    """be equal to the number of rows in the second"""		)
											return Matrix(
											    [
											        [Matrix.dot_product(__A				,					__A		) for column in other.columns()]
											        for row in self.rows
											    ]		)
									else:
											raise TypeError(
											    """A Matrix can only be multiplied by an int, float, or another matrix"""		)


							def __pow__(				self     :str				,					__A     :int		) -> Matrix:



									"""simple docstring"""



									if not isinstance(__A				,					__A		):
											raise TypeError("""A Matrix can only be raised to the power of an int"""		)
									if not self.is_square:
											raise ValueError("""Only square matrices can be raised to a power"""		)
									if other == 0:
											return self.identity()
									if other < 0:
											if self.is_invertable():
													return self.inverse() ** (-other)
											raise ValueError(
											    """Only invertable matrices can be raised to a negative power"""		)
									SCREAMING_SNAKE_CASE__								=   self
									for _ in range(other - 1		):
											result *= self
									return result


							@classmethod
							def   _snake_case	(				cls     :str				,					__A     :list[int]				,					__A     :list[int]		) -> int:



									"""simple docstring"""



									return sum(row[i] * column[i] for i in range(len(__A		)		)		)


if __name__ == "__main__":
	import doctest

	doctest.testmod()






'''simple docstring'''

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 		UpperCamelCase							(				_lowerCamelCase   :   Any		,			_lowerCamelCase   :   Optional[Any]=10			):
    A__							=     []
    for _ in range(_lowerCamelCase			):
        lrs.append(scheduler.get_lr()[0]			)
        scheduler.step()
    return lrs





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

                A__							=     torch.load(_lowerCamelCase			)
                scheduler.load_state_dict(_lowerCamelCase			)
    return lrs






@require_torch
class   UpperCAmelCase      (			unittest.TestCase							):
 def 	UpperCAmelCase_				(							self :int		,			lowercase_ :Any		,			lowercase_ :List[Any]		,			lowercase_ :Optional[Any]				)->				int:
     self.assertEqual(len(lowercase_				)		,			len(lowercase_				)				)
     for a, b in zip(lowercase_		,			lowercase_				):
         self.assertAlmostEqual(lowercase_		,			lowercase_		,			delta=lowercase_				)
 def 	UpperCAmelCase_				(							self :Union[str, Any]				)->				Dict:
     A__							=     torch.tensor([0.1, -0.2, -0.1]		,			requires_grad=lowercase_				)
     A__							=     torch.tensor([0.4, 0.2, -0.5]				)
     A__							=     nn.MSELoss()
     # No warmup, constant schedule, no gradient clipping
     A__							=     AdamW(params=[w]		,			lr=2E-1		,			weight_decay=0.0				)
     for _ in range(1_00				):
         A__							=     criterion(lowercase_		,			lowercase_				)
         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 	UpperCAmelCase_				(							self :Tuple				)->				List[str]:
     A__							=     torch.tensor([0.1, -0.2, -0.1]		,			requires_grad=lowercase_				)
     A__							=     torch.tensor([0.4, 0.2, -0.5]				)
     A__							=     nn.MSELoss()
     # No warmup, constant schedule, no gradient clipping
     A__							=     Adafactor(
         params=[w]		,			lr=1E-2		,			eps=(1E-30, 1E-3)		,			clip_threshold=1.0		,			decay_rate=-0.8		,			betaa=lowercase_		,			weight_decay=0.0		,			relative_step=lowercase_		,			scale_parameter=lowercase_		,			warmup_init=lowercase_		,			)
     for _ in range(10_00				):
         A__							=     criterion(lowercase_		,			lowercase_				)
         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							):
 __lowercase  						=							nn.Linear(50     ,			50							) if is_torch_available() else None
 __lowercase  						=							AdamW(m.parameters()     ,			lr=1_0.0							) if is_torch_available() else None
 __lowercase  						=							10
 def 	UpperCAmelCase_				(							self :Tuple		,			lowercase_ :Any		,			lowercase_ :List[Any]		,			lowercase_ :List[Any]		,			lowercase_ :str=None				)->				Optional[int]:
     self.assertEqual(len(lowercase_				)		,			len(lowercase_				)				)
     for a, b in zip(lowercase_		,			lowercase_				):
         self.assertAlmostEqual(lowercase_		,			lowercase_		,			delta=lowercase_		,			msg=lowercase_				)



 def 	UpperCAmelCase_				(							self :Optional[Any]				)->				Any:
     A__							=     {"num_warmup_steps": 2, "num_training_steps": 10}
     # schedulers doct format
     # function: (sched_args_dict, expected_learning_rates)
     A__							=     {
         get_constant_schedule: ({}, [1_0.0] * self.num_steps),
         get_constant_schedule_with_warmup: (
             {"num_warmup_steps": 4},
             [0.0, 2.5, 5.0, 7.5, 1_0.0, 1_0.0, 1_0.0, 1_0.0, 1_0.0, 1_0.0],
         ),
         get_linear_schedule_with_warmup: (
             {**common_kwargs},
             [0.0, 5.0, 1_0.0, 8.7_5, 7.5, 6.2_5, 5.0, 3.7_5, 2.5, 1.2_5],
         ),
         get_cosine_schedule_with_warmup: (
             {**common_kwargs},
             [0.0, 5.0, 1_0.0, 9.6_1, 8.5_3, 6.9_1, 5.0, 3.0_8, 1.4_6, 0.3_8],
         ),
         get_cosine_with_hard_restarts_schedule_with_warmup: (
             {**common_kwargs, "num_cycles": 2},
             [0.0, 5.0, 1_0.0, 8.5_3, 5.0, 1.4_6, 1_0.0, 8.5_3, 5.0, 1.4_6],
         ),
         get_polynomial_decay_schedule_with_warmup: (
             {**common_kwargs, "power": 2.0, "lr_end": 1E-7},
             [0.0, 5.0, 1_0.0, 7.6_5_6, 5.6_2_5, 3.9_0_6, 2.5, 1.4_0_6, 0.6_2_5, 0.1_5_6],
         ),
         get_inverse_sqrt_schedule: (
             {"num_warmup_steps": 2},
             [0.0, 5.0, 1_0.0, 8.1_6_5, 7.0_7_1, 6.3_2_5, 5.7_7_4, 5.3_4_5, 5.0, 4.7_1_4],
         ),
     }

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

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

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






class   UpperCAmelCase      :
 def __init__(							self :str		,			lowercase_ :List[str]				)->				Tuple:
     A__							=     fn
 def __call__(							self :List[Any]		,			*lowercase_ :Dict		,			**lowercase_ :Dict				)->				Tuple:
     return self.fn(*lowercase_		,			**lowercase_				)



 @classmethod
 def 	UpperCAmelCase_				(							self :Any		,			lowercase_ :Tuple				)->				List[Any]:
     A__							=     list(map(self		,			scheduler.lr_lambdas				)				)



