






'''simple docstring'''




import json
import os
from dataclasses import dataclass
from functools import partial
from typing import Callable

import flax.linen as nn
import jax
import jax.numpy as jnp
import joblib
import optax
import wandb
from flax import jax_utils, struct, traverse_util
from flax.serialization import from_bytes, to_bytes
from flax.training import train_state
from flax.training.common_utils import shard
from tqdm.auto import tqdm

from transformers import BigBirdConfig, FlaxBigBirdForQuestionAnswering
from transformers.models.big_bird.modeling_flax_big_bird import FlaxBigBirdForQuestionAnsweringModule







class       __lowercase					(__lowerCamelCase    ):
	_lowerCamelCase              =  42
	_lowerCamelCase              =  jnp.floataa
	_lowerCamelCase              =  True

	def      __UpperCamelCase							(      self   :						Optional[Any]):
			super().setup()
			UpperCamelCase__				:					int					=					nn.Dense(5  ,					dtype=self.dtype)





	def __call__(      self   :						Tuple  ,					*UpperCAmelCase_   :						Optional[int]  ,					**UpperCAmelCase_   :						Dict):
			UpperCamelCase__				:					str					=					super().__call__(*UpperCAmelCase_  ,					**UpperCAmelCase_)
			UpperCamelCase__				:					str					=					self.cls(outputs[2])
			return outputs[:2] + (cls_out,)







class       __lowercase					(__lowerCamelCase    ):
	_lowerCamelCase              =  FlaxBigBirdForNaturalQuestionsModule







def       __UpperCAmelCase						(  lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_)							->     Any:
		def cross_entropy(lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_=None):
				UpperCamelCase__				:					Tuple					=					logits.shape[-1]
				UpperCamelCase__				:					Any					=					(labels[..., None] == jnp.arange(lowerCamelCase_)[None]).astype('f4')
				UpperCamelCase__				:					Tuple					=					jax.nn.log_softmax(lowerCamelCase_     ,      axis=-1)
				UpperCamelCase__				:					List[str]					=					-jnp.sum(labels * logits     ,      axis=-1)
				if reduction is not None:
						UpperCamelCase__				:					List[str]					=					reduction(lowerCamelCase_)
				return loss

		UpperCamelCase__				:					int					=					partial(lowerCamelCase_     ,      reduction=jnp.mean)
		UpperCamelCase__				:					int					=					cross_entropy(lowerCamelCase_     ,      lowerCamelCase_)
		UpperCamelCase__				:					str					=					cross_entropy(lowerCamelCase_     ,      lowerCamelCase_)
		UpperCamelCase__				:					Dict					=					cross_entropy(lowerCamelCase_     ,      lowerCamelCase_)
		return (start_loss + end_loss + pooled_loss) / 3







@dataclass
class       __lowercase					:
	_lowerCamelCase              =  "google/bigbird-roberta-base"
	_lowerCamelCase              =  3000
	_lowerCamelCase              =  10500

	_lowerCamelCase              =  128
	_lowerCamelCase              =  3

	_lowerCamelCase              =  1
	_lowerCamelCase              =  5

	# tx_args
	_lowerCamelCase              =  3E-5
	_lowerCamelCase              =  0.0
	_lowerCamelCase              =  20000
	_lowerCamelCase              =  0.0095

	_lowerCamelCase              =  "bigbird-roberta-natural-questions"
	_lowerCamelCase              =  "training-expt"
	_lowerCamelCase              =  "data/nq-training.jsonl"
	_lowerCamelCase              =  "data/nq-validation.jsonl"

	def      __UpperCamelCase							(      self   :						List[Any]):
			os.makedirs(self.base_dir  ,					exist_ok=UpperCAmelCase_)
			UpperCamelCase__				:					str					=					os.path.join(self.base_dir  ,					self.save_dir)
			UpperCamelCase__				:					Optional[int]					=					self.batch_size_per_device * jax.device_count()







@dataclass
class       __lowercase					:
	_lowerCamelCase              =  42
	_lowerCamelCase              =  4096  # no dynamic padding on TPUs

	def __call__(      self   :						Dict  ,					UpperCAmelCase_   :						int):
			UpperCamelCase__				:					Optional[Any]					=					self.collate_fn(UpperCAmelCase_)
			UpperCamelCase__				:					Tuple					=					jax.tree_util.tree_map(UpperCAmelCase_  ,					UpperCAmelCase_)
			return batch

	def      __UpperCamelCase							(      self   :						List[Any]  ,					UpperCAmelCase_   :						str):
			UpperCamelCase__,	UpperCamelCase__				:					List[Any]					=					self.fetch_inputs(features['input_ids'])
			UpperCamelCase__				:					Union[str, Any]					=					{
			    'input_ids': jnp.array(UpperCAmelCase_  ,					dtype=jnp.intaa),
			    'attention_mask': jnp.array(UpperCAmelCase_  ,					dtype=jnp.intaa),
			    'start_labels': jnp.array(features['start_token']  ,					dtype=jnp.intaa),
			    'end_labels': jnp.array(features['end_token']  ,					dtype=jnp.intaa),
			    'pooled_labels': jnp.array(features['category']  ,					dtype=jnp.intaa),
			}
			return batch

	def      __UpperCamelCase							(      self   :						Union[str, Any]  ,					UpperCAmelCase_   :						list):
			UpperCamelCase__				:					int					=					[self._fetch_inputs(UpperCAmelCase_) for ids in input_ids]
			return zip(*UpperCAmelCase_)





	def      __UpperCamelCase							(      self   :						Dict  ,					UpperCAmelCase_   :						list):
			UpperCamelCase__				:					Dict					=					[1 for _ in range(len(UpperCAmelCase_))]
			while len(UpperCAmelCase_) < self.max_length:
					input_ids.append(self.pad_id)
					attention_mask.append(0)
			return input_ids, attention_mask







def       __UpperCAmelCase						(  lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_=None)							->     Any:
		if seed is not None:
				UpperCamelCase__				:					str					=					dataset.shuffle(seed=lowerCamelCase_)
		for i in range(len(lowerCamelCase_) // batch_size):
				UpperCamelCase__				:					Any					=					dataset[i * batch_size : (i + 1) * batch_size]
				yield dict(lowerCamelCase_)







@partial(jax.pmap     ,      axis_name='batch')
def       __UpperCAmelCase						(  lowerCamelCase_     ,      lowerCamelCase_     ,      **lowerCamelCase_)							->     Optional[Any]:
		def loss_fn(lowerCamelCase_):
				UpperCamelCase__				:					List[Any]					=					model_inputs.pop('start_labels')
				UpperCamelCase__				:					Any					=					model_inputs.pop('end_labels')
				UpperCamelCase__				:					Optional[Any]					=					model_inputs.pop('pooled_labels')

				UpperCamelCase__				:					int					=					state.apply_fn(**lowerCamelCase_     ,      params=lowerCamelCase_     ,      dropout_rng=lowerCamelCase_     ,      train=lowerCamelCase_)
				UpperCamelCase__,	UpperCamelCase__,	UpperCamelCase__				:					Any					=					outputs

				return state.loss_fn(
				    lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      )

		UpperCamelCase__,	UpperCamelCase__				:					str					=					jax.random.split(lowerCamelCase_)
		UpperCamelCase__				:					str					=					jax.value_and_grad(lowerCamelCase_)
		UpperCamelCase__,	UpperCamelCase__				:					Any					=					grad_fn(state.params)
		UpperCamelCase__				:					Tuple					=					jax.lax.pmean({'loss': loss}     ,      axis_name='batch')
		UpperCamelCase__				:					Optional[Any]					=					jax.lax.pmean(lowerCamelCase_     ,      'batch')

		UpperCamelCase__				:					List[Any]					=					state.apply_gradients(grads=lowerCamelCase_)
		return state, metrics, new_drp_rng







@partial(jax.pmap     ,      axis_name='batch')
def       __UpperCAmelCase						(  lowerCamelCase_     ,      **lowerCamelCase_)							->     Dict:
		UpperCamelCase__				:					Tuple					=					model_inputs.pop('start_labels')
		UpperCamelCase__				:					Dict					=					model_inputs.pop('end_labels')
		UpperCamelCase__				:					Any					=					model_inputs.pop('pooled_labels')

		UpperCamelCase__				:					Optional[Any]					=					state.apply_fn(**lowerCamelCase_     ,      params=state.params     ,      train=lowerCamelCase_)
		UpperCamelCase__,	UpperCamelCase__,	UpperCamelCase__				:					str					=					outputs

		UpperCamelCase__				:					str					=					state.loss_fn(lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_)
		UpperCamelCase__				:					Union[str, Any]					=					jax.lax.pmean({'loss': loss}     ,      axis_name='batch')
		return metrics







class       __lowercase					(train_state.TrainState    ):
	_lowerCamelCase              =  struct.field(pytree_node=__lowerCamelCase    )







@dataclass
class       __lowercase					:
	_lowerCamelCase              =  42
	_lowerCamelCase              =  42
	_lowerCamelCase              =  42
	_lowerCamelCase              =  42
	_lowerCamelCase              =  42
	_lowerCamelCase              =  42
	_lowerCamelCase              =  None

	def      __UpperCamelCase							(      self   :						str  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						Union[str, Any]  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						Optional[int]=None):
			UpperCamelCase__				:					Any					=					model.params
			UpperCamelCase__				:					str					=					TrainState.create(
			    apply_fn=model.__call__  ,					params=UpperCAmelCase_  ,					tx=UpperCAmelCase_  ,					loss_fn=UpperCAmelCase_  ,					)
			if ckpt_dir is not None:
					UpperCamelCase__,	UpperCamelCase__,	UpperCamelCase__,	UpperCamelCase__,	UpperCamelCase__				:					Optional[int]					=					restore_checkpoint(UpperCAmelCase_  ,					UpperCAmelCase_)
					UpperCamelCase__				:					Tuple					=					{
					    'lr': args.lr,
					    'init_lr': args.init_lr,
					    'warmup_steps': args.warmup_steps,
					    'num_train_steps': num_train_steps,
					    'weight_decay': args.weight_decay,
					}
					UpperCamelCase__,	UpperCamelCase__				:					Optional[Any]					=					build_tx(**UpperCAmelCase_)
					UpperCamelCase__				:					List[Any]					=					train_state.TrainState(
					    step=UpperCAmelCase_  ,					apply_fn=model.__call__  ,					params=UpperCAmelCase_  ,					tx=UpperCAmelCase_  ,					opt_state=UpperCAmelCase_  ,					)
					UpperCamelCase__				:					Tuple					=					args
					UpperCamelCase__				:					Optional[Any]					=					data_collator
					UpperCamelCase__				:					str					=					lr
					UpperCamelCase__				:					Any					=					params
			UpperCamelCase__				:					Any					=					jax_utils.replicate(UpperCAmelCase_)
			return state

	def      __UpperCamelCase							(      self   :						Dict  ,					UpperCAmelCase_   :						List[Any]  ,					UpperCAmelCase_   :						str  ,					UpperCAmelCase_   :						str):
			UpperCamelCase__				:					int					=					self.args
			UpperCamelCase__				:					str					=					len(UpperCAmelCase_) // args.batch_size

			UpperCamelCase__				:					Tuple					=					jax.random.PRNGKey(0)
			UpperCamelCase__				:					Optional[Any]					=					jax.random.split(UpperCAmelCase_  ,					jax.device_count())
			for epoch in range(args.max_epochs):
					UpperCamelCase__				:					Union[str, Any]					=					jnp.array(0  ,					dtype=jnp.floataa)
					UpperCamelCase__				:					Optional[int]					=					get_batched_dataset(UpperCAmelCase_  ,					args.batch_size  ,					seed=UpperCAmelCase_)
					UpperCamelCase__				:					Dict					=					0
					for batch in tqdm(UpperCAmelCase_  ,					total=UpperCAmelCase_  ,					desc=F'Running EPOCH-{epoch}'):
							UpperCamelCase__				:					str					=					self.data_collator(UpperCAmelCase_)
							UpperCamelCase__,	UpperCamelCase__,	UpperCamelCase__				:					Dict					=					self.train_step_fn(UpperCAmelCase_  ,					UpperCAmelCase_  ,					**UpperCAmelCase_)
							running_loss += jax_utils.unreplicate(metrics['loss'])
							i += 1
							if i % args.logging_steps == 0:
									UpperCamelCase__				:					Optional[Any]					=					jax_utils.unreplicate(state.step)
									UpperCamelCase__				:					List[Any]					=					running_loss.item() / i
									UpperCamelCase__				:					Optional[Any]					=					self.scheduler_fn(state_step - 1)

									UpperCamelCase__				:					List[str]					=					self.evaluate(UpperCAmelCase_  ,					UpperCAmelCase_)
									UpperCamelCase__				:					Dict					=					{
									    'step': state_step.item(),
									    'eval_loss': eval_loss.item(),
									    'tr_loss': tr_loss,
									    'lr': lr.item(),
									}
									tqdm.write(str(UpperCAmelCase_))
									self.logger.log(UpperCAmelCase_  ,					commit=UpperCAmelCase_)

							if i % args.save_steps == 0:
									self.save_checkpoint(args.save_dir + F'-e{epoch}-s{i}'  ,					state=UpperCAmelCase_)

	def      __UpperCamelCase							(      self   :						Dict  ,					UpperCAmelCase_   :						str  ,					UpperCAmelCase_   :						int):
			UpperCamelCase__				:					str					=					get_batched_dataset(UpperCAmelCase_  ,					self.args.batch_size)
			UpperCamelCase__				:					Any					=					len(UpperCAmelCase_) // self.args.batch_size
			UpperCamelCase__				:					Optional[Any]					=					jnp.array(0  ,					dtype=jnp.floataa)
			UpperCamelCase__				:					Optional[Any]					=					0
			for batch in tqdm(UpperCAmelCase_  ,					total=UpperCAmelCase_  ,					desc='Evaluating ... '):
					UpperCamelCase__				:					Optional[Any]					=					self.data_collator(UpperCAmelCase_)
					UpperCamelCase__				:					str					=					self.val_step_fn(UpperCAmelCase_  ,					**UpperCAmelCase_)
					running_loss += jax_utils.unreplicate(metrics['loss'])
					i += 1
			return running_loss / i





	def      __UpperCamelCase							(      self   :						Optional[int]  ,					UpperCAmelCase_   :						Optional[Any]  ,					UpperCAmelCase_   :						Optional[Any]):
			UpperCamelCase__				:					Union[str, Any]					=					jax_utils.unreplicate(UpperCAmelCase_)
			print(F'SAVING CHECKPOINT IN {save_dir}'  ,					end=' ... ')
			self.model_save_fn(UpperCAmelCase_  ,					params=state.params)
			with open(os.path.join(UpperCAmelCase_  ,					'opt_state.msgpack')  ,					'wb') as f:
					f.write(to_bytes(state.opt_state))
			joblib.dump(self.args  ,					os.path.join(UpperCAmelCase_  ,					'args.joblib'))
			joblib.dump(self.data_collator  ,					os.path.join(UpperCAmelCase_  ,					'data_collator.joblib'))
			with open(os.path.join(UpperCAmelCase_  ,					'training_state.json')  ,					'w') as f:
					json.dump({'step': state.step.item()}  ,					UpperCAmelCase_)
			print('DONE')







def       __UpperCAmelCase						(  lowerCamelCase_     ,      lowerCamelCase_)							->     Dict:
		print(f'RESTORING CHECKPOINT FROM {save_dir}'     ,      end=' ... ')
		with open(os.path.join(lowerCamelCase_     ,      'flax_model.msgpack')     ,      'rb') as f:
				UpperCamelCase__				:					Optional[Any]					=					from_bytes(state.params     ,      f.read())

		with open(os.path.join(lowerCamelCase_     ,      'opt_state.msgpack')     ,      'rb') as f:
				UpperCamelCase__				:					Any					=					from_bytes(state.opt_state     ,      f.read())

		UpperCamelCase__				:					Union[str, Any]					=					joblib.load(os.path.join(lowerCamelCase_     ,      'args.joblib'))
		UpperCamelCase__				:					int					=					joblib.load(os.path.join(lowerCamelCase_     ,      'data_collator.joblib'))

		with open(os.path.join(lowerCamelCase_     ,      'training_state.json')     ,      'r') as f:
				UpperCamelCase__				:					str					=					json.load(lowerCamelCase_)
		UpperCamelCase__				:					Optional[int]					=					training_state['step']

		print('DONE')
		return params, opt_state, step, args, data_collator







def       __UpperCAmelCase						(  lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_)							->     Optional[Any]:
		UpperCamelCase__				:					List[str]					=					num_train_steps - warmup_steps
		UpperCamelCase__				:					List[Any]					=					optax.linear_schedule(init_value=lowerCamelCase_     ,      end_value=lowerCamelCase_     ,      transition_steps=lowerCamelCase_)
		UpperCamelCase__				:					Dict					=					optax.linear_schedule(init_value=lowerCamelCase_     ,      end_value=1e-7     ,      transition_steps=lowerCamelCase_)
		UpperCamelCase__				:					Optional[int]					=					optax.join_schedules(schedules=[warmup_fn, decay_fn]     ,      boundaries=[warmup_steps])
		return lr







def       __UpperCAmelCase						(  lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_)							->     List[Any]:
		def weight_decay_mask(lowerCamelCase_):
				UpperCamelCase__				:					int					=					traverse_util.flatten_dict(lowerCamelCase_)
				UpperCamelCase__				:					Dict					=					{k: (v[-1] != 'bias' and v[-2:] != ('LayerNorm', 'scale')) for k, v in params.items()}
				return traverse_util.unflatten_dict(lowerCamelCase_)

		UpperCamelCase__				:					str					=					scheduler_fn(lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_)

		UpperCamelCase__				:					str					=					optax.adamw(learning_rate=lowerCamelCase_     ,      weight_decay=lowerCamelCase_     ,      mask=lowerCamelCase_)
		return tx, lr












'''simple docstring'''




from __future__ import annotations







class       __lowercase					:

	def __init__(      self   :						Union[str, Any]  ,					UpperCAmelCase_   :						list[list[int]]):
			UpperCamelCase__				:					int					=					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(UpperCAmelCase_) != 0:
					UpperCamelCase__				:					str					=					len(rows[0])
					if cols == 0:
							raise error
					for row in rows:
							if len(UpperCAmelCase_) != cols:
									raise error
							for value in row:
									if not isinstance(UpperCAmelCase_  ,					(int, float)):
											raise error
					UpperCamelCase__				:					Optional[int]					=					rows
			else:
					UpperCamelCase__				:					Optional[Any]					=					[]

	def      __UpperCamelCase							(      self   :						Union[str, Any]):
			return [[row[i] for row in self.rows] for i in range(len(self.rows[0]))]

	@property
	def      __UpperCamelCase							(      self   :						Dict):
			return len(self.rows)

	@property
	def      __UpperCamelCase							(      self   :						Tuple):
			return len(self.rows[0])

	@property
	def      __UpperCamelCase							(      self   :						List[Any]):
			return (self.num_rows, self.num_columns)

	@property
	def      __UpperCamelCase							(      self   :						Any):
			return self.order[0] == self.order[1]

	def      __UpperCamelCase							(      self   :						Any):
			UpperCamelCase__				:					Optional[int]					=					[
			    [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(UpperCAmelCase_)

	def      __UpperCamelCase							(      self   :						Dict):
			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      __UpperCamelCase							(      self   :						str):
			return bool(self.determinant())

	def      __UpperCamelCase							(      self   :						List[str]  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int):
			UpperCamelCase__				:					Optional[Any]					=					[
			    [
			        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(UpperCAmelCase_).determinant()

	def      __UpperCamelCase							(      self   :						Any  ,					UpperCAmelCase_   :						int  ,					UpperCAmelCase_   :						int):
			if (row + column) % 2 == 0:
					return self.get_minor(UpperCAmelCase_  ,					UpperCAmelCase_)
			return -1 * self.get_minor(UpperCAmelCase_  ,					UpperCAmelCase_)

	def      __UpperCamelCase							(      self   :						List[Any]):
			return Matrix(
			    [
			        [self.get_minor(UpperCAmelCase_  ,					UpperCAmelCase_) for column in range(self.num_columns)]
			        for row in range(self.num_rows)
			    ])

	def      __UpperCamelCase							(      self   :						Optional[int]):
			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      __UpperCamelCase							(      self   :						Dict):
			UpperCamelCase__				:					Dict					=					[
			    [self.cofactors().rows[column][row] for column in range(self.num_columns)]
			    for row in range(self.num_rows)
			]
			return Matrix(UpperCAmelCase_)

	def      __UpperCamelCase							(      self   :						int):
			UpperCamelCase__				:					List[Any]					=					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):
			return str(self.rows)

	def __str__(      self   :						List[Any]):
			if self.num_rows == 0:
					return "[]"
			if self.num_rows == 1:
					return "[[" + ". ".join(str(self.rows[0])) + "]]"
			return (
			    "["
			    + "\n ".join(
			        [
			            '[' + '. '.join([str(UpperCAmelCase_) for value in row]) + '.]'
			            for row in self.rows
			        ])
			    + "]"
			)

	def      __UpperCamelCase							(      self   :						Dict  ,					UpperCAmelCase_   :						list[int]  ,					UpperCAmelCase_   :						int | None = None):
			UpperCamelCase__				:					List[str]					=					TypeError('Row must be a list containing all ints and/or floats')
			if not isinstance(UpperCAmelCase_  ,					UpperCAmelCase_):
					raise type_error
			for value in row:
					if not isinstance(UpperCAmelCase_  ,					(int, float)):
							raise type_error
			if len(UpperCAmelCase_) != 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(UpperCAmelCase_)
			else:
					UpperCamelCase__				:					Tuple					=					self.rows[0:position] + [row] + self.rows[position:]

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

	def __eq__(      self   :						List[Any]  ,					UpperCAmelCase_   :						object):
			if not isinstance(UpperCAmelCase_  ,					UpperCAmelCase_):
					return NotImplemented
			return self.rows == other.rows

	def __ne__(      self   :						Any  ,					UpperCAmelCase_   :						object):
			return not self == other

	def __neg__(      self   :						Union[str, Any]):
			return self * -1

	def __add__(      self   :						Optional[int]  ,					UpperCAmelCase_   :						Matrix):
			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   :						Tuple  ,					UpperCAmelCase_   :						Matrix):
			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   :						Any  ,					UpperCAmelCase_   :						Matrix | int | float):
			if isinstance(UpperCAmelCase_  ,					(int, float)):
					return Matrix(
					    [[int(element * other) for element in row] for row in self.rows])
			elif isinstance(UpperCAmelCase_  ,					UpperCAmelCase_):
					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(UpperCAmelCase_  ,					UpperCAmelCase_) 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   :						Dict  ,					UpperCAmelCase_   :						int):
			if not isinstance(UpperCAmelCase_  ,					UpperCAmelCase_):
					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')
			UpperCamelCase__				:					str					=					self
			for _ in range(other - 1):
					result *= self
			return result





	@classmethod
	def      __UpperCamelCase							(      cls   :						Optional[int]  ,					UpperCAmelCase_   :						list[int]  ,					UpperCAmelCase_   :						list[int]):
			return sum(row[i] * column[i] for i in range(len(UpperCAmelCase_)))


if __name__ == "__main__":
		import doctest

		doctest.testmod()




