


"""simple docstring"""



import math
import time
from typing import Dict, List, Optional

from torch.utils.data import Dataset

from transformers import SeqaSeqTrainer, is_torch_tpu_available
from transformers.trainer_utils import PredictionOutput, speed_metrics


if is_torch_tpu_available(check_device=False):
 import torch_xla.core.xla_model as xm
 import torch_xla.debug.metrics as met
class 					__magic_name__		(			__snake_case     ):






       def __init__(   self  :    str  ,     *snake_case__  :    Optional[int]  ,     snake_case__  :    Dict=None  ,     snake_case__  :    int=None  ,     **snake_case__  :    Tuple				):

              '''simple docstring'''






              super().__init__(*_lowercase  ,     **_lowercase				)
              lowercase		:int       							=				eval_examples
              lowercase		:Optional[Any]       							=				post_process_function






       def  __snake_case						(   self  :    int  ,     snake_case__  :    Dict = None  ,     snake_case__  :    Optional[int]=None  ,     snake_case__  :    List[str] = None  ,     snake_case__  :    Any = "eval"  ,     **snake_case__  :    Any  ,     ):

              '''simple docstring'''






              lowercase		:Any       							=				gen_kwargs.copy()
              lowercase		:int       							=				(
                  gen_kwargs["""max_length"""] if gen_kwargs.get('''max_length'''				) is not None else self.args.generation_max_length
              )
              lowercase		:Optional[int]       							=				(
                  gen_kwargs["""num_beams"""] if gen_kwargs.get('''num_beams'''				) is not None else self.args.generation_num_beams
              )
              lowercase		:Tuple       							=				gen_kwargs

              lowercase		:Optional[int]       							=				self.eval_dataset if eval_dataset is None else eval_dataset
              lowercase		:Optional[Any]       							=				self.get_eval_dataloader(_lowercase				)
              lowercase		:Dict       							=				self.eval_examples if eval_examples is None else eval_examples

              # Temporarily disable metric computation, we will do it in the loop here.
              lowercase		:Dict       							=				self.compute_metrics
              lowercase		:List[Any]       							=				None
              lowercase		:Dict       							=				time.time()
              lowercase		:Tuple       							=				self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
              try:
                     lowercase		:Optional[Any]       							=				eval_loop(
                         _lowercase  ,     description='''Evaluation'''  ,     prediction_loss_only=True if compute_metrics is None else None  ,     ignore_keys=_lowercase  ,     metric_key_prefix=_lowercase  ,     )
              finally:
                     lowercase		:List[str]       							=				compute_metrics
              lowercase		:Any       							=				self.args.eval_batch_size * self.args.world_size
              if f"""{metric_key_prefix}_jit_compilation_time""" in output.metrics:
                     start_time += output.metrics[f"""{metric_key_prefix}_jit_compilation_time"""]
              output.metrics.update(
                  speed_metrics(
                      _lowercase  ,     _lowercase  ,     num_samples=output.num_samples  ,     num_steps=math.ceil(output.num_samples / total_batch_size				)  ,     )				)

              if self.post_process_function is not None and self.compute_metrics is not None and self.args.should_save:
                     # Only the main node write the results by default
                     lowercase		:Union[str, Any]       							=				self.post_process_function(_lowercase  ,     _lowercase  ,     _lowercase				)
                     lowercase		:Tuple       							=				self.compute_metrics(_lowercase				)

                     # Prefix all keys with metric_key_prefix + '_'
                     for key in list(metrics.keys()				):
                            if not key.startswith(f"""{metric_key_prefix}_"""				):
                                   lowercase		:int       							=				metrics.pop(_lowercase				)

                     metrics.update(output.metrics				)
              else:
                     lowercase		:Any       							=				output.metrics

              if self.args.should_log:
                     # Only the main node log the results by default
                     self.log(_lowercase				)

              if self.args.tpu_metrics_debug or self.args.debug:
                     # tpu-comment: Logging debug metrics for PyTorch/XLA (compile, execute times, ops, etc.)
                     xm.master_print(met.metrics_report()				)

              lowercase		:str       							=				self.callback_handler.on_evaluate(self.args  ,     self.state  ,     self.control  ,     _lowercase				)
              return metrics







       def  __snake_case						(   self  :    Optional[int]  ,     snake_case__  :    Optional[int]  ,     snake_case__  :    Union[str, Any]  ,     snake_case__  :    Optional[Any]=None  ,     snake_case__  :    List[Any] = "test"  ,     **snake_case__  :    str				):

              '''simple docstring'''






              lowercase		:Dict       							=				gen_kwargs.copy()

              lowercase		:Tuple       							=				self.get_test_dataloader(_lowercase				)

              # Temporarily disable metric computation, we will do it in the loop here.
              lowercase		:Dict       							=				self.compute_metrics
              lowercase		:List[str]       							=				None
              lowercase		:Union[str, Any]       							=				time.time()
              lowercase		:List[Any]       							=				self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
              try:
                     lowercase		:str       							=				eval_loop(
                         _lowercase  ,     description='''Prediction'''  ,     prediction_loss_only=True if compute_metrics is None else None  ,     ignore_keys=_lowercase  ,     metric_key_prefix=_lowercase  ,     )
              finally:
                     lowercase		:Optional[int]       							=				compute_metrics

              lowercase		:Any       							=				self.args.eval_batch_size * self.args.world_size
              if f"""{metric_key_prefix}_jit_compilation_time""" in output.metrics:
                     start_time += output.metrics[f"""{metric_key_prefix}_jit_compilation_time"""]
              output.metrics.update(
                  speed_metrics(
                      _lowercase  ,     _lowercase  ,     num_samples=output.num_samples  ,     num_steps=math.ceil(output.num_samples / total_batch_size				)  ,     )				)
              if self.post_process_function is None or self.compute_metrics is None:
                     return output

              lowercase		:str       							=				self.post_process_function(_lowercase  ,     _lowercase  ,     _lowercase  ,     '''predict'''				)
              lowercase		:Tuple       							=				self.compute_metrics(_lowercase				)

              # Prefix all keys with metric_key_prefix + '_'
              for key in list(metrics.keys()				):
                     if not key.startswith(f"""{metric_key_prefix}_"""				):
                            lowercase		:Any       							=				metrics.pop(_lowercase				)
              metrics.update(output.metrics				)
              return PredictionOutput(predictions=predictions.predictions  ,     label_ids=predictions.label_ids  ,     metrics=_lowercase				)





"""simple docstring"""



import unittest

import numpy as np






def       lowerCamelCase					(a_						:np.ndarray				,				a_						:np.ndarray				,				a_						:np.ndarray				,				a_						:np.ndarray | None = None				,				)     ->							np.ndarray:
       lowercase		:str       							=				np.shape(a_)
       lowercase		:Dict       							=				np.shape(a_)
       lowercase		:Optional[int]       							=				np.shape(a_)

       if shape_a[0] != shape_b[0]:
              lowercase		:List[str]       							=				(
                  '''Expected the same number of rows for A and B. '''
                  F"""Instead found A of size {shape_a} and B of size {shape_b}"""
              )
              raise ValueError(a_)

       if shape_b[1] != shape_c[1]:
              lowercase		:List[str]       							=				(
                  '''Expected the same number of columns for B and C. '''
                  F"""Instead found B of size {shape_b} and C of size {shape_c}"""
              )
              raise ValueError(a_)

       lowercase		:Optional[Any]       							=				pseudo_inv
       if a_inv is None:
              try:
                     lowercase		:int       							=				np.linalg.inv(a_)
              except np.linalg.LinAlgError:
                     raise ValueError(
                         '''Input matrix A is not invertible. Cannot compute Schur complement.''')

       return mat_c - mat_b.T @ a_inv @ mat_b
class 					__magic_name__		(			unittest.TestCase     ):






       def  __snake_case						(   self  :    int				):

              '''simple docstring'''






              lowercase		:Dict       							=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]				)
              lowercase		:List[str]       							=				np.array([[0, 3], [3, 0], [2, 3]]				)
              lowercase		:List[str]       							=				np.array([[2, 1], [6, 3]]				)

              lowercase		:Any       							=				schur_complement(snake_case__  ,     snake_case__  ,     snake_case__				)

              lowercase		:int       							=				np.block([[a, b], [b.T, c]]				)

              lowercase		:Tuple       							=				np.linalg.det(snake_case__				)
              lowercase		:Any       							=				np.linalg.det(snake_case__				)
              lowercase		:List[Any]       							=				np.linalg.det(snake_case__				)

              self.assertAlmostEqual(snake_case__  ,     det_a * det_s				)






       def  __snake_case						(   self  :    Optional[int]				):

              '''simple docstring'''






              lowercase		:Union[str, Any]       							=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]				)
              lowercase		:Union[str, Any]       							=				np.array([[0, 3], [3, 0], [2, 3]]				)
              lowercase		:List[str]       							=				np.array([[2, 1], [6, 3]]				)

              with self.assertRaises(snake_case__				):
                     schur_complement(snake_case__  ,     snake_case__  ,     snake_case__				)







       def  __snake_case						(   self  :    List[Any]				):

              '''simple docstring'''






              lowercase		:List[str]       							=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]				)
              lowercase		:int       							=				np.array([[0, 3], [3, 0], [2, 3]]				)
              lowercase		:List[Any]       							=				np.array([[2, 1, 3], [6, 3, 5]]				)

              with self.assertRaises(snake_case__				):
                     schur_complement(snake_case__  ,     snake_case__  ,     snake_case__				)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 unittest.main()

