

import unittest

import numpy as np





def      A__					(			__A  :						np.ndarray     ,				__A  :						np.ndarray     ,				__A  :						np.ndarray     ,				__A  :						np.ndarray | None = None     ,				)					->np.ndarray:
      __A    =np.shape(__A			)
      __A    =np.shape(__A			)
      __A    =np.shape(__A			)

      if shape_a[0] != shape_b[0]:
            __A    =(
                '''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]:
            __A    =(
                '''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			)

      __A    =pseudo_inv
      if a_inv is None:
            try:
                  __A    =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        lowerCAmelCase__  (					unittest.TestCase			):



       '''simple docstring'''







       def     __UpperCamelCase     (							self     ):







             '''simple docstring'''



             __A    =np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
             __A    =np.array([[0, 3], [3, 0], [2, 3]]     )
             __A    =np.array([[2, 1], [6, 3]]     )

             __A    =schur_complement(lowercase__ ,   lowercase__ ,   lowercase__     )

             __A    =np.block([[a, b], [b.T, c]]     )

             __A    =np.linalg.det(lowercase__     )
             __A    =np.linalg.det(lowercase__     )
             __A    =np.linalg.det(lowercase__     )

             self.assertAlmostEqual(lowercase__ ,   det_a * det_s     )

       def     __UpperCamelCase     (							self     ):







             '''simple docstring'''



             __A    =np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
             __A    =np.array([[0, 3], [3, 0], [2, 3]]     )
             __A    =np.array([[2, 1], [6, 3]]     )

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


       def     __UpperCamelCase     (							self     ):







             '''simple docstring'''



             __A    =np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
             __A    =np.array([[0, 3], [3, 0], [2, 3]]     )
             __A    =np.array([[2, 1, 3], [6, 3, 5]]     )

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


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   unittest.main()





import gc
import threading
import time

import psutil
import torch





class        lowerCAmelCase__  :



       '''simple docstring'''







       def __init__(							self     ):







             '''simple docstring'''



             __A    =psutil.Process()
             __A    =False

       def     __UpperCamelCase     (							self     ):







             '''simple docstring'''



             __A    =-1

             while True:
                   __A    =max(self.process.memory_info().rss ,   self.cpu_memory_peak     )

                   # can't sleep or will not catch the peak right (this comment is here on purpose)
                   if not self.peak_monitoring:
                         break

       def     __UpperCamelCase     (							self     ):







             '''simple docstring'''



             __A    =True
             __A    =threading.Thread(target=self.peak_monitor     )
             __A    =True
             self.thread.start()


       def     __UpperCamelCase     (							self     ):







             '''simple docstring'''



             __A    =False
             self.thread.join()
             return self.cpu_memory_peak

_lowerCamelCase      :					Union[str, Any]					    =      PeakCPUMemory()





def      A__					(			)					->Dict:
      # Time
      __A    ={'''time''': time.time()}

      gc.collect()
      torch.cuda.empty_cache()

      # CPU mem
      __A    =psutil.Process().memory_info().rss
      cpu_peak_tracker.start()

      # GPU mem
      for i in range(torch.cuda.device_count()			):
            __A    =torch.cuda.memory_allocated(__A			)
      torch.cuda.reset_peak_memory_stats()

      return measures





def      A__					(			__A  :						Any			)					->Any:
      # Time
      __A    ={'''time''': time.time() - start_measures['''time''']}

      gc.collect()
      torch.cuda.empty_cache()

      # CPU mem
      __A    =(psutil.Process().memory_info().rss - start_measures['''cpu''']) / 2**20
      __A    =(cpu_peak_tracker.stop() - start_measures['''cpu''']) / 2**20

      # GPU mem
      for i in range(torch.cuda.device_count()			):
            __A    =(torch.cuda.memory_allocated(__A			) - start_measures[str(__A			)]) / 2**20
            __A    =(torch.cuda.max_memory_allocated(__A			) - start_measures[str(__A			)]) / 2**20

      return measures





def      A__					(			__A  :						Union[str, Any]     ,				__A  :						Any			)					->Union[str, Any]:
      print(F'''{description}:'''			)
      print(F'''- Time: {measures['time']:.2f}s'''			)
      for i in range(torch.cuda.device_count()			):
            print(F'''- GPU {i} allocated: {measures[str(__A			)]:.2f}MiB'''			)
            __A    =measures[F'''{i}-peak''']
            print(F'''- GPU {i} peak: {peak:.2f}MiB'''			)
      print(F'''- CPU RAM allocated: {measures['cpu']:.2f}MiB'''			)
      print(F'''- CPU RAM peak: {measures['cpu-peak']:.2f}MiB'''			)


