




"""simple docstring"""




#
# This a `torch.distributed` diagnostics script that checks that all GPUs in the cluster (one or
# many nodes) can talk to each other via nccl and allocate gpu memory.
#
# To run first adjust the number of processes and nodes:
#
# python -m torch.distributed.run --nproc_per_node 2 --nnodes 1 torch-distributed-gpu-test.py
#
# You may need to add --master_addr $MASTER_ADDR --master_port $MASTER_PORT if using a custom addr:port
#
# You can also use the rdzv API: --rdzv_endpoint $MASTER_ADDR:$MASTER_PORT --rdzv_backend c10d
#
# use torch.distributed.launch instead of torch.distributed.run for torch < 1.9
#
# If you get a hanging in `barrier` calls you have some network issues, you may try to debug this with:
#
# NCCL_DEBUG=INFO python -m torch.distributed.run --nproc_per_node 2 --nnodes 1 torch-distributed-gpu-test.py
#
# which should tell you what's going on behind the scenes.
#
#
# This script can be run via `srun` in the SLURM environment as well. Here is a SLURM script that
# runs on 2 nodes of 4 gpus per node:
#
# #SBATCH --job-name=test-nodes        # name
# #SBATCH --nodes=2                    # nodes
# #SBATCH --ntasks-per-node=1          # crucial - only 1 task per dist per node!
# #SBATCH --cpus-per-task=10           # number of cores per tasks
# #SBATCH --gres=gpu:4                 # number of gpus
# #SBATCH --time 0:05:00               # maximum execution time (HH:MM:SS)
# #SBATCH --output=%x-%j.out           # output file name
#
# GPUS_PER_NODE=4
# MASTER_ADDR=$(scontrol show hostnames $SLURM_JOB_NODELIST | head -n 1)
# MASTER_PORT=6000
#
# srun --jobid $SLURM_JOBID bash -c 'python -m torch.distributed.run \
# --nproc_per_node $GPUS_PER_NODE --nnodes $SLURM_NNODES --node_rank $SLURM_PROCID \
# --master_addr $MASTER_ADDR --master_port $MASTER_PORT \
# torch-distributed-gpu-test.py'
#

import fcntl
import os
import socket

import torch
import torch.distributed as dist







def      __UpperCAmelCase     ( *__UpperCamelCase	):
			with open(__UpperCamelCase	,				'''r'''	) as fh:
						fcntl.flock(__UpperCamelCase	,				fcntl.LOCK_EX	)
						try:
									print(*__UpperCamelCase	)
						finally:
									fcntl.flock(__UpperCamelCase	,				fcntl.LOCK_UN	)


a_        =       int(os.environ['LOCAL_RANK'])
torch.cuda.set_device(local_rank)
a_        =       torch.device('cuda', local_rank)
a_        =       socket.gethostname()

a_        =       F"[{hostname}-{local_rank}]"

try:
			# test distributed
			dist.init_process_group('nccl')
			dist.all_reduce(torch.ones(1).to(device), op=dist.ReduceOp.SUM)
			dist.barrier()

			# test cuda is available and can allocate memory
			torch.cuda.is_available()
			torch.ones(1).cuda(local_rank)

			# global rank
			a_        =       dist.get_rank()
			a_        =       dist.get_world_size()

			printflock(F"{gpu} is OK (global rank: {rank}/{world_size})")

			dist.barrier()
			if rank == 0:
						printflock(F"pt={torch.__version__}, cuda={torch.version.cuda}, nccl={torch.cuda.nccl.version()}")

except Exception:
			printflock(F"{gpu} is broken")
			raise











"""simple docstring"""
import numpy as np






def       __UpperCamelCase						(		snake_case__ , snake_case__ , snake_case__ = 1E-12 , snake_case__ = 100 , ):
	assert np.shape(snake_case__       )[0] == np.shape(snake_case__       )[1]
	# Ensure proper dimensionality.
	assert np.shape(snake_case__       )[0] == np.shape(snake_case__       )[0]
	# Ensure inputs are either both complex or both real
	assert np.iscomplexobj(snake_case__       ) == np.iscomplexobj(snake_case__       )
	A_		:    Union[str, Any]						     = np.iscomplexobj(snake_case__       )
	if is_complex:
		# Ensure complex input_matrix is Hermitian
		assert np.array_equal(snake_case__ , input_matrix.conj().T       )

	# Set convergence to False. Will define convergence when we exceed max_iterations
	# or when we have small changes from one iteration to next.

	A_		:    List[str]						     = False
	A_		:    int						     = 0
	A_		:    List[Any]						     = 0
	A_		:    Tuple						     = 1E12

	while not convergence:
		# Multiple matrix by the vector.
		A_		:    Dict						     = np.dot(snake_case__ , snake_case__       )
		# Normalize the resulting output vector.
		A_		:    str						     = w / np.linalg.norm(snake_case__       )
		# Find rayleigh quotient
		# (faster than usual b/c we know vector is normalized already)
		A_		:    str						     = vector.conj().T if is_complex else vector.T
		A_		:    Optional[Any]						     = np.dot(snake_case__ , np.dot(snake_case__ , snake_case__       )       )

		# Check convergence.
		A_		:    Any						     = np.abs(lambda_ - lambda_previous       ) / lambda_
		iterations += 1

		if error <= error_tol or iterations >= max_iterations:
			A_		:    Optional[Any]						     = True

		A_		:    Union[str, Any]						     = lambda_

	if is_complex:
		A_		:    str						     = np.real(lambda_       )

	return lambda_, vector






def       __UpperCamelCase						(		):
	A_		:    Optional[int]						     = np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]       )
	A_		:    Tuple						     = np.array([41, 4, 20]       )
	A_		:    Tuple						     = real_input_matrix.astype(np.complexaaa       )
	A_		:    List[Any]						     = np.triu(1J * complex_input_matrix , 1       )
	complex_input_matrix += imag_matrix
	complex_input_matrix += -1 * imag_matrix.T
	A_		:    Any						     = np.array([41, 4, 20]       ).astype(np.complexaaa       )

	for problem_type in ["real", "complex"]:
		if problem_type == "real":
			A_		:    Optional[int]						     = real_input_matrix
			A_		:    List[str]						     = real_vector
		elif problem_type == "complex":
			A_		:    List[Any]						     = complex_input_matrix
			A_		:    str						     = complex_vector

		# Our implementation.
		A_     ,  A_		:    Dict						     = power_iteration(snake_case__ , snake_case__       )

		# Numpy implementation.

		# Get eigenvalues and eigenvectors using built-in numpy
		# eigh (eigh used for symmetric or hermetian matrices).
		A_     ,  A_		:    Optional[Any]						     = np.linalg.eigh(snake_case__       )
		# Last eigenvalue is the maximum one.
		A_		:    List[Any]						     = eigen_values[-1]
		# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
		A_		:    Optional[Any]						     = eigen_vectors[:, -1]

		# Check our implementation and numpy gives close answers.
		assert np.abs(eigen_value - eigen_value_max       ) <= 1E-6
		# Take absolute values element wise of each eigenvector.
		# as they are only unique to a minus sign.
		assert np.linalg.norm(np.abs(snake_case__       ) - np.abs(snake_case__       )       ) <= 1E-6


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							test_power_iteration()

