'''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       lowerCAmelCase					(		*UpperCamelCase__				:   Optional[Any]       ):


	"""simple docstring"""
	with open(UpperCamelCase__    ,					'''r'''       ) as fh:
		fcntl.flock(UpperCamelCase__    ,					fcntl.LOCK_EX       )
		try:
			print(*UpperCamelCase__       )
		finally:
			fcntl.flock(UpperCamelCase__    ,					fcntl.LOCK_UN       )


__lowerCAmelCase	:       Tuple						       =	int(os.environ["LOCAL_RANK"])
torch.cuda.set_device(local_rank)
__lowerCAmelCase	:       Union[str, Any]						       =	torch.device("cuda", local_rank)
__lowerCAmelCase	:       str						       =	socket.gethostname()

__lowerCAmelCase	:       int						       =	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
					__lowerCAmelCase	:       Union[str, Any]						       =	dist.get_rank()
					__lowerCAmelCase	:       int						       =	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'''


from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
__lowerCAmelCase	:       str						       =	299_792_458

# Symbols
__lowerCAmelCase       ,	__lowerCAmelCase       ,	__lowerCAmelCase       ,	__lowerCAmelCase	:       Any						       =	symbols("ct x y z")





def       lowerCAmelCase					(		UpperCamelCase__				:   float       ):


	"""simple docstring"""
	if velocity > c:
		raise ValueError('''Speed must not exceed light speed 299,792,458 [m/s]!'''       )
	elif velocity < 1:
		# Usually the speed should be much higher than 1 (c order of magnitude)
		raise ValueError('''Speed must be greater than or equal to 1!'''       )

	return velocity / c





def       lowerCAmelCase					(		UpperCamelCase__				:   float       ):


	"""simple docstring"""
	return 1 / sqrt(1 - beta(UpperCamelCase__       ) ** 2       )





def       lowerCAmelCase					(		UpperCamelCase__				:   float       ):


	"""simple docstring"""
	return np.array(
	    [
	        [gamma(UpperCamelCase__       ), -gamma(UpperCamelCase__       ) * beta(UpperCamelCase__       ), 0, 0],
	        [-gamma(UpperCamelCase__       ) * beta(UpperCamelCase__       ), gamma(UpperCamelCase__       ), 0, 0],
	        [0, 0, 1, 0],
	        [0, 0, 0, 1],
	    ]       )





def       lowerCAmelCase					(		UpperCamelCase__				:   float    ,					UpperCamelCase__				:   np.ndarray | None = None       ):


	"""simple docstring"""
	# Ensure event is not empty
	if event is None:
		__UpperCAmelCase							=			np.array([ct, x, y, z]       )  # Symbolic four vector
	else:
		event[0] *= c  # x0 is ct (speed of light * time)

	return transformation_matrix(UpperCamelCase__       ) @ event


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					# Example of symbolic vector:
					__lowerCAmelCase	:       Dict						       =	transform(29_979_245)
					print("Example of four vector: ")
					print(F"""ct' = {four_vector[0]}""")
					print(F"""x' = {four_vector[1]}""")
					print(F"""y' = {four_vector[2]}""")
					print(F"""z' = {four_vector[3]}""")

					# Substitute symbols with numerical values
					__lowerCAmelCase	:       Union[str, Any]						       =	{ct: c, x: 1, y: 1, z: 1}
					__lowerCAmelCase	:       Optional[int]						       =	[four_vector[i].subs(sub_dict) for i in range(4)]

					print(F"""\n{numerical_vector}""")
