


"""simple docstring"""
from .constants import (
    MODEL_NAME,
    OPTIMIZER_NAME,
    RNG_STATE_NAME,
    SAFE_WEIGHTS_INDEX_NAME,
    SAFE_WEIGHTS_NAME,
    SCALER_NAME,
    SCHEDULER_NAME,
    TORCH_LAUNCH_PARAMS,
    WEIGHTS_INDEX_NAME,
    WEIGHTS_NAME,
)
from .dataclasses import (
    BnbQuantizationConfig,
    ComputeEnvironment,
    CustomDtype,
    DeepSpeedPlugin,
    DistributedDataParallelKwargs,
    DistributedType,
    DynamoBackend,
    FPaRecipeKwargs,
    FullyShardedDataParallelPlugin,
    GradientAccumulationPlugin,
    GradScalerKwargs,
    InitProcessGroupKwargs,
    KwargsHandler,
    LoggerType,
    MegatronLMPlugin,
    PrecisionType,
    ProjectConfiguration,
    RNGType,
    SageMakerDistributedType,
    TensorInformation,
    TorchDynamoPlugin,
)
from .environment import get_int_from_env, parse_choice_from_env, parse_flag_from_env
from .imports import (
    get_ccl_version,
    is_abit_bnb_available,
    is_abit_bnb_available,
    is_aim_available,
    is_bfaa_available,
    is_bnb_available,
    is_botoa_available,
    is_ccl_available,
    is_comet_ml_available,
    is_datasets_available,
    is_deepspeed_available,
    is_fpa_available,
    is_ipex_available,
    is_megatron_lm_available,
    is_mlflow_available,
    is_mps_available,
    is_npu_available,
    is_rich_available,
    is_safetensors_available,
    is_sagemaker_available,
    is_tensorboard_available,
    is_tpu_available,
    is_transformers_available,
    is_wandb_available,
    is_xpu_available,
)
from .modeling import (
    check_device_map,
    check_tied_parameters_in_config,
    check_tied_parameters_on_same_device,
    compute_module_sizes,
    convert_file_size_to_int,
    dtype_byte_size,
    find_tied_parameters,
    get_balanced_memory,
    get_max_layer_size,
    get_max_memory,
    get_mixed_precision_context_manager,
    id_tensor_storage,
    infer_auto_device_map,
    load_checkpoint_in_model,
    load_offloaded_weights,
    load_state_dict,
    named_module_tensors,
    retie_parameters,
    set_module_tensor_to_device,
    shard_checkpoint,
)
from .offload import (
    OffloadedWeightsLoader,
    PrefixedDataset,
    extract_submodules_state_dict,
    load_offloaded_weight,
    offload_state_dict,
    offload_weight,
    save_offload_index,
)
from .operations import (
    broadcast,
    broadcast_object_list,
    concatenate,
    convert_outputs_to_fpaa,
    convert_to_fpaa,
    find_batch_size,
    find_device,
    gather,
    gather_object,
    get_data_structure,
    honor_type,
    initialize_tensors,
    is_namedtuple,
    is_tensor_information,
    is_torch_tensor,
    listify,
    pad_across_processes,
    recursively_apply,
    reduce,
    send_to_device,
    slice_tensors,
)
from .versions import compare_versions, is_torch_version


if is_deepspeed_available():
			from .deepspeed import (
			    DeepSpeedEngineWrapper,
			    DeepSpeedOptimizerWrapper,
			    DeepSpeedSchedulerWrapper,
			    DummyOptim,
			    DummyScheduler,
			    HfDeepSpeedConfig,
			)

from .bnb import has_abit_bnb_layers, load_and_quantize_model
from .fsdp_utils import load_fsdp_model, load_fsdp_optimizer, save_fsdp_model, save_fsdp_optimizer
from .launch import (
    PrepareForLaunch,
    _filter_args,
    prepare_deepspeed_cmd_env,
    prepare_multi_gpu_env,
    prepare_sagemager_args_inputs,
    prepare_simple_launcher_cmd_env,
    prepare_tpu,
)
from .megatron_lm import (
    AbstractTrainStep,
    BertTrainStep,
    GPTTrainStep,
    MegatronEngine,
    MegatronLMDummyDataLoader,
    MegatronLMDummyScheduler,
    MegatronLMOptimizerWrapper,
    MegatronLMSchedulerWrapper,
    TaTrainStep,
    avg_losses_across_data_parallel_group,
    gather_across_data_parallel_groups,
)
from .megatron_lm import initialize as megatron_lm_initialize
from .megatron_lm import prepare_data_loader as megatron_lm_prepare_data_loader
from .megatron_lm import prepare_model as megatron_lm_prepare_model
from .megatron_lm import prepare_optimizer as megatron_lm_prepare_optimizer
from .megatron_lm import prepare_scheduler as megatron_lm_prepare_scheduler
from .memory import find_executable_batch_size, release_memory
from .other import (
    extract_model_from_parallel,
    get_pretty_name,
    is_port_in_use,
    merge_dicts,
    patch_environment,
    save,
    wait_for_everyone,
    write_basic_config,
)
from .random import set_seed, synchronize_rng_state, synchronize_rng_states
from .torch_xla import install_xla
from .tqdm import tqdm
from .transformer_engine import convert_model, has_transformer_engine_layers









"""simple docstring"""
from __future__ import annotations

from scipy.special import comb  # type: ignore



class 			_UpperCAmelCase :






		'''simple docstring'''

		def __init__(self				,       a_					):





			'''simple docstring'''

			__snake_case	:						List[str]						=				list_of_points
			# Degree determines the flexibility of the curve.
			# Degree = 1 will produce a straight line.
			__snake_case	:						Optional[Any]						=				len(a_					) - 1



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			assert 0 <= t <= 1, "Time t must be between 0 and 1."
			__snake_case	:						list[float]						=				[]
			for i in range(len(self.list_of_points					)					):
				# basis function for each i
				output_values.append(
				    comb(self.degree				,       a_					) * ((1 - t) ** (self.degree - i)) * (t**i)					)
			# the basis must sum up to 1 for it to produce a valid Bezier curve.
			assert round(sum(a_					)				,       5					) == 1
			return output_values



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			assert 0 <= t <= 1, "Time t must be between 0 and 1."

			__snake_case	:						List[str]						=				self.basis_function(a_					)
			__snake_case	:						str						=				0.0
			__snake_case	:						Union[str, Any]						=				0.0
			for i in range(len(self.list_of_points					)					):
				# For all points, sum up the product of i-th basis function and i-th point.
				x += basis_function[i] * self.list_of_points[i][0]
				y += basis_function[i] * self.list_of_points[i][1]
			return (x, y)



		def 				SCREAMING_SNAKE_CASE  (self				,       a_ = 0.01					):





			'''simple docstring'''

			from matplotlib import pyplot as plt  # type: ignore

			__snake_case	:						list[float]						=				[]  # x coordinates of points to plot
			__snake_case	:						list[float]						=				[]  # y coordinates of points to plot

			__snake_case	:						int						=				0.0
			while t <= 1:
				__snake_case	:						Union[str, Any]						=				self.bezier_curve_function(a_					)
				to_plot_x.append(value[0]					)
				to_plot_y.append(value[1]					)
				t += step_size

			__snake_case	:						List[Any]						=				[i[0] for i in self.list_of_points]
			__snake_case	:						Any						=				[i[1] for i in self.list_of_points]

			plt.plot(
			    a_				,       a_				,       color='''blue'''				,       label='''Curve of Degree ''' + str(self.degree					)				,       )
			plt.scatter(a_				,       a_				,       color='''red'''				,       label='''Control Points'''					)
			plt.legend()
			plt.show()


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			BezierCurve([(1, 2), (3, 5)]).plot_curve()  # degree 1
			BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve()  # degree 2
			BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve()  # degree 3





