






import argparse
import inspect
import logging
from typing import Tuple

import numpy as np
import torch

from transformers import (
    AutoTokenizer,
    BloomForCausalLM,
    BloomTokenizerFast,
    CTRLLMHeadModel,
    CTRLTokenizer,
    GenerationMixin,
    GPTaLMHeadModel,
    GPTaTokenizer,
    GPTJForCausalLM,
    LlamaForCausalLM,
    LlamaTokenizer,
    OpenAIGPTLMHeadModel,
    OpenAIGPTTokenizer,
    OPTForCausalLM,
    TransfoXLLMHeadModel,
    TransfoXLTokenizer,
    XLMTokenizer,
    XLMWithLMHeadModel,
    XLNetLMHeadModel,
    XLNetTokenizer,
)
from transformers.modeling_outputs import CausalLMOutputWithPast


logging.basicConfig(
    format='%(asctime)s - %(levelname)s - %(name)s - %(message)s',
    datefmt='%m/%d/%Y %H:%M:%S',
    level=logging.INFO,
)
A										=      logging.getLogger(__name__)

A										=      int(1_0000)  # Hardcoded max length to avoid infinite loop

A										=      {
    'gpt2': (GPTaLMHeadModel, GPTaTokenizer),
    'ctrl': (CTRLLMHeadModel, CTRLTokenizer),
    'openai-gpt': (OpenAIGPTLMHeadModel, OpenAIGPTTokenizer),
    'xlnet': (XLNetLMHeadModel, XLNetTokenizer),
    'transfo-xl': (TransfoXLLMHeadModel, TransfoXLTokenizer),
    'xlm': (XLMWithLMHeadModel, XLMTokenizer),
    'gptj': (GPTJForCausalLM, AutoTokenizer),
    'bloom': (BloomForCausalLM, BloomTokenizerFast),
    'llama': (LlamaForCausalLM, LlamaTokenizer),
    'opt': (OPTForCausalLM, GPTaTokenizer),
}

# Padding text to help Transformer-XL and XLNet with short prompts as proposed by Aman Rusia
# in https://github.com/rusiaaman/XLNet-gen#methodology
# and https://medium.com/@amanrusia/xlnet-speaks-comparison-to-gpt-2-ea1a4e9ba39e
A										=      'In 1991, the remains of Russian Tsar Nicholas II and his family\n(except for Alexei and Maria) are discovered.\nThe voice of Nicholas\'s young son, Tsarevich Alexei Nikolaevich, narrates the\nremainder of the story. 1883 Western Siberia,\na young Grigori Rasputin is asked by his father and a group of men to perform magic.\nRasputin has a vision and denounces one of the men as a horse thief. Although his\nfather initially slaps him for making such an accusation, Rasputin watches as the\nman is chased outside and beaten. Twenty years later, Rasputin sees a vision of\nthe Virgin Mary, prompting him to become a priest. Rasputin quickly becomes famous,\nwith people, even a bishop, begging for his blessing. <eod> </s> <eos>'



def        _lowerCamelCase(      lowerCAmelCase__					:		int   ):





				'''simple docstring'''







				np.random.seed(args.seed   )
				torch.manual_seed(args.seed   )
				if args.n_gpu > 0:
								torch.cuda.manual_seed_all(args.seed   )



def        _lowerCamelCase(      lowerCAmelCase__					:		Any     ,     lowerCAmelCase__					:		Dict     ,     lowerCAmelCase__					:		Optional[Any]     ,     lowerCAmelCase__					:		List[Any]   ):





				'''simple docstring'''







				if args.temperature > 0.7:
								logger.info('CTRL typically works better with lower temperatures (and lower top_k).'   )

				SCREAMING_SNAKE_CASE_ :						List[Any]    				= tokenizer.encode(lowerCAmelCase__     ,     add_special_tokens=lowerCAmelCase__   )
				if not any(encoded_prompt[0] == x for x in tokenizer.control_codes.values()   ):
								logger.info('WARNING! You are not starting your generation from a control code so you won\'t get good results'   )
				return prompt_text



def        _lowerCamelCase(      lowerCAmelCase__					:		int     ,     lowerCAmelCase__					:		Union[str, Any]     ,     lowerCAmelCase__					:		List[str]     ,     lowerCAmelCase__					:		Any   ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_ :						int    				= hasattr(model.config     ,     'use_lang_emb'   ) and model.config.use_lang_emb
				if hasattr(model.config     ,     'lang2id'   ) and use_lang_emb:
								SCREAMING_SNAKE_CASE_ :						Union[str, Any]    				= model.config.langaid.keys()
								if args.xlm_language in available_languages:
												SCREAMING_SNAKE_CASE_ :						Union[str, Any]    				= args.xlm_language
								else:
												SCREAMING_SNAKE_CASE_ :						Optional[int]    				= None
												while language not in available_languages:
																SCREAMING_SNAKE_CASE_ :						Tuple    				= input('Using XLM. Select language in ' + str(list(lowerCAmelCase__   )   ) + ' >>> '   )

								SCREAMING_SNAKE_CASE_ :						Tuple    				= model.config.langaid[language]
								# kwargs["language"] = tokenizer.lang2id[language]

				# TODO fix mask_token_id setup when configurations will be synchronized between models and tokenizers
				# XLM masked-language modeling (MLM) models need masked token
				# is_xlm_mlm = "mlm" in args.model_name_or_path
				# if is_xlm_mlm:
				#     kwargs["mask_token_id"] = tokenizer.mask_token_id

				return prompt_text



def        _lowerCamelCase(      lowerCAmelCase__					:		Dict     ,     lowerCAmelCase__					:		Optional[int]     ,     lowerCAmelCase__					:		List[str]     ,     lowerCAmelCase__					:		Tuple   ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_ :						Union[str, Any]    				= args.prefix if args.prefix else args.padding_text if args.padding_text else PREFIX
				SCREAMING_SNAKE_CASE_ :						Optional[int]    				= prefix + prompt_text
				return prompt_text



def        _lowerCamelCase(      lowerCAmelCase__					:		List[str]     ,     lowerCAmelCase__					:		Union[str, Any]     ,     lowerCAmelCase__					:		List[Any]     ,     lowerCAmelCase__					:		Optional[int]   ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_ :						List[Any]    				= args.prefix if args.prefix else args.padding_text if args.padding_text else PREFIX
				SCREAMING_SNAKE_CASE_ :						List[str]    				= prefix + prompt_text
				return prompt_text


A										=      {
    'ctrl': prepare_ctrl_input,
    'xlm': prepare_xlm_input,
    'xlnet': prepare_xlnet_input,
    'transfo-xl': prepare_transfoxl_input,
}



def        _lowerCamelCase(      lowerCAmelCase__					:		Any     ,     lowerCAmelCase__					:		Union[str, Any]   ):





				'''simple docstring'''







				if length < 0 and max_sequence_length > 0:
								SCREAMING_SNAKE_CASE_ :						Dict    				= max_sequence_length
				elif 0 < max_sequence_length < length:
								SCREAMING_SNAKE_CASE_ :						str    				= max_sequence_length  # No generation bigger than model size
				elif length < 0:
								SCREAMING_SNAKE_CASE_ :						Dict    				= MAX_LENGTH  # avoid infinite loop
				return length



def        _lowerCamelCase(      lowerCAmelCase__					:		Dict   ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_ :						Optional[int]    				= None
				if hasattr(lowerCAmelCase__     ,     'hidden_size'   ):
								SCREAMING_SNAKE_CASE_ :						str    				= model_config.hidden_size
				elif hasattr(lowerCAmelCase__     ,     'n_embed'   ):
								SCREAMING_SNAKE_CASE_ :						int    				= model_config.n_embed
				elif hasattr(lowerCAmelCase__     ,     'n_embd'   ):
								SCREAMING_SNAKE_CASE_ :						Union[str, Any]    				= model_config.n_embd

				SCREAMING_SNAKE_CASE_ :						List[Any]    				= None
				if hasattr(lowerCAmelCase__     ,     'num_attention_heads'   ):
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= model_config.num_attention_heads
				elif hasattr(lowerCAmelCase__     ,     'n_head'   ):
								SCREAMING_SNAKE_CASE_ :						List[str]    				= model_config.n_head

				if embedding_size is None or num_head is None or num_head == 0:
								raise ValueError('Check the model config'   )

				SCREAMING_SNAKE_CASE_ :						Tuple    				= int(embedding_size / num_head   )
				if hasattr(lowerCAmelCase__     ,     'n_layer'   ):
								SCREAMING_SNAKE_CASE_ :						int    				= model_config.n_layer
				elif hasattr(lowerCAmelCase__     ,     'num_hidden_layers'   ):
								SCREAMING_SNAKE_CASE_ :						Optional[Any]    				= model_config.num_hidden_layers
				else:
								raise ValueError('Number of hidden layers couldn\'t be determined from the model config'   )

				return num_layer, num_head, num_embedding_size_per_head



def        _lowerCamelCase(      lowerCAmelCase__					:		Tuple     ,     lowerCAmelCase__					:		str     ,     lowerCAmelCase__					:		str   ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_ :						Any    				= sparse_model_config(model.config   )
				if model.config.model_type == "bloom":
								SCREAMING_SNAKE_CASE_ :						int    				= tuple(
								    (
								        torch.empty(int(num_attention_heads * batch_size   )     ,     lowerCAmelCase__     ,     lowerCAmelCase__   )
								        .to(model.dtype   )
								        .to(model.device   ),
								        torch.empty(int(num_attention_heads * batch_size   )     ,     lowerCAmelCase__     ,     lowerCAmelCase__   )
								        .to(model.dtype   )
								        .to(model.device   ),
								    )
								    for _ in range(lowerCAmelCase__   )   )
				else:
								SCREAMING_SNAKE_CASE_ :						Optional[Any]    				= tuple(
								    (
								        torch.empty(lowerCAmelCase__     ,     lowerCAmelCase__     ,     lowerCAmelCase__     ,     lowerCAmelCase__   )
								        .to(model.dtype   )
								        .to(model.device   ),
								        torch.empty(lowerCAmelCase__     ,     lowerCAmelCase__     ,     lowerCAmelCase__     ,     lowerCAmelCase__   )
								        .to(model.dtype   )
								        .to(model.device   ),
								    )
								    for _ in range(lowerCAmelCase__   )   )
				return past_key_values



def        _lowerCamelCase(      lowerCAmelCase__					:		List[str]     ,     lowerCAmelCase__					:		str     ,     lowerCAmelCase__					:		Any   ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_ :						int    				= len(lowerCAmelCase__   )
				SCREAMING_SNAKE_CASE_ :						str    				= tokenizer.batch_encode_plus(lowerCAmelCase__     ,     return_tensors='pt'   )
				SCREAMING_SNAKE_CASE_ :						Any    				= dummy_input.to(model.device   )
				if model.config.use_cache:
								SCREAMING_SNAKE_CASE_ :						Optional[Any]    				= generate_past_key_values(lowerCAmelCase__     ,     lowerCAmelCase__     ,     1   )
				SCREAMING_SNAKE_CASE_ :						Dict    				= torch.cat(
				    [
				        torch.zeros(dummy_input['attention_mask'].shape[0]     ,     1   )
				        .to(dummy_input['attention_mask'].dtype   )
				        .to(model.device   ),
				        dummy_input['attention_mask'],
				    ]     ,     -1     ,     )
				return dummy_input


class 				__a				(	__A    ):





		'''simple docstring'''



		UpperCAmelCase__   :					Any					     =    ("""_optimized""", """_default""")


		def __init__(    self			,     UpperCamelCase__			,     UpperCamelCase__							):
						SCREAMING_SNAKE_CASE_ :						str    				= optimized
						SCREAMING_SNAKE_CASE_ :						Union[str, Any]    				= default


		def __call__(    self			,     *UpperCamelCase__			,     **UpperCamelCase__							):
						if kwargs["past_key_values"] is None and self._default.config.use_cache:
										SCREAMING_SNAKE_CASE_ :						List[Any]    				= generate_past_key_values(self._default			,     kwargs['input_ids'].shape[0]			,     0							)
						kwargs.pop('position_ids'			,     UpperCamelCase__							)
						for k in list(kwargs.keys()							):
										if kwargs[k] is None or isinstance(kwargs[k]			,     UpperCamelCase__							):
														kwargs.pop(UpperCamelCase__							)
						SCREAMING_SNAKE_CASE_ :						Union[str, Any]    				= self._optimized(**UpperCamelCase__							)
						SCREAMING_SNAKE_CASE_ :						int    				= outputs[0]
						SCREAMING_SNAKE_CASE_ :						str    				= outputs[1]
						SCREAMING_SNAKE_CASE_ :						str    				= CausalLMOutputWithPast(
						    loss=UpperCamelCase__			,     logits=UpperCamelCase__			,     past_key_values=UpperCamelCase__			,     hidden_states=UpperCamelCase__			,     attentions=UpperCamelCase__			,     )
						return fixed_output


		def __getattr__(    self			,     UpperCamelCase__							):
						return getattr(self._default			,     UpperCamelCase__							)


		def 	__snake_case      (    self			,     UpperCamelCase__			,     UpperCamelCase__=None			,     UpperCamelCase__=None			,     UpperCamelCase__=None			,     **UpperCamelCase__							):
						return self._default.prepare_inputs_for_generation(
						    UpperCamelCase__			,     past_key_values=UpperCamelCase__			,     inputs_embeds=UpperCamelCase__			,     use_cache=UpperCamelCase__			,     **UpperCamelCase__							)






		def 	__snake_case      (    self			,     UpperCamelCase__			,     UpperCamelCase__							):
						return self._default._reorder_cache(UpperCamelCase__			,     UpperCamelCase__							)






def        _lowerCamelCase(      ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_ :						Union[str, Any]    				= argparse.ArgumentParser()
				parser.add_argument(
				    '--model_type'     ,     default=lowerCAmelCase__     ,     type=lowerCAmelCase__     ,     required=lowerCAmelCase__     ,     help='Model type selected in the list: ' + ', '.join(MODEL_CLASSES.keys()   )     ,     )
				parser.add_argument(
				    '--model_name_or_path'     ,     default=lowerCAmelCase__     ,     type=lowerCAmelCase__     ,     required=lowerCAmelCase__     ,     help='Path to pre-trained model or shortcut name selected in the list: ' + ', '.join(MODEL_CLASSES.keys()   )     ,     )

				parser.add_argument('--prompt'     ,     type=lowerCAmelCase__     ,     default=''   )
				parser.add_argument('--length'     ,     type=lowerCAmelCase__     ,     default=20   )
				parser.add_argument('--stop_token'     ,     type=lowerCAmelCase__     ,     default=lowerCAmelCase__     ,     help='Token at which text generation is stopped'   )

				parser.add_argument(
				    '--temperature'     ,     type=lowerCAmelCase__     ,     default=1.0     ,     help='temperature of 1.0 has no effect, lower tend toward greedy sampling'     ,     )
				parser.add_argument(
				    '--repetition_penalty'     ,     type=lowerCAmelCase__     ,     default=1.0     ,     help='primarily useful for CTRL model; in that case, use 1.2'   )
				parser.add_argument('--k'     ,     type=lowerCAmelCase__     ,     default=0   )
				parser.add_argument('--p'     ,     type=lowerCAmelCase__     ,     default=0.9   )

				parser.add_argument('--prefix'     ,     type=lowerCAmelCase__     ,     default=''     ,     help='Text added prior to input.'   )
				parser.add_argument('--padding_text'     ,     type=lowerCAmelCase__     ,     default=''     ,     help='Deprecated, the use of `--prefix` is preferred.'   )
				parser.add_argument('--xlm_language'     ,     type=lowerCAmelCase__     ,     default=''     ,     help='Optional language when used with the XLM model.'   )

				parser.add_argument('--seed'     ,     type=lowerCAmelCase__     ,     default=42     ,     help='random seed for initialization'   )
				parser.add_argument('--no_cuda'     ,     action='store_true'     ,     help='Avoid using CUDA when available'   )
				parser.add_argument('--num_return_sequences'     ,     type=lowerCAmelCase__     ,     default=1     ,     help='The number of samples to generate.'   )
				parser.add_argument(
				    '--fp16'     ,     action='store_true'     ,     help='Whether to use 16-bit (mixed) precision (through NVIDIA apex) instead of 32-bit'     ,     )
				parser.add_argument('--jit'     ,     action='store_true'     ,     help='Whether or not to use jit trace to accelerate inference'   )
				SCREAMING_SNAKE_CASE_ :						Dict    				= parser.parse_args()

				SCREAMING_SNAKE_CASE_ :						Any    				= torch.device('cuda' if torch.cuda.is_available() and not args.no_cuda else 'cpu'   )
				SCREAMING_SNAKE_CASE_ :						Tuple    				= 0 if args.no_cuda else torch.cuda.device_count()

				logger.warning(F'''device: {args.device}, n_gpu: {args.n_gpu}, 16-bits training: {args.fpaa}'''   )

				set_seed(lowerCAmelCase__   )

				# Initialize the model and tokenizer
				try:
								SCREAMING_SNAKE_CASE_ :						int    				= args.model_type.lower()
								SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_ :						str    				= MODEL_CLASSES[args.model_type]
				except KeyError:
								raise KeyError('the model {} you specified is not supported. You are welcome to add it and open a PR :)'   )

				SCREAMING_SNAKE_CASE_ :						Optional[int]    				= tokenizer_class.from_pretrained(args.model_name_or_path   )
				if tokenizer.pad_token is None:
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= tokenizer.eos_token
				SCREAMING_SNAKE_CASE_ :						List[Any]    				= model_class.from_pretrained(args.model_name_or_path   )
				model.to(args.device   )

				if args.fpaa:
								model.half()
				SCREAMING_SNAKE_CASE_ :						Dict    				= getattr(model.config     ,     'max_position_embeddings'     ,     0   )
				SCREAMING_SNAKE_CASE_ :						Any    				= adjust_length_to_model(args.length     ,     max_sequence_length=lowerCAmelCase__   )
				logger.info(lowerCAmelCase__   )

				SCREAMING_SNAKE_CASE_ :						str    				= args.prompt if args.prompt else input('Model prompt >>> '   )

				# Different models need different input formatting and/or extra arguments
				SCREAMING_SNAKE_CASE_ :						int    				= args.model_type in PREPROCESSING_FUNCTIONS.keys()
				if requires_preprocessing:
								SCREAMING_SNAKE_CASE_ :						Dict    				= PREPROCESSING_FUNCTIONS.get(args.model_type   )
								SCREAMING_SNAKE_CASE_ :						Any    				= prepare_input(lowerCAmelCase__     ,     lowerCAmelCase__     ,     lowerCAmelCase__     ,     lowerCAmelCase__   )

								if model.__class__.__name__ in ["TransfoXLLMHeadModel"]:
												SCREAMING_SNAKE_CASE_ :						List[Any]    				= {'add_space_before_punct_symbol': True}
								else:
												SCREAMING_SNAKE_CASE_ :						Any    				= {}

								SCREAMING_SNAKE_CASE_ :						Dict    				= tokenizer.encode(
								    lowerCAmelCase__     ,     add_special_tokens=lowerCAmelCase__     ,     return_tensors='pt'     ,     **lowerCAmelCase__   )
				else:
								SCREAMING_SNAKE_CASE_ :						List[str]    				= args.prefix if args.prefix else args.padding_text
								SCREAMING_SNAKE_CASE_ :						str    				= tokenizer.encode(prefix + prompt_text     ,     add_special_tokens=lowerCAmelCase__     ,     return_tensors='pt'   )
				SCREAMING_SNAKE_CASE_ :						Optional[int]    				= encoded_prompt.to(args.device   )

				if encoded_prompt.size()[-1] == 0:
								SCREAMING_SNAKE_CASE_ :						Tuple    				= None
				else:
								SCREAMING_SNAKE_CASE_ :						List[Any]    				= encoded_prompt

				if args.jit:
								SCREAMING_SNAKE_CASE_ :						int    				= ['enable jit']
								SCREAMING_SNAKE_CASE_ :						List[str]    				= prepare_jit_inputs(lowerCAmelCase__     ,     lowerCAmelCase__     ,     lowerCAmelCase__   )
								torch._C._jit_set_texpr_fuser_enabled(lowerCAmelCase__   )
								SCREAMING_SNAKE_CASE_ :						Union[str, Any]    				= False
								if hasattr(lowerCAmelCase__     ,     'forward'   ):
												SCREAMING_SNAKE_CASE_ :						Tuple    				= inspect.signature(model.forward   )
								else:
												SCREAMING_SNAKE_CASE_ :						Optional[Any]    				= inspect.signature(model.__call__   )
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= tuple(jit_inputs[key] for key in sig.parameters if jit_inputs.get(lowerCAmelCase__     ,     lowerCAmelCase__   ) is not None   )
								SCREAMING_SNAKE_CASE_ :						Dict    				= torch.jit.trace(lowerCAmelCase__     ,     lowerCAmelCase__     ,     strict=lowerCAmelCase__   )
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= torch.jit.freeze(traced_model.eval()   )
								traced_model(*lowerCAmelCase__   )
								traced_model(*lowerCAmelCase__   )

								SCREAMING_SNAKE_CASE_ :						Dict    				= _ModelFallbackWrapper(lowerCAmelCase__     ,     lowerCAmelCase__   )

				SCREAMING_SNAKE_CASE_ :						Dict    				= model.generate(
				    input_ids=lowerCAmelCase__     ,     max_length=args.length + len(encoded_prompt[0]   )     ,     temperature=args.temperature     ,     top_k=args.k     ,     top_p=args.p     ,     repetition_penalty=args.repetition_penalty     ,     do_sample=lowerCAmelCase__     ,     num_return_sequences=args.num_return_sequences     ,     )

				# Remove the batch dimension when returning multiple sequences
				if len(output_sequences.shape   ) > 2:
								output_sequences.squeeze_()

				SCREAMING_SNAKE_CASE_ :						List[str]    				= []

				for generated_sequence_idx, generated_sequence in enumerate(lowerCAmelCase__   ):
								print(F'''=== GENERATED SEQUENCE {generated_sequence_idx + 1} ==='''   )
								SCREAMING_SNAKE_CASE_ :						List[Any]    				= generated_sequence.tolist()

								# Decode text
								SCREAMING_SNAKE_CASE_ :						Optional[Any]    				= tokenizer.decode(lowerCAmelCase__     ,     clean_up_tokenization_spaces=lowerCAmelCase__   )

								# Remove all text after the stop token
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= text[: text.find(args.stop_token   ) if args.stop_token else None]

								# Add the prompt at the beginning of the sequence. Remove the excess text that was used for pre-processing
								SCREAMING_SNAKE_CASE_ :						List[str]    				= (
								    prompt_text + text[len(tokenizer.decode(encoded_prompt[0]     ,     clean_up_tokenization_spaces=lowerCAmelCase__   )   ) :]
								)

								generated_sequences.append(lowerCAmelCase__   )
								print(lowerCAmelCase__   )

				return generated_sequences


if __name__ == "__main__":
				main()







from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve



def        _lowerCamelCase(      lowerCAmelCase__					:		np.ndarray     ,     lowerCAmelCase__					:		np.ndarray     ,     lowerCAmelCase__					:		np.ndarray   ):





				'''simple docstring'''







				SCREAMING_SNAKE_CASE_ :						List[Any]    				= np.stack((horizontal_flow, vertical_flow)     ,     2   )

				# Create a grid of all pixel coordinates and subtract the flow to get the
				# target pixels coordinates
				SCREAMING_SNAKE_CASE_ :						List[Any]    				= np.stack(
				    np.meshgrid(np.arange(0     ,     image.shape[1]   )     ,     np.arange(0     ,     image.shape[0]   )   )     ,     2   )
				SCREAMING_SNAKE_CASE_ :						List[str]    				= np.round(grid - flow   ).astype(np.intaa   )

				# Find the locations outside of the original image
				SCREAMING_SNAKE_CASE_ :						str    				= (grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]]   ))
				SCREAMING_SNAKE_CASE_ :						Dict    				= 0

				SCREAMING_SNAKE_CASE_ :						Optional[Any]    				= image[grid[:, :, 1], grid[:, :, 0]]

				# Set pixels at invalid locations to 0
				SCREAMING_SNAKE_CASE_ :						Optional[int]    				= 0

				return warped



def        _lowerCamelCase(      lowerCAmelCase__					:		np.ndarray     ,     lowerCAmelCase__					:		np.ndarray     ,     lowerCAmelCase__					:		SupportsIndex     ,     lowerCAmelCase__					:		float | None = None     ,     ):





				'''simple docstring'''







				if alpha is None:
								SCREAMING_SNAKE_CASE_ :						Any    				= 0.1

				# Initialize flow
				SCREAMING_SNAKE_CASE_ :						List[Any]    				= np.zeros_like(lowerCAmelCase__   )
				SCREAMING_SNAKE_CASE_ :						Any    				= np.zeros_like(lowerCAmelCase__   )

				# Prepare kernels for the calculation of the derivatives and the average velocity
				SCREAMING_SNAKE_CASE_ :						Optional[int]    				= np.array([[-1, 1], [-1, 1]]   ) * 0.25
				SCREAMING_SNAKE_CASE_ :						Tuple    				= np.array([[-1, -1], [1, 1]]   ) * 0.25
				SCREAMING_SNAKE_CASE_ :						Optional[int]    				= np.array([[1, 1], [1, 1]]   ) * 0.25
				SCREAMING_SNAKE_CASE_ :						Tuple    				= np.array(
				    [[1 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]]   )

				# Iteratively refine the flow
				for _ in range(lowerCAmelCase__   ):
								SCREAMING_SNAKE_CASE_ :						Union[str, Any]    				= warp(lowerCAmelCase__     ,     lowerCAmelCase__     ,     lowerCAmelCase__   )
								SCREAMING_SNAKE_CASE_ :						Any    				= convolve(lowerCAmelCase__     ,     lowerCAmelCase__   ) + convolve(lowerCAmelCase__     ,     lowerCAmelCase__   )
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= convolve(lowerCAmelCase__     ,     lowerCAmelCase__   ) + convolve(lowerCAmelCase__     ,     lowerCAmelCase__   )
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= convolve(lowerCAmelCase__     ,     lowerCAmelCase__   ) + convolve(lowerCAmelCase__     ,     -kernel_t   )

								SCREAMING_SNAKE_CASE_ :						List[str]    				= convolve(lowerCAmelCase__     ,     lowerCAmelCase__   )
								SCREAMING_SNAKE_CASE_ :						Optional[Any]    				= convolve(lowerCAmelCase__     ,     lowerCAmelCase__   )

								# This updates the flow as proposed in the paper (Step 12)
								SCREAMING_SNAKE_CASE_ :						Tuple    				= (
								    derivative_x * avg_horizontal_velocity
								    + derivative_y * avg_vertical_velocity
								    + derivative_t
								)
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= update / (alpha**2 + derivative_x**2 + derivative_y**2)

								SCREAMING_SNAKE_CASE_ :						List[str]    				= avg_horizontal_velocity - derivative_x * update
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= avg_vertical_velocity - derivative_y * update

				return horizontal_flow, vertical_flow


if __name__ == "__main__":
				import doctest

				doctest.testmod()