




'''simple docstring'''
from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve
def     snake_case_  (       a__		:     np.ndarray   ,a__		:     np.ndarray   ,a__		:     np.ndarray      ):



    """simple docstring"""




    __lowercase          =						np.stack((horizontal_flow, vertical_flow)   ,2      )

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

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

    __lowercase          =						image[grid[:, :, 1], grid[:, :, 0]]

    # Set pixels at invalid locations to 0
    __lowercase          =						0

    return warped
def     snake_case_  (       a__		:     np.ndarray   ,a__		:     np.ndarray   ,a__		:     SupportsIndex   ,a__		:     float | None = None   ,):



    """simple docstring"""




    if alpha is None:
        __lowercase          =						0.1

    # Initialize flow
    __lowercase          =						np.zeros_like(a__      )
    __lowercase          =						np.zeros_like(a__      )

    # Prepare kernels for the calculation of the derivatives and the average velocity
    __lowercase          =						np.array([[-1, 1], [-1, 1]]      ) * 0.2_5
    __lowercase          =						np.array([[-1, -1], [1, 1]]      ) * 0.2_5
    __lowercase          =						np.array([[1, 1], [1, 1]]      ) * 0.2_5
    __lowercase          =						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(a__      ):
        __lowercase          =						warp(a__   ,a__   ,a__      )
        __lowercase          =						convolve(a__   ,a__      ) + convolve(a__   ,a__      )
        __lowercase          =						convolve(a__   ,a__      ) + convolve(a__   ,a__      )
        __lowercase          =						convolve(a__   ,a__      ) + convolve(a__   ,-kernel_t      )

        __lowercase          =						convolve(a__   ,a__      )
        __lowercase          =						convolve(a__   ,a__      )

        # This updates the flow as proposed in the paper (Step 12)
        __lowercase          =						(
            derivative_x * avg_horizontal_velocity
            + derivative_y * avg_vertical_velocity
            + derivative_t
        )
        __lowercase          =						update / (alpha**2 + derivative_x**2 + derivative_y**2)

        __lowercase          =						avg_horizontal_velocity - derivative_x * update
        __lowercase          =						avg_vertical_velocity - derivative_y * update

    return horizontal_flow, vertical_flow


if __name__ == "__main__":
  import doctest

  doctest.testmod()










'''simple docstring'''
import random
from typing import List, Optional, Union

import numpy as np
import torch

from ..state import AcceleratorState
from .constants import CUDA_DISTRIBUTED_TYPES
from .dataclasses import DistributedType, RNGType
from .imports import is_npu_available, is_tpu_available, is_xpu_available


if is_tpu_available(check_device=False):
  import torch_xla.core.xla_model as xm
def     snake_case_  (       a__		:     int   ,a__		:     bool = False      ):



    """simple docstring"""




    if device_specific:
        seed += AcceleratorState().process_index
    random.seed(a__      )
    np.random.seed(a__      )
    torch.manual_seed(a__      )
    if is_xpu_available():
        torch.xpu.manual_seed_all(a__      )
    elif is_npu_available():
        torch.npu.manual_seed_all(a__      )
    else:
        torch.cuda.manual_seed_all(a__      )
    # ^^ safe to call this function even if cuda is not available
    if is_tpu_available():
        xm.set_rng_state(a__      )
def     snake_case_  (       a__		:     Optional[RNGType] = None   ,a__		:     Optional[torch.Generator] = None      ):



    """simple docstring"""




    if rng_type == RNGType.TORCH:
        __lowercase          =						torch.get_rng_state()
    elif rng_type == RNGType.CUDA:
        __lowercase          =						torch.cuda.get_rng_state()
    elif rng_type == RNGType.XLA:
        assert is_tpu_available(), "Can't synchronize XLA seeds on an environment without TPUs."
        __lowercase          =						torch.tensor(xm.get_rng_state()      )
    elif rng_type == RNGType.NPU:
        assert is_npu_available(), "Can't synchronize NPU seeds on an environment without NPUs."
        __lowercase          =						torch.npu.get_rng_state()
    elif rng_type == RNGType.XPU:
        assert is_xpu_available(), "Can't synchronize XPU seeds on an environment without XPUs."
        __lowercase          =						torch.xpu.get_rng_state()
    elif rng_type == RNGType.GENERATOR:
        assert generator is not None, "Need a generator to synchronize its seed."
        __lowercase          =						generator.get_state()

    # Broadcast the rng state from device 0 to other devices
    __lowercase          =						AcceleratorState()
    if state.distributed_type == DistributedType.TPU:
        __lowercase          =						rng_state.to(xm.xla_device()      )
        xm.collective_broadcast([rng_state]      )
        xm.mark_step()
        __lowercase          =						rng_state.cpu()
    elif (
        state.distributed_type in CUDA_DISTRIBUTED_TYPES
        or state.distributed_type == DistributedType.MULTI_NPU
        or state.distributed_type == DistributedType.MULTI_XPU
    ):
        __lowercase          =						rng_state.to(state.device      )
        torch.distributed.broadcast(a__   ,0      )
        __lowercase          =						rng_state.cpu()
    elif state.distributed_type == DistributedType.MULTI_CPU:
        torch.distributed.broadcast(a__   ,0      )

    # Set the broadcast rng state
    if rng_type == RNGType.TORCH:
        torch.set_rng_state(a__      )
    elif rng_type == RNGType.CUDA:
        torch.cuda.set_rng_state(a__      )
    elif rng_type == RNGType.NPU:
        torch.npu.set_rng_state(a__      )
    elif rng_type == RNGType.XPU:
        torch.xpu.set_rng_state(a__      )
    elif rng_type == RNGType.XLA:
        xm.set_rng_state(rng_state.item()      )
    elif rng_type == RNGType.GENERATOR:
        generator.set_state(a__      )



def     snake_case_  (       a__		:     List[Union[str, RNGType]]   ,a__		:     Optional[torch.Generator] = None      ):



    """simple docstring"""




    for rng_type in rng_types:
        synchronize_rng_state(RNGType(a__      )   ,generator=a__      )




