Implement Volume Bars Sampling

Implement volume bars sampling, an alternative bar sampling method used in financial machine learning. Unlike traditional time-based bars (e.g., daily or hourly candles), volume bars form a new bar whenever a predefined cumulative volume threshold is reached.

Given an array of trade prices, an array of corresponding trade volumes, and a volume threshold, generate volume bars. Each bar should contain:

• Open: The first price in the bar
• High: The maximum price in the bar
• Low: The minimum price in the bar
• Close: The last price in the bar
• Volume: The total volume accumulated in the bar

When the cumulative volume reaches or exceeds the threshold, close the current bar and start a new one. If there is remaining data that does not reach the threshold, include it as an incomplete bar at the end.

Return a list of bars, where each bar is represented as [open, high, low, close, volume] with values rounded to 4 decimal places.

import numpy as np

def volume_bars_sampling(prices: np.ndarray, volumes: np.ndarray, volume_threshold: float) -> list:
    """
    Generate volume bars from tick/trade data.
    
    Args:
        prices: Array of trade prices for each trade/tick
        volumes: Array of trade volumes corresponding to each price
        volume_threshold: Volume threshold that triggers formation of a new bar
    
    Returns:
        List of bars, where each bar is [open, high, low, close, total_volume]
        All values rounded to 4 decimal places
    """
    pass