Use Python and Sprak to find the area above the curve and the X-axis

有n组标本(1, 2, 3, 4), 每组由m个( , , ...)元素( , )组成(m值不定), . 各组样本的分布 曲线如下图所示. 通过程序近似实现各曲线与oc, cd直线围成的⾯积.

train of thought

1. The image can be divided into several trapezoids. The length of the bottom of each trapezoid is (Xn+1 - Xn-1), and the area is half of the rectangle. Its area = (length of the bottom X height)/2, that is, S = (Xn +1 - Xn-1) * (Yn+1 + Yn+2), for the entire figure, the area is the sum of the areas of all trapezoids.
   [picture]
2. Finding the area of ​​the curve and the x-axis below it is essentially a process of integration. All points can be integrated, and np.tapz(x, y) can be called to find

the code

"""Calculate the area between the coordinates and the X-axis
"""

import typing
from pandas import read_parquet

def calc_area(file_name: str) -> typing.Any:
    """⾯积计算.
    Args:
    file_name: parquet⽂件路径, eg: data.parquet
    Returns:
    计算后的结果
    """

    res = []

    # Load data from .parquet
    initial_data = read_parquet(file_name)

    # Get number of groups
    group_numbers = initial_data["gid"].drop_duplicates().unique()

    # Loop through the results for each group
    for i in group_numbers:
        data = initial_data[initial_data["gid"] == i]
        data = data.reset_index(drop=True)

        # Extract the list of x\y
        x_coordinates = data["x"]
        y_coordinates = data["y"]

        # Calculate area between (x[i], y[i]) and (x[i+1], y[i+1])
        rect_areas = [
            (x_coordinates[i + 1] - x_coordinates[i])
            * (y_coordinates[i + 1] + y_coordinates[i])
            / 2
            for i in range(len(x_coordinates) - 1)
        ]

        # Sum the total area
        result = sum(rect_areas)
        res.append(result)

        # Also we can use np for convenience
        # import numpy as np
        # result_np = np.trapz(y_coordinates, x_coordinates)
    return res

calc_area("./data.parquet")

or use pyspark

"""Calculate the area between the coordinates and the X-axis
"""

import typing
from pyspark.sql import Window
from pyspark.sql.functions import lead, lit
from pyspark.sql import SparkSession

def calc_area(file_name: str) -> typing.Any:
    """⾯积计算.
    Args:
    file_name: parquet⽂件路径, eg: data.parquet
    Returns:
    计算后的结果
    """

    res = []

    # Create a session with spark
    spark = SparkSession.builder.appName("Area Calculation").getOrCreate()

    # Load data from .parquet
    initial_data = spark.read.parquet(file_name, header=True)

    # Get number of groups
    df_unique = initial_data.dropDuplicates(subset=["gid"]).select("gid")
    group_numbers = df_unique.collect()

    # Loop through the results for each group
    for row in group_numbers:
        # Select a set of data
        data = initial_data.filter(initial_data["gid"] == row[0])

        # Adds a column of delta_x to the data frame representing difference
        # from the x value of an adjacent data point
        window = Window.orderBy(data["x"])
        data = data.withColumn("delta_x", lead("x").over(window) - data["x"])

        # Calculated trapezoidal area
        data = data.withColumn(
            "trap",
            (
                data["delta_x"]
                * (data["y"] + lit(0.5) * (lead("y").over(window) - data["y"]))
            ),
        )

        result = data.agg({
    
    "trap": "sum"}).collect()[0][0]

        res.append(result)
    return res

calc_area("./data.parquet")

Improve computing efficiency

• More efficient algorithms can be used, such as the adaptive Simpson method or other faster integration methods
• It is possible to perform parallel processing on the data, partition the pd DataFrame\spark DataFrame and use distributed computing
• When using spark, you can specify partitions for window operations to improve performance
• The following are general efficiency-improving methods that are not relevant to this example:

1. Parallel computing: use multi-core CPU or distributed computing system to decompose tasks into multiple subtasks for parallel processing.
2. Data Compression: Compress large data to reduce storage space and bandwidth, and speed up reading and writing.
3. Data chunking: Chunking large data can reduce memory requirements and speed up processing.
4. Cache optimization: optimize the cache strategy, reduce disk access and reading, and improve computing efficiency.
5. Algorithm optimization: Using high-efficiency algorithms, such as tree-based algorithms and matrix algorithms, can improve computational efficiency.