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Python結(jié)合Sprak實現(xiàn)計算曲線與X軸上方的面積

更新時間：2023年02月25日 10:22:16 作者：夢實現(xiàn)了嗎

這篇文章主要介紹了Python結(jié)合Sprak實現(xiàn)計算曲線與X軸上方的面積，文中通過示例代碼介紹的非常詳細(xì)，對大家的學(xué)習(xí)或者工作具有一定的參考學(xué)習(xí)價值，需要的朋友們下面隨著小編來一起學(xué)習(xí)吧

思路

可以將圖像分成若干個梯形，每個梯形的底邊長為(Xn+1 - Xn-1)，面積為矩形的一半，其面積 = (底邊長 X 高)/2，即S = (Xn+1 - Xn-1) * （Yn+1 + Yn+2），對于整個圖形，面積為所有梯形面積之和。

[圖片]求曲線與其下方x軸的面積，本質(zhì)上是一個求積分的過程。可以對所有點進(jìn)行積分，可以調(diào)用np.tapz(x, y)來求

代碼

"""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:
    """?積計算.
    Args:
    file_name: parquet?件路徑, eg: data.parquet
    Returns:
    計算后的結(jié)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")

或者使用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:
    """?積計算.
    Args:
    file_name: parquet?件路徑, eg: data.parquet
    Returns:
    計算后的結(jié)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")