Python 为什么在计算两条曲线之间的面积时，在下面的数值积分中不进行累积和？

说明：

在下面的python代码中，我将生成一个高斯PDF，即p（y）。我试图通过矩形求和的方法，找到[min_p，max_p]范围内曲线和任何水平线之间的区域。我的主要问题在于函数的实现，该函数应该为p数组中的任何特定元素（如代码中定义的）迭代计算该区域，并将其绘制为上述范围内给定值的函数

问题:

代码运行良好，但不会生成所需的单调递增/递减函数

import matplotlib
from scipy.stats import norm
from scipy import integrate
import matplotlib.pyplot as pyplot
import numpy as np


N  = 10                                         # Number of sigmas away from central value
M, K = 2**10, 2**10                             # Number of grid points along y and p(y)

mean, sigma = 10.0, 1.0                         #Mean value and standard deviation of a Gaussian probability distribuiton (PDF)
ymin, ymax = -N*sigma+mean, N*sigma+mean        #Minimum and maximum and spacing between grid points along y-axis
ylims = [ymin, ymax]

y = np.linspace(ylims[0],ylims[1],M)            #The values of y-axis on grid points
pdf = norm.pdf(y,loc=mean,scale=sigma)          # Definiton of the normalized probability distribuiton function (PDF)
min_p , max_p = min(pdf), max(pdf)              #The maximum, minimum value of p(y) 

p = np.linspace(min_p, max_p, K)                #The values of p(y)-axis on grid points                                                                                               


def Area(p):                                    #Calculating the area under the PDF for which probability is more than pj-value for a particular jth index in pj_array above
    Areas = []                                
    for yi in y.flat:
        for p_j in p.flat:
            Area = 0.0
            delta_y = (ymax - ymin) / (M-1)    #The spacing beteen grid points along y-axis
            if (pdf[yi] > p_j): Area += (delta_y * pdf.sum())
            else: Area += 0.0
        Areas.append(Area)
    return Areas

pyplot.plot(p, Area(p), '-')
pyplot.axis([min_p, max_p, 0, 1])
pyplot.show()

---

在做了很多更改之后，我认为您正在尝试生成以下代码：

from scipy.stats import norm
import numpy as np
import pylab as p 
%matplotlib inline


N  = 10                                         # Number of sigmas away from central value
M, K = 2**10, 2**10                             # Number of grid points along x and y

mean, sigma = 10.0, 1.0                         #Mean value and standard deviation of a Gaussian probability distribuiton (PDF)
xmin, xmax = -N*sigma+mean, N*sigma+mean        #Minimum and maximum and spacing between grid points along y-axis

xx = np.linspace(xmin,xmax,M)                    #The values of x-axis on grid points
pdf = norm.pdf(xx,loc=mean,scale=sigma )          # Definiton of the normalized probability distribuiton function (PDF)


min_p , max_p = min(pdf), max(pdf)  
pp = np.linspace(min_p,max_p, K)                        #The values of y-axis on grid points                                                                                               


delta_x = xx[1]-xx[0]    # spacing beteen grid points along x-axis
delta_p = pp[1]-pp[0]    # spacing between grid points on y-axis


def Area(p):                                    #Calculating the area under the PDF for which probability is more than pj-value for a particular jth index in pj_array above
    areas = []                                
    area=0
    for i in range(nx):

        for pi  in pp :
            if (pi< pdf[i]): 
                area +=  delta_x * delta_p 
        areas.append(area)
    return areas

p.subplot(121)
p.plot(xx,pdf)
p.subplot(122)
p.plot(xx, Area(p), '-')

---

要在任何给定的p=const行上进行积分，您只需从

pdf[i]

中减去该固定值，并可能根据您在特定上下文中对积分的含义添加一个条件（减去负数或忽略负数）

打印

区域（p）

，您将看到它不是您声称的1D数组是。我只是注意到了。我想知道为什么它没有更新p的任何元素。你会建议我编辑这个问题吗？你的问题现在很难读。你的回溯是混乱的，你有一个巨大的段落在顶部感谢roadrunner的澄清。现在，至少我知道代码出了什么问题。但是，我仍然没有得到这个函数。对于p_j，假设它是一个单调递减函数，其最大值为1，最小值在[0,1]范围内为0。所以，这就是为什么我编辑了这个问题，使它比以前更好地描述了这个问题。再次感谢，

from scipy.stats import norm
import numpy as np
import pylab as p 
%matplotlib inline


N  = 10                                         # Number of sigmas away from central value
M, K = 2**10, 2**10                             # Number of grid points along x and y

mean, sigma = 10.0, 1.0                         #Mean value and standard deviation of a Gaussian probability distribuiton (PDF)
xmin, xmax = -N*sigma+mean, N*sigma+mean        #Minimum and maximum and spacing between grid points along y-axis

xx = np.linspace(xmin,xmax,M)                    #The values of x-axis on grid points
pdf = norm.pdf(xx,loc=mean,scale=sigma )          # Definiton of the normalized probability distribuiton function (PDF)

delta_x = xx[1]-xx[0]    # spacing between grid points along x-axis

def Area(p):                                    #Calculating the area under the PDF for which probability is more than pj-value for a particular jth index in pj_array above
    areas = []                                
    area=0
    for i in range(nx):
        area +=  delta_x * pdf[i] 
        areas.append(area)
    return areas

p.subplot(121)
p.plot(xx,pdf)
p.subplot(122)
p.plot(xx, Area(p), '-')