Question

我需要计算拟合高斯曲线下的粒子数。拟合曲线的面积可以通过将函数积分在极限（平均-3 *西格玛）与（平均值+ 3 *西格玛）之间来找到。你能帮我解决一下吗？谢谢你的好意。

import pylab as py
import numpy as np
from scipy import optimize
from scipy.stats import stats
import matplotlib.pyplot as plt
import pandas as pd

BackPFT='T067.csv'
df_180 = pd.read_csv(BackPFT, error_bad_lines=False, header=1)
x_180=df_180.iloc[:,3]
y_180=df_180.iloc[:,4]

#want  to plot the distribution of s calculated by the following equation 
s=np.sqrt((((16*x_180**2*38.22**2)/((4*38.22**2-y_180**2)**2))+1))-1
#Shape of this distribution is Gaussian 
#I need to fit this distribution by following parameter
mean=0.433
sigma=0.014
draw=s
#Definition of bin number
bi=np.linspace(0.01,8, 1000)
data = py.hist(draw.dropna(), bins = bi)
#Definition of Gaussian function 
def f(x, a, b, c):
    return (a * py.exp(-(x - mean)**2.0 / (2 *sigma**2)))
x = [0.5 * (data[1][i] + data[1][i+1]) for i in xrange(len(data[1])-1)]
y = data[0]
#Fitting the peak of the distribution
popt, pcov = optimize.curve_fit(f, x, y)
chi2, p = stats.chisquare(popt)
x_fit = py.linspace(x[0], x[-1], 80000)
y_fit = f(x_fit, *popt)
plot(x_fit, y_fit, lw=3, color="r",ls="--")
plt.xlim(0,2)
plt.tick_params(axis='both', which='major', labelsize=20)
plt.show()

问题是如何整合定义的函数（f）并计算该区域下的数字。在这里，我附上文件T067.csv。提前感谢您的好意。

Answer 1

BackPFT='T061.csv'

df_180 = pd.read_csv(BackPFT, skip_blank_lines=True ,skiprows=1,header=None,skipfooter=None,engine='python')

x_180=df_180.iloc[:,3]
y_180=df_180.iloc[:,4]

b=42.4
E=109.8
LET=24.19
REL=127.32

mean=0.339; m1=0.259
sigma=0.012; s1=0.015

s=np.sqrt((((16*x_180**2*b**2)/((4*b**2-y_180**2)**2))+1))-1
draw=s
bi=np.linspace(0,8, 2000)
binwidth=0.004
#I want to plot the dsitribution of s. This distribution has three gaussian peaks
data = py.hist(draw.dropna(), bins = bi,color='gray',)
#first Gaussian function for the first peak (peaks counted from the right)
def f(x, a, b, c):
    return (a * py.exp(-(x - mean)**2.0 / (2 *sigma**2)))
#  fitting the function (Gaussian)
x = [0.5 * (data[1][i] + data[1][i+1]) for i in xrange(len(data[1])-1)]
y = data[0]
popt, pcov = optimize.curve_fit(f, x, y)
chi, p = stats.chisquare(popt)
x_fit = py.linspace(x[0], x[-1], 80000)
y_fit = f(x_fit, *popt)
plot(x_fit, y_fit, lw=5, color="r",ls="--")

#integration of first function f
gaussF = lambda x, a: f(x, a, sigma, mean)
bins=((6*sigma)/(binwidth))
delta = ((mean+3*sigma) - (mean-3*sigma))/bins 
f1 = lambda x : f(x, popt[0], sigma, mean)
result = quad(f1,mean-3*sigma,mean+3*sigma)
area = result[0] # this give the area after integration of the gaussian
numPar = area / delta # this gives the number of particle under the integrated area
print"\n\tArea under curve = ", area, "\n\tNumber of particel= ", numPar

此处有T061.csv个文件。感谢I Putu Susila博士的合作和兴趣。

集成高斯函数以计算面积下的粒子数

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