Question

我有以下代码可以为三组不同的时间范围绘制三组数据，即计数率与时间的关系：

#!/usr/bin/env python

from pylab import rc, array, subplot, zeros, savefig, ylim, xlabel, ylabel, errorbar, FormatStrFormatter, gca, axis
from scipy import optimize, stats
import numpy as np
import pyfits, os, re, glob, sys

rc('font',**{'family':'serif','serif':['Helvetica']})
rc('ps',usedistiller='xpdf')
rc('text', usetex=True)
#------------------------------------------------------

tmin=56200
tmax=56249

data=pyfits.open('http://heasarc.gsfc.nasa.gov/docs/swift/results/transients/weak/GX304-1.orbit.lc.fits')

time  = data[1].data.field(0)/86400. + data[1].header['MJDREFF'] + data[1].header['MJDREFI']
rate  = data[1].data.field(1)
error = data[1].data.field(2)
data.close()

cond = ((time > tmin-5) & (time < tmax))
time=time[cond]
rate=rate[cond]
error=error[cond]

errorbar(time, rate, error, fmt='r.', capsize=0)
gca().xaxis.set_major_formatter(FormatStrFormatter('%5.1f'))

axis([tmin-10,tmax,-0.00,0.45])
xlabel('Time, MJD')
savefig("sync.eps",orientation='portrait',papertype='a4',format='eps')

因为这样，情节太混乱，我认为适合曲线。我尝试使用UnivariateSpline，但这完全弄乱了我的数据。有什么建议吗？我应该首先定义一个适合这些数据的函数吗？我也寻找“最小平方”：这是解决这个问题的最佳方法吗？

Answer 1

这就是我解决的问题：

#!/usr/bin/env python

import pyfits, os, re, glob, sys
from scipy.optimize import leastsq
from numpy import *
from pylab import *
from scipy import *
rc('font',**{'family':'serif','serif':['Helvetica']})
rc('ps',usedistiller='xpdf')
rc('text', usetex=True)
#------------------------------------------------------

tmin = 56200
tmax = 56249
pi = 3.14
data=pyfits.open('http://heasarc.gsfc.nasa.gov/docs/swift/results/transients/weak/GX304-1.orbit.lc.fits')

time  = data[1].data.field(0)/86400. + data[1].header['MJDREFF'] + data[1].header['MJDREFI']
rate  = data[1].data.field(1)
error = data[1].data.field(2)
data.close()

cond = ((time > tmin-5) & (time < tmax))
time=time[cond]
rate=rate[cond]
error=error[cond]

gauss_fit = lambda p, x: p[0]*(1/(2*pi*(p[2]**2))**(1/2))*exp(-(x-p[1])**2/(2*p[2]**2))+p[3]*(1/sqrt(2*pi*(p[5]**2)))*exp(-(x-p[4])**2/(2*p[5]**2)) #1d Gaussian func
e_gauss_fit = lambda p, x, y: (gauss_fit(p, x) -y) #1d Gaussian fit
v0= [0.20, 56210.0, 1, 0.40, 56234.0, 1] #inital guesses for Gaussian Fit, just do it around the peaks
out = leastsq(e_gauss_fit, v0[:], args=(time, rate), maxfev=100000, full_output=1) #Gauss Fit
v = out[0] #fit parameters out
xxx = arange(min(time), max(time), time[1] - time[0])
ccc = gauss_fit(v, xxx) # this will only work if the units are pixel and not wavelength
fig = figure(figsize=(9, 9)) #make a plot
ax1 = fig.add_subplot(111)
ax1.plot(time, rate, 'g.') #spectrum
ax1.plot(xxx, ccc, 'b-') #fitted spectrum
savefig("plotfitting.png")

axis([tmin-10,tmax,-0.00,0.45])

来自here。

如果我想在曲线的上升和衰减部分中使用不同的函数呢？

Answer 2

我用它来装配。它改编自互联网上的某个地方，但我忘记了。

from __future__ import print_function
from __future__ import division
from __future__ import absolute_import

import numpy

from scipy.optimize.minpack import leastsq

### functions ###

def eq_cos(A, t):
    """
    4 parameters
    function: A[0] + A[1] * numpy.cos(2 * numpy.pi * A[2] * t + A[3])
    A[0]: offset
    A[1]: amplitude
    A[2]: frequency
    A[3]: phase
    """
    return A[0] + A[1] * numpy.cos(2 * numpy.pi * A[2] * t + numpy.pi*A[3])

def linear(A, t):
    """
    A[0]: y-offset
    A[1]: slope
    """
    return A[0] + A[1] * t  

### fitting routines ###

def minimize(A, t, y0, function):
    """
    Needed for fit
    """
    return y0 - function(A, t)

def fit(x_array, y_array, function, A_start):
    """
    Fit data

    20101209/RB: started
    20130131/RB: added example to doc-string

    INPUT:
    x_array: the array with time or something
    y-array: the array with the values that have to be fitted
    function: one of the functions, in the format as in the file "Equations"
    A_start: a starting point for the fitting

    OUTPUT:
    A_final: the final parameters of the fitting

    EXAMPLE:
    Fit some data to this function above
    def linear(A, t):
        return A[0] + A[1] * t  

    ### 
    x = x-axis
    y = some data
    A = [0,1] # initial guess
    A_final = fit(x, y, linear, A)
    ###

    WARNING:
    Always check the result, it might sometimes be sensitive to a good starting point.

    """
    param = (x_array, y_array, function)

    A_final, cov_x, infodict, mesg, ier = leastsq(minimize, A_start, args=param, full_output = True)

    return A_final



if __name__ == '__main__':

    # data
    x = numpy.arange(10)
    y = x + numpy.random.rand(10) # values between 0 and 1

    # initial guesss
    A = [0,0.5]

    # fit 
    A_final = fit(x, y, linear, A)

    # result is linear with a little offset
    print(A_final)

Python：如何拟合曲线

2 个答案: