Trying to fit some data with to a log curve however my output is not valid and I don't understand what is causing the error. IT's weird cause when omitting the b of the fit it converges and all fields are green.
import matplotlib
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
def logis(x,a,b): #function to fit
return (1+x*np.log(b/x))*a
xlat=np.array([81.96100485, 64.96427609, 38.15520137, 45.75992993,
27.38344029, 23.41742996, 18.73586921, 18.07486749,
9.20589292, 4.83878931, 72.17070899, 71.08083681,
39.57647386, 31.63373626]) #xdata
lo=logis(xlat,92,30) #ydata
p=np.concatenate((np.array([92,30]),xlat,lo),axis=0) #all parameters
def chi(pa): #chisquare
chis=sum((92-pa[0:1])**2)+sum((30-p[1:2])**2)+sum((xlat-pa[2:16])**2)+sum((lo-pa[16:30])**2)
return chis
#minuit part
m = Minuit.from_array_func(chi,p,errordef=1)
fmin,para=m.migrad()
print(m.values)
print(fmin)
xn=[]
xtra=np.sort(xlat)
for i in range(2,16):
xn.append(m.values[i])
xr=np.array(xn)
#plot part
xp=np.linspace(min(xr),max(xr),14)
plt.figure(figsize=(14,8.5))
plt.plot(xp,logis(xp,m.values[0],m.values[1]))
plt.show
Here are some figures:
Nevermind I found the problem, had written sum((30-p[1:2])**2) instead of sum((30-pa[1:2])**2). Thank you for your time!
Related
I'm trying to do a guassian fit for some experimental data but I keep running into error after error. I've followed a few different threads online but either the fit isn't good (it's just a horizontal line) or the code just won't run. I'm following this code from another thread. Below is my code.
I apologize if my code seems a bit messy. There are some bits from other attempts when I tried making it work. Hence the "astropy" import.
import math as m
import matplotlib.pyplot as plt
import numpy as np
from scipy import optimize as opt
import pandas as pd
import statistics as stats
from astropy import modeling
def gaus(x,a,x0,sigma, offset):
return a*m.exp(-(x-x0)**2/(2*sigma**2)) + offset
# Python program to get average of a list
def Average(lst):
return sum(lst) / len(lst)
wavelengths = [391.719, 391.984, 392.248, 392.512, 392.777, 393.041, 393.306, 393.57, 393.835, 394.099, 391.719, 391.455, 391.19, 390.926, 390.661, 390.396]
intensities = [511.85, 1105.85, 1631.85, 1119.85, 213.85, 36.85, 10.85, 6.85, 13.85, 7.85, 511.85, 200.85, 80.85, 53.85, 14.85, 24.85]
n=sum(intensities)
mean = sum(wavelengths*intensities)/n
sigma = m.sqrt(sum(intensities*(wavelengths-mean)**2)/n)
def gaus(x,a,x0,sigma):
return a*m.exp(-(x-x0)**2/(2*sigma**2))
popt,pcov = opt.curve_fit(gaus,wavelengths,intensities,p0=[1,mean,sigma])
print(popt)
plt.scatter(wavelengths, intensities)
plt.title("Helium Spectral Line Peak 1")
plt.xlabel("Wavelength (nm)")
plt.ylabel("Intensity (a.u.)")
plt.show()
Thanks to the kind user, my curve seems to be working more reasonably well. However, one of the points seems to be back connecting to an earlier point? Screenshot below:
There are two problems with your code. The first is that you are performing vector operation on list which gives you the first error in the line mean = sum(wavelengths*intensities)/n. Therefore, you should use np.array instead. The second is that you take math.exp on python list which again throws an error as it takes a real number, so you should use np.exp here instead.
The following code solves your problem:
import matplotlib.pyplot as plt
import numpy as np
from scipy import optimize as opt
wavelengths = [391.719, 391.984, 392.248, 392.512, 392.777, 393.041,
393.306, 393.57, 393.835, 394.099, 391.719, 391.455,
391.19, 390.926, 390.661, 390.396]
intensities = [511.85, 1105.85, 1631.85, 1119.85, 213.85, 36.85, 10.85, 6.85,
13.85, 7.85, 511.85, 200.85, 80.85, 53.85, 14.85, 24.85]
wavelengths_new = np.array(wavelengths)
intensities_new = np.array(intensities)
n=sum(intensities)
mean = sum(wavelengths_new*intensities_new)/n
sigma = np.sqrt(sum(intensities_new*(wavelengths_new-mean)**2)/n)
def gaus(x,a,x0,sigma):
return a*np.exp(-(x-x0)**2/(2*sigma**2))
popt,pcov = opt.curve_fit(gaus,wavelengths_new,intensities_new,p0=[1,mean,sigma])
print(popt)
plt.scatter(wavelengths_new, intensities_new, label="data")
plt.plot(wavelengths_new, gaus(wavelengths_new, *popt), label="fit")
plt.title("Helium Spectral Line Peak 1")
plt.xlabel("Wavelength (nm)")
plt.ylabel("Intensity (a.u.)")
plt.show()
I am trying to fit different data set with different non-linear function that shared some parameters and it look something like this:
import matplotlib
from matplotlib import pyplot as plt
from scipy import optimize
import numpy as np
#some non-linear function
def Sigma1x(x,C11,C111,C1111,C11111):
return C11*x+1/2*C111*pow(x,2)+1/6*C1111*pow(x,3)+1/24*C11111*pow(x,4)
def Sigma2x(x,C12,C112,C1112,C11112):
return C12*x+1/2*C112*pow(x,2)+1/6*C1112*pow(x,3)+1/24*C11112*pow(x,4)
def Sigma1y(y,C12,C111,C222,C112,C1111,C1112,C2222,C12222):
return C12*y+1/2*(C111-C222+C112)*pow(y,2)+1/12*(C111+2*C1112-C2222)*pow(y,3)+1/24*C12222*pow(y,4)
def Sigma2y(y,C11,C222,C222,C2222):
return C11*y+1/2*C222*pow(y,2)+1/6*C2222*pow(y,3)+1/24*C22222*pow(y,4)
def Sigmaz(z,C11,C12,C111,C222,C112,C1111,C1112,C2222,C1122,C11111,C11112,C122222,C11122,C22222):
return (C11+C12)*z+1/2*(2*C111-C222+3*C112)*pow(z,2)+1/6*(3/2*C1111+4*C1112-1/2*C222+3*C1122)*pow(z,3)+\
1/24*(3*C11111+10*C11112-5*C12222+10*C11122-2*C22222)*pow(z,4)
# Experimental datasets
Xdata=np.loadtxt('x-direction.txt') #This contain x axis and two other dataset, should be fitted with Sigma1x and Sigma2x
Ydata=np.loadtxt('y-direction.txt') #his contain yaxis and two other dataset, should be fitted with Sigma1yand Sigma2y
Zdata=nploadtxt('z-direction.txt')#This contain z axis and one dataset fitted with Sigmaz
The question is how to use optimize.leastsq or other packages to fit the data with the appropriate function, knowing that they share multiple paramaters?
I was able to solve ( partially the initial question). I found symfit a very comprehensive and easy to use. So i wrote the following code
import matplotlib.pyplot as plt
from symfit import *
import numpy as np
from symfit.core.minimizers import DifferentialEvolution, BFGS
Y_strain = np.genfromtxt('Y_strain.csv', delimiter=',')
X_strain=np.genfromtxt('X_strain.csv', delimiter=',')
xmax=max(X_strain[:,0])
xmin=min(X_strain[:,0])
xdata = np.linspace(xmin, xmax, 50)
ymax=max(Y_strain[:,0])
ymin=max(Y_strain[:,0])
ydata=np.linspace(ymin, ymax, 50)
x,y,Sigma1x,Sigma2x,Sigma1y,Sigma2y= variables('x,y,Sigma1x,Sigma2x,Sigma1y,Sigma2y')
C11,C111,C1111,C11111,C12,C112,C1112,C11112,C222,C2222,C12222,C22222 = parameters('C11,C111,C1111,C11111,C12,C112,C1112,C11112,C222,C2222,C12222,C22222')
model =Model({
Sigma1x:C11*x+1/2*C111*pow(x,2)+1/6*C1111*pow(x,3)+1/24*C11111*pow(x,4),
Sigma2x:C12*x+1/2*C112*pow(x,2)+1/6*C1112*pow(x,3)+1/24*C11112*pow(x,4),
#Sigma1y:C12*y+1/2*(C111-C222+C112)*pow(y,2)+1/12*(C111+2*C1112-C2222)*pow(y,3)+1/24*C12222*pow(y,4),
#Sigma2y:C11*y+1/2*C222*pow(y,2)+1/6*C2222*pow(y,3)+1/24*C22222*pow(y,4),
})
fit = Fit(model, x=X_strain[:,0], Sigma1x=X_strain[:,1],Sigma2x=X_strain[:,2])
fit_result = fit.execute()
print(fit_result)
plt.scatter(Y_strain[:,0],Y_strain[:,2])
plt.scatter(Y_strain[:,0],Y_strain[:,1])
plt.plot(xdata, model(x=xdata, **fit_result.params).Sigma1x)
plt.plot(xdata, model(x=xdata, **fit_result.params).Sigma2x)
However, The resulting fit is very bad :
Parameter Value Standard Deviation
C11 1.203919e+02 3.988977e+00
C111 -6.541505e+02 5.643111e+01
C1111 1.520749e+03 3.713742e+02
C11111 -7.824107e+02 1.015887e+03
C11112 4.451211e+03 1.015887e+03
C1112 -1.435071e+03 3.713742e+02
C112 9.207923e+01 5.643111e+01
C12 3.272248e+01 3.988977e+00
Status message Desired error not necessarily achieved due to precision loss.
Number of iterations 59
Objective <symfit.core.objectives.LeastSquares object at 0x000001CC00C0A508>
Minimizer <symfit.core.minimizers.BFGS object at 0x000001CC7F84A548>
Goodness of fit qualifiers:
chi_squared 6.230510793023184
objective_value 3.115255396511592
r_squared 0.991979767376565
Any idea's how to improve the fit?
Here is my first steps within the NumPy world.
As a matter of fact the target is plotting below 2-D function as a 3-D mesh:
N = \frac{n}{2\sigma\sqrt{\pi}}\exp^{-\frac{n^{2}x^{2}}{4\sigma^{2}}}
That could been done as a piece a cake in Matlab with below snippet:
[x,n] = meshgrid(0:0.1:20, 1:1:100);
mu = 0;
sigma = sqrt(2)./n;
f = normcdf(x,mu,sigma);
mesh(x,n,f);
But the bloody result is ugly enough to drive me trying Python capabilities to generate scientific plots.
I searched something and found that the primary steps to hit above mark in Pyhton might be acquired by below snippet:
from matplotlib.patches import Polygon
import numpy as np
from scipy.integrate import quad
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
sigma = 1
def integrand(x,n):
return (n/(2*sigma*np.sqrt(np.pi)))*np.exp(-(n**2*x**2)/(4*sigma**2))
t = np.linespace(0, 20, 0.01)
n = np.linespace(1, 100, 1)
lower_bound = -100000000000000000000 #-inf
upper_bound = t
tt, nn = np.meshgrid(t,n)
real_integral = quad(integrand(tt,nn), lower_bound, upper_bound)
Axes3D.plot_trisurf(real_integral, tt,nn)
Edit: With due attention to more investigations on Greg's advices, above code is the most updated snippet.
Here is the generated exception:
RuntimeError: infinity comparisons don't work for you
It is seemingly referring to the quad call...
Would you please helping me to handle this integrating-plotting problem?!...
Best
Just a few hints to get you in the right direction.
numpy.meshgrid can do the same as MatLABs function:
http://docs.scipy.org/doc/numpy/reference/generated/numpy.meshgrid.html
When you have x and n you can do math just like in matlab:
sigma = numpy.sqrt(2)/n
(in python multiplication/division is default index by index - no dot needed)
scipy has a lot more advanced functions, see for example How to calculate cumulative normal distribution in Python for a 1D case.
For plotting you can use matplotlibs pcolormesh:
import matplotlib.pyplot as plt
plt.pcolormesh(x,n,real_integral)
Hope this helps until someone can give you a more detailed answer.
I am new to python and trying to fit data using lmfit. I am following on the lmfit tutorial here:
http://lmfit.github.io/lmfit-py/parameters.html
and this is my code (based on the code explained in the above link):
import numpy as np
import lmfit
import matplotlib.pyplot as plt
from numpy import exp, sqrt, pi
from lmfit import minimize,Parameters,Parameter,report_fit
data=np.genfromtxt('test.txt',delimiter=',')
x=data[:,][:,0]
y=data[:,][:,1]
def fcn2fit(params,x,y):
"""model decaying sine wave, subtract data"""
S1=params['S1'].value
t0=params['t0'].value
T1=params['T1'].value
S2=params['S2'].value
T2=params['T2'].value
model = 1-(1-S1)*exp(-(x-t0)/T1)+S2*(1-exp(-(x-t0)/T2)
return model - y
params = Parameters()
params.add('S1', value=0.85, min=0.8, max=0.9)
params.add('t0', value=0.05, min=0.01, max=0.1)
params.add('T1', value=0.2, min=0.1, max=0.3)
params.add('S2', value=0.03, min=0.01, max=0.05)
params.add('T2', value=0.3, min=0.2, max=0.4)
result = minimize(fcn2fit, params, args=(x,y))
final = y + result.residual
report_fit (params)
try:
import pylab
pylab.plot(x,y, 'k+')
pylab.plot(x,final, 'r')
pylab.show()
except:
pass
Problem:
it return syntax error for line return model-y
I appreciate if you could please let me to right direction.
I think there is a parenthesis problem in the previous line. This causes the return to be included in the formula. I think there's a ) missing at the end.
You have forgotten a right parenthesis ")" in the previous line (result= ...). Opening and closing parentheses are unbalanced causing a syntax error.
I'm trying to plot a simple signal in python, and when i run this it doesn't show any error only 'Restart' and a blank space
from pymatlab import*
import numpy as np
from numpy import sqrt
import matplotlib.pyplot as plt
import scipy as sp
import math
(hashtags) n, coef, freq, phase
def sinyal(N,c,f,p):
y=np.zeros(N)
t=np.linspace(0,2*pi,N)
Nf=len(c)
for i in range(Nf):
y+=c[i]*np.sin(f[i]*t)
return y;
# Signal Generator
c=[2,5,10]
f=[50, 150, 300]
p=[0,0]
N=2000
x=np.linspace(0,2.0*math.pi,N)
y=sinyal(N,c,f,p)
plt.plot(x[:100],y[:100])
plt.show()
The code you posted has a logical indentation error. The call to sinyal is indented one level, placing it inside the definition of sinyal itself. So although sinyal gets defined, it never gets called.
Using 4 spaces for indentation may help you avoid this error in the future.
Your code basically works (apart from some formatting errors and other oddities). I don't have pymatlab but it isn't necessary for this.
import numpy as np
from numpy import sqrt
import matplotlib.pyplot as plt
import scipy as sp
import math
def sinyal(N,c,f,p):
y=np.zeros(N)
t=np.linspace(0,2*np.pi,N)
Nf=len(c)
for i in range(Nf):
y+=c[i]*np.sin(f[i]*t)
return y;
# Signal Generator
c=[2,5,10]
f=[50, 150, 300]
p=[0,0]
N=2000
x=np.linspace(0,2.0*math.pi,N)
y=sinyal(N,c,f,p)
plt.plot(x[:100],y[:100])
plt.show()