CODEWITHSUNDEEP
pythonmatplotlibplotcurve-fittingexponential
Essex
Essex

Reputation: 6118

How to fit data by exponential curve

I get a little problem with my project because I have a set of data, I plot it in order to get 2 curves and I would like to fit this plots by an exponential curve.

I watched this post : fitting exponential decay with no initial guessing. But my example is kind different.

This is what I'm getting with data :

enter image description here

My script is as following :

mask_G = np.bitwise_and( tbdata['G'] < 99.99, tbdata['GERR'] < 0.2)
mask_R = np.bitwise_and( tbdata['R'] < 99.99, tbdata['RERR'] < 0.2)

G_corrected = tbdata[mask_G]
R_corrected = tbdata[mask_R]


fig13 = plt.gcf()
fig13.set_size_inches(16, 9)


fig13, (ax1,ax2) = plt.subplots(1,2)

fig_error_g = ax1.plot(G_corrected['G'], G_corrected['GERR'], '.')
ax1.set_xlabel('G')
ax1.set_ylabel('GERR')
ax1.set_title('Evolution de GERR en fonction de G')

fig_error_r = ax2.plot(R_corrected['R'], R_corrected['RERR'], '.')
ax2.set_xlabel('R')
ax2.set_ylabel('RERR')
ax2.set_title('Evolution de RERR en fonction de R')

fig13.tight_layout() 

plt.savefig('graphique.png')

plt.show()

I tried to write that, which based on scipy doc :

def exponential(x,a,b,c) :
    return a * np.exp(-b * x) + c

xdata = G_corrected['G']
y = G_corrected['GERR']
ydata = y + 0.2 * np.random.normal(size=len(xdata))

popt, pcov = curve_fit(exponential, xdata, ydata)

but I get :

/home/user/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/optimize/minpack.py:601: OptimizeWarning: Covariance of the parameters could not be estimated
category=OptimizeWarning)

Do you have any idea on how I can process ?

Thank you so much ;)

EDIT :

I tried to fit my plot like that :

mask_G = np.bitwise_and( tbdata['G'] < 99.99, tbdata['GERR'] < 0.2)
mask_R = np.bitwise_and( tbdata['R'] < 99.99, tbdata['RERR'] < 0.2)

G_corrected = tbdata[mask_G]
R_corrected = tbdata[mask_R]


params = np.polyfit(G_corrected['G'], np.log(G_corrected['GERR']),1)
a = params[0]
A = np.exp(params[1])


fig13 = plt.gcf()
fig13.set_size_inches(16, 9)


fig13, (ax1,ax2) = plt.subplots(1,2)

fig_error_g = ax1.plot(G_corrected['G'], (G_corrected['GERR']), '.')
fig_error_g = ax1.plot(G_corrected['G'], (A*np.exp(a*G_corrected['G'])),'.')

ax1.set_xlabel('G')
ax1.set_ylabel('GERR')
ax1.set_title('Evolution de GERR en fonction de G')

fig_error_r = ax2.plot(R_corrected['R'], np.log(R_corrected['RERR']), '.')
ax2.set_xlabel('R')
ax2.set_ylabel('RERR')
ax2.set_title('Evolution de RERR en fonction de R')

fig13.tight_layout() 

plt.savefig('graphique.png')

plt.show()

and I get :

enter image description here

What do you think about the result ?

Upvotes: 1

Views: 591

Answers (1)

Frank
Frank

Reputation: 404

easiest way is to apply logarithmic scaling to your plot. As you certainly know log(exp(x)) = x, i.e. if you apply log() to your y-values and plot that you should get a linear plot. Once you have that, you can fit it with your linear toolbox (Gaussian Least Square method). The resulting slope is the prefactor in exp(ax), which you try to obtain.

If you have another dependency on the x-axis, it might be beneficial to make a log-log plot of your data to figure out all dependencies.

Upvotes: 4

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