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I'm trying to fit a set of data with a function (see the example below) using scipy.optimize.curvefit, but when I use bounds (documentation) the fit fails and I simply get the initial guess parameters as output. As soon as I substitute -np.inf ad np.inf as bounds for the second parameter (dt in the function), the fit works. What am I doing wrong?

import numpy as np import matplotlib.pyplot as plt import scipy.optimize as opt #Generate data crc=np.array([-1.4e-14, 7.3e-14, 1.9e-13, 3.9e-13, 6.e-13, 8.0e-13, 9.2e-13, 9.9e-13, 1.e-12, 1.e-12, 1.e-12, 1.0e-12, 1.1e-12, 1.1e-12, 1.1e-12, 1.0e-12, 1.1e-12]) time=np.array([0., 368., 648., 960., 1520.,1864., 2248., 2655., 3031., 3384., 3688., 4048., 4680., 5343., 6055., 6928., 8120.]) #Define the function for the fit def testcurve(x, Dp, dt): k = -Dp*(x+dt)*2e11 curve = 1e-12 * (1+2*(-np.exp(k) + np.exp(4*k) - np.exp(9*k) + np.exp(16*k))) curve[0]= 0 return curve #Set fit bounds dtmax=time[2] param_bounds = ((-np.inf, -dtmax),(np.inf, dtmax)) #Perform fit (par, par_cov) = opt.curve_fit(testcurve, time, crc, p0 = (5e-15, 0), bounds = param_bounds) #Print and plot output print(par) plt.plot(time, crc, 'o') plt.plot(time, testcurve(time, par[0], par[1]), 'r-') plt.show()
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  • What are your bounds when not inf? Commented Apr 22, 2017 at 9:35
  • They're the ones in the example, +/- time[2], i.e. -648. and 648. But I also tried manually entering different values, it still doesn't work. Commented Apr 22, 2017 at 9:40
  • I have the same problem as well, without bounds, all my fits fail (with curve_fit, least_squares, and even minimize and a directly defined loss function), but with bounds, they all fail. Commented Nov 30, 2021 at 17:09

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I encountered the same behavior today in a different fitting problem. After some searching online, I found this link quite helpful: Why does scipy.optimize.curve_fit not fit to the data?

The short answer is that: using extremely small (or large) numbers in numerical fitting is not robust and scale them leads to a much better fitting.

In your case, both crc and Dp are extremely small numbers which could be scaled up. You could play with the scale factors and within certain range the fitting looks quite robust. Full example:

import numpy as np import matplotlib.pyplot as plt import scipy.optimize as opt #Generate data crc=np.array([-1.4e-14, 7.3e-14, 1.9e-13, 3.9e-13, 6.e-13, 8.0e-13, 9.2e-13, 9.9e-13, 1.e-12, 1.e-12, 1.e-12, 1.0e-12, 1.1e-12, 1.1e-12, 1.1e-12, 1.0e-12, 1.1e-12]) time=np.array([0., 368., 648., 960., 1520.,1864., 2248., 2655., 3031., 3384., 3688., 4048., 4680., 5343., 6055., 6928., 8120.]) # add scale factors to the data as well as the fitting parameter scale_factor_1 = 1e12 # 1./np.mean(crc) also works if you don't want to set the scale factor manually scale_factor_2 = 1./2e11 #Define the function for the fit def testcurve(x, Dp, dt): k = -Dp*(x+dt)*2e11 * scale_factor_2 curve = 1e-12 * (1+2*(-np.exp(k) + np.exp(4*k) - np.exp(9*k) + np.exp(16*k))) * scale_factor_1 curve[0]= 0 return curve #Set fit bounds dtmax=time[2] param_bounds = ((-np.inf, -dtmax),(np.inf, dtmax)) #Perform fit (par, par_cov) = opt.curve_fit(testcurve, time, crc*scale_factor_1, p0 = (5e-15/scale_factor_2, 0), bounds = param_bounds) #Print and plot output print(par[0]*scale_factor_2, par[1]) plt.plot(time, crc*scale_factor_1, 'o') plt.plot(time, testcurve(time, par[0], par[1]), 'r-') plt.show()

Fitting results: [6.273102923176595e-15, -21.12202697564494], which gives a reasonable fitting and also is very close to the result without any bounds: [6.27312512e-15, -2.11307470e+01]

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2 Comments

Shouldn't this be independent of whether there are bounds or not however? In my case, I have the same problem as the poster; without bounds I get a normal fit as expected, with bounds it fails. Do you know what it is about bounds that would make these "small number problem" suddenly show up?
Also in your solution, in func, scale_factor_2 cancels out with the 2e11 and same with scale_factor_1. This doesn't seem right? What's supposed to be going on there?

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