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    <p>Numerical algorithms tend to work better when not fed extremely small (or large) numbers.</p> <p>In this case, the graph shows your data has extremely small x and y values. If you scale them, the fit is remarkable better:</p> <pre><code>xData = np.load('xData.npy')*10**5 yData = np.load('yData.npy')*10**5 </code></pre> <hr> <pre><code>from __future__ import division import os os.chdir(os.path.expanduser('~/tmp')) import numpy as np import scipy.optimize as optimize import matplotlib.pyplot as plt def func(x,a,b,c): return a*np.exp(-b*x)-c xData = np.load('xData.npy')*10**5 yData = np.load('yData.npy')*10**5 print(xData.min(), xData.max()) print(yData.min(), yData.max()) trialX = np.linspace(xData[0], xData[-1], 1000) # Fit a polynomial fitted = np.polyfit(xData, yData, 10)[::-1] y = np.zeros(len(trialX)) for i in range(len(fitted)): y += fitted[i]*trialX**i # Fit an exponential popt, pcov = optimize.curve_fit(func, xData, yData) print(popt) yEXP = func(trialX, *popt) plt.figure() plt.plot(xData, yData, label='Data', marker='o') plt.plot(trialX, yEXP, 'r-',ls='--', label="Exp Fit") plt.plot(trialX, y, label = '10 Deg Poly') plt.legend() plt.show() </code></pre> <p><img src="https://i.stack.imgur.com/C7Zxy.png" alt="enter image description here"></p> <p>Note that after rescaling <code>xData</code> and <code>yData</code>, the parameters returned by <code>curve_fit</code> must also be rescaled. In this case, <code>a</code>, <code>b</code> and <code>c</code> each must be divided by 10**5 to obtain fitted parameters for the original data.</p> <hr> <p>One objection you might have to the above is that the scaling has to be chosen rather "carefully". (Read: Not every reasonable choice of scale works!)</p> <p>You can improve the robustness of <code>curve_fit</code> by providing a reasonable initial guess for the parameters. Usually you have some <em>a priori</em> knowledge about the data which can motivate ballpark / back-of-the envelope type guesses for reasonable parameter values.</p> <p>For example, calling <code>curve_fit</code> with</p> <pre><code>guess = (-1, 0.1, 0) popt, pcov = optimize.curve_fit(func, xData, yData, guess) </code></pre> <p>helps improve the range of scales on which <code>curve_fit</code> succeeds in this case.</p>
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    1. POWhy does scipy.optimize.curve_fit not fit to the data?
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    1. POWhy does scipy.optimize.curve_fit not fit to the data?
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    1. COThat's much better! is there a reason that it doesn't like small numbers?
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    2. COI haven't studied `curve_fit's` algorithm closely enough to tell you exactly why. But in general, these algorithms need to test a guess for the parameter values, then tweak the guess. The size of initial tweak may work well if the data have magnitude around 1, but may overshoot the correct answer completely if the data has magnitude around 10**-6.
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    3. CO@unutbu You were right about the initial guess being around 1. From http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html#scipy.optimize.curve_fit `p0 : None, scalar, or M-length sequence Initial guess for the parameters. If None, then the initial values will all be 1 (if the number of parameters for the function can be determined using introspection, otherwise a ValueError is raised).` Where `scipy.optimize.curve_fit(f, xdata, ydata, p0=None, sigma=None, **kw)[source]`
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