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POSciPy leastsq fit to a sine wave failing
 

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  1. POSciPy leastsq fit to a sine wave failing
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    <p>I am trying to figure out what it is I don't understand here.</p> <p>I am following <a href="http://www.scipy.org/Cookbook/FittingData" rel="nofollow noreferrer">http://www.scipy.org/Cookbook/FittingData</a> and trying to fit a sine wave. The real problem is satellite magnetometer data which makes a nice sine wave on a spinning spacecraft. I created a dataset then am trying to fit it to recover the inputs.</p> <p>Here is my code:</p> <pre><code>import numpy as np from scipy import optimize from scipy.optimize import curve_fit, leastsq import matplotlib.pyplot as plt class Parameter: def __init__(self, value): self.value = value def set(self, value): self.value = value def __call__(self): return self.value def fit(function, parameters, y, x = None): def f(params): i = 0 for p in parameters: p.set(params[i]) i += 1 return y - function(x) if x is None: x = np.arange(y.shape[0]) p = [param() for param in parameters] return optimize.leastsq(f, p, full_output=True, ftol=1e-6, xtol=1e-6) # generate a perfect data set (my real data have tiny error) def mysine(x, a1, a2, a3): return a1 * np.sin(a2 * x + a3) xReal = np.arange(500)/10. a1 = 200. a2 = 2*np.pi/10.5 # omega, 10.5 is the period a3 = np.deg2rad(10.) # 10 degree phase offset yReal = mysine(xReal, a1, a2, a3) # plot the real data plt.figure(figsize=(15,5)) plt.plot(xReal, yReal, 'r', label='Real Values') # giving initial parameters amplitude = Parameter(175.) frequency = Parameter(2*np.pi/8.) phase = Parameter(0.0) # define your function: def f(x): return amplitude() * np.sin(frequency() * x + phase()) # fit! (given that data is an array with the data to fit) out = fit(f, [amplitude, frequency, phase], yReal, xReal) period = 2*np.pi/frequency() print amplitude(), period, np.rad2deg(phase()) xx = np.linspace(0, np.max(xReal), 50) plt.plot( xx, f(xx) , label='fit') plt.legend(shadow=True, fancybox=True) </code></pre> <p>Which makes this plot: <img src="https://i.stack.imgur.com/91cGN.png" alt="enter image description here"></p> <p>The recovered fit parameters of <code>[44.2434221897 8.094832581 -61.6204033699]</code> have no resemblance to what I started with.</p> <p>Any thoughts on what I am not understanding or doing wrong?</p> <pre><code>scipy.__version__ '0.10.1' </code></pre> <hr> <p>Edit: Fixing one parameter was suggested. In the example above fixing the amplitude to <code>np.histogram(yReal)[1][-1]</code> still produces unacceptable output. Fits: <code>[175.0 8.31681375217 6.0]</code> Should I try a different fitting method? Suggestions on which?</p> <p><img src="https://i.stack.imgur.com/KFEwf.png" alt="enter image description here"></p>
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