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@mstankie
Created November 11, 2016 15:00
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Fitting two curves with some common parameters. From http://scipy-cookbook.readthedocs.io/items/FittingData.html
# Target function
fitfunc = lambda T, p, x: p[0]*np.cos(2*np.pi/T*x+p[1]) + p[2]*x
# Initial guess for the first set's parameters
p1 = r_[-15., 0., -1.]
# Initial guess for the second set's parameters
p2 = r_[-15., 0., -1.]
# Initial guess for the common period
T = 0.8
# Vector of the parameters to fit, it contains all the parameters of the problem, and the period of the oscillation is not there twice !
p = r_[T, p1, p2]
# Cost function of the fit, compare it to the previous example.
errfunc = lambda p, x1, y1, x2, y2: r_[
fitfunc(p[0], p[1:4], x1) - y1,
fitfunc(p[0], p[4:7], x2) - y2
]
# This time we need to pass the two sets of data, there are thus four "args".
p,success = optimize.leastsq(errfunc, p, args=(Tx, tX, Ty, tY))
time = np.linspace(Tx.min(), Tx.max(), 100) # Plot of the first data and the fit
plt.plot(Tx, tX, "ro", time, fitfunc(p[0], p[1:4], time),"r-")
# Plot of the second data and the fit
time = np.linspace(Ty.min(), Ty.max(),100)
plt.plot(Ty, tY, "b^", time, fitfunc(p[0], p[4:7], time),"b-")
# Legend the plot
plt.title("Oscillations in the compressed trap")
plt.xlabel("time [ms]")
plt.ylabel("displacement [um]")
plt.legend(('x position', 'x fit', 'y position', 'y fit'))
ax = plt.axes()
plt.text(0.8, 0.07,
'x freq : %.3f kHz' % (1/p[0]),
fontsize=16,
horizontalalignment='center',
verticalalignment='center',
transform=ax.transAxes)
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