Le lundi 06 juillet 2009 à 17:57 +0200, Fabrice Silva a écrit : > Le lundi 06 juillet 2009 à 17:13 +0200, Nils Wagner a écrit : > > IIRC, the coefficients of your polynomial are complex. > > So, you cannot guarantee that the roots are complex > > conjugate pairs. > > Correct! If the construction is done with X1 and X1* treated separately, > the coefficients appear to be complex. But if their processing is done > simultaneously, the combination gives real coefficients. Let me modify > this point and come back to tell you if it is the breakpoint...
Alright, the coefficients are now all real (I still wonder how it passed the check tests I have). You can find attached a simple test. Looking at the evolution of a.r, it seems there really is a trouble with the representation of high order polynomial. 'a' is initialized with its roots, but a.r is far from equal to the input roots... -- Fabrice Silva Laboratory of Mechanics and Acoustics - CNRS 31 chemin Joseph Aiguier, 13402 Marseille, France.
import matplotlib.pyplot as plt
import numpy as np
import numpy.lib.polynomial as pol
plt.figure()
S1 = plt.subplot(111)
for n in np.arange(50):
a = pol.poly1d(np.arange(n)*1.,r=True)
print n,np.all(np.diff(a.r)==1), a.r
b = pol.poly1d(a.c, r=False)
sol = b.r
S1.plot(sol, n*np.ones_like(sol), 'r+')
plt.xlabel('roots')
plt.ylabel('order of polynomial')
plt.show()
<<attachment: test_roots.png>>
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