[Numpy-discussion] polynomial fromroots
josef.pktd@gmai...
josef.pktd@gmai...
Sat Oct 9 20:47:06 CDT 2010
I'm trying to see whether I can do this without reading the full manual.
Is it intended that fromroots normalizes the highest order term
instead of the lowest?
>>> import numpy.polynomial as poly
>>> p = poly.Polynomial([1, -1.88494037, 0.0178126 ])
>>> p
Polynomial([ 1. , -1.88494037, 0.0178126 ], [-1., 1.])
>>> pr = p.roots()
>>> pr
array([ 0.53320748, 105.28741219])
>>> poly.Polynomial.fromroots(pr)
Polynomial([ 56.14003571, -105.82061967, 1. ], [-1., 1.])
>>>
renormalizing
>>> p2 = poly.Polynomial.fromroots(pr)
>>> p2/p2.coef[0]
Polynomial([ 1. , -1.88494037, 0.0178126 ], [-1., 1.])
this is, I think what I want to do, invert roots that are
inside/outside the unit circle (whatever that means
>>> pr[np.abs(pr)<1] = 1./pr[np.abs(pr)<1]
>>> p3 = poly.Polynomial.fromroots(pr)
>>> p3/p3.coef[0]
Polynomial([ 1. , -0.54270529, 0.0050643 ], [-1., 1.])
Josef
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