[Numpy-discussion] polynomial fromroots

Charles R Harris charlesr.harris@gmail....
Sat Oct 9 21:01:09 CDT 2010


On Sat, Oct 9, 2010 at 7:47 PM, <josef.pktd@gmail.com> wrote:

> 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.])
>
>
Wrong function ;) You defined the polynomial by its coefficients. What you
want to do is

In [1]: import numpy.polynomial as poly

In [2]: p = poly.Polynomial.fromroots([1, -1.88494037,  0.0178126 ])

In [3]: p
Out[3]: Polynomial([ 0.03357569, -1.90070346,  0.86712777,  1.        ],
[-1.,  1.])

In [4]: p.roots()
Out[4]: array([-1.88494037,  0.0178126 ,  1.        ])

Chuck
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