[Numpy-discussion] polynomial fromroots
Charles R Harris
charlesr.harris@gmail....
Sat Oct 9 21:05:08 CDT 2010
On Sat, Oct 9, 2010 at 8:01 PM, Charles R Harris
<charlesr.harris@gmail.com>wrote:
>
>
> 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. ])
>
>
Oh, and least squares follows the same convention:
In [5]: x = linspace(-1,1,10)
In [6]: y = (x - 1)*( x + 1.88494037)*(x - 0.0178126)
In [7]: p = poly.Polynomial.fit(x, y, 3)
In [8]: p
Out[8]: Polynomial([ 0.03357569, -1.90070346, 0.86712777, 1. ],
[-1., 1.])
Chuck
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