On Sat, Oct 9, 2010 at 8:01 PM, Charles R Harris <[email protected]>wrote:
> > > On Sat, Oct 9, 2010 at 7:47 PM, <[email protected]> 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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