On Sat, Oct 9, 2010 at 10:01 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
My coefficients are from a lag-polynomial in time series analysis (ARMA), and they really are the (estimated) coefficients. It is essentially the same as the model for scipy.signal.lfilter. I just need to check the roots to see whether the process is stationary and invertible. If one of the two lag-polynomials (moving average) has roots on the wrong side of the unit circle, then I can invert them. I'm coding from memory of how this is supposed to work, so maybe I'm back to RTFM and RTFTB (TB=text book). (I think what I really would need is a z-transform, but I don't have much of an idea how to do this on a computer) Thanks, the main thing I need to do is check the convention or definition for the normalization. And as btw, I like that the coef are in increasing order e.g. seasonal differencing multiplied with 1 lag autoregressive poly.Polynomial([1.,0,0,-1])*poly.Polynomial([1,0.8]) (I saw your next message: Last time I played with function approximation, I didn't figure out what the basis does, but it worked well without touching it) Josef > > 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 > > > _______________________________________________ > NumPy-Discussion mailing list > [email protected] > http://mail.scipy.org/mailman/listinfo/numpy-discussion > > _______________________________________________ NumPy-Discussion mailing list [email protected] http://mail.scipy.org/mailman/listinfo/numpy-discussion
