On Thu, Sep 24, 2009 at 2:34 PM, Pauli Virtanen <p...@iki.fi> wrote: > to, 2009-09-24 kello 13:53 -0600, Charles R Harris kirjoitti: > > [clip] > > I was thinking of storing the chebyshev internally as the values at > > the chebyschev points. This makes multiplication, differentiation and > > such quite easy (resample and multiply/divide appropriatately). Its > > equivalent to working in the fourier domain for convolution and > > differentiation. The transform back and forth is likewise othogonal, > > so stable. The intepolation also becomes simple using the barycentric > > version. > > Sounds like you know this stuff well :) > > The internal representation of each orthogonal polynomial type can > probably be whatever works best for each case. It should be no problem > to sugar ChebyPoly up after the main work has been done. > > > As a side note, should the cheby* versions of `polyval`, > > `polymul` etc. just be dropped to reduce namespace clutter? > > You can do the same things already within just class methods > > and arithmetic. > > > > What do you mean? The evaluation can use various stable methods > > appropriate to the chebyshev series. > > This comment was just on the API -- the implementation of course should > be appropriate. > > > I have a set of functions that does the first (works on > > multidimensional arrays of coefficients, actually), but I am open to > > ideas of what such a chebyschev class with these methods should look > > like. An interval of definition should probably be part of the ctor. > > Thoughts? > > Having the following features could be useful: > > - __call__, .roots, .order: as in poly1d > - .data -> whatever is the internal representation > - .coef -> Chebyshev coefficients? > - .limits -> The interval > - arithmetic: chebyshev <op> chebyshev -> chebyshev > - arithmetic: scalar <op> chebyshev -> chebyshev > - arithmetic: poly1d <op> chebyshev -> chebyshev/poly1d (??) > > Multiplying by poly1d should be easy, just interpolate at the chebyshev points and multiply. Going the other way is a bit trickier.
I'm wondering if having support for complex would be justified? Chuck
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