[Numpy-discussion] polynomial package update
Charles R Harris
charlesr.harris at gmail.com
Tue Jan 3 08:21:04 EST 2012
On Mon, Jan 2, 2012 at 10:46 PM, <josef.pktd at gmail.com> wrote:
> On Mon, Jan 2, 2012 at 9:44 PM, Charles R Harris
> <charlesr.harris at gmail.com> wrote:
> > Hi All,
> >
> > I've made a pull request for a rather large update of the polynomial
> > package. The new features are
> >
> > 1) Bug fixes
> > 2) Improved documentation in the numpy reference
> > 3) Preliminary support for multi-dimensional coefficient arrays
> > 4) Support for NA in the fitting routines
> > 5) Improved testing and test coverage
> > 6) Gauss quadrature
> > 7) Weight functions
> > 8) (Mostly) Symmetrized companion matrices
> > 9) Add cast and basis as static functions of convenience classes
> > 10) Remove deprecated import from package init.py
> >
> > If anyone has an interest in that package, please take some time and
> review
> > it here.
>
> (Since I'm not setup for compiling numpy I cannot try it out. Just
> some spotty reading of the code.)
>
> The two things I'm most interested in are the 2d, 3d enhancements and
> the quadrature.
>
> What's the return of the 2d vander functions?
>
> If I read it correctly, it's:
>
> >>> xyn = np.array([['x^%d*y^%d'%(px,py) for py in range(5)] for px in
> range(3)])
> >>> xyn
> array([['x^0*y^0', 'x^0*y^1', 'x^0*y^2', 'x^0*y^3', 'x^0*y^4'],
> ['x^1*y^0', 'x^1*y^1', 'x^1*y^2', 'x^1*y^3', 'x^1*y^4'],
> ['x^2*y^0', 'x^2*y^1', 'x^2*y^2', 'x^2*y^3', 'x^2*y^4']],
> dtype='|S7')
> >>> xyn.ravel()
> array(['x^0*y^0', 'x^0*y^1', 'x^0*y^2', 'x^0*y^3', 'x^0*y^4', 'x^1*y^0',
> 'x^1*y^1', 'x^1*y^2', 'x^1*y^3', 'x^1*y^4', 'x^2*y^0', 'x^2*y^1',
> 'x^2*y^2', 'x^2*y^3', 'x^2*y^4'],
> dtype='|S7')
>
>
Yes, that's right.
> Are the normalization constants available in explicit form to get an
> orthonormal basis?
>
No, not at the moment. I haven't quite figured out how I want to expose
them but I agree that they should be available.
> The test_100 look like good recipes for getting the normalization and
> the integration constants.
>
>
Yes, that works. There are also explicit formulas, but I don't know that
they
would work better. Some of the factors get very large, for Laguerre of
degree
100 the can be up in the 10^100 range
> Are the quads weights and points the same as in scipy.special (up to
> floating point differences)?
>
>
Yes, but more accurate. For instance, the scipy.special values for
Gauss-Laguerre integration die at around degree 40.
> Looks very useful and I'm looking forward to trying it out, and I will
> borrow some code like test_100 as recipes.
> (For densities, I still need mostly orthonormal basis and integration
> normalized to 1.)
>
>
Let me know what would be useful and I'll try to put it in.
Chuck
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