[SciPy-Dev] Splines

Charles R Harris charlesr.harris@gmail....
Wed Mar 13 11:19:16 CDT 2013


On Wed, Mar 13, 2013 at 9:47 AM, denis <denis-bz-py@t-online.de> wrote:

> Pauli Virtanen <pav <at> iki.fi> writes:
>
> > However, map_coordinates is only for splines on uniform set of knots,
> > you can't evaluate it on a grid efficiently, etc.
>
> Pauli,
>   It's easy to uniformize non-uniform grids, see
> [Intergrid](http://denis-bz.github.com/docs/intergrid.html)
> (comments welcome).
> Sure, for order > 1 this is not as smooth as real non-uniform splines
> but very simple, low-memory too, fast:
>     in 4d, 5d, 6d, Intergrid does around 3M, 2M, .8M interpolations /
> second.
>
> a bird in the hand.
>
>
I'm not sure you are interpreting 'prefilter' correctly. I haven't looked
at the scipy code, but the uniform spline coefficients can be gotten by
filtering forward and back along each axis. It essentially factors the fit
matrix into lower/upper factors with constant diagonals modulo boundary
conditions, and forward/reverse substitution reduces to IIR filtering. This
is also used for other interpolation schemes, for instance variance
preserving interpolation which is useful when matching scenes using mutual
information.

Chuck
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