[SciPy-User] Gradient of spline interpolation at a point wrt changing the knot points

Pauli Virtanen pav@iki...
Sat Jun 15 08:23:06 CDT 2013


15.06.2013 02:03, Daπid kirjoitti:
> On 14 June 2013 23:47, Pauli Virtanen <pav@iki.fi> wrote:
>> Sorry, wrote it too fast. Computing the spline coefficients
>> is IIRC is a global process, and it is affected by knot locations,
>> so I doubt there is a simple formula for the derivative.
>
> Actually, it only depends on the surrounding points, and with linear
> properties. See, for example, its matrix form [1]: a multi-diagonal
> fixed matrix A multiplying a vector of coefficients b.
>
> A b = y

The matrix A depends here on the knot locations, so taking derivative 
with respect to them is not so straightforward?

Ah, but I now read the original mail and it says the derivatives should 
be taken with respect to knot values. This is not so much of a problem...

-- 
Pauli Virtanen




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