Spline fitting
1. ..\..\interpolation\Cubic Spline Interpolation.doc Press’s presentation of the codes SPLINE.FOR and SPLINT.FOR. These use x, y, and y” to interpolate a set of data points. The y” is solved for by requiring continuity of the first derivatives. A part labeled Bob’s thoughts flirts with midpoint knots, picture showing effects of end point derivatives.
2. doc1/ypp.htm .doc – Bob’s Lagrange derivation of the Press result -- details the Lagrange interpolation of y and y”, produces the same results as doc1/Cubic Spline Interpolation.htm .doc based on Press
3.
doc1/The two forms.htm .doc Detailed derivation of YPPTOC.FOR for converting x,y,y” to sum on c and d
terms.
The partials with respect to cj, dk, and xk
are easy to evaluate in this form making it appropriate for fitting the data
This code is used in CNMFIT.FOR
(this is code from bkgfit that needs to be modified and simplified for use in
class)
4. doc1/Fitting Sections.htm .doc. Considers the boundary conditions for fitting data in short sections. doc1\Fitting Sections 2.htm .doc A bit more detail. In fact the fitting method actually used was to vary a knot, the six above it and the six below it. The knots were moved toward lower channels 2 knots at a time. The idea is that the top two knots and the bottom 2 represent the boundary conditions, while the rest are local. In fact, the non-local effect of each knot on regions much lower is probably the primary reason for the method working. The fact that this limits the number of constants to 26 makes the matrix invertible which possibly is more important than any other consideration.
5. doc1/Alpha for bkg.htm .doc The notion that the error should be increased introduced in the general reference above is implemented here by solving for alpha such that 2N=(f-fA)**2/((alpha*f)**2+e2)
6. doc1/Adding knots.htm .doc A penalty is added to keep knots from drifting outside the fitting region.
Fortran codes