fnjmp

Examples

fnjmp(ppmak(1:4,1:3),1:4)returns the vector[0,1,1,0]since the页function here is 1 on [1 .. 2], 2 on [2 .. 3], and 3 on [3 .. 4], hence has zero jump at 1 and 4 and a jump of 1 across both 2 and 3.

Ifxiscos([4:-1:0]*pi/4), thenfnjmp(fnder(spmak(x,1),3),x)returns the vector[12 -24 24 -24 12](up to round-off). This is consistent with the fact that the spline in question is a so calledperfect cubic B-spline, i.e., has an absolutely constant third derivative (on its basic interval). The modified command

fnjmp(fnder(fn2fm(spmak(x,1),'pp'),3),x)

returns instead the vector[0 -24 24 -24 0], consistent with the fact that, in contrast to the B-form, a spline in ppform does not have a discontinuity in any of its derivatives at the endpoints of itsbasic interval. Note thatfnjmp(fnder(spmak(x,1),3),-x)returns the vector[12,0,0,0,12]since-x, though theoretically equal tox, differs fromxby round-off, hence the third derivative of the B-spline provided byspmak(x,1)does not have a jump across-x(2),- x (3), and-x(4).