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Jumps, i.e., f(x+)-f(x-)

`jumps = fnjmp(f,x) `

`jumps = fnjmp(f,x) ` is
like `fnval(f,x)` except that it returns the jump *f*(*x*+)
– *f*(*x*–) across `x` (rather
than the value at `x`) of the function *f* described
by `f` and that it only works for univariate functions.

This is a function for spline specialists.

`fnjmp(ppmak(1:4,1:3),1:4)` returns the vector `[0,1,1,0]` since
the `pp` 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.

If `x` is `cos([4:-1:0]*pi/4)`,
then `fnjmp(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 called perfect 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 its basic interval. Note that `fnjmp(fnder(spmak(x,1),3),-x) `returns
the vector `[12,0,0,0,12]` since `-x`,
though theoretically equal to `x,` differs from `x` by
roundoff, hence the third derivative of the B-spline provided by `spmak(x,1)` does
not have a jump across `-x(2)`,`-x(3)`,
and `-x(4)`.

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