fnjmp - Jumps, i.e., f(x+)-f(x-)
Syntax
jumps = fnjmp(f,x)
Description
jumps = fnjmp(f,x) is
like fnval(f,x), -- except that it returns the
jump
across x (rather than the
value at x) of the function
described by f and
that it only works for univariate functions.
This is a function for spline specialists.
Examples
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).
 | fnint | | fnmin |  |
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