This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.


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


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 round-off, 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).