Spline Toolbox

Construction

A piecewise-polynomial is usually constructed by some command, through a process of interpolation or approximation, or conversion from some other form e.g., from the B-form, and is output as a variable. But it is also possible to make one up from scratch, using the statement

• pp = ppmak(breaks,coefs)
  

For example, we might say pp=ppmak(-5:-1,-22:-11), or, more explicitly,

• breaks = -5:-1;
  coefs = -22:-11;
  pp = ppmak(breaks,coefs);
  

thus supplying the uniform break sequence -5:-1 and the coefficient sequence -22:-11. Since this break sequence has 5 entries, hence 4 break intervals, while the coefficient sequence has 12 entries, we have, in effect, specified a piecewise-polynomial of order 3 (= 12/4). The command

• fnbrk(pp)
  

prints out all the constituent parts of this piecewise-polynomial, as follows:

• breaks(1:l+1) 
     -5 -4 -3 -2 -1 
  coefficients(d*l,k) 
     -22 -21 -20 
     -19 -18 -17
     -16 -15 -14 
     -13 -12 -11 
  pieces number l
     4
  order k
     3
  dimension d of target
     1
  

Further, fnbrk can be used to supply each of these parts separately. But the point of the Spline Toolbox is that you usually need not concern yourself with these details. You simply use pp as an argument to commands that evaluate, differentiate, integrate, convert, or plot the piecewise-polynomial whose description is contained in pp.

ppform

Use