Spline Toolbox

Use

Once you have constructed an approximating or interpolating thin-plate spline st with the aid of tpaps (or directly via stmak), you can use fnbrk to obtain its parts or change its basic interval, fnval to evaluate it, fnplt to plot it, and fnder to construct its two first partial derivatives, but no higher-order derivatives as they become infinite at the centers. This is just one indication that the stform is quite different in nature from the other forms in this toolbox, hence other fn... commands by and large don't work with stforms. For example, it makes no sense to use fnjmp, and fnmin or fnzeros only work for univariate functions. It also makes no sense to use fnint on a function in stform since such functions cannot be integrated in closed form. The command Ast = fncmb(st,A) can be used on st, provided A is something that can be applied to the values of the function described by st. For example, A might be 'sin', in which case Ast is the stform of the function whose coefficients are the sine of the coefficients of st. In effect, Ast describes the function obtained by composing A with st. But, because of the singularities in the higher-order derivatives of a thin-plate spline, there seems little point to make fndir or fntlr applicable to such a st.

stform

Example: A Nonlinear ODE