Functions

Functions are defined by a finite number of $x$ and the corresponding values of $f(x)$. We do not assume that these $x$ are equally spaced, but this case is also considered, since it simplifies sometimes the definition of functions or their computation. We assume that the functions are continuous, linear between two successive $x$ where they are defined, and constant before the first $x$ and after the last one. However, for Fourier or Bessel transforms we assume that the functions vanish after the last $x$ and before the first.

The program is able to make operations (such as sum, product, composition, derivation, integration, convolution) on functions which are not necessary defined on the same $x$. For example if we want to compute the sum of $f_1(x)$ and $f_2(x)$ we will define a new function $g(x)$ (with a well defined x-range) and the sum of the two first functions will be computed exactly at the points of the x-range of $g$ and stored in this function.

Two kinds of tranforms are implemented in funct : Fourier transforms and Bessel transforms. There are two kinds of Fourier tranforms : the FFT transform, and the precise Fourier transform (cf. 3.3.1). Here also we don't assume that the x-ranges of a function and of its transform are related.

The expression evaluator accepts in funct 81 numerical functions. Those who are not in the standard math library come from the cephes package (see 1.2). These numerical functions can of course be used to define or modify the functions in funct.