Complex data structures

Figaro defines a `complex data structure' in a fairly precise way. A complex data structure is a structure containing two arrays, one holding the real part of the complex data, and one holding the imaginary part. These arrays have to be the same size and shape, although they may have any number of dimensions. The dimensions of the arrays must be such that the Fast Fourier Transform algorithm (Cooley & Tukey, 1965) may be applied to them. Different implementations of the FFT have different restrictions-many require that the number of elements be a power of 2. The NAG library used by Figaro before version 5.0 required that, in each dimension, the number of elements had to have fewer than 20 prime factors, none greater than 19. The routines used from version 5.0 onwards have no restrictions. They are in the Starlink PDA library, the algorithms come originally from the FFTPACK library.

In a Figaro complex data structure the main data array is the real part of the complex data. This means that most of the Figaro routines may be applied to a complex data structure, and if this is done it will be the real part of the data that they operate on. For example, an easy way to look at complex data is with `splot', which will happily plot the real part of the data, quite ignorant of the fact that the data structure in question is complex. To plot the imaginary part, or the modulus of the data, these will first have to be extracted using `cmplx2m' or `cmplx2i'. It is important to note that if an ordinary Figaro function is used to change this data, for example by

   ICL> icmult cmplxdata 2 cmplxdata

which multiplies the real array by 2, the imaginary part will be unchanged. Generally, to avoid unnecessary conversions before using the FFT routines, the real and imaginary arrays are held in double precision. However, this is not a strict requirement.