The workhorse for the generation of surrogate data within the TISEAN package is the program surrogates. It implements the iterative Fourier based scheme introduced in Ref. [30] and discussed in Sec. 4.3. It has been extended to be able to handle multivariate data as discussed in Sec. 4.6. An FFT routine is used that can handle data sets of N points if N can be factorised using prime factors 2, 3, and 5 only. Routines that take arbitrary N will end up doing a slow Fourier transform if N is not factorisable with small factors. Occasionally, the length restriction results in the loss of a few points.
The routine starts with a random scramble as 
,
performs as many iterates as necessary to reach a fixed point and then prints
out 
or 
, as
desired. Further, the number of iterations is shown and the residual root mean
squared discrepancy between and
. The number of iterations can be limited by an
option. In particular, i=0 gives the initial scramble as
or a non-rescaled FFT surrogate as
. The first iterate, 
, is
approximately (but not quite) equivalent to an AAFT surrogate. It is advisable
to evaluate the residual discrepancy whenever the algorithm took more than a
few iterations. In cases of doubt if the accuracy is sufficient, it may be
useful to plot the autocorrelation function (corr or autocor)
of the data and , and, in the multivariate case,
the cross-correlation function (xcor) between the channels.
The routine can generate up to 999 surrogates in one call.
be a sub-sequence of length
and offset 
. The program then computes the contribution of the
end-to-end mismatch 
to the total power
in the sub-sequence:
is used.
Now the program goes through a sequence of decreasing 
, and for each determines 
such that
is minimal. The values of , ,
and are printed whenever 
has
decreased. One can thus easily find a sub-sequence that achieves negligible end
point mismatch with the minimal loss of data.