ref: b548687a8ed1d0a159c9d3f3f921d93bbb56908e
dir: /module/ffts.m/
FFTs: module{
PATH: con "/dis/math/ffts.dis";
ffts: fn(a,b:array of real, ntot,n,nspan,isn:int);
};
# multivariate complex fourier transform, computed in place
# using mixed-radix fast fourier transform algorithm.
# arrays a and b originally hold the real and imaginary
# components of the data, and return the real and
# imaginary components of the resulting fourier coefficients.
# multivariate data is indexed according to the fortran
# array element successor function, without limit
# on the number of implied multiple subscripts.
# the subroutine is called once for each variate.
# the calls for a multivariate transform may be in any order.
# ntot is the total number of complex data values.
# n is the dimension of the current variable.
# nspan/n is the spacing of consecutive data values
# while indexing the current variable.
# the sign of isn determines the sign of the complex
# exponential, and the magnitude of isn is normally one.
# univariate transform:
# ffts(a,b,n,n,n,1)
# trivariate transform with a(n1,n2,n3), b(n1,n2,n3):
# ffts(a,b,n1*n2*n3,n1,n1,1)
# ffts(a,b,n1*n2*n3,n2,n1*n2,1)
# ffts(a,b,n1*n2*n3,n3,n1*n2*n3,1)
# the data can alternatively be stored in a single vector c
# alternating real and imaginary parts. the magnitude of isn changed
# to two to give correct indexing increment, and a[0:] and a[1:] used
# for a and b