I read the text about rlft3 (Fortran 77 version) over and over, but I still could not understand how the output array was arranged. Fig. 12.5.1 does not help, I am not sure why the complex array spec
appears to begin (1,1) at the center (N/2, N/2) of the input array, leaving 3/4 of the original data array blank.

I also try to write a code to test, but this does not
help me either. I tried a 2d version (i.e. set N3=1).
However, I am confused even for the simplest case,
i.e. a function f(i,j) = constant. The fourier transform
of this should be some const for the 0,0 component,
i.e. i=1, j=1 component, all other components should
be 0. This is not the case, I found that in addition
to (i=1, j=1), there are also three other points which
are non-zero, namely (i=1, j=N/2+1), (i=2, j=1),
(i=2, j=N/2+1).

Could someone help me to understand this? I am truly frustrated.