fft(x, direction)  
             fft(x, ljdir, rjdir)  
          or fft(x, ljdir, rjdir, setup=workspace)  
  
     returns the complex Fast Fourier Transform of array X.  
     The DIRECTION determines which direction the transform is in --  
     e.g.- from time to frequency or vice-versa -- as follows:  
  
     DIRECTION    meaning  
     ---------    -------  
         1        "forward" transform (coefficients of exp(+i * 2*pi*kl/N))  
	          on every dimension of X  
        -1        "backward" transform (coefficients of exp(-i * 2*pi*kl/N))  
	          on every dimension of X  
     [1,-1,1]     forward transform on first and third dimensions of X,  
                  backward transform on second dimension of X (any other  
		  dimensions remain untransformed)  
     [-1,0,0,1]   backward transform on first dimension of X, forward  
                  transform on fourth dimension of X  
	etc.  
  
     The third positional argument, if present, allows the direction  
     of dimensions of X to be specified relative to the final dimension  
     of X, instead of relative to the first dimension of X.  In this  
     case, both LJDIR and RJDIR must be vectors of integers -- the  
     scalar form is illegal:  
  
        LJDIR    RJDIR      meaning  
        -----    -----      -------  
	[]        [1]       forward transform last dimension of X  
	[1]        []       forward transform first dimension of X  
	[]        [-1,-1]   backward transform last two dimensions of X,  
	                    leaving any other dimensions untransformed  
     [-1,0,0,1]    []       backward transform on first dimension of X,  
                            forward transform on fourth dimension of X  
        []      [-1,0,0,1]  backward transform on 4th to last dimension of X,  
                            forward transform on last dimension of X  
	etc.  
  
     Note that the final element of RJDIR corresponds to the last dimension  
     of X, while the initial element of LJDIR corresponds to the first  
     dimension of X.  
  
     The explicit meaning of "forward" transform -- the coefficients of  
     exp(+i * 2*pi*kl/N) -- is:  
  
     result for j=1,...,n  
  
                result(j)=the sum from k=1,...,n of  
  
                      x(k)*exp(-i*(j-1)*(k-1)*2*pi/n)  
  
                            where i=sqrt(-1)  
  
     Note that the result is unnormalized.  Applying the "backward"  
     transform to the result of a "forward" transform returns N times  
     the original vector of length N.  Equivalently, applying either  
     the "forward" or "backward" transform four times in succession  
     yields N^2 times the original vector of length N.  
  
     Performing the transform requires some WORKSPACE, which can be  
     set up beforehand by calling fft_setup, if fft is to be called  
     more than once with arrays X of the same shape.  If no setup  
     keyword argument is supplied, the workspace allocation and setup  
     must be repeated for each call.  
  

unknown type function, documented at startup/fft.i   line 93