functions in fft.i - f

             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.  

interpreted function, defined at i0/fft.i   line 20  

             fft_braw, n, c, wsave  
 
     Swarztrauber's cfftb.  You can use this to avoid the additional  
     2*N storage incurred by fft_setup.  

builtin function, documented at i0/fft.i   line 237  

 fft_dirs  
 
  

interpreted function, defined at i0/fft.i   line 192  

             fft_fraw, n, c, wsave  
 
     Swarztrauber's cfftf.  You can use this to avoid the additional  
     2*N storage incurred by fft_setup.  

builtin function, documented at i0/fft.i   line 228  

             fft_init, n, wsave  
 
     Swarztrauber's cffti.  This actually requires wsave=array(0.0, 4*n+15),  
     instead of the 6*n+15 doubles of storage used by fft_raw to handle the  
     possibility of multidimensional arrays.  If the storage matters, you  
     can call cfftf and/or cfftb as the Yorick functions fft_fraw and/or  
     fft_braw.  

builtin function, documented at i0/fft.i   line 216  

             fft_inplace, x, direction  
          or fft_inplace, x, ljdir, rjdir  
 	 or fft_inplace, x, ljdir, rjdir, setup=workspace  
 
     is the same as the fft function, except that the transform is  
     performed "in_place" on the array X, which must be of type complex.  

interpreted function, defined at i0/fft.i   line 94  

 fft_raw  
 
  

builtin function, documented at i0/fft.i   line 246  

             workspace= fft_setup(dimsof(x))  
          or workspace= fft_setup(dimsof(x), direction)  
          or workspace= fft_setup(dimsof(x), ljdir, rjdir)  
 
     allocates and sets up the workspace for a subsequent call to  
            fft(X, DIRECTION, setup=WORKSPACE)  
     or  
            fft(X, LJDIR, RJDIR, setup=WORKSPACE)  
     The DIRECTION or LJDIR, RJDIR arguments compute WORKSPACE only for  
     the dimensions which will actually be transformed.  If only the  
     dimsof(x) argument is supplied, then WORKSPACE will be enough to  
     transform any or all dimensions of X.  With DIRECTION or LJDIR, RJDIR  
     supplied, WORKSPACE will only be enough to compute the dimensions  
     which are actually to be transformed.  The WORKSPACE does not  
     depend on the sign of any element in the DIRECTION (or LJDIR, RJDIR),  
     so you can use the same WORKSPACE for both "forward" and "backward"  
     transforms.  
     Furthermore, as long as the length of any dimensions of the array  
     X to be transformed are present in WORKSPACE, it may be used in  
     a call to fft with the array.  Thus, if X were a 25-by-64 array,  
     and Y were a 64-vector, the following sequence is legal:  
          ws= fft_setup(dimsof(x));  
	  xf= fft(x, 1, setup=ws);  
	  yf= fft(y, -1, setup=ws);  
     The WORKSPACE required for a dimension of length N is 6*N+15 doubles.  

interpreted function, defined at i0/fft.i   line 137