section f of routines in fft.i

Home Manual Packages Global Index Keywords Quick Reference | # functions in fft.i - f
fft |
                 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
SEE ALSO: | roll, fft_setup, fft_inplace
fft_braw |
                 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 |
     fft_dirs

    interpreted function, defined at i0/fft.i   line 192
fft_fraw |
                 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 |
                 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 |
                 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
SEE ALSO: | fft, fft_setup
fft_raw |
     fft_raw

    builtin function, documented at i0/fft.i   line 246
fft_setup |
                 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
SEE ALSO: | fft, dimsof, fft_inplace