SCFFT,DZFFT(3)              MathKeisan FFT routine              SCFFT,DZFFT(3)



NAME
       scfft, dzfft - one-dimensional real-to-complex FFT

SYNOPSIS
       libfft.a

          INTEGER isign, n, isys
          COMPLEX y(n/2 + 1)
          REAL    scale, x(n+2), table(2*n+64), work(4*n)
          CALL SCFFT ( isign, n, scale, x, y, table, work, isys )

          INTEGER         isign, n, isys
          COMPLEX(kind=8) y(n/2 + 1)
          REAL(kind=8)    scale, x(n+2), table(2*n+64), work(4*n)
          CALL DZFFT ( isign, n, scale, x, y, table, work, isys )

       libfft_64.a

          INTEGER(kind=8) isign, n, isys
          COMPLEX(kind=8) y(n/2 + 1)
          REAL(kind=8)    scale, x(n+2), table(2*n+64), work(4*n)
          CALL SCFFT ( isign, n, scale, x, y, table, work, isys )

          INTEGER(kind=8) isign, n, isys
          COMPLEX(kind=8) y(n/2 + 1)
          REAL(kind=8)    scale, x(n+2), table(2*n+64), work(4*n)
          CALL DZFFT ( isign, n, scale, x, y, table, work, isys )

DESCRIPTION
       This subroutine computes the one-dimensional discrete Fourier transform
       of the given real array x; the transformed data is stored in  the  com-
       plex  array  y.   If  we take x and y to be dimensioned as x(0:n-1) and
       y(0:n/2), the transform is expressed by the following formula:


                      n-1

       y(k) = scale * Sum x(j) * exp(isign*j*k*2*pi*i/n)

                      j=0


       for k = 0, ..., n/2, where i = sqrt(-1).

       In order to accomodate multiple calls of the same size to this routine,
       an  additional initialization step is required prior to the computation
       of any transforms.  Hence, whenever it is desired to use  [(SC)(DZ)]FFT
       in a program, it must be called at least twice.

       A  result  of Fourier theory is that a transform of real data is conju-
       gate symmetric; hence, only the first n/2 + 1 complex data points  will
       be output by this routine.

       Note that this routine currently provides only serial functionality.


ARGUMENTS
       Input

       isign  Option flag:

              If  isign = 0, the routine is initialized for the given value of
              n.

              If isign = (+/-) 1, isign is the sign of the exponential in  the
              transform.

       n      Number of data points (n>0).


       scale  Scaling factor for the transform.

              Not used if isign = 0.

       x      Array of data to be transformed.

              Not used if isign = 0.

       isys   Currently unused.

       Working Storage

       table  If  isign  = 0, table is initialized for computing transforms of
              length n.

              If isign != 0, table must have been initialized  by  a  previous
              call with this value of n in which isign was 0.

       work   Workspace for computing the transform.

              Not used if isign = 0.

       Output

       y      Transformed data.

              Not used if isign = 0.



SciLib routine                                                  SCFFT,DZFFT(3)