CSFFT,ZDFFT(3)              MathKeisan FFT routine              CSFFT,ZDFFT(3)



NAME
       csfft, zdfft - one-dimensional complex-to-real FFT

SYNOPSIS
       libfft.a

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

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

       libfft_64.a

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

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

DESCRIPTION
       This subroutine computes the one-dimensional discrete Fourier transform
       of the given complex array x; the transformed data  is  stored  in  the
       real  array  y.   If  we take x and y to be dimensioned as x(0:n/2) and
       y(0:n-1), 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-1, where i = sqrt(-1).

       (The additional values of x can be determined by conjugate symmetry.)

       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  [(CS)(ZD)]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  are
       to be input to 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                                                  CSFFT,ZDFFT(3)