CSFFTM,ZDFFTM(3)            MathKeisan FFT routine            CSFFTM,ZDFFTM(3)



NAME
       csfftm,  zdfftm - one-dimensional multiple complex-to-real FFT. (OpenMP
       Parallel Support).

SYNOPSIS
       libfft.a

          INTEGER isign, n, lot, ldx, ldy, isys
          COMPLEX x(ldx,lot)
          REAL    scale, y(ldy,lot), table(2*n+64), work(4*n*lot)
          CALL CSFFTM ( isign, n, lot,  scale,  x,  ldx,  y,  ldy,
          table, work, isys )

          INTEGER         isign, n, lot, ldx, ldy, isys
          COMPLEX(kind=8) x(ldx,lot)
          REAL(kind=8)    scale, y(ldy,lot), table(2*n+64), work(4*n*lot)
          CALL  ZDFFTM  (  isign,  n,  lot,  scale, x, ldx, y, ldy,
          table, work, isys )

       libfft_64.a

          INTEGER(kind=8) isign, n, lot, ldx, ldy, isys
          COMPLEX(kind=8) x(ldx,lot)
          REAL(kind=8)    scale, y(ldy,lot), table(2*n+64), work(4*n*lot)
          CALL CSFFTM ( isign, n, lot,  scale,  x,  ldx,  y,  ldy,
          table, work, isys )

          INTEGER(kind=8) isign, n, lot, ldx, ldy, isys
          COMPLEX(kind=8) x(ldx,lot)
          REAL(kind=8)    scale, y(ldy,lot), table(2*n+64), work(4*n*lot)
          CALL  ZDFFTM  (  isign,  n,  lot,  scale, x, ldx, y, ldy,
          table, work, isys )

DESCRIPTION
       This subroutine computes the one-dimensional discrete Fourier transform
       of  the lot complex vectors stored in x; the transformed data is stored
       in the real array y.  Examining a single vector to be  transformed,  if
       we  take x and y to be dimensioned as x(0:n/2) and y(0:n-1), the trans-
       form is expressed by the following formula:


                      n/2

       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).

       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)]FFTM
       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  of
       each data set are to be input to this routine.

       Set  the OpenMP environmental variable OMP_NUM_THREADS to the number of
       threads you would like to use.



ARGUMENTS
       Input

       isign  Option flag:

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

              If  isign  =  +1,  the transform is calculated, and isign is the
              sign of the exponential in the transform.

       n      Number of data points in a given data set (n>0).

       lot    Number of data sets to transform (lot>0).

       scale  Scaling factor for the transform.

              Not used if isign = 0.

       x      Array of data to be transformed.

              Not used if isign = 0.

       ldx    Leading dimension of x.  ldx >= n/2 + 1.

       ldy    Leading dimension of y.  ldy >= n.

       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                                                CSFFTM,ZDFFTM(3)