Contents


NAME

     cfftc3 - initialize  the  trigonometric  weight  and  factor
     tables   or   compute  the  three-dimensional  Fast  Fourier
     Transform (forward or inverse) of a  three-dimensional  com-
     plex array.

SYNOPSIS

     SUBROUTINE CFFTC3(IOPT, N1, N2, N3, SCALE, X, LDX1, LDX2, Y, LDY1, LDY2, TRIGS, IFAC, WORK, LWORK, IERR)

     INTEGER IOPT, N1, N2, N3, LDX1, LDX2, LDY1,  LDY2,  IFAC(*),
     LWORK, IERR
     COMPLEX X(LDX1, LDX2, *), Y(LDY1, LDY2, *)
     REAL SCALE, TRIGS(*), WORK(*)

     SUBROUTINE CFFTC3_64(IOPT, N1, N2, N3, SCALE, X, LDX1, LDX2, Y, LDY1, LDY2, TRIGS, IFAC, WORK, LWORK, IERR)

     INTEGER*8 IOPT, N1, N2, N3, LDX1, LDX2, LDY1, LDY2, IFAC(*),
     LWORK, IERR
     COMPLEX X(LDX1, LDX2, *), Y(LDY1, LDY2, *)
     REAL SCALE, TRIGS(*), WORK(*)

  F95 INTERFACE
     SUBROUTINE FFT3(IOPT, [N1], [N2], [N3], [SCALE], X, [LDX1], LDX2, Y, [LDY1], LDY2, TRIGS,
               IFAC, WORK, [LWORK], IERR)

     INTEGER*4, INTENT(IN) :: IOPT, LDX2, LDY2
     INTEGER*4, INTENT(IN), OPTIONAL :: N1, N2, N3,  LDX1,  LDY1,
     LWORK
     REAL, INTENT(IN), OPTIONAL :: SCALE
     COMPLEX, INTENT(IN), DIMENSION(:,:) :: X
     COMPLEX, INTENT(OUT), DIMENSION(:,:) :: Y
     REAL, INTENT(INOUT), DIMENSION(:) :: TRIGS
     INTEGER*4, INTENT(INOUT), DIMENSION(:) :: IFAC
     REAL, INTENT(OUT), DIMENSION(:) :: WORK
     INTEGER*4, INTENT(OUT) :: IERR

     SUBROUTINE FFT3_64(IOPT, [N1], [N2], [N3], [SCALE], X, [LDX1], LDX2, Y, [LDY1], LDY2, TRIGS,
               IFAC, WORK, [LWORK], IERR)

     INTEGER(8), INTENT(IN) :: IOPT, LDX2, LDY2
     INTEGER(8), INTENT(IN), OPTIONAL :: N1, N2, N3, LDX1,  LDY1,
     LWORK
     REAL, INTENT(IN), OPTIONAL :: SCALE
     COMPLEX, INTENT(IN), DIMENSION(:,:) :: X
     COMPLEX, INTENT(OUT), DIMENSION(:,:) :: Y
     REAL, INTENT(INOUT), DIMENSION(:) :: TRIGS
     INTEGER(8), INTENT(INOUT), DIMENSION(:) :: IFAC
     REAL, INTENT(OUT), DIMENSION(:) :: WORK
     INTEGER(8), INTENT(OUT) :: IERR
  C INTERFACE
     #include <sunperf.h>

     void cfftc3_ (int *iopt, int *n1, int *n2,  int  *n3,  float
               *scale,  complex *x, int *ldx1, int *ldx2, complex
               *y, int *ldy1, int *ldy2, float *trigs, int *ifac,
               float *work, int *lwork, int *ierr);

     void cfftc3_64_ (long *iopt, long *n1, long *n2,  long  *n3,
               float  *scale, complex *x, long *ldx1, long *ldx2,
               complex *y, long *ldy1, long *ldy2, float  *trigs,
               long *ifac, float *work, long *lwork, long *ierr);

PURPOSE

     cfftc3  initializes  the  trigonometric  weight  and  factor
     tables   or  computes  the  three-dimensional  Fast  Fourier
     Transform (forward or inverse) of a  three-dimensional  com-
     plex array.

                           N3-1  N2-1  N1-1
     Y(k1,k2,k3) = scale * SUM   SUM   SUM   W3*W2*W1*X(j1,j2,j3)
                           j3=0  j2=0  j1=0

     where
     k1 ranges from 0 to N1-1; k2 ranges from 0 to  N2-1  and  k3
     ranges from 0 to N3-1
     i = sqrt(-1)
     isign = 1 for inverse transform or -1 for forward transform
     W1 = exp(isign*i*j1*k1*2*pi/N1)
     W2 = exp(isign*i*j2*k2*2*pi/N2)
     W3 = exp(isign*i*j3*k3*2*pi/N3)

ARGUMENTS

     IOPT (input)
               Integer specifying the operation to be performed:
               IOPT = 0 computes the trigonometric  weight  table
               and factor table
               IOPT = -1 computes forward FFT
               IOPT = +1 computes inverse FFT

     N1 (input)
               Integer specifying length of the transform in  the
               first  dimension.  N1 is most efficient when it is
               a product of small primes.  N1 >= 0.  Unchanged on
               exit.

     N2 (input)
               Integer specifying length of the transform in  the
               second dimension.  N2 is most efficient when it is
               a product of small primes.  N2 >= 0.  Unchanged on
               exit.

     N3 (input)
               Integer specifying length of the transform in  the
               third  dimension.  N3 is most efficient when it is
               a product of small primes.  N3 >= 0.  Unchanged on
               exit.

     SCALE (input)
               Real scalar by which transform results are scaled.
               Unchanged  on exit.  SCALE is defaulted to 1.0 for
               F95 INTERFACE.

     X (input) X is a complex array of  dimensions  (LDX1,  LDX2,
               N3) that contains input data to be transformed.

     LDX1 (input)
               first dimension of X.  LDX1  >=  N1  Unchanged  on
               exit.

     LDX2 (input)
               second dimension of X.  LDX2 >=  N2  Unchanged  on
               exit.

     Y (output)
               Y is a complex array of  dimensions  (LDY1,  LDY2,
               N3)  that contains the transform results.  X and Y
               can be the same array starting at the same  memory
               location,   in  which  case  the  input  data  are
               overwritten by their  transform  results.   Other-
               wise,  it  is  assumed  that  there  is no overlap
               between X and Y in memory.

     LDY1 (input)
               first dimension of Y.  If X and  Y  are  the  same
               array,  LDY1  =  LDX1 Else LDY1 >= N1 Unchanged on
               exit.

     LDY2 (input)
               second dimension of Y.  If X and Y  are  the  same
               array,  LDY2  =  LDX2 Else LDY2 >= N2 Unchanged on
               exit.

     TRIGS (input/output)
               Real array of length  2*(N1+N2+N3)  that  contains
               the  trigonometric  weights.  The weights are com-
               puted when the routine is called with IOPT = 0 and
               they are used in subsequent calls when IOPT = 1 or
               IOPT = -1.  Unchanged on exit.

     IFAC (input/output)
               Integer array of dimension  at  least  3*128  that
               contains  the  factors of N1, N2 and N3.  The fac-
               tors are computed when the routine is called  with
               IOPT  =  0  and  they are used in subsequent calls
               when IOPT = 1 or IOPT = -1.  Unchanged on exit.

     WORK (workspace)
               Real array of dimension at least (2*MAX(N,N2,N3) +
               32*N3)  *  NCPUS  where  NCPUS  is  the  number of
               threads used to execute the routine.  The user can
               also  choose  to have the routine allocate its own
               workspace (see LWORK).

     LWORK (input)
               Integer specifying workspace size.  If LWORK =  0,
               the routine will allocate its own workspace.

     IERR (output)
               On exit, integer IERR has  one  of  the  following
               values:
               0 = normal return
               -1 = IOPT is not 0, 1 or -1
               -2 = N1 < 0
               -3 = N2 < 0
               -4 = N3 < 0
               -5 = (LDX1 < N1)
               -6 = (LDX2 < N2)
               -7 = (LDY1 < N1) or (LDY1 not equal  LDX1  when  X
               and Y are same array)
               -8 = (LDY2 < N2) or (LDY2 not equal  LDX2  when  X
               and Y are same array)
               -9  =  (LWORK  not   equal   0)   and   (LWORK   <
               (2*MAX(N,N2,N3) + 16*N3) * NCPUS)
               -10 = memory allocation failed

SEE ALSO

     fft

CAUTIONS

     This routine uses Y(N1+1:LDY1,:,:) as scratch space.  There-
     fore,  the  original  contents of this subarray will be lost
     upon returning from routine while subarray Y(1:N1,1:N2,1:N3)
     contains the transform results.