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dfftz3(3P)		    Sun Performance Library		    dfftz3(3P)

NAME
       dfftz3  - initialize the trigonometric weight and factor tables or com‐
       pute the three-dimensional forward Fast Fourier Transform of  a	three-
       dimensional double complex array.

SYNOPSIS
       SUBROUTINE DFFTZ3(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
       DOUBLE COMPLEX Y(LDY1, LDY2, *)
       DOUBLE PRECISION X(LDX1, LDX2, *), SCALE, TRIGS(*), WORK(*)

       SUBROUTINE DFFTZ3_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
       DOUBLE COMPLEX Y(LDY1, LDY2, *)
       DOUBLE PRECISION X(LDX1, LDX2, *), SCALE, TRIGS(*), WORK(*)

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

       INTEGER, INTENT(IN) :: IOPT, LDX2, LDY2
       INTEGER, INTENT(IN), OPTIONAL :: N1, N2, N3, LDX1, LDY1, LWORK
       REAL(8), INTENT(IN), OPTIONAL :: SCALE
       REAL(8), INTENT(IN), DIMENSION(:,:,:) :: X
       COMPLEX(8), INTENT(OUT), DIMENSION(:,:,:) :: Y
       REAL(8), INTENT(INOUT), DIMENSION(:) :: TRIGS
       INTEGER, INTENT(INOUT), DIMENSION(:) :: IFAC
       REAL(8), INTENT(OUT), DIMENSION(:) :: WORK
       INTEGER, 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(8), INTENT(IN), OPTIONAL :: SCALE
       REAL(8), INTENT(IN), DIMENSION(:,:,:) :: X
       COMPLEX(8), INTENT(OUT), DIMENSION(:,:,:) :: Y
       REAL(8), INTENT(INOUT), DIMENSION(:) :: TRIGS
       INTEGER(8), INTENT(INOUT), DIMENSION(:) :: IFAC
       REAL(8), INTENT(OUT), DIMENSION(:) :: WORK
       INTEGER(8), INTENT(OUT) :: IERR

   C INTERFACE
       #include <sunperf.h>

       void dfftz3_ (int *iopt, int *n1, int *n2, int *n3, double *scale, dou‐
		 ble  *x,  int	*ldx1, int *ldx2, doublecomplex *y, int *ldy1,
		 int *ldy2,  double  *trigs,  int  *ifac,  double  *work,  int
		 *lwork, int *ierr);

       void  dfftz3_64_	 (long	*iopt,	long  *n1,  long *n2, long *n3, double
		 *scale, double *x, long *ldx1, long *ldx2, doublecomplex  *y,
		 long  *ldy1,  long  *ldy2,  double *trigs, long *ifac, double
		 *work, long *lwork, long *ierr);

PURPOSE
       dfftz3 initializes the trigonometric weight and factor tables  or  com‐
       putes  the  three-dimensional  forward  Fast  Fourier  Transform	 of  a
       three-dimensional double complex 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 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

       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)
		 Double	 precision  scalar  by	which  transform  results  are
		 scaled.   Unchanged on exit.  SCALE is defaulted to 1.0D0 for
		 F95 INTERFACE.

       X (input) X is a double precision array of dimensions (LDX1, LDX2,  N3)
		 that  contains	 input	data to be transformed.	 X can be same
		 array as Y.

       LDX1 (input)
		 first dimension of X.	If X is not same array as Y,  LDX1  >=
		 N1 Else, LDX1 = 2*LDY1 Unchanged on exit.

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

       Y (output)
		 Y  is	a  double 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.	  Oth‐
		 erwise,  it is assumed that there is no overlap between X and
		 Y in memory.

       LDY1 (input)
		 first dimension of Y.	LDY1 >= N1/2+1 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)
		 Double	 precision  array of length 2*(N1+N2+N3) that contains
		 the trigonometric weights.  The weights are computed when the
		 routine  is  called with IOPT = 0 and they are used in subse‐
		 quent calls when 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 factors are computed when the
		 routine is called with IOPT = 0 and they are used  in	subse‐
		 quent calls when IOPT = -1.  Unchanged on exit.

       WORK (workspace)
		 Double	   precision	array	 of    dimension    at	 least
		 (MAX(N,2*N2,2*N3) + 16*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 or -1
		 -2 = N1 < 0
		 -3 = N2 < 0
		 -4 = N3 < 0
		 -5 = (LDX1 < N1) or (LDX not equal 2*LDY when	X  and	Y  are
		 same array)
		 -6 = (LDX2 < N2)
		 -7 = (LDY1 < N1/2+1)
		 -8  =	(LDY2  <  N2) or (LDY2 not equal LDX2 when X and Y are
		 same array)
		 -9 = (LWORK not equal 0) and  (LWORK  <  (MAX(N,2*N2,2*N3)  +
		 16*N3))
		 -10 = memory allocation failed

SEE ALSO
       fft

CAUTIONS
       On exit, output subarray Y(1:LDY1, 1:N2, 1:N3) is overwritten.

				  6 Mar 2009			    dfftz3(3P)
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