Contents


NAME

     dfftz2 - initialize  the  trigonometric  weight  and  factor
     tables  or  compute the two-dimensional forward Fast Fourier
     Transform of a two-dimensional double precision array.

SYNOPSIS

     SUBROUTINE DFFTZ2(IOPT, N1, N2, SCALE, X, LDX, Y, LDY, TRIGS, IFAC, WORK, LWORK, IERR)

     INTEGER IOPT, N1, N2, LDX, LDY, IFAC(*), LWORK, IERR
     DOUBLE COMPLEX Y(LDY, *)
     DOUBLE PRECISION X(LDX, *), SCALE, TRIGS(*), WORK(*)

     SUBROUTINE DFFTZ2_64(IOPT, N1, N2, SCALE, X, LDX, Y, LDY, TRIGS, IFAC, WORK, LWORK, IERR)

     INTEGER*8 IOPT, N1, N2, LDX, LDY, IFAC(*), LWORK, IERR
     DOUBLE COMPLEX Y(LDY, *)
     DOUBLE PRECISION X(LDX, *), SCALE, TRIGS(*), WORK(*)

  F95 INTERFACE
     SUBROUTINE FFT2(IOPT, [N1], [N2], [SCALE], X, [LDX], Y, [LDY], TRIGS,
               IFAC, WORK, [LWORK], IERR)

     INTEGER, INTENT(IN) :: IOPT
     INTEGER, INTENT(IN), OPTIONAL :: N1, N2, LDX, LDY, 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 FFT2_64(IOPT, [N1], [N2], [SCALE], X, [LDX], Y, [LDY], TRIGS, IFAC, WORK, [LWORK], IERR)

     INTEGER(8), INTENT(IN) :: IOPT
     INTEGER(8), INTENT(IN), OPTIONAL :: N1, N2, LDX, LDY, 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 dfftz2_ (int *iopt, int *n1, int  *n2,  double  *scale,
               double  *x,  int *ldx, doublecomplex *y, int *ldy,
               double  *trigs,  int  *ifac,  double  *work,   int
               *lwork, int *ierr);

     void dfftz2_64_ (long *iopt,  long  *n1,  long  *n2,  double
               *scale,  double  *x,  long *ldx, doublecomplex *y,
               long  *ldy,  double  *trigs,  long  *ifac,  double
               *work, long *lwork, long *ierr);

PURPOSE

     dfftz2  initializes  the  trigonometric  weight  and  factor
     tables  or computes the two-dimensional forward Fast Fourier
     Transform of a two-dimensional double precision  array.   In
     computing  the two-dimensional FFT, one-dimensional FFTs are
     computed   along   the   columns   of   the   input   array.
     One-dimensional FFTs are then computed along the rows of the
     intermediate results.

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

     where
     k1 ranges from 0 to N1-1 and k2 ranges from 0 to N2-1
     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)
     In real-to-complex transform of length N1, the (N1/2+1) com-
     plex  output  data  points stored are the positive-frequency
     half of the spectrum of the Discrete Fourier Transform.  The
     other  half  can be obtained through complex conjugation and
     therefore is not stored.

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.

     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 complex array  of  dimensions  (LDX,
               N2) that contains input data to be transformed.  X
               and Y can be the same array.

     LDX (input)
               Leading dimension of X.  LDX >= N1 if X is not the
               same  array as Y. Else, LDX = 2*LDY.  Unchanged on
               exit.

     Y (output)
               Y is a double complex array  of  dimensions  (LDY,
               N2)  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.

     LDY (input)
               Leading dimension of Y.  LDY >=  N1/2+1  Unchanged
               on exit.

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

     IFAC (input/output)
               Integer array of dimension  at  least  2*128  that
               contains  the  factors  of N1 and N2.  The factors
               are computed when the routine is called with  IOPT
               =  0  and  they  are used in subsequent calls when
               IOPT = -1.  Unchanged on exit.

     WORK (workspace)
               Double  precision  array  of  dimension  at  least
               MAX(N1, 2*N2) 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 = (LDX < N1) or (LDX not equal 2*LDY when X and
               Y are same array)
               -5 = (LDY < N1/2+1)
               -6  =  (LWORK  not   equal   0)   and   (LWORK   <
               MAX(N1,2*N2))
               -7 = memory allocation failed

SEE ALSO

     fft

CAUTIONS

     On exit, output array Y(1:LDY, 1:N2) is overwritten.