Contents
zfftz3 - initialize the trigonometric weight and factor
tables or compute the three-dimensional Fast Fourier
Transform (forward or inverse) of a three-dimensional double
complex array.
SUBROUTINE ZFFTZ3(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 X(LDX1, LDX2, *), Y(LDY1, LDY2, *)
DOUBLE PRECISION SCALE, TRIGS(*), WORK(*)
SUBROUTINE ZFFTZ3_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 X(LDX1, LDX2, *), Y(LDY1, LDY2, *)
DOUBLE PRECISION 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
COMPLEX(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
COMPLEX(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 zfftz3_ (int *iopt, int *n1, int *n2, int *n3, double
*scale, doublecomplex *x, int *ldx1, int *ldx2,
doublecomplex *y, int *ldy1, int *ldy2, double
*trigs, int *ifac, double *work, int *lwork, int
*ierr);
void zfftz3_64_ (long *iopt, long *n1, long *n2, long *n3,
double *scale, doublecomplex *x, long *ldx1, long
*ldx2, doublecomplex *y, long *ldy1, long *ldy2,
double *trigs, long *ifac, double *work, long
*lwork, long *ierr);
zfftz3 initializes the trigonometric weight and factor
tables or computes the three-dimensional Fast Fourier
Transform (forward or inverse) 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 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)
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)
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 (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 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. 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)
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 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)
Double precision 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 allo-
cate 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
fft
On exit, output subarray Y(1:LDY1, 1:N2, 1:N3) is overwrit-
ten.