Contents
dfftz2 - initialize the trigonometric weight and factor
tables or compute the two-dimensional forward Fast Fourier
Transform of a two-dimensional double precision array.
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);
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.
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
fft
On exit, output array Y(1:LDY, 1:N2) is overwritten.