dfftz2(3P) Sun Performance Library dfftz2(3P)NAMEdfftz2 - initialize the trigonometric weight and factor tables or com‐
pute the two-dimensional forward Fast Fourier Transform of a two-dimen‐
sional 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);
PURPOSEdfftz2 initializes the trigonometric weight and factor tables or com‐
putes the two-dimensional forward Fast Fourier Transform of a
two-dimensional double precision array. In computing the two-dimen‐
sional 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) complex 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 precision 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 con‐
tains 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. Otherwise,
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 subse‐
quent 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 rou‐
tine 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 rou‐
tine. 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.
6 Mar 2009 dfftz2(3P)
