NAME

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. =head1 SYNOPSIS

  SUBROUTINE DFFTZ2( IOPT, N1, N2, SCALE, X, LDX, Y, LDY, TRIGS, IFAC, 
 *      WORK, LWORK, IERR)
  DOUBLE COMPLEX Y(LDY,*)
  INTEGER IOPT, N1, N2, LDX, LDY, LWORK, IERR
  INTEGER IFAC(*)
  DOUBLE PRECISION SCALE
  DOUBLE PRECISION X(LDX,*), TRIGS(*), WORK(*)

  SUBROUTINE DFFTZ2_64( IOPT, N1, N2, SCALE, X, LDX, Y, LDY, TRIGS, 
 *      IFAC, WORK, LWORK, IERR)
  DOUBLE COMPLEX Y(LDY,*)
  INTEGER*8 IOPT, N1, N2, LDX, LDY, LWORK, IERR
  INTEGER*8 IFAC(*)
  DOUBLE PRECISION SCALE
  DOUBLE PRECISION X(LDX,*), TRIGS(*), WORK(*)

F95 INTERFACE

  SUBROUTINE FFT2( IOPT, [N1], [N2], [SCALE], X, [LDX], Y, [LDY], 
 *       TRIGS, IFAC, WORK, [LWORK], IERR)
  COMPLEX(8), DIMENSION(:,:) :: Y
  INTEGER :: IOPT, N1, N2, LDX, LDY, LWORK, IERR
  INTEGER, DIMENSION(:) :: IFAC
  REAL(8) :: SCALE
  REAL(8), DIMENSION(:) :: TRIGS, WORK
  REAL(8), DIMENSION(:,:) :: X

  SUBROUTINE FFT2_64( IOPT, [N1], [N2], [SCALE], X, [LDX], Y, [LDY], 
 *       TRIGS, IFAC, WORK, [LWORK], IERR)
  COMPLEX(8), DIMENSION(:,:) :: Y
  INTEGER(8) :: IOPT, N1, N2, LDX, LDY, LWORK, IERR
  INTEGER(8), DIMENSION(:) :: IFAC
  REAL(8) :: SCALE
  REAL(8), DIMENSION(:) :: TRIGS, WORK
  REAL(8), DIMENSION(:,:) :: X

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. .Ve

                   N2-1  N1-1

Y(k1,k2) = scale * SUM SUM W2*W1*X(j1,j2)

                   j2=0  j1=0
.Ve

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.
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. 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 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 (output)
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

CAUTIONS