• NAME
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS
• SEE ALSO
• CAUTIONS

NAME

cffts3 - initialize the trigonometric weight and factor tables or compute the three-dimensional inverse Fast Fourier Transform of a three-dimensional complex array. =head1 SYNOPSIS

  SUBROUTINE CFFTS3( IOPT, N1, N2, N3, SCALE, X, LDX1, LDX2, Y, LDY1, 
 *      LDY2, TRIGS, IFAC, WORK, LWORK, IERR)
  COMPLEX X(LDX1,LDX2,*)
  INTEGER IOPT, N1, N2, N3, LDX1, LDX2, LDY1, LDY2, LWORK, IERR
  INTEGER IFAC(*)
  REAL SCALE
  REAL Y(LDY1,LDY2,*), TRIGS(*), WORK(*)

  SUBROUTINE CFFTS3_64( IOPT, N1, N2, N3, SCALE, X, LDX1, LDX2, Y, 
 *      LDY1, LDY2, TRIGS, IFAC, WORK, LWORK, IERR)
  COMPLEX X(LDX1,LDX2,*)
  INTEGER*8 IOPT, N1, N2, N3, LDX1, LDX2, LDY1, LDY2, LWORK, IERR
  INTEGER*8 IFAC(*)
  REAL SCALE
  REAL Y(LDY1,LDY2,*), TRIGS(*), WORK(*)

F95 INTERFACE

  SUBROUTINE FFT3( IOPT, N1, [N2], [N3], [SCALE], X, [LDX1], LDX2, Y, 
 *       [LDY1], LDY2, TRIGS, IFAC, WORK, [LWORK], IERR)
  COMPLEX, DIMENSION(:,:,:) :: X
  INTEGER :: IOPT, N1, N2, N3, LDX1, LDX2, LDY1, LDY2, LWORK, IERR
  INTEGER, DIMENSION(:) :: IFAC
  REAL :: SCALE
  REAL, DIMENSION(:) :: TRIGS, WORK
  REAL, DIMENSION(:,:,:) :: Y

  SUBROUTINE FFT3_64( IOPT, N1, [N2], [N3], [SCALE], X, [LDX1], LDX2, 
 *       Y, [LDY1], LDY2, TRIGS, IFAC, WORK, [LWORK], IERR)
  COMPLEX, DIMENSION(:,:,:) :: X
  INTEGER(8) :: IOPT, N1, N2, N3, LDX1, LDX2, LDY1, LDY2, LWORK, IERR
  INTEGER(8), DIMENSION(:) :: IFAC
  REAL :: SCALE
  REAL, DIMENSION(:) :: TRIGS, WORK
  REAL, DIMENSION(:,:,:) :: Y

C INTERFACE

#include <sunperf.h>

void cffts3(int iopt, int n1, int n2, int n3, float scale, complex *x, int ldx1, int ldx2, float *y, int ldy1, int ldy2, float *trigs, int *ifac, float *work, int lwork, int *ierr);

void cffts3_64(long iopt, long n1, long n2, long n3, float scale, complex *x, long ldx1, long ldx2, float *y, long ldy1, long ldy2, float *trigs, long *ifac, float *work, long lwork, long *ierr);

PURPOSE

cffts3 initializes the trigonometric weight and factor tables or computes the three-dimensional inverse Fast Fourier Transform of a three-dimensional complex array. .Ve

                      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
.Ve

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

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)

ARGUMENTS

• IOPT (input)
  Integer specifying the operation to be performed:

  IOPT = 0 computes the trigonometric weight table and factor table

  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)
  Real scalar by which transform results are scaled. Unchanged on exit.

• X (input)
  X is a complex array of dimensions (LDX1, LDX2, N3) that contains input data to be transformed.

• LDX1 (input)
  first dimension of X. LDX1 > = N1/2+1 Unchanged on exit.

• LDX2 (input)
  second dimension of X. LDX2 > = N2 Unchanged on exit.

• Y (output)
  Y is a 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. Otherwise, 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 = 2*LDX1 Else LDY1 > = 2*LDX1 and LDY1 is even 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)
  Real 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. Unchanged on exit.

• IFAC (input/output)
  Integer array of dimension at least 3*128 that contains the factors of N1, N2 and N3. 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)
  Real array of dimension at least (MAX(N,2*N2,2*N3) + 16*N3) * NCPUS 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 = N3 < 0

  -5 = (LDX1 < N1/2+1)

  -6 = (LDX2 < N2)

  -7 = LDY1 not equal 2*LDX1 when X and Y are same array

  -8 = (LDY1 < 2*LDX1) or (LDY1 is odd) when X and Y are not same array

  -9 = (LDY2 < N2) or (LDY2 not equal LDX2) when X and Y are same array

  -10 = (LWORK not equal 0) and ((LWORK < MAX(N,2*N2,2*N3) + 16*N3)*NCPUS)

  -11 = memory allocation failed

SEE ALSO

fft

CAUTIONS

This routine uses Y(N1+1:LDY1,:,:) as scratch space. Therefore, the original contents of this subarray will be lost upon returning from routine while subarray Y(1:N1,1:N2,1:N3) contains the transform results.