Three-Dimensional Fourier Synthesis

Calling Sequence

CALL RFFT3B	(PLACE, M, N, K, RX, LDX, LD2X, RY, LDY, LD2Y, RWSAVE, LWSAVE)
CALL DFFT3B	(PLACE, M, N, K, DX, LDX, LD2X, DY, LDY, LD2Y, DWSAVE, LWSAVE)
CALL CFFT3B	(M, N, K, CX, LDX, LD2X, CWSAVE, LWSAVE)
CALL ZFFT3B	(M, N, K, ZX, LDX, LD2X, ZWSAVE, LWSAVE)
void rfft3b	(char place, int m, int n, int k, float *rx, int ldx, int ld2x, float *ry, int ldy, int ld2y, float *wsave, int lwsave)
void dfft3b	(char place, int m, int n, int k, double *dx, int ldx, int ld2x, double *dy, int ldy, int ld2y, double *wsave, int lwsave)
void cfft3b	(char place, int m, int n, int k, complex *cx, int ldx, int ld2x, complex *cy, int ldy, int ld2y, complex *wsave, int lwsave)
void zfft3b	(char place, int m, int n, int k, doublecomplex *zx, int ldx, int ld2x, doublecomplex *zy, int ldy, int ld2y, doublecomplex *wsave, int lwsave)

Arguments

PLACE	Indicates whether the transform should be performed in place or out-of-place. The legal values for PLACE are listed below. Any values not listed below are illegal. `I' or `i' In-place. Input is supplied in xX and the transformed input is returned in xX. xY is not referenced. `O' or `o' Out-of-place. Input is supplied in xX and the transformed input is returned in xY.
M	Number of rows to be transformed. These subroutines are most efficient when M is a product of small primes. M 0.
N	Number of columns to be transformed. These subroutines are most efficient when N is a product of small primes. N 0.
K	Number of planes to be transformed. These subroutines are most efficient when K is a product of small primes. K 0.
xX	On entry, if the caller selected an in-place transform then xX is a three-dimensional array xX(LDX,N,K) that contains the sequences to be transformed. On exit, the transformed sequences.
LDX	Leading dimension of the array containing the data to be transformed. LDX M.
LD2X	Second dimension of the array containing the data to be transformed. LDX N.
xY	On entry, if the caller selected an out-of-place transform then xY is a three-dimensional array xY(LDY,N,K) that contains the sequences to be transformed. If the caller selected an in-place transform then this argument is never referenced.
LDY	Leading dimension of the array for an out-of-place transform. LDY M.
LD2Y	Second dimension of the array for an out-of-place transform. LDY N.
xWSAVE	On entry, an array with dimension of at least (M + N + MAX(M,N,K) + 45). The array must have been initialized by xFFT3I.
LWSAVE	Length of the WSAVE array.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LWSAVE, M, N, K

PARAMETER (K = 2)

PARAMETER (M = 2)

PARAMETER (N = 4)

PARAMETER (LWSAVE = 4 * (M + N + N) + 45)

C

INTEGER I, J, L

REAL PI, WSAVE(LWSAVE)

REAL X, Y

COMPLEX C(M,N,K)

C

EXTERNAL CFFT3B, CFFT3F, CFFT3I

INTRINSIC ACOS, CMPLX, COS, SIN

C

C Initialize the array C to a complex sequence.

C

PI = ACOS (-1.0)

DO 120, L = 1, K

DO 110, J = 1, N

DO 100, I = 1, M

X = SIN ((I - 1.0) * 2.0 * PI / N)

Y = COS ((J - 1.0) * 2.0 * PI / M)

C(I,J,L) = CMPLX (X, Y)

100 CONTINUE

110 CONTINUE

120 CONTINUE

C

PRINT 1000

DO 210, L = 1, K

PRINT 1010, L

DO 200, I = 1, M

PRINT 1020, (C(I,J,L), J = 1, N)

200 CONTINUE

210 CONTINUE

CALL CFFT3I (M, N, K, WSAVE)

CALL CFFT3F (M, N, K, C, M, N, WSAVE, LWSAVE)

PRINT 1030

DO 310, L = 1, K

PRINT 1010, L

DO 300, I = 1, M

PRINT 1020, (C(I,J,L), J = 1, N)

300 CONTINUE

310 CONTINUE

CALL CFFT3B (M, N, K, C, M, N, WSAVE, LWSAVE)

PRINT 1040

DO 410, L = 1, K

PRINT 1010, L

DO 400, I = 1, M

PRINT 1020, (C(I,J,L), J = 1, N)

400 CONTINUE

410 CONTINUE

C

1000 FORMAT (1X, 'Original Sequences:')

1010 FORMAT (1X, ' Plane', I2)

1020 FORMAT (5X, 100(F5.1' +',F5.1,'i '))

1030 FORMAT (/1X, 'Transformed Sequences:')

1040 FORMAT (/1X, 'Recovered Sequences:')

C

END

Sample Output

Original Sequences:

Plane 1

0.0 + 1.0i 0.0 + -1.0i 0.0 + 1.0i 0.0 + -1.0i

1.0 + 1.0i 1.0 + -1.0i 1.0 + 1.0i 1.0 + -1.0i

Plane 2

0.0 + 1.0i 0.0 + -1.0i 0.0 + 1.0i 0.0 + -1.0i

1.0 + 1.0i 1.0 + -1.0i 1.0 + 1.0i 1.0 + -1.0i

Transformed Sequences:

Plane 1

8.0 + 0.0i 0.0 + 0.0i 0.0 + 16.0i 0.0 + 0.0i

-8.0 + 0.0i 0.0 + 0.0i 0.0 + 0.0i 0.0 + 0.0i

Plane 2

0.0 + 0.0i 0.0 + 0.0i 0.0 + 0.0i 0.0 + 0.0i

0.0 + 0.0i 0.0 + 0.0i 0.0 + 0.0i 0.0 + 0.0i

Recovered Sequences:

Plane 1

0.0 + 16.0i 0.0 +-16.0i 0.0 + 16.0i 0.0 +-16.0i

16.0 + 16.0i 16.0 +-16.0i 16.0 + 16.0i 16.0 +-16.0i

Plane 2

0.0 + 16.0i 0.0 +-16.0i 0.0 + 16.0i 0.0 +-16.0i

16.0 + 16.0i 16.0 +-16.0i 16.0 + 16.0i 16.0 +-16.0i