Initialize Three-Dimensional Fourier Transform or Synthesis

Calling Sequence

CALL RFFT3I	(M, N, K, RWSAVE)
CALL DFFT3I	(M, N, K, DWSAVE)
CALL CFFT3I	(M, N, K, CWSAVE)
CALL ZFFT3I	(M, N, K, ZWSAVE)
void rfft3i	(int m, int n, int k, float *wsave)
void dfft3i	(int m, int n, int k, double *wsave)
void cfft3i	(int m, int n, int k, complex *wsave)
void zfft3i	(int m, int n, int k, doublecomplex *wsave)

Arguments

M	Number of rows to be transformed. M 0.
N	Number of columns to be transformed. N 0.
K	Number of planes to be transformed. K 0.
xWSAVE	On entry, an array with dimension of at least (M + N + MAX(M,N,K) + 45). The same work array can be used for both xFFT3F and xFFT3B as long as M, N, and K remain unchanged. Different xWSAVE arrays are required for different values of M, N, or K. This initialization does not have to be repeated between calls to xFFT3F or xFFT3B as long as M, N, K, and xWSAVE remain unchanged, thus subsequent transforms can be obtained faster than the first.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LWORK, M, N, K

PARAMETER (K = 2)

PARAMETER (M = 2)

PARAMETER (N = 4)

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

C

INTEGER I, J, L

REAL PI, WSAVE(LWORK)

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, LWORK)

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, LWORK)

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