FFTCI
Computes parameters needed by FFTCF and FFTCB.
Required Arguments
N — Length of the sequence to be transformed. (Input)
WFFTC — Array of length 4N + 15 containing parameters needed by FFTCF and FFTCB. (Output)
FORTRAN 90 Interface
Generic: CALL FFTCI (N, WFFTC)
Specific: The specific interface names are S_FFTCI and D_FFTCI.
FORTRAN 77 Interface
Single: CALL FFTCI (N, WFFTC)
Double: The double precision name is DFFTCI.
Description
The routine FFTCI initializes the functions FFTCF and FFTCB. An efficient way to make multiple calls for the same N to IMSL routine FFTCF or FFTCB is to use routine FFTCI for initialization. (In this case, replace FFTCF or FFTCB with F2TCF or F2TCB, respectively.) The routine FFTCI is based on the routine CFFTI in FFTPACK. The package FFTPACK was developed by Paul Swarztrauber at the National Center for Atmospheric Research.
If the Intel® Math Kernel Library, Sun Performance Library or IBM Engineering and Scientific Subroutine Library is used, parameters computed by FFTCI are not used. In this case, there is no need to call FFTCI.
Comments
Different WFFTC arrays are needed for different values of N.
Example
In this example, we compute a two-dimensional complex FFT by making one call to FFTCI followed by 2N calls to F2TCF.
USE FFTCI_INT
USE CONST_INT
USE F2TCF_INT
USE UMACH_INT
IMPLICIT NONE
! SPECIFICATIONS FOR PARAMETERS
INTEGER N
PARAMETER (N=4)
!
INTEGER I, IR, IS, J, NOUT
REAL FLOAT, TWOPI, WFFTC(35), CPY(2*N)
COMPLEX CEXP, CMPLX, COEF(N,N), H, SEQ(N,N), TEMP
INTRINSIC CEXP, CMPLX, FLOAT
!
TWOPI = CONST('PI')
TWOPI = 2*TWOPI
IR = 3
IS = 1
! Here we compute e**(2*pi*i/N)
TEMP = CMPLX(0.0,TWOPI/FLOAT(N))
H = CEXP(TEMP)
! Fill SEQ with data
DO 20 I=1, N
DO 10 J=1, N
SEQ(I,J) = H**((I-1)*(IR-1)+(J-1)*(IS-1))
10 CONTINUE
20 CONTINUE
! Print out SEQ
! Get output unit number
CALL UMACH (2, NOUT)
WRITE (NOUT,99997)
DO 30 I=1, N
WRITE (NOUT,99998) (SEQ(I,J),J=1,N)
30 CONTINUE
! Set initialization vector
CALL FFTCI (N, WFFTC)
! Transform the columns of SEQ
DO 40 I=1, N
CALL F2TCF (N, SEQ(1:,I), COEF(1:,I), WFFTC, CPY)
40 CONTINUE
! Take transpose of the result
DO 60 I=1, N
DO 50 J=I + 1, N
TEMP = COEF(I,J)
COEF(I,J) = COEF(J,I)
COEF(J,I) = TEMP
50 CONTINUE
60 CONTINUE
! Transform the columns of this result
DO 70 I=1, N
CALL F2TCF (N, COEF(1:,I), SEQ(1:,I), WFFTC, CPY)
70 CONTINUE
! Take transpose of the result
DO 90 I=1, N
DO 80 J=I + 1, N
TEMP = SEQ(I,J)
SEQ(I,J) = SEQ(J,I)
SEQ(J,I) = TEMP
80 CONTINUE
90 CONTINUE
! Print results
WRITE (NOUT,99999)
DO 100 I=1, N
WRITE (NOUT,99998) (SEQ(I,J),J=1,N)
100 CONTINUE
!
99997 FORMAT (1X, 'The input matrix is below')
99998 FORMAT (1X, 4(' (',F5.2,',',F5.2,')'))
99999 FORMAT (/, 1X, 'Result of two-dimensional transform')
END
The input matrix is below
( 1.00, 0.00) ( 1.00, 0.00) ( 1.00, 0.00) ( 1.00, 0.00)
(-1.00, 0.00) (-1.00, 0.00) (-1.00, 0.00) (-1.00, 0.00)
( 1.00, 0.00) ( 1.00, 0.00) ( 1.00, 0.00) ( 1.00, 0.00)
(-1.00, 0.00) (-1.00, 0.00) (-1.00, 0.00) (-1.00, 0.00)
Result of two-dimensional transform
( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00)
( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00)
(16.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00)
( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00)
