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 routines 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.

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

Output

 

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)

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