Computes parameters needed by FFTRF and FFTRB.

Required Arguments

N — Length of the sequence to be transformed.   (Input)

WFFTR — Array of length 2N + 15 containing parameters needed by FFTRF and FFTRB.   (Output)

FORTRAN 90 Interface

Generic:          CALL FFTRI (N, WFFTR)

Specific:         The specific interface names are S_FFTRI and D_FFTRI.

FORTRAN 77 Interface

Single:            CALL FFTRI (N, WFFTR)

Double:          The double precision name is DFFTRI.

Description

The routine FFTRI initializes the routines FFTRF and FFTRB. An efficient way to make multiple calls for the same N to routine FFTRF or FFTRB, is to use routine FFTRI for initialization. (In this case, replace FFTRF or FFTRB with F2TRF or F2TRB, respectively.) The routine FFTRI is based on the routine RFFTI in FFTPACK. The package FFTPACK was developed by Paul Swarztrauber at the National Center for Atmospheric Research.

Comments

Different WFFTR arrays are needed for different values of N.

Example

In this example, we compute three distinct real FFTs by calling FFTRI once and then calling F2TRF three times.

 

      USE FFTRI_INT

      USE CONST_INT

      USE F2TRF_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

      INTEGER    N

      PARAMETER  (N=7)

!

      INTEGER    I, K, NOUT

      REAL       COEF(N), COS, FLOAT, TWOPI, WFFTR(29), SEQ(N)

      INTRINSIC  COS, FLOAT

!

      TWOPI = CONST('PI')

      TWOPI = 2* TWOPI

!                                 Get output unit number

      CALL UMACH (2, NOUT)

!                                 Set the work vector

      CALL FFTRI (N, WFFTR)

!

      DO 20  K=1, 3

!                                 This loop fills out the data vector

!                                 with a pure exponential signal

         DO 10  I=1, N

            SEQ(I) = COS(FLOAT(K*(I-1))*TWOPI/FLOAT(N))

   10 CONTINUE

!                                 Compute the Fourier transform of SEQ

         CALL F2TRF (N, SEQ, COEF, WFFTR)

!                                 Print results

         WRITE (NOUT,99998)

99998    FORMAT (/, 9X, 'INDEX', 5X, 'SEQ', 6X, 'COEF')

         WRITE (NOUT,99999) (I, SEQ(I), COEF(I), I=1,N)

99999    FORMAT (1X, I11, 5X, F5.2, 5X, F5.2)

!

   20 CONTINUE

      END

Output

 

INDEX     SEQ      COEF
  1      1.00      0.00
  2      0.62      3.50
  3     -0.22      0.00
  4     -0.90      0.00
  5     -0.90      0.00
  6     -0.22      0.00
  7      0.62      0.00

INDEX     SEQ      COEF
  1      1.00      0.00
  2     -0.22      0.00
  3     -0.90      0.00
  4      0.62      3.50
  5      0.62      0.00
  6     -0.90      0.00
  7     -0.22      0.00


INDEX     SEQ      COEF
1      1.00      0.00
2     -0.90      0.00
3      0.62      0.00
4     -0.22      0.00
5     -0.22      0.00
6      0.62      3.50
7     -0.90      0.00

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