DG01OD

Scrambled discrete Hartley transform of a real signal

Purpose

  To compute the (scrambled) discrete Hartley transform of
  a real signal.

      SUBROUTINE DG01OD( SCR, WGHT, N, A, W, INFO )
C     .. Scalar Arguments ..
      CHARACTER         SCR, WGHT
      INTEGER           INFO, N
C     .. Array Arguments ..
      DOUBLE PRECISION  A(*), W(*)

Mode Parameters

  SCR     CHARACTER*1
          Indicates whether the signal is scrambled on input or
          on output as follows:
          = 'N':  the signal is not scrambled at all;
          = 'I':  the input signal is bit-reversed;
          = 'O':  the output transform is bit-reversed.

  WGHT    CHARACTER*1
          Indicates whether the precomputed weights are available
          or not, as follows:
          = 'A':  available;
          = 'N':  not available.
          Note that if N > 1 and WGHT = 'N' on entry, then WGHT is
          set to 'A' on exit.

  N       (input) INTEGER
          Number of real samples. N must be a power of 2.
          N >= 0.

  A       (input/output) DOUBLE PRECISION array, dimension (N)
          On entry with SCR = 'N' or SCR = 'O', this array must
          contain the input signal.
          On entry with SCR = 'I', this array must contain the
          bit-reversed input signal.
          On exit with SCR = 'N' or SCR = 'I', this array contains
          the Hartley transform of the input signal.
          On exit with SCR = 'O', this array contains the
          bit-reversed Hartley transform.

  W       (input/output) DOUBLE PRECISION array,
                         dimension (N - LOG2(N))
          On entry with WGHT = 'A', this array must contain the long
          weight vector computed by a previous call of this routine
          with the same value of N. If WGHT = 'N', the contents of
          this array on entry is ignored.
          On exit, this array contains the long weight vector.

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value.

  This routine uses a Hartley butterfly algorithm as described
  in [1].

  [1] Van Loan, Charles.
      Computational frameworks for the fast Fourier transform.
      SIAM, 1992.

  The algorithm is backward stable and requires O(N log(N))
  floating point operations.

  None

Program Text

*     DG01OD EXAMPLE PROGRAM TEXT
*     Copyright (c) 2002-2017 NICONET e.V.
*
*     .. Parameters ..
      INTEGER          NIN, NOUT
      PARAMETER        ( NIN = 5, NOUT = 6 )
      INTEGER          NMAX
      PARAMETER        ( NMAX = 128 )
*     .. Local Scalars ..
      INTEGER          I, INFO, N
      CHARACTER*1      SCR, WGHT
*     .. Local Arrays ..
      DOUBLE PRECISION A(NMAX), W(NMAX)
*     .. External Subroutines ..
      EXTERNAL         DG01OD
*     .. Executable Statements ..
*
      WRITE ( NOUT, FMT = 99999 )
*     Skip the heading in the data file and read the data.
      READ ( NIN, FMT = '()' )
      READ ( NIN, FMT = * ) N, SCR, WGHT
      IF ( N.LT.0 .OR. N.GT.NMAX ) THEN
         WRITE ( NOUT, FMT = 99995 ) N
      ELSE
         READ ( NIN, FMT = * ) ( A(I), I = 1,N )
*        Compute the Hartley transform.
         CALL DG01OD( SCR, WGHT, N, A, W, INFO )
         IF ( INFO.NE.0 ) THEN
            WRITE ( NOUT, FMT = 99998 ) INFO
         ELSE
            WRITE ( NOUT, FMT = 99997 )
            DO 10 I = 1, N
               WRITE ( NOUT, FMT = 99996 ) I, A(I)
   10       CONTINUE
         END IF
      END IF
      STOP
*
99999 FORMAT (' DG01OD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from DG01OD = ',I2)
99997 FORMAT ('   Hartley transform ',//'   i    A(i)',/)
99996 FORMAT (I4,1X,F8.4)
99995 FORMAT (/' N is out of range.',/' N = ',I5)
      END

 DG01OD EXAMPLE
  16      N      N
 1.0
 2.0
 3.0
 4.0
 5.0
 6.0
 7.0
 8.0
 9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0

 DG01OD EXAMPLE PROGRAM RESULTS

   Hartley transform 

   i    A(i)

   1 136.0000
   2 -48.2187
   3 -27.3137
   4 -19.9728
   5 -16.0000
   6 -13.3454
   7 -11.3137
   8  -9.5913
   9  -8.0000
  10  -6.4087
  11  -4.6863
  12  -2.6546
  13   0.0000
  14   3.9728
  15  11.3137
  16  32.2187

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