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NAME
     dfft2b - compute a periodic sequence from its Fourier  coef-
     ficients.   The  xFFT operations are unnormalized, so a call
     of xFFT2F followed by a call of  xFFT2B  will  multiply  the
     input sequence by M*N.

SYNOPSIS
     SUBROUTINE RFFT2B (PLACE, M, N, RX, LDX,  RY,  LDY,  RWSAVE,
               LWSAVE)

     SUBROUTINE DFFT2B (PLACE, M, N, DX, LDX,  DY,  LDY,  DWSAVE,
               LWSAVE)

     SUBROUTINE CFFT2B (M, N, CX, LDX, RWSAVE, LWSAVE)

     SUBROUTINE ZFFT2B (M, N, ZX, LDX, DWSAVE, LWSAVE)



     #include <sunperf.h>

     void rfft2b (char place, int m, int n, float *rx,  int  ldx,
               float *ry, int ldy, float *wsave, int lwsave);

     void dfft2b (char place, int m, int n, double *ry, int  ldx,
               double *wsave, int lwsave);

     void cfft2b (int m, int n, complex  *cx,  int  ldx,  complex
               *wsave, int lwsave);

     void zfft2b (int m, int n, doublecomplex *zx, int ldx, doub-
               lecomplex *wsave, int lwsave);

ARGUMENTS
     PLACE     Determines whether  an  in-place  or  out-of-place
               transform  is  to  be performed.  'I' or 'i' if an
               in-place transform is to be performed, 'O' or  'o'
               if an out-of-place transform is to be performed.

     M         Number of rows to be transformed.   These  subrou-
               tines  are  most  efficient when M is a product of
               small primes.  M >= 0.

     N         Number of columns to be transformed.   These  sub-
               routines are most efficient when N is a product of
               small primes.  N >= 0.

     xX        On entry, a  two-dimensional  array  xX(M,N)  that
               contains the sequences to be transformed.

     LDX       Leading dimension of the array containing the data
               to be transformed.  LDX >= M.

     xY         On entry, the data to be transformed if PLACE  is
                'O'  or  'o', otherwise this argument is ignored.
                Undefined on exit.

     LDY        Leading dimension of  the  array  containing  the
                data   to  be  transformed  in  the  out-of-place
                transform case.  LDX >= M.

     xWSAVE    On entry, an array  with  dimension  of  at  least
               LWSAVE.   xWSAVE  must  have  been  initialized by
               xFFT2I.

     LWSAVE    Length of WSAVE.  LWSAVE >= (M+N+MAX(M,N)+45)  for
               real  inputs or LWSAVE >= (2*(M+N+MAX(M,N)+45) for
               complex inputs.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           LWSAVE, M, N
           PARAMETER        (LWSAVE = 4 * (M + N + K) + 45)
           PARAMETER        (M = 2)
           PARAMETER        (N = 4)
     C
           INTEGER           I, J
           REAL              PI, WSAVE(LWSAVE)
           REAL              X, Y
           COMPLEX           C(M,N)
     C
           EXTERNAL          CFFT2B, CFFT2F, CFFT2I
           INTRINSIC         ACOS, CMPLX, COS, SIN
     C
     C     Initialize the array C to a complex sequence.
     C
           PI = ACOS (-1.0)
           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) = CMPLX (X, Y)
       100   CONTINUE
       110 CONTINUE
     C
           PRINT 1000
           DO 200, I = 1, M
             PRINT 1010, (C(I,J), J = 1, N)
       200 CONTINUE
           CALL CFFT2I (M, N, WSAVE)
           CALL CFFT2F (M, N, C, M, WSAVE, LWSAVE)
           PRINT 1020
           DO 300, I = 1, M
             PRINT 1010, (C(I,J), J = 1, N)
       300 CONTINUE
           CALL CFFT2B (M, N, C, M, WSAVE, LWSAVE)
           PRINT 1030
           DO 400, I = 1, M
             PRINT 1010, (C(I,J), J = 1, N)
       400 CONTINUE
     C
      1000 FORMAT (1X, 'Original Sequences:')
      1010 FORMAT (1X, 100(F4.1' +',F4.1,'i  '))
      1020 FORMAT (1X, 'Transformed Sequences:')
      1030 FORMAT (1X, 'Recovered Sequences:')
     C
           END

SAMPLE OUTPUT
       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:
       4.0 + 0.0i   0.0 + 0.0i   0.0 + 8.0i   0.0 + 0.0i
      -4.0 + 0.0i   0.0 + 0.0i   0.0 + 0.0i   0.0 + 0.0i
      Recovered Sequences:
       0.0 + 8.0i   0.0 +-8.0i   0.0 + 8.0i   0.0 +-8.0i
       8.0 + 8.0i   8.0 +-8.0i   8.0 + 8.0i   8.0 +-8.0i

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