# cfftb.f

          SUBROUTINE CFFTB (N, C, WSAVE)
    C***BEGIN PROLOGUE  CFFTB
    ....
    ....
    Warning:   this routine is not intended to be user-callable.
    ....
    ....
    C***SUBSIDIARY
    C***PURPOSE  Compute the unnormalized inverse of CFFTF.
    C***LIBRARY   SLATEC (FFTPACK)
    C***CATEGORY  J1A2
    C***TYPE      COMPLEX (RFFTB-S, CFFTB-C)
    C***KEYWORDS  FFTPACK, FOURIER TRANSFORM
    C***AUTHOR  Swarztrauber, P. N., (NCAR)
    C***DESCRIPTION
    C
    C  ********************************************************************
    C  *   NOTICE   NOTICE   NOTICE   NOTICE   NOTICE   NOTICE   NOTICE   *
    C  ********************************************************************
    C  *                                                                  *
    C  *   This routine uses non-standard Fortran 77 constructs and will  *
    C  *   be removed from the library at a future date.  You are         *
    C  *   requested to use CFFTB1.                                       *
    C  *                                                                  *
    C  ********************************************************************
    C
    C  Subroutine CFFTB computes the backward complex discrete Fourier
    C  transform (the Fourier synthesis).  Equivalently, CFFTB computes
    C  a complex periodic sequence from its Fourier coefficients.
    C  The transform is defined below at output parameter C.
    C
    C  A call of CFFTF followed by a call of CFFTB will multiply the
    C  sequence by N.
    C
    C  The array WSAVE which is used by subroutine CFFTB must be
    C  initialized by calling subroutine CFFTI(N,WSAVE).
    C
    C  Input Parameters
    C
    C  N       the length of the complex sequence C.  The method is
    C          more efficient when N is the product of small primes.
    C
    C  C       a complex array of length N which contains the sequence
    C
    C  WSAVE   a real work array which must be dimensioned at least 4*N+15
    C          in the program that calls CFFTB.  The WSAVE array must be
    C          initialized by calling subroutine CFFTI(N,WSAVE), and a
    C          different WSAVE array must be used for each different
    C          value of N.  This initialization does not have to be
    C          repeated so long as N remains unchanged.  Thus subsequent
    C          transforms can be obtained faster than the first.
    C          The same WSAVE array can be used by CFFTF and CFFTB.
    C
    C  Output Parameters
    C
    C  C       For J=1,...,N
    C
    C              C(J)=the sum from K=1,...,N of
    C
    C                 C(K)*EXP(I*(J-1)*(K-1)*2*PI/N)
    C
    C                         where I=SQRT(-1)
    C
    C  WSAVE   contains initialization calculations which must not be
    C          destroyed between calls of subroutine CFFTF or CFFTB
    C
    C***REFERENCES  P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
    C                 Computations (G. Rodrigue, ed.), Academic Press,
    C                 1982, pp. 51-83.
    C***ROUTINES CALLED  CFFTB1
    C***REVISION HISTORY  (YYMMDD)
    C   790601  DATE WRITTEN
    C   830401  Modified to use SLATEC library source file format.
    C   860115  Modified by Ron Boisvert to adhere to Fortran 77 by
    C           changing dummy array size declarations (1) to (*).
    C   861211  REVISION DATE from Version 3.2
    C   881128  Modified by Dick Valent to meet prologue standards.
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   900131  Routine changed from user-callable to subsidiary
    C           because of non-standard Fortran 77 arguments in the
    C           call to CFFTB1.  (WRB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  CFFTB