SLATEC Routines --- CFFTF1 ---

*DECK CFFTF1
      SUBROUTINE CFFTF1 (N, C, CH, WA, IFAC)
C***BEGIN PROLOGUE  CFFTF1
C***PURPOSE  Compute the forward transform of a complex, periodic
C            sequence.
C***LIBRARY   SLATEC (FFTPACK)
C***CATEGORY  J1A2
C***TYPE      COMPLEX (RFFTF1-S, CFFTF1-C)
C***KEYWORDS  FFTPACK, FOURIER TRANSFORM
C***AUTHOR  Swarztrauber, P. N., (NCAR)
C***DESCRIPTION
C
C  Subroutine CFFTF1 computes the forward complex discrete Fourier
C  transform (the Fourier analysis).  Equivalently, CFFTF1 computes
C  the Fourier coefficients of a complex periodic sequence.
C  The transform is defined below at output parameter C.
C
C  The transform is not normalized.  To obtain a normalized transform
C  the output must be divided by N.  Otherwise a call of CFFTF1
C  followed by a call of CFFTB1 will multiply the sequence by N.
C
C  The arrays WA and IFAC which are used by subroutine CFFTB1 must be
C  initialized by calling subroutine CFFTI1 (N, WA, IFAC).
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  CH      a real work array of length at least 2*N
C
C  WA      a real work array which must be dimensioned at least 2*N.
C
C  IFAC    an integer work array which must be dimensioned at least 15.
C
C          The WA and IFAC arrays must be initialized by calling
C          subroutine CFFTI1 (N, WA, IFAC), and different WA and IFAC
C          arrays must be used for each different value of N.  This
C          initialization does not have to be repeated so long as N
C          remains unchanged.  Thus subsequent transforms can be
C          obtained faster than the first.  The same WA and IFAC arrays
C          can be used by CFFTF1 and CFFTB1.
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  NOTE:   WA and IFAC contain initialization calculations which must
C          not be destroyed between calls of subroutine CFFTF1 or CFFTB1
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  PASSF, PASSF2, PASSF3, PASSF4, PASSF5
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   881128  Modified by Dick Valent to meet prologue standards.
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900131  Routine changed from subsidiary to user-callable.  (WRB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  CFFTF1