*DECK CFFTF
SUBROUTINE CFFTF (N, C, WSAVE)
C***BEGIN PROLOGUE CFFTF
C***SUBSIDIARY
C***PURPOSE Compute the forward transform of a complex, periodic
C sequence.
C***LIBRARY SLATEC (FFTPACK)
C***CATEGORY J1A2
C***TYPE COMPLEX (RFFTF-S, CFFTF-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 CFFTF1. *
C * *
C ********************************************************************
C
C Subroutine CFFTF computes the forward complex discrete Fourier
C transform (the Fourier analysis). Equivalently, CFFTF 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 CFFTF
C followed by a call of CFFTB will multiply the sequence by N.
C
C The array WSAVE which is used by subroutine CFFTF 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 CFFTF. 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 CFFTF1
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 CFFTF
COMPLEX C
DIMENSION C(*), WSAVE(*)
C***FIRST EXECUTABLE STATEMENT CFFTF
IF (N .EQ. 1) RETURN
IW1 = N+N+1
IW2 = IW1+N+N
CALL CFFTF1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2))
RETURN
END