*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