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- *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
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