CFFTF(3)

SYNOPSIS
SUBROUTINE CFFTF (N, C, WSAVE)

NAME
cfftf - Compute the forward transform of a complex, periodic sequence.

LIBRARY
SLATEC (FFTPACK)

CATEGORY
J1A2

TYPE
COMPLEX (RFFTF-S, CFFTF-C)

KEYWORDS
FFTPACK, FOURIER TRANSFORM

AUTHOR
Swarztrauber, P. N., (NCAR)

DESCRIPTION
******************************************************************** * NOTICE NOTICE NOTICE NOTICE NOTICE NOTICE NOTICE * ******************************************************************** * * * This routine uses non-standard Fortran 77 constructs and will * * be removed from the library at a future date. You are * * requested to use CFFTF1. * * * ******************************************************************** Subroutine CFFTF computes the forward complex discrete Fourier transform (the Fourier analysis). Equivalently, CFFTF computes the Fourier coefficients of a complex periodic sequence. The transform is defined below at output parameter C. The transform is not normalized. To obtain a normalized transform the output must be divided by N. Otherwise a call of CFFTF followed by a call of CFFTB will multiply the sequence by N. The array WSAVE which is used by subroutine CFFTF must be initialized by calling subroutine CFFTI(N,WSAVE). Input Parameters N the length of the complex sequence C. The method is more efficient when N is the product of small primes. C a complex array of length N which contains the sequence WSAVE a real work array which must be dimensioned at least 4*N+15 in the program that calls CFFTF. The WSAVE array must be initialized by calling subroutine CFFTI(N,WSAVE), and a different WSAVE array must be used for each different value of N. This initialization does not have to be repeated so long as N remains unchanged. Thus subsequent transforms can be obtained faster than the first. The same WSAVE array can be used by CFFTF and CFFTB. Output Parameters C For J=1,...,N C(J)=the sum from K=1,...,N of C(K)*EXP(-I*(J-1)*(K-1)*2*PI/N) where I=SQRT(-1) WSAVE contains initialization calculations which must not be destroyed between calls of subroutine CFFTF or CFFTB

REFERENCES
P. N. Swarztrauber, Vectorizing the FFTs, in Parallel Computations (G. Rodrigue, ed.), Academic Press, 1982, pp. 51-83.

ROUTINES CALLED
CFFTF1

REVISION HISTORY (YYMMDD)
790601 DATE WRITTEN
830401 Modified to use SLATEC library source file format.
860115 Modified by Ron Boisvert to adhere to Fortran 77 by changing dummy array size declarations (1) to (*).
861211 REVISION DATE from Version 3.2
881128 Modified by Dick Valent to meet prologue standards.
891214 Prologue converted to Version 4.0 format. (BAB)
900131 Routine changed from user-callable to subsidiary because of non-standard Fortran 77 arguments in the call to CFFTB1. (WRB)
920501 Reformatted the REFERENCES section. (WRB)