*DECK RFFTF
SUBROUTINE RFFTF (N, R, WSAVE)
C***BEGIN PROLOGUE RFFTF
C***SUBSIDIARY
C***PURPOSE Compute the forward transform of a real, periodic sequence.
C***LIBRARY SLATEC (FFTPACK)
C***CATEGORY J1A1
C***TYPE SINGLE PRECISION (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 RFFTF1. *
C * *
C ********************************************************************
C
C Subroutine RFFTF computes the Fourier coefficients of a real
C periodic sequence (Fourier analysis). The transform is defined
C below at output parameter R.
C
C Input Arguments
C
C N the length of the array R to be transformed. The method
C is most efficient when N is a product of small primes.
C N may change so long as different work arrays are provided.
C
C R a real array of length N which contains the sequence
C to be transformed.
C
C WSAVE a work array which must be dimensioned at least 2*N+15
C in the program that calls RFFTF. The WSAVE array must be
C initialized by calling subroutine RFFTI, and a different
C WSAVE array must be used for each different value of N.
C This initialization does not have to be repeated so long as
C remains unchanged. Thus subsequent transforms can be
C obtained faster than the first. Moreover, the same WSAVE
C array can be used by RFFTF and RFFTB as long as N remains
C unchanged.
C
C Output Argument
C
C R R(1) = the sum from I=1 to I=N of R(I)
C
C If N is even set L = N/2; if N is odd set L = (N+1)/2
C
C then for K = 2,...,L
C
C R(2*K-2) = the sum from I = 1 to I = N of
C
C R(I)*COS((K-1)*(I-1)*2*PI/N)
C
C R(2*K-1) = the sum from I = 1 to I = N of
C
C -R(I)*SIN((K-1)*(I-1)*2*PI/N)
C
C If N is even
C
C R(N) = the sum from I = 1 to I = N of
C
C (-1)**(I-1)*R(I)
C
C Note: This transform is unnormalized since a call of RFFTF
C followed by a call of RFFTB will multiply the input
C sequence by N.
C
C WSAVE contains results which must not be destroyed between
C calls of RFFTF or RFFTB.
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 RFFTF1
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 RFFTF
DIMENSION R(*), WSAVE(*)
C***FIRST EXECUTABLE STATEMENT RFFTF
IF (N .EQ. 1) RETURN
CALL RFFTF1 (N,R,WSAVE,WSAVE(N+1),WSAVE(2*N+1))
RETURN
END