SLATEC Routines --- RFFTF1 ---

*DECK RFFTF1
      SUBROUTINE RFFTF1 (N, C, CH, WA, IFAC)
C***BEGIN PROLOGUE  RFFTF1
C***PURPOSE  Compute the forward transform of a real, periodic sequence.
C***LIBRARY   SLATEC (FFTPACK)
C***CATEGORY  J1A1
C***TYPE      SINGLE PRECISION (RFFTF1-S, CFFTF1-C)
C***KEYWORDS  FFTPACK, FOURIER TRANSFORM
C***AUTHOR  Swarztrauber, P. N., (NCAR)
C***DESCRIPTION
C
C   Subroutine RFFTF1 computes the Fourier coefficients of a real
C   periodic sequence (Fourier analysis).  The transform is defined
C   below at output parameter C.
C
C   The arrays WA and IFAC which are used by subroutine RFFTB1 must be
C   initialized by calling subroutine RFFTI1.
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   C       a real array of length N which contains the sequence
C           to be transformed.
C
C   CH      a real work array of length at least N.
C
C   WA      a real work array which must be dimensioned at least N.
C
C   IFAC    an integer work array which must be dimensioned at least 15.
C
C           The WA and IFAC arrays must be initialized by calling
C           subroutine RFFTI1, and different WA and IFAC arrays must be
C           used for each different value of N.  This initialization
C           does not have to be repeated so long as N remains unchanged.
C           Thus subsequent transforms can be obtained faster than the
C           first.  The same WA and IFAC arrays can be used by RFFTF1
C           and RFFTB1.
C
C   Output Argument
C
C   C       C(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                C(2*K-2) = the sum from I = 1 to I = N of
C
C                     C(I)*COS((K-1)*(I-1)*2*PI/N)
C
C                C(2*K-1) = the sum from I = 1 to I = N of
C
C                    -C(I)*SIN((K-1)*(I-1)*2*PI/N)
C
C           If N is even
C
C                C(N) = the sum from I = 1 to I = N of
C
C                     (-1)**(I-1)*C(I)
C
C   Notes:  This transform is unnormalized since a call of RFFTF1
C           followed by a call of RFFTB1 will multiply the input
C           sequence by N.
C
C           WA and IFAC contain initialization calculations which must
C           not be destroyed between calls of subroutine RFFTF1 or
C           RFFTB1.
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  RADF2, RADF3, RADF4, RADF5, RADFG
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   881128  Modified by Dick Valent to meet prologue standards.
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900131  Routine changed from subsidiary to user-callable.  (WRB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  RFFTF1