rfftf1.f
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