SLATEC Routines --- RFFTB1 ---

*DECK RFFTB1
      SUBROUTINE RFFTB1 (N, C, CH, WA, IFAC)
C***BEGIN PROLOGUE  RFFTB1
C***PURPOSE  Compute the backward fast Fourier transform of a real
C            coefficient array.
C***LIBRARY   SLATEC (FFTPACK)
C***CATEGORY  J1A1
C***TYPE      SINGLE PRECISION (RFFTB1-S, CFFTB1-C)
C***KEYWORDS  FFTPACK, FOURIER TRANSFORM
C***AUTHOR  Swarztrauber, P. N., (NCAR)
C***DESCRIPTION
C
C   Subroutine RFFTB1 computes the real periodic sequence from its
C   Fourier coefficients (Fourier synthesis).  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       For N even and for I = 1,...,N
C
C                C(I) = C(1)+(-1)**(I-1)*C(N)
C
C                     plus the sum from K=2 to K=N/2 of
C
C                      2.*C(2*K-2)*COS((K-1)*(I-1)*2*PI/N)
C
C                     -2.*C(2*K-1)*SIN((K-1)*(I-1)*2*PI/N)
C
C           For N odd and for I = 1,...,N
C
C                C(I) = C(1) plus the sum from K=2 to K=(N+1)/2 of
C
C                     2.*C(2*K-2)*COS((K-1)*(I-1)*2*PI/N)
C
C                    -2.*C(2*K-1)*SIN((K-1)*(I-1)*2*PI/N)
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  RADB2, RADB3, RADB4, RADB5, RADBG
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  RFFTB1