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*DECK RFFTB
SUBROUTINE RFFTB (N, R, WSAVE)
C***BEGIN PROLOGUE RFFTB
C***SUBSIDIARY
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 (RFFTB-S, CFFTB-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 RFFTB1. *
C * *
C ********************************************************************
C
C Subroutine RFFTB computes the real periodic sequence from its
C Fourier coefficients (Fourier synthesis). 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 RFFTB. 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 For N even and for I = 1,...,N
C
C R(I) = R(1)+(-1)**(I-1)*R(N)
C
C plus the sum from K=2 to K=N/2 of
C
C 2.*R(2*K-2)*COS((K-1)*(I-1)*2*PI/N)
C
C -2.*R(2*K-1)*SIN((K-1)*(I-1)*2*PI/N)
C
C For N odd and for I = 1,...,N
C
C R(I) = R(1) plus the sum from K=2 to K=(N+1)/2 of
C
C 2.*R(2*K-2)*COS((K-1)*(I-1)*2*PI/N)
C
C -2.*R(2*K-1)*SIN((K-1)*(I-1)*2*PI/N)
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 RFFTB or RFFTF.
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 RFFTB1
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 RFFTB
DIMENSION R(*), WSAVE(*)
C***FIRST EXECUTABLE STATEMENT RFFTB
IF (N .EQ. 1) RETURN
CALL RFFTB1 (N,R,WSAVE,WSAVE(N+1),WSAVE(2*N+1))
RETURN
END
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