*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