*DECK CFFTB SUBROUTINE CFFTB (N, C, WSAVE) C***BEGIN PROLOGUE CFFTB C***SUBSIDIARY C***PURPOSE Compute the unnormalized inverse of CFFTF. C***LIBRARY SLATEC (FFTPACK) C***CATEGORY J1A2 C***TYPE COMPLEX (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 CFFTB1. * C * * C ******************************************************************** C C Subroutine CFFTB computes the backward complex discrete Fourier C transform (the Fourier synthesis). Equivalently, CFFTB computes C a complex periodic sequence from its Fourier coefficients. C The transform is defined below at output parameter C. C C A call of CFFTF followed by a call of CFFTB will multiply the C sequence by N. C C The array WSAVE which is used by subroutine CFFTB must be C initialized by calling subroutine CFFTI(N,WSAVE). C C Input Parameters C C N the length of the complex sequence C. The method is C more efficient when N is the product of small primes. C C C a complex array of length N which contains the sequence C C WSAVE a real work array which must be dimensioned at least 4*N+15 C in the program that calls CFFTB. The WSAVE array must be C initialized by calling subroutine CFFTI(N,WSAVE), and a C different WSAVE array must be used for each different C value of N. This initialization does not have to be C repeated so long as N remains unchanged. Thus subsequent C transforms can be obtained faster than the first. C The same WSAVE array can be used by CFFTF and CFFTB. C C Output Parameters C C C For J=1,...,N C C C(J)=the sum from K=1,...,N of C C C(K)*EXP(I*(J-1)*(K-1)*2*PI/N) C C where I=SQRT(-1) C C WSAVE contains initialization calculations which must not be C destroyed between calls of subroutine CFFTF or CFFTB 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 CFFTB1 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 CFFTB COMPLEX C DIMENSION C(*), WSAVE(*) C***FIRST EXECUTABLE STATEMENT CFFTB IF (N .EQ. 1) RETURN IW1 = N+N+1 IW2 = IW1+N+N CALL CFFTB1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2)) RETURN END