*DECK CFFTB1 SUBROUTINE CFFTB1 (N, C, CH, WA, IFAC) C***BEGIN PROLOGUE CFFTB1 C***PURPOSE Compute the unnormalized inverse of CFFTF1. C***LIBRARY SLATEC (FFTPACK) C***CATEGORY J1A2 C***TYPE COMPLEX (RFFTB1-S, CFFTB1-C) C***KEYWORDS FFTPACK, FOURIER TRANSFORM C***AUTHOR Swarztrauber, P. N., (NCAR) C***DESCRIPTION C C Subroutine CFFTB1 computes the backward complex discrete Fourier C transform (the Fourier synthesis). Equivalently, CFFTB1 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 CFFTF1 followed by a call of CFFTB1 will multiply the C sequence by N. C C The arrays WA and IFAC which are used by subroutine CFFTB1 must be C initialized by calling subroutine CFFTI1 (N, WA, IFAC). 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 CH a real work array of length at least 2*N C C WA a real work array which must be dimensioned at least 2*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 CFFTI1 (N, WA, IFAC), and different WA and IFAC C arrays must be used for each different value of N. This C initialization does not have to be repeated so long as N C remains unchanged. Thus subsequent transforms can be C obtained faster than the first. The same WA and IFAC arrays C can be used by CFFTF1 and CFFTB1. 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 NOTE: WA and IFAC contain initialization calculations which must C not be destroyed between calls of subroutine CFFTF1 or CFFTB1 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 PASSB, PASSB2, PASSB3, PASSB4, PASSB5 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 CFFTB1 DIMENSION CH(*), C(*), WA(*), IFAC(*) C***FIRST EXECUTABLE STATEMENT CFFTB1 NF = IFAC(2) NA = 0 L1 = 1 IW = 1 DO 116 K1=1,NF IP = IFAC(K1+2) L2 = IP*L1 IDO = N/L2 IDOT = IDO+IDO IDL1 = IDOT*L1 IF (IP .NE. 4) GO TO 103 IX2 = IW+IDOT IX3 = IX2+IDOT IF (NA .NE. 0) GO TO 101 CALL PASSB4 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3)) GO TO 102 101 CALL PASSB4 (IDOT,L1,CH,C,WA(IW),WA(IX2),WA(IX3)) 102 NA = 1-NA GO TO 115 103 IF (IP .NE. 2) GO TO 106 IF (NA .NE. 0) GO TO 104 CALL PASSB2 (IDOT,L1,C,CH,WA(IW)) GO TO 105 104 CALL PASSB2 (IDOT,L1,CH,C,WA(IW)) 105 NA = 1-NA GO TO 115 106 IF (IP .NE. 3) GO TO 109 IX2 = IW+IDOT IF (NA .NE. 0) GO TO 107 CALL PASSB3 (IDOT,L1,C,CH,WA(IW),WA(IX2)) GO TO 108 107 CALL PASSB3 (IDOT,L1,CH,C,WA(IW),WA(IX2)) 108 NA = 1-NA GO TO 115 109 IF (IP .NE. 5) GO TO 112 IX2 = IW+IDOT IX3 = IX2+IDOT IX4 = IX3+IDOT IF (NA .NE. 0) GO TO 110 CALL PASSB5 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4)) GO TO 111 110 CALL PASSB5 (IDOT,L1,CH,C,WA(IW),WA(IX2),WA(IX3),WA(IX4)) 111 NA = 1-NA GO TO 115 112 IF (NA .NE. 0) GO TO 113 CALL PASSB (NAC,IDOT,IP,L1,IDL1,C,C,C,CH,CH,WA(IW)) GO TO 114 113 CALL PASSB (NAC,IDOT,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW)) 114 IF (NAC .NE. 0) NA = 1-NA 115 L1 = L2 IW = IW+(IP-1)*IDOT 116 CONTINUE IF (NA .EQ. 0) RETURN N2 = N+N DO 117 I=1,N2 C(I) = CH(I) 117 CONTINUE RETURN END