*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