*DECK RFFTB1
SUBROUTINE RFFTB1 (N, C, CH, WA, IFAC)
C***BEGIN PROLOGUE RFFTB1
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 (RFFTB1-S, CFFTB1-C)
C***KEYWORDS FFTPACK, FOURIER TRANSFORM
C***AUTHOR Swarztrauber, P. N., (NCAR)
C***DESCRIPTION
C
C Subroutine RFFTB1 computes the real periodic sequence from its
C Fourier coefficients (Fourier synthesis). The transform is defined
C below at output parameter C.
C
C The arrays WA and IFAC which are used by subroutine RFFTB1 must be
C initialized by calling subroutine RFFTI1.
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 C a real array of length N which contains the sequence
C to be transformed.
C
C CH a real work array of length at least N.
C
C WA a real work array which must be dimensioned at least 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 RFFTI1, and different WA and IFAC arrays must be
C used for each different value of N. This initialization
C does not have to be repeated so long as N remains unchanged.
C Thus subsequent transforms can be obtained faster than the
C first. The same WA and IFAC arrays can be used by RFFTF1
C and RFFTB1.
C
C Output Argument
C
C C For N even and for I = 1,...,N
C
C C(I) = C(1)+(-1)**(I-1)*C(N)
C
C plus the sum from K=2 to K=N/2 of
C
C 2.*C(2*K-2)*COS((K-1)*(I-1)*2*PI/N)
C
C -2.*C(2*K-1)*SIN((K-1)*(I-1)*2*PI/N)
C
C For N odd and for I = 1,...,N
C
C C(I) = C(1) plus the sum from K=2 to K=(N+1)/2 of
C
C 2.*C(2*K-2)*COS((K-1)*(I-1)*2*PI/N)
C
C -2.*C(2*K-1)*SIN((K-1)*(I-1)*2*PI/N)
C
C Notes: This transform is unnormalized since a call of RFFTF1
C followed by a call of RFFTB1 will multiply the input
C sequence by N.
C
C WA and IFAC contain initialization calculations which must
C not be destroyed between calls of subroutine RFFTF1 or
C RFFTB1.
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 RADB2, RADB3, RADB4, RADB5, RADBG
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 RFFTB1
DIMENSION CH(*), C(*), WA(*), IFAC(*)
C***FIRST EXECUTABLE STATEMENT RFFTB1
NF = IFAC(2)
NA = 0
L1 = 1
IW = 1
DO 116 K1=1,NF
IP = IFAC(K1+2)
L2 = IP*L1
IDO = N/L2
IDL1 = IDO*L1
IF (IP .NE. 4) GO TO 103
IX2 = IW+IDO
IX3 = IX2+IDO
IF (NA .NE. 0) GO TO 101
CALL RADB4 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3))
GO TO 102
101 CALL RADB4 (IDO,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 RADB2 (IDO,L1,C,CH,WA(IW))
GO TO 105
104 CALL RADB2 (IDO,L1,CH,C,WA(IW))
105 NA = 1-NA
GO TO 115
106 IF (IP .NE. 3) GO TO 109
IX2 = IW+IDO
IF (NA .NE. 0) GO TO 107
CALL RADB3 (IDO,L1,C,CH,WA(IW),WA(IX2))
GO TO 108
107 CALL RADB3 (IDO,L1,CH,C,WA(IW),WA(IX2))
108 NA = 1-NA
GO TO 115
109 IF (IP .NE. 5) GO TO 112
IX2 = IW+IDO
IX3 = IX2+IDO
IX4 = IX3+IDO
IF (NA .NE. 0) GO TO 110
CALL RADB5 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4))
GO TO 111
110 CALL RADB5 (IDO,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 RADBG (IDO,IP,L1,IDL1,C,C,C,CH,CH,WA(IW))
GO TO 114
113 CALL RADBG (IDO,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW))
114 IF (IDO .EQ. 1) NA = 1-NA
115 L1 = L2
IW = IW+(IP-1)*IDO
116 CONTINUE
IF (NA .EQ. 0) RETURN
DO 117 I=1,N
C(I) = CH(I)
117 CONTINUE
RETURN
END