+*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