+++ /dev/null
-*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