C************************************************************************** C FFTPACK: Available at http://www.scd.ucar.edu/softlib/mathlib.html C C ***NOTE (C.T.) *** this is a subset of FFTPACK, which only includes C the routines for the complex FFT (forward & inverse). C C Modified: November 1999 by Arjan van Dijk to include IMPLICIT NONE and C to convert all routines to DOUBLE precision. C************************************************************************** C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C * * C * FFTPACK * C * * C * A package of Fortran subprograms for calculating * C * fast Fourier transforms for both complex and real * C * periodic sequences and certain other symmetric * C * sequences that are listed below * C * (Version 4.1 November 1988) * C * by * C * Paul Swarztrauber * C * of * C * The National Center for Atmospheric Research * C * Boulder, Colorado (80307) U.S.A. * C * which is sponsored by * C * the National Science Foundation * C * * C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C C Any source code available through this distribution interface at NCAR C is free of charge, but there is no guarantee. C C FFTPACK breaks the FORTRAN 77 ANSI Standard C by passing REAL arrays to subroutines and using the arrays within C the subroutines as DOUBLE PRECISION or other types. This infraction C may cause data alignment problems when the source code is compiled C and loaded in an executable. C**************************************************************************** C SUBROUTINE CFFTI(N,WSAVE) C C SUBROUTINE CFFTI INITIALIZES THE ARRAY WSAVE WHICH IS USED IN C BOTH CFFTF AND CFFTB. THE PRIME FACTORIZATION OF N TOGETHER WITH C A TABULATION OF THE TRIGONOMETRIC FUNCTIONS ARE COMPUTED AND C STORED IN WSAVE. C C INPUT PARAMETER C C N THE LENGTH OF THE SEQUENCE TO BE TRANSFORMED C C OUTPUT PARAMETER C C WSAVE A WORK ARRAY WHICH MUST BE DIMENSIONED AT LEAST 4*N+15 C THE SAME WORK ARRAY CAN BE USED FOR BOTH CFFTF AND CFFTB C AS LONG AS N REMAINS UNCHANGED. DIFFERENT WSAVE ARRAYS C ARE REQUIRED FOR DIFFERENT VALUES OF N. THE CONTENTS OF C WSAVE MUST NOT BE CHANGED BETWEEN CALLS OF CFFTF OR CFFTB. C SUBROUTINE CFFTI (N,WSAVE) IMPLICIT NONE INTEGER N,IW1,IW2 DOUBLE PRECISION WSAVE DIMENSION WSAVE(*) C IF (N .EQ. 1) RETURN IW1 = N+N+1 IW2 = IW1+N+N CALL CFFTI1 (N,WSAVE(IW1),WSAVE(IW2)) RETURN END C**************************************************************************** C SUBROUTINE CFFTF(N,C,WSAVE) C C SUBROUTINE CFFTF COMPUTES THE FORWARD COMPLEX DISCRETE FOURIER C TRANSFORM (THE FOURIER ANALYSIS). EQUIVALENTLY , CFFTF COMPUTES C THE FOURIER COEFFICIENTS OF A COMPLEX PERIODIC SEQUENCE. C THE TRANSFORM IS DEFINED BELOW AT OUTPUT PARAMETER C. C C THE TRANSFORM IS NOT NORMALIZED. TO OBTAIN A NORMALIZED TRANSFORM C THE OUTPUT MUST BE DIVIDED BY N. OTHERWISE A CALL OF CFFTF C FOLLOWED BY A CALL OF CFFTB WILL MULTIPLY THE SEQUENCE BY N. C C THE ARRAY WSAVE WHICH IS USED BY SUBROUTINE CFFTF MUST BE C INITIALIZED BY CALLING SUBROUTINE CFFTI(N,WSAVE). C C INPUT PARAMETERS C C C N THE LENGTH OF THE COMPLEX SEQUENCE C. THE METHOD IS C MORE EFFICIENT WHEN N IS THE PRODUCT OF SMALL PRIMES. N C C C A COMPLEX ARRAY OF LENGTH N WHICH CONTAINS THE SEQUENCE C C WSAVE A REAL WORK ARRAY WHICH MUST BE DIMENSIONED AT LEAST 4N+15 C IN THE PROGRAM THAT CALLS CFFTF. THE WSAVE ARRAY MUST BE C INITIALIZED BY CALLING SUBROUTINE CFFTI(N,WSAVE) AND A C DIFFERENT WSAVE ARRAY MUST BE USED FOR EACH DIFFERENT C VALUE OF N. THIS INITIALIZATION DOES NOT HAVE TO BE C REPEATED SO LONG AS N REMAINS UNCHANGED THUS SUBSEQUENT C TRANSFORMS CAN BE OBTAINED FASTER THAN THE FIRST. C THE SAME WSAVE ARRAY CAN BE USED BY CFFTF AND CFFTB. 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 WSAVE CONTAINS INITIALIZATION CALCULATIONS WHICH MUST NOT BE C DESTROYED BETWEEN CALLS OF SUBROUTINE CFFTF OR CFFTB C SUBROUTINE CFFTF (N,C,WSAVE) IMPLICIT NONE INTEGER N,IW1,IW2 DOUBLE PRECISION C,WSAVE DIMENSION C(*) ,WSAVE(*) C IF (N .EQ. 1) RETURN IW1 = N+N+1 IW2 = IW1+N+N CALL CFFTF1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2)) RETURN END C**************************************************************************** C SUBROUTINE CFFTB(N,C,WSAVE) C C SUBROUTINE CFFTB COMPUTES THE BACKWARD COMPLEX DISCRETE FOURIER C TRANSFORM (THE FOURIER SYNTHESIS). EQUIVALENTLY , CFFTB 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 CFFTF FOLLOWED BY A CALL OF CFFTB WILL MULTIPLY THE C SEQUENCE BY N. C C THE ARRAY WSAVE WHICH IS USED BY SUBROUTINE CFFTB MUST BE C INITIALIZED BY CALLING SUBROUTINE CFFTI(N,WSAVE). C C INPUT PARAMETERS C 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 WSAVE A REAL WORK ARRAY WHICH MUST BE DIMENSIONED AT LEAST 4N+15 C IN THE PROGRAM THAT CALLS CFFTB. THE WSAVE ARRAY MUST BE C INITIALIZED BY CALLING SUBROUTINE CFFTI(N,WSAVE) AND A C DIFFERENT WSAVE ARRAY MUST BE USED FOR EACH DIFFERENT C VALUE OF N. THIS INITIALIZATION DOES NOT HAVE TO BE C REPEATED SO LONG AS N REMAINS UNCHANGED THUS SUBSEQUENT C TRANSFORMS CAN BE OBTAINED FASTER THAN THE FIRST. C THE SAME WSAVE ARRAY CAN BE USED BY CFFTF AND CFFTB. 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 WSAVE CONTAINS INITIALIZATION CALCULATIONS WHICH MUST NOT BE C DESTROYED BETWEEN CALLS OF SUBROUTINE CFFTF OR CFFTB C SUBROUTINE CFFTB (N,C,WSAVE) IMPLICIT NONE INTEGER N,IW1,IW2 DOUBLE PRECISION C,WSAVE DIMENSION C(*) ,WSAVE(*) C IF (N .EQ. 1) RETURN IW1 = N+N+1 IW2 = IW1+N+N CALL CFFTB1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2)) RETURN END C**************************************************************************** SUBROUTINE CFFTI1 (N,WA,WIFAC) IMPLICIT NONE INTEGER N,NTRYH,NL,NF,J,NTRY,NQ,NR,IB,I,L1,K1,IP,LD,L2, & IDO,IDOT,IPM,I1,II DOUBLE PRECISION WA,TPI,ARGH,FI,ARGLD,ARG,WIFAC DIMENSION WA(*) ,WIFAC(*) ,NTRYH(4) DATA NTRYH(1),NTRYH(2),NTRYH(3),NTRYH(4)/3,4,2,5/ NL = N NF = 0 J = 0 101 J = J+1 IF (J-4) 102,102,103 102 NTRY = NTRYH(J) GO TO 104 103 NTRY = NTRY+2 104 NQ = NL/NTRY NR = NL-NTRY*NQ IF (NR) 101,105,101 105 NF = NF+1 WIFAC(NF+2) = DBLE(NTRY) NL = NQ IF (NTRY .NE. 2) GO TO 107 IF (NF .EQ. 1) GO TO 107 DO 106 I=2,NF IB = NF-I+2 WIFAC(IB+2) = WIFAC(IB+1) 106 CONTINUE WIFAC(3) = 2.D0 107 IF (NL .NE. 1) GO TO 104 WIFAC(1) = DBLE(N) WIFAC(2) = DBLE(NF) TPI = 2.D0*(4.D0*ATAN(1.D0)) ARGH = TPI/DBLE(N) I = 2 L1 = 1 DO 110 K1=1,NF IP = NINT(WIFAC(K1+2)) LD = 0 L2 = L1*IP IDO = N/L2 IDOT = IDO+IDO+2 IPM = IP-1 DO 109 J=1,IPM I1 = I WA(I-1) = 1.D0 WA(I) = 0.D0 LD = LD+L1 FI = 0.D0 ARGLD = DBLE(LD)*ARGH DO 108 II=4,IDOT,2 I = I+2 FI = FI+1.D0 ARG = FI*ARGLD WA(I-1) = COS(ARG) WA(I) = SIN(ARG) 108 CONTINUE IF (IP .LE. 5) GO TO 109 WA(I1-1) = WA(I-1) WA(I1) = WA(I) 109 CONTINUE L1 = L2 110 CONTINUE RETURN END C**************************************************************************** SUBROUTINE CFFTF1 (N,C,CH,WA,WIFAC) IMPLICIT NONE INTEGER N,NF,NA,L1,IW,K1,IP,L2,IDO,IDOT,IDL1,IX2,IX3,IX4,N2, & I,NAC DOUBLE PRECISION C,CH,WA,WIFAC DIMENSION CH(*) ,C(*) ,WA(*) ,WIFAC(*) NF = NINT(WIFAC(2)) NA = 0 L1 = 1 IW = 1 DO 116 K1=1,NF IP = NINT(WIFAC(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 PASSF4 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3)) GO TO 102 101 CALL PASSF4 (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 PASSF2 (IDOT,L1,C,CH,WA(IW)) GO TO 105 104 CALL PASSF2 (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 PASSF3 (IDOT,L1,C,CH,WA(IW),WA(IX2)) GO TO 108 107 CALL PASSF3 (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 PASSF5 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4)) GO TO 111 110 CALL PASSF5 (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 PASSF (NAC,IDOT,IP,L1,IDL1,C,C,C,CH,CH,WA(IW)) GO TO 114 113 CALL PASSF (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 C**************************************************************************** SUBROUTINE CFFTB1 (N,C,CH,WA,WIFAC) IMPLICIT NONE INTEGER N,NF,NA,L1,IW,K1,IP,L2,IDO,IDOT,IDL1,IX2,IX3,IX4,N2, & I,NAC DOUBLE PRECISION C,CH,WA,WIFAC DIMENSION CH(*) ,C(*) ,WA(*) ,WIFAC(*) NF = NINT(WIFAC(2)) NA = 0 L1 = 1 IW = 1 DO 116 K1=1,NF IP = NINT(WIFAC(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 C**************************************************************************** SUBROUTINE PASSB (NAC,IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA) IMPLICIT NONE INTEGER NAC,IDO,IP,L1,IDL1,IDOT,IPP2,IPPH,IDP,J,K,I,IDL,LC,L, & IK,IDLJ,JC,INC,IDIJ,IDJ DOUBLE PRECISION CC,C1,C2,CH,CH2,WA,WAR,WAI DIMENSION CH(IDO,L1,IP) ,CC(IDO,IP,L1) , 1 C1(IDO,L1,IP) ,WA(*) ,C2(IDL1,IP), 2 CH2(IDL1,IP) IDOT = IDO/2 IPP2 = IP+2 IPPH = (IP+1)/2 IDP = IP*IDO C IF (IDO .LT. L1) GO TO 106 DO 103 J=2,IPPH JC = IPP2-J DO 102 K=1,L1 DO 101 I=1,IDO CH(I,K,J) = CC(I,J,K)+CC(I,JC,K) CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K) 101 CONTINUE 102 CONTINUE 103 CONTINUE DO 105 K=1,L1 DO 104 I=1,IDO CH(I,K,1) = CC(I,1,K) 104 CONTINUE 105 CONTINUE GO TO 112 106 DO 109 J=2,IPPH JC = IPP2-J DO 108 I=1,IDO DO 107 K=1,L1 CH(I,K,J) = CC(I,J,K)+CC(I,JC,K) CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K) 107 CONTINUE 108 CONTINUE 109 CONTINUE DO 111 I=1,IDO DO 110 K=1,L1 CH(I,K,1) = CC(I,1,K) 110 CONTINUE 111 CONTINUE 112 IDL = 2-IDO INC = 0 DO 116 L=2,IPPH LC = IPP2-L IDL = IDL+IDO DO 113 IK=1,IDL1 C2(IK,L) = CH2(IK,1)+WA(IDL-1)*CH2(IK,2) C2(IK,LC) = WA(IDL)*CH2(IK,IP) 113 CONTINUE IDLJ = IDL INC = INC+IDO DO 115 J=3,IPPH JC = IPP2-J IDLJ = IDLJ+INC IF (IDLJ .GT. IDP) IDLJ = IDLJ-IDP WAR = WA(IDLJ-1) WAI = WA(IDLJ) DO 114 IK=1,IDL1 C2(IK,L) = C2(IK,L)+WAR*CH2(IK,J) C2(IK,LC) = C2(IK,LC)+WAI*CH2(IK,JC) 114 CONTINUE 115 CONTINUE 116 CONTINUE DO 118 J=2,IPPH DO 117 IK=1,IDL1 CH2(IK,1) = CH2(IK,1)+CH2(IK,J) 117 CONTINUE 118 CONTINUE DO 120 J=2,IPPH JC = IPP2-J DO 119 IK=2,IDL1,2 CH2(IK-1,J) = C2(IK-1,J)-C2(IK,JC) CH2(IK-1,JC) = C2(IK-1,J)+C2(IK,JC) CH2(IK,J) = C2(IK,J)+C2(IK-1,JC) CH2(IK,JC) = C2(IK,J)-C2(IK-1,JC) 119 CONTINUE 120 CONTINUE NAC = 1 IF (IDO .EQ. 2) RETURN NAC = 0 DO 121 IK=1,IDL1 C2(IK,1) = CH2(IK,1) 121 CONTINUE DO 123 J=2,IP DO 122 K=1,L1 C1(1,K,J) = CH(1,K,J) C1(2,K,J) = CH(2,K,J) 122 CONTINUE 123 CONTINUE IF (IDOT .GT. L1) GO TO 127 IDIJ = 0 DO 126 J=2,IP IDIJ = IDIJ+2 DO 125 I=4,IDO,2 IDIJ = IDIJ+2 DO 124 K=1,L1 C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)-WA(IDIJ)*CH(I,K,J) C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)+WA(IDIJ)*CH(I-1,K,J) 124 CONTINUE 125 CONTINUE 126 CONTINUE RETURN 127 IDJ = 2-IDO DO 130 J=2,IP IDJ = IDJ+IDO DO 129 K=1,L1 IDIJ = IDJ DO 128 I=4,IDO,2 IDIJ = IDIJ+2 C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)-WA(IDIJ)*CH(I,K,J) C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)+WA(IDIJ)*CH(I-1,K,J) 128 CONTINUE 129 CONTINUE 130 CONTINUE RETURN END C**************************************************************************** SUBROUTINE PASSB2 (IDO,L1,CC,CH,WA1) IMPLICIT NONE INTEGER IDO,L1,K,I DOUBLE PRECISION CC,CH,WA1,TR2,TI2 DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) , 1 WA1(1) IF (IDO .GT. 2) GO TO 102 DO 101 K=1,L1 CH(1,K,1) = CC(1,1,K)+CC(1,2,K) CH(1,K,2) = CC(1,1,K)-CC(1,2,K) CH(2,K,1) = CC(2,1,K)+CC(2,2,K) CH(2,K,2) = CC(2,1,K)-CC(2,2,K) 101 CONTINUE RETURN 102 DO 104 K=1,L1 DO 103 I=2,IDO,2 CH(I-1,K,1) = CC(I-1,1,K)+CC(I-1,2,K) TR2 = CC(I-1,1,K)-CC(I-1,2,K) CH(I,K,1) = CC(I,1,K)+CC(I,2,K) TI2 = CC(I,1,K)-CC(I,2,K) CH(I,K,2) = WA1(I-1)*TI2+WA1(I)*TR2 CH(I-1,K,2) = WA1(I-1)*TR2-WA1(I)*TI2 103 CONTINUE 104 CONTINUE RETURN END C**************************************************************************** SUBROUTINE PASSB3 (IDO,L1,CC,CH,WA1,WA2) IMPLICIT NONE INTEGER IDO,L1,K,I DOUBLE PRECISION CC,CH,WA1,WA2,TAUR,TAUI,TR2,CR2,TI2,CI2,CR3,CI3, & DR2,DR3,DI2,DI3 DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) , 1 WA1(*) ,WA2(*) DATA TAUR,TAUI /-.5D0,.866025403784439D0/ IF (IDO .NE. 2) GO TO 102 DO 101 K=1,L1 TR2 = CC(1,2,K)+CC(1,3,K) CR2 = CC(1,1,K)+TAUR*TR2 CH(1,K,1) = CC(1,1,K)+TR2 TI2 = CC(2,2,K)+CC(2,3,K) CI2 = CC(2,1,K)+TAUR*TI2 CH(2,K,1) = CC(2,1,K)+TI2 CR3 = TAUI*(CC(1,2,K)-CC(1,3,K)) CI3 = TAUI*(CC(2,2,K)-CC(2,3,K)) CH(1,K,2) = CR2-CI3 CH(1,K,3) = CR2+CI3 CH(2,K,2) = CI2+CR3 CH(2,K,3) = CI2-CR3 101 CONTINUE RETURN 102 DO 104 K=1,L1 DO 103 I=2,IDO,2 TR2 = CC(I-1,2,K)+CC(I-1,3,K) CR2 = CC(I-1,1,K)+TAUR*TR2 CH(I-1,K,1) = CC(I-1,1,K)+TR2 TI2 = CC(I,2,K)+CC(I,3,K) CI2 = CC(I,1,K)+TAUR*TI2 CH(I,K,1) = CC(I,1,K)+TI2 CR3 = TAUI*(CC(I-1,2,K)-CC(I-1,3,K)) CI3 = TAUI*(CC(I,2,K)-CC(I,3,K)) DR2 = CR2-CI3 DR3 = CR2+CI3 DI2 = CI2+CR3 DI3 = CI2-CR3 CH(I,K,2) = WA1(I-1)*DI2+WA1(I)*DR2 CH(I-1,K,2) = WA1(I-1)*DR2-WA1(I)*DI2 CH(I,K,3) = WA2(I-1)*DI3+WA2(I)*DR3 CH(I-1,K,3) = WA2(I-1)*DR3-WA2(I)*DI3 103 CONTINUE 104 CONTINUE RETURN END C**************************************************************************** SUBROUTINE PASSB4 (IDO,L1,CC,CH,WA1,WA2,WA3) IMPLICIT NONE INTEGER IDO,L1,K,I DOUBLE PRECISION CC,CH,WA1,WA2,WA3,TI1,TI2,TI3,TI4,TR1,TR2,TR3, & TR4,CR3,CR2,CI3,CR4,CI4,CI2 DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) , 1 WA1(*) ,WA2(*) ,WA3(*) IF (IDO .NE. 2) GO TO 102 DO 101 K=1,L1 TI1 = CC(2,1,K)-CC(2,3,K) TI2 = CC(2,1,K)+CC(2,3,K) TR4 = CC(2,4,K)-CC(2,2,K) TI3 = CC(2,2,K)+CC(2,4,K) TR1 = CC(1,1,K)-CC(1,3,K) TR2 = CC(1,1,K)+CC(1,3,K) TI4 = CC(1,2,K)-CC(1,4,K) TR3 = CC(1,2,K)+CC(1,4,K) CH(1,K,1) = TR2+TR3 CH(1,K,3) = TR2-TR3 CH(2,K,1) = TI2+TI3 CH(2,K,3) = TI2-TI3 CH(1,K,2) = TR1+TR4 CH(1,K,4) = TR1-TR4 CH(2,K,2) = TI1+TI4 CH(2,K,4) = TI1-TI4 101 CONTINUE RETURN 102 DO 104 K=1,L1 DO 103 I=2,IDO,2 TI1 = CC(I,1,K)-CC(I,3,K) TI2 = CC(I,1,K)+CC(I,3,K) TI3 = CC(I,2,K)+CC(I,4,K) TR4 = CC(I,4,K)-CC(I,2,K) TR1 = CC(I-1,1,K)-CC(I-1,3,K) TR2 = CC(I-1,1,K)+CC(I-1,3,K) TI4 = CC(I-1,2,K)-CC(I-1,4,K) TR3 = CC(I-1,2,K)+CC(I-1,4,K) CH(I-1,K,1) = TR2+TR3 CR3 = TR2-TR3 CH(I,K,1) = TI2+TI3 CI3 = TI2-TI3 CR2 = TR1+TR4 CR4 = TR1-TR4 CI2 = TI1+TI4 CI4 = TI1-TI4 CH(I-1,K,2) = WA1(I-1)*CR2-WA1(I)*CI2 CH(I,K,2) = WA1(I-1)*CI2+WA1(I)*CR2 CH(I-1,K,3) = WA2(I-1)*CR3-WA2(I)*CI3 CH(I,K,3) = WA2(I-1)*CI3+WA2(I)*CR3 CH(I-1,K,4) = WA3(I-1)*CR4-WA3(I)*CI4 CH(I,K,4) = WA3(I-1)*CI4+WA3(I)*CR4 103 CONTINUE 104 CONTINUE RETURN END C**************************************************************************** SUBROUTINE PASSB5 (IDO,L1,CC,CH,WA1,WA2,WA3,WA4) IMPLICIT NONE INTEGER IDO,L1,K,I DOUBLE PRECISION CC,CH,WA1,WA2,WA3,WA4,TR11,TI11,TR12,TI12, & TI2,TI3,TI4,TI5,TR2,TR3,TR4,TR5,CR2,CI2,CR3,CI3,CR4,CI4,CR5,CI5, & DR3,DI3,DR4,DI4,DR5,DI5,DR2,DI2 DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) , 1 WA1(*) ,WA2(*) ,WA3(*) ,WA4(*) DATA TR11,TI11,TR12,TI12 /.309016994374947D0,.951056516295154D0, 1-.809016994374947D0,.587785252292473D0/ IF (IDO .NE. 2) GO TO 102 DO 101 K=1,L1 TI5 = CC(2,2,K)-CC(2,5,K) TI2 = CC(2,2,K)+CC(2,5,K) TI4 = CC(2,3,K)-CC(2,4,K) TI3 = CC(2,3,K)+CC(2,4,K) TR5 = CC(1,2,K)-CC(1,5,K) TR2 = CC(1,2,K)+CC(1,5,K) TR4 = CC(1,3,K)-CC(1,4,K) TR3 = CC(1,3,K)+CC(1,4,K) CH(1,K,1) = CC(1,1,K)+TR2+TR3 CH(2,K,1) = CC(2,1,K)+TI2+TI3 CR2 = CC(1,1,K)+TR11*TR2+TR12*TR3 CI2 = CC(2,1,K)+TR11*TI2+TR12*TI3 CR3 = CC(1,1,K)+TR12*TR2+TR11*TR3 CI3 = CC(2,1,K)+TR12*TI2+TR11*TI3 CR5 = TI11*TR5+TI12*TR4 CI5 = TI11*TI5+TI12*TI4 CR4 = TI12*TR5-TI11*TR4 CI4 = TI12*TI5-TI11*TI4 CH(1,K,2) = CR2-CI5 CH(1,K,5) = CR2+CI5 CH(2,K,2) = CI2+CR5 CH(2,K,3) = CI3+CR4 CH(1,K,3) = CR3-CI4 CH(1,K,4) = CR3+CI4 CH(2,K,4) = CI3-CR4 CH(2,K,5) = CI2-CR5 101 CONTINUE RETURN 102 DO 104 K=1,L1 DO 103 I=2,IDO,2 TI5 = CC(I,2,K)-CC(I,5,K) TI2 = CC(I,2,K)+CC(I,5,K) TI4 = CC(I,3,K)-CC(I,4,K) TI3 = CC(I,3,K)+CC(I,4,K) TR5 = CC(I-1,2,K)-CC(I-1,5,K) TR2 = CC(I-1,2,K)+CC(I-1,5,K) TR4 = CC(I-1,3,K)-CC(I-1,4,K) TR3 = CC(I-1,3,K)+CC(I-1,4,K) CH(I-1,K,1) = CC(I-1,1,K)+TR2+TR3 CH(I,K,1) = CC(I,1,K)+TI2+TI3 CR2 = CC(I-1,1,K)+TR11*TR2+TR12*TR3 CI2 = CC(I,1,K)+TR11*TI2+TR12*TI3 CR3 = CC(I-1,1,K)+TR12*TR2+TR11*TR3 CI3 = CC(I,1,K)+TR12*TI2+TR11*TI3 CR5 = TI11*TR5+TI12*TR4 CI5 = TI11*TI5+TI12*TI4 CR4 = TI12*TR5-TI11*TR4 CI4 = TI12*TI5-TI11*TI4 DR3 = CR3-CI4 DR4 = CR3+CI4 DI3 = CI3+CR4 DI4 = CI3-CR4 DR5 = CR2+CI5 DR2 = CR2-CI5 DI5 = CI2-CR5 DI2 = CI2+CR5 CH(I-1,K,2) = WA1(I-1)*DR2-WA1(I)*DI2 CH(I,K,2) = WA1(I-1)*DI2+WA1(I)*DR2 CH(I-1,K,3) = WA2(I-1)*DR3-WA2(I)*DI3 CH(I,K,3) = WA2(I-1)*DI3+WA2(I)*DR3 CH(I-1,K,4) = WA3(I-1)*DR4-WA3(I)*DI4 CH(I,K,4) = WA3(I-1)*DI4+WA3(I)*DR4 CH(I-1,K,5) = WA4(I-1)*DR5-WA4(I)*DI5 CH(I,K,5) = WA4(I-1)*DI5+WA4(I)*DR5 103 CONTINUE 104 CONTINUE RETURN END C**************************************************************************** SUBROUTINE PASSF (NAC,IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA) IMPLICIT NONE INTEGER NAC,IDO,IP,L1,IDL1,IDOT,IPP2,IPPH,IDP,J,JC,K,I,IDL, & INC,L,LC,IK,IDLJ,IDIJ,IDJ DOUBLE PRECISION CC,C1,C2,CH,CH2,WA,WAR,WAI DIMENSION CH(IDO,L1,IP) ,CC(IDO,IP,L1) , 1 C1(IDO,L1,IP) ,WA(*) ,C2(IDL1,IP), 2 CH2(IDL1,IP) IDOT = IDO/2 IPP2 = IP+2 IPPH = (IP+1)/2 IDP = IP*IDO C IF (IDO .LT. L1) GO TO 106 DO 103 J=2,IPPH JC = IPP2-J DO 102 K=1,L1 DO 101 I=1,IDO CH(I,K,J) = CC(I,J,K)+CC(I,JC,K) CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K) 101 CONTINUE 102 CONTINUE 103 CONTINUE DO 105 K=1,L1 DO 104 I=1,IDO CH(I,K,1) = CC(I,1,K) 104 CONTINUE 105 CONTINUE GO TO 112 106 DO 109 J=2,IPPH JC = IPP2-J DO 108 I=1,IDO DO 107 K=1,L1 CH(I,K,J) = CC(I,J,K)+CC(I,JC,K) CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K) 107 CONTINUE 108 CONTINUE 109 CONTINUE DO 111 I=1,IDO DO 110 K=1,L1 CH(I,K,1) = CC(I,1,K) 110 CONTINUE 111 CONTINUE 112 IDL = 2-IDO INC = 0 DO 116 L=2,IPPH LC = IPP2-L IDL = IDL+IDO DO 113 IK=1,IDL1 C2(IK,L) = CH2(IK,1)+WA(IDL-1)*CH2(IK,2) C2(IK,LC) = -WA(IDL)*CH2(IK,IP) 113 CONTINUE IDLJ = IDL INC = INC+IDO DO 115 J=3,IPPH JC = IPP2-J IDLJ = IDLJ+INC IF (IDLJ .GT. IDP) IDLJ = IDLJ-IDP WAR = WA(IDLJ-1) WAI = WA(IDLJ) DO 114 IK=1,IDL1 C2(IK,L) = C2(IK,L)+WAR*CH2(IK,J) C2(IK,LC) = C2(IK,LC)-WAI*CH2(IK,JC) 114 CONTINUE 115 CONTINUE 116 CONTINUE DO 118 J=2,IPPH DO 117 IK=1,IDL1 CH2(IK,1) = CH2(IK,1)+CH2(IK,J) 117 CONTINUE 118 CONTINUE DO 120 J=2,IPPH JC = IPP2-J DO 119 IK=2,IDL1,2 CH2(IK-1,J) = C2(IK-1,J)-C2(IK,JC) CH2(IK-1,JC) = C2(IK-1,J)+C2(IK,JC) CH2(IK,J) = C2(IK,J)+C2(IK-1,JC) CH2(IK,JC) = C2(IK,J)-C2(IK-1,JC) 119 CONTINUE 120 CONTINUE NAC = 1 IF (IDO .EQ. 2) RETURN NAC = 0 DO 121 IK=1,IDL1 C2(IK,1) = CH2(IK,1) 121 CONTINUE DO 123 J=2,IP DO 122 K=1,L1 C1(1,K,J) = CH(1,K,J) C1(2,K,J) = CH(2,K,J) 122 CONTINUE 123 CONTINUE IF (IDOT .GT. L1) GO TO 127 IDIJ = 0 DO 126 J=2,IP IDIJ = IDIJ+2 DO 125 I=4,IDO,2 IDIJ = IDIJ+2 DO 124 K=1,L1 C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)+WA(IDIJ)*CH(I,K,J) C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)-WA(IDIJ)*CH(I-1,K,J) 124 CONTINUE 125 CONTINUE 126 CONTINUE RETURN 127 IDJ = 2-IDO DO 130 J=2,IP IDJ = IDJ+IDO DO 129 K=1,L1 IDIJ = IDJ DO 128 I=4,IDO,2 IDIJ = IDIJ+2 C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)+WA(IDIJ)*CH(I,K,J) C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)-WA(IDIJ)*CH(I-1,K,J) 128 CONTINUE 129 CONTINUE 130 CONTINUE RETURN END C**************************************************************************** SUBROUTINE PASSF2 (IDO,L1,CC,CH,WA1) IMPLICIT NONE INTEGER IDO,L1,K,I DOUBLE PRECISION CC,CH,WA1,TR2,TI2 DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) , 1 WA1(*) IF (IDO .GT. 2) GO TO 102 DO 101 K=1,L1 CH(1,K,1) = CC(1,1,K)+CC(1,2,K) CH(1,K,2) = CC(1,1,K)-CC(1,2,K) CH(2,K,1) = CC(2,1,K)+CC(2,2,K) CH(2,K,2) = CC(2,1,K)-CC(2,2,K) 101 CONTINUE RETURN 102 DO 104 K=1,L1 DO 103 I=2,IDO,2 CH(I-1,K,1) = CC(I-1,1,K)+CC(I-1,2,K) TR2 = CC(I-1,1,K)-CC(I-1,2,K) CH(I,K,1) = CC(I,1,K)+CC(I,2,K) TI2 = CC(I,1,K)-CC(I,2,K) CH(I,K,2) = WA1(I-1)*TI2-WA1(I)*TR2 CH(I-1,K,2) = WA1(I-1)*TR2+WA1(I)*TI2 103 CONTINUE 104 CONTINUE RETURN END C**************************************************************************** SUBROUTINE PASSF3 (IDO,L1,CC,CH,WA1,WA2) IMPLICIT NONE INTEGER IDO,L1,K,I DOUBLE PRECISION CC,CH,WA1,WA2,TAUR,TAUI,TR2,CR2,TI2,CI2,CR3,CI3, & DR2,DR3,DI2,DI3 DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) , 1 WA1(*) ,WA2(*) DATA TAUR,TAUI /-.5D0,-.866025403784439D0/ IF (IDO .NE. 2) GO TO 102 DO 101 K=1,L1 TR2 = CC(1,2,K)+CC(1,3,K) CR2 = CC(1,1,K)+TAUR*TR2 CH(1,K,1) = CC(1,1,K)+TR2 TI2 = CC(2,2,K)+CC(2,3,K) CI2 = CC(2,1,K)+TAUR*TI2 CH(2,K,1) = CC(2,1,K)+TI2 CR3 = TAUI*(CC(1,2,K)-CC(1,3,K)) CI3 = TAUI*(CC(2,2,K)-CC(2,3,K)) CH(1,K,2) = CR2-CI3 CH(1,K,3) = CR2+CI3 CH(2,K,2) = CI2+CR3 CH(2,K,3) = CI2-CR3 101 CONTINUE RETURN 102 DO 104 K=1,L1 DO 103 I=2,IDO,2 TR2 = CC(I-1,2,K)+CC(I-1,3,K) CR2 = CC(I-1,1,K)+TAUR*TR2 CH(I-1,K,1) = CC(I-1,1,K)+TR2 TI2 = CC(I,2,K)+CC(I,3,K) CI2 = CC(I,1,K)+TAUR*TI2 CH(I,K,1) = CC(I,1,K)+TI2 CR3 = TAUI*(CC(I-1,2,K)-CC(I-1,3,K)) CI3 = TAUI*(CC(I,2,K)-CC(I,3,K)) DR2 = CR2-CI3 DR3 = CR2+CI3 DI2 = CI2+CR3 DI3 = CI2-CR3 CH(I,K,2) = WA1(I-1)*DI2-WA1(I)*DR2 CH(I-1,K,2) = WA1(I-1)*DR2+WA1(I)*DI2 CH(I,K,3) = WA2(I-1)*DI3-WA2(I)*DR3 CH(I-1,K,3) = WA2(I-1)*DR3+WA2(I)*DI3 103 CONTINUE 104 CONTINUE RETURN END C**************************************************************************** SUBROUTINE PASSF4 (IDO,L1,CC,CH,WA1,WA2,WA3) IMPLICIT NONE INTEGER IDO,L1,K,I DOUBLE PRECISION CC,CH,WA1,WA2,WA3,TI1,TI2,TI3,TI4,TR1,TR2,TR3, & TR4,CR2,CR3,CR4,CI2,CI3,CI4 DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) , 1 WA1(*) ,WA2(*) ,WA3(*) IF (IDO .NE. 2) GO TO 102 DO 101 K=1,L1 TI1 = CC(2,1,K)-CC(2,3,K) TI2 = CC(2,1,K)+CC(2,3,K) TR4 = CC(2,2,K)-CC(2,4,K) TI3 = CC(2,2,K)+CC(2,4,K) TR1 = CC(1,1,K)-CC(1,3,K) TR2 = CC(1,1,K)+CC(1,3,K) TI4 = CC(1,4,K)-CC(1,2,K) TR3 = CC(1,2,K)+CC(1,4,K) CH(1,K,1) = TR2+TR3 CH(1,K,3) = TR2-TR3 CH(2,K,1) = TI2+TI3 CH(2,K,3) = TI2-TI3 CH(1,K,2) = TR1+TR4 CH(1,K,4) = TR1-TR4 CH(2,K,2) = TI1+TI4 CH(2,K,4) = TI1-TI4 101 CONTINUE RETURN 102 DO 104 K=1,L1 DO 103 I=2,IDO,2 TI1 = CC(I,1,K)-CC(I,3,K) TI2 = CC(I,1,K)+CC(I,3,K) TI3 = CC(I,2,K)+CC(I,4,K) TR4 = CC(I,2,K)-CC(I,4,K) TR1 = CC(I-1,1,K)-CC(I-1,3,K) TR2 = CC(I-1,1,K)+CC(I-1,3,K) TI4 = CC(I-1,4,K)-CC(I-1,2,K) TR3 = CC(I-1,2,K)+CC(I-1,4,K) CH(I-1,K,1) = TR2+TR3 CR3 = TR2-TR3 CH(I,K,1) = TI2+TI3 CI3 = TI2-TI3 CR2 = TR1+TR4 CR4 = TR1-TR4 CI2 = TI1+TI4 CI4 = TI1-TI4 CH(I-1,K,2) = WA1(I-1)*CR2+WA1(I)*CI2 CH(I,K,2) = WA1(I-1)*CI2-WA1(I)*CR2 CH(I-1,K,3) = WA2(I-1)*CR3+WA2(I)*CI3 CH(I,K,3) = WA2(I-1)*CI3-WA2(I)*CR3 CH(I-1,K,4) = WA3(I-1)*CR4+WA3(I)*CI4 CH(I,K,4) = WA3(I-1)*CI4-WA3(I)*CR4 103 CONTINUE 104 CONTINUE RETURN END C**************************************************************************** SUBROUTINE PASSF5 (IDO,L1,CC,CH,WA1,WA2,WA3,WA4) IMPLICIT NONE INTEGER IDO,L1,K,I DOUBLE PRECISION CC,CH,WA1,WA2,WA3,WA4,TR11,TI11,TR12,TI12, & TI2,TI3,TI4,TI5,TR2,TR3,TR4,TR5,CI2,CI3,CI4,CI5,CR2,CR3,CR4, & CR5,DI2,DI3,DI4,DI5,DR2,DR3,DR4,DR5 DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) , 1 WA1(*) ,WA2(*) ,WA3(*) ,WA4(*) DATA TR11,TI11,TR12,TI12 /.309016994374947D0,-.951056516295154D0, 1-.809016994374947D0,-.587785252292473D0/ IF (IDO .NE. 2) GO TO 102 DO 101 K=1,L1 TI5 = CC(2,2,K)-CC(2,5,K) TI2 = CC(2,2,K)+CC(2,5,K) TI4 = CC(2,3,K)-CC(2,4,K) TI3 = CC(2,3,K)+CC(2,4,K) TR5 = CC(1,2,K)-CC(1,5,K) TR2 = CC(1,2,K)+CC(1,5,K) TR4 = CC(1,3,K)-CC(1,4,K) TR3 = CC(1,3,K)+CC(1,4,K) CH(1,K,1) = CC(1,1,K)+TR2+TR3 CH(2,K,1) = CC(2,1,K)+TI2+TI3 CR2 = CC(1,1,K)+TR11*TR2+TR12*TR3 CI2 = CC(2,1,K)+TR11*TI2+TR12*TI3 CR3 = CC(1,1,K)+TR12*TR2+TR11*TR3 CI3 = CC(2,1,K)+TR12*TI2+TR11*TI3 CR5 = TI11*TR5+TI12*TR4 CI5 = TI11*TI5+TI12*TI4 CR4 = TI12*TR5-TI11*TR4 CI4 = TI12*TI5-TI11*TI4 CH(1,K,2) = CR2-CI5 CH(1,K,5) = CR2+CI5 CH(2,K,2) = CI2+CR5 CH(2,K,3) = CI3+CR4 CH(1,K,3) = CR3-CI4 CH(1,K,4) = CR3+CI4 CH(2,K,4) = CI3-CR4 CH(2,K,5) = CI2-CR5 101 CONTINUE RETURN 102 DO 104 K=1,L1 DO 103 I=2,IDO,2 TI5 = CC(I,2,K)-CC(I,5,K) TI2 = CC(I,2,K)+CC(I,5,K) TI4 = CC(I,3,K)-CC(I,4,K) TI3 = CC(I,3,K)+CC(I,4,K) TR5 = CC(I-1,2,K)-CC(I-1,5,K) TR2 = CC(I-1,2,K)+CC(I-1,5,K) TR4 = CC(I-1,3,K)-CC(I-1,4,K) TR3 = CC(I-1,3,K)+CC(I-1,4,K) CH(I-1,K,1) = CC(I-1,1,K)+TR2+TR3 CH(I,K,1) = CC(I,1,K)+TI2+TI3 CR2 = CC(I-1,1,K)+TR11*TR2+TR12*TR3 CI2 = CC(I,1,K)+TR11*TI2+TR12*TI3 CR3 = CC(I-1,1,K)+TR12*TR2+TR11*TR3 CI3 = CC(I,1,K)+TR12*TI2+TR11*TI3 CR5 = TI11*TR5+TI12*TR4 CI5 = TI11*TI5+TI12*TI4 CR4 = TI12*TR5-TI11*TR4 CI4 = TI12*TI5-TI11*TI4 DR3 = CR3-CI4 DR4 = CR3+CI4 DI3 = CI3+CR4 DI4 = CI3-CR4 DR5 = CR2+CI5 DR2 = CR2-CI5 DI5 = CI2-CR5 DI2 = CI2+CR5 CH(I-1,K,2) = WA1(I-1)*DR2+WA1(I)*DI2 CH(I,K,2) = WA1(I-1)*DI2-WA1(I)*DR2 CH(I-1,K,3) = WA2(I-1)*DR3+WA2(I)*DI3 CH(I,K,3) = WA2(I-1)*DI3-WA2(I)*DR3 CH(I-1,K,4) = WA3(I-1)*DR4+WA3(I)*DI4 CH(I,K,4) = WA3(I-1)*DI4-WA3(I)*DR4 CH(I-1,K,5) = WA4(I-1)*DR5+WA4(I)*DI5 CH(I,K,5) = WA4(I-1)*DI5-WA4(I)*DR5 103 CONTINUE 104 CONTINUE RETURN END