c fftpack is public domain, available from netlib.org c minor change: replace (dimension|integer|real) var(1) -> (dimension|integer|real) var(*) c to avoid gfortran warnings 9/23/2020: Wesley Ebisuzaki c c ****************************************************************** c ****************************************************************** c ****** ****** c ****** FFTPACK ****** c ****** ****** c ****************************************************************** c ****************************************************************** c SUBROUTINE RFFTF (N,R,WSAVE) DIMENSION R(1) ,WSAVE(*) IF (N .EQ. 1) RETURN CALL RFFTF1 (N,R,WSAVE,WSAVE(N+1),WSAVE(2*N+1)) RETURN END SUBROUTINE RFFTB (N,R,WSAVE) DIMENSION R(1) ,WSAVE(*) IF (N .EQ. 1) RETURN CALL RFFTB1 (N,R,WSAVE,WSAVE(N+1),WSAVE(2*N+1)) RETURN END SUBROUTINE RFFTI (N,WSAVE) DIMENSION WSAVE(*) IF (N .EQ. 1) RETURN CALL RFFTI1 (N,WSAVE(N+1),WSAVE(2*N+1)) RETURN END SUBROUTINE RFFTB1 (N,C,CH,WA,IFAC) DIMENSION CH(*) ,C(*) ,WA(*) ,IFAC(*) 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 SUBROUTINE RFFTF1 (N,C,CH,WA,IFAC) DIMENSION CH(*) ,C(*) ,WA(*) ,IFAC(*) NF = IFAC(2) NA = 1 L2 = N IW = N DO 111 K1=1,NF KH = NF-K1 IP = IFAC(KH+3) L1 = L2/IP IDO = N/L2 IDL1 = IDO*L1 IW = IW-(IP-1)*IDO NA = 1-NA IF (IP .NE. 4) GO TO 102 IX2 = IW+IDO IX3 = IX2+IDO IF (NA .NE. 0) GO TO 101 CALL RADF4 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3)) GO TO 110 101 CALL RADF4 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3)) GO TO 110 102 IF (IP .NE. 2) GO TO 104 IF (NA .NE. 0) GO TO 103 CALL RADF2 (IDO,L1,C,CH,WA(IW)) GO TO 110 103 CALL RADF2 (IDO,L1,CH,C,WA(IW)) GO TO 110 104 IF (IP .NE. 3) GO TO 106 IX2 = IW+IDO IF (NA .NE. 0) GO TO 105 CALL RADF3 (IDO,L1,C,CH,WA(IW),WA(IX2)) GO TO 110 105 CALL RADF3 (IDO,L1,CH,C,WA(IW),WA(IX2)) GO TO 110 106 IF (IP .NE. 5) GO TO 108 IX2 = IW+IDO IX3 = IX2+IDO IX4 = IX3+IDO IF (NA .NE. 0) GO TO 107 CALL RADF5 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4)) GO TO 110 107 CALL RADF5 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3),WA(IX4)) GO TO 110 108 IF (IDO .EQ. 1) NA = 1-NA IF (NA .NE. 0) GO TO 109 CALL RADFG (IDO,IP,L1,IDL1,C,C,C,CH,CH,WA(IW)) NA = 1 GO TO 110 109 CALL RADFG (IDO,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW)) NA = 0 110 L2 = L1 111 CONTINUE IF (NA .EQ. 1) RETURN DO 112 I=1,N C(I) = CH(I) 112 CONTINUE RETURN END SUBROUTINE RFFTI1 (N,WA,IFAC) DIMENSION WA(*) ,IFAC(*) ,NTRYH(4) DATA NTRYH(1),NTRYH(2),NTRYH(3),NTRYH(4)/4,2,3,5/ 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 IFAC(NF+2) = 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 IFAC(IB+2) = IFAC(IB+1) 106 CONTINUE IFAC(3) = 2 107 IF (NL .NE. 1) GO TO 104 IFAC(1) = N IFAC(2) = NF TPI = 6.28318530717959 ARGH = TPI/FLOAT(N) IS = 0 NFM1 = NF-1 L1 = 1 IF (NFM1 .EQ. 0) RETURN DO 110 K1=1,NFM1 IP = IFAC(K1+2) LD = 0 L2 = L1*IP IDO = N/L2 IPM = IP-1 DO 109 J=1,IPM LD = LD+L1 I = IS ARGLD = FLOAT(LD)*ARGH FI = 0 DO 108 II=3,IDO,2 I = I+2 FI = FI+1 ARG = FI*ARGLD WA(I-1) = COS(ARG) WA(I) = SIN(ARG) 108 CONTINUE IS = IS+IDO 109 CONTINUE L1 = L2 110 CONTINUE RETURN END SUBROUTINE RADB2 (IDO,L1,CC,CH,WA1) DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) , 1 WA1(*) DO 101 K=1,L1 CH(1,K,1) = CC(1,1,K)+CC(IDO,2,K) CH(1,K,2) = CC(1,1,K)-CC(IDO,2,K) 101 CONTINUE IF (IDO-2) 107,105,102 102 IDP2 = IDO+2 DO 104 K=1,L1 DO 103 I=3,IDO,2 IC = IDP2-I CH(I-1,K,1) = CC(I-1,1,K)+CC(IC-1,2,K) TR2 = CC(I-1,1,K)-CC(IC-1,2,K) CH(I,K,1) = CC(I,1,K)-CC(IC,2,K) TI2 = CC(I,1,K)+CC(IC,2,K) CH(I-1,K,2) = WA1(I-2)*TR2-WA1(I-1)*TI2 CH(I,K,2) = WA1(I-2)*TI2+WA1(I-1)*TR2 103 CONTINUE 104 CONTINUE IF (MOD(IDO,2) .EQ. 1) RETURN 105 DO 106 K=1,L1 CH(IDO,K,1) = CC(IDO,1,K)+CC(IDO,1,K) CH(IDO,K,2) = -(CC(1,2,K)+CC(1,2,K)) 106 CONTINUE 107 RETURN END SUBROUTINE RADB3 (IDO,L1,CC,CH,WA1,WA2) DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) , 1 WA1(*) ,WA2(*) DATA TAUR,TAUI /-.5,.866025403784439/ DO 101 K=1,L1 TR2 = CC(IDO,2,K)+CC(IDO,2,K) CR2 = CC(1,1,K)+TAUR*TR2 CH(1,K,1) = CC(1,1,K)+TR2 CI3 = TAUI*(CC(1,3,K)+CC(1,3,K)) CH(1,K,2) = CR2-CI3 CH(1,K,3) = CR2+CI3 101 CONTINUE IF (IDO .EQ. 1) RETURN IDP2 = IDO+2 DO 103 K=1,L1 DO 102 I=3,IDO,2 IC = IDP2-I TR2 = CC(I-1,3,K)+CC(IC-1,2,K) CR2 = CC(I-1,1,K)+TAUR*TR2 CH(I-1,K,1) = CC(I-1,1,K)+TR2 TI2 = CC(I,3,K)-CC(IC,2,K) CI2 = CC(I,1,K)+TAUR*TI2 CH(I,K,1) = CC(I,1,K)+TI2 CR3 = TAUI*(CC(I-1,3,K)-CC(IC-1,2,K)) CI3 = TAUI*(CC(I,3,K)+CC(IC,2,K)) DR2 = CR2-CI3 DR3 = CR2+CI3 DI2 = CI2+CR3 DI3 = CI2-CR3 CH(I-1,K,2) = WA1(I-2)*DR2-WA1(I-1)*DI2 CH(I,K,2) = WA1(I-2)*DI2+WA1(I-1)*DR2 CH(I-1,K,3) = WA2(I-2)*DR3-WA2(I-1)*DI3 CH(I,K,3) = WA2(I-2)*DI3+WA2(I-1)*DR3 102 CONTINUE 103 CONTINUE RETURN END SUBROUTINE RADB4 (IDO,L1,CC,CH,WA1,WA2,WA3) DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) , 1 WA1(*) ,WA2(*) ,WA3(*) DATA SQRT2 /1.414213562373095/ DO 101 K=1,L1 TR1 = CC(1,1,K)-CC(IDO,4,K) TR2 = CC(1,1,K)+CC(IDO,4,K) TR3 = CC(IDO,2,K)+CC(IDO,2,K) TR4 = CC(1,3,K)+CC(1,3,K) CH(1,K,1) = TR2+TR3 CH(1,K,2) = TR1-TR4 CH(1,K,3) = TR2-TR3 CH(1,K,4) = TR1+TR4 101 CONTINUE IF (IDO-2) 107,105,102 102 IDP2 = IDO+2 DO 104 K=1,L1 DO 103 I=3,IDO,2 IC = IDP2-I TI1 = CC(I,1,K)+CC(IC,4,K) TI2 = CC(I,1,K)-CC(IC,4,K) TI3 = CC(I,3,K)-CC(IC,2,K) TR4 = CC(I,3,K)+CC(IC,2,K) TR1 = CC(I-1,1,K)-CC(IC-1,4,K) TR2 = CC(I-1,1,K)+CC(IC-1,4,K) TI4 = CC(I-1,3,K)-CC(IC-1,2,K) TR3 = CC(I-1,3,K)+CC(IC-1,2,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-2)*CR2-WA1(I-1)*CI2 CH(I,K,2) = WA1(I-2)*CI2+WA1(I-1)*CR2 CH(I-1,K,3) = WA2(I-2)*CR3-WA2(I-1)*CI3 CH(I,K,3) = WA2(I-2)*CI3+WA2(I-1)*CR3 CH(I-1,K,4) = WA3(I-2)*CR4-WA3(I-1)*CI4 CH(I,K,4) = WA3(I-2)*CI4+WA3(I-1)*CR4 103 CONTINUE 104 CONTINUE IF (MOD(IDO,2) .EQ. 1) RETURN 105 CONTINUE DO 106 K=1,L1 TI1 = CC(1,2,K)+CC(1,4,K) TI2 = CC(1,4,K)-CC(1,2,K) TR1 = CC(IDO,1,K)-CC(IDO,3,K) TR2 = CC(IDO,1,K)+CC(IDO,3,K) CH(IDO,K,1) = TR2+TR2 CH(IDO,K,2) = SQRT2*(TR1-TI1) CH(IDO,K,3) = TI2+TI2 CH(IDO,K,4) = -SQRT2*(TR1+TI1) 106 CONTINUE 107 RETURN END SUBROUTINE RADB5 (IDO,L1,CC,CH,WA1,WA2,WA3,WA4) DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) , 1 WA1(*) ,WA2(*) ,WA3(*) ,WA4(*) DATA TR11,TI11,TR12,TI12 /.309016994374947,.951056516295154, 1-.809016994374947,.587785252292473/ DO 101 K=1,L1 TI5 = CC(1,3,K)+CC(1,3,K) TI4 = CC(1,5,K)+CC(1,5,K) TR2 = CC(IDO,2,K)+CC(IDO,2,K) TR3 = CC(IDO,4,K)+CC(IDO,4,K) CH(1,K,1) = CC(1,1,K)+TR2+TR3 CR2 = CC(1,1,K)+TR11*TR2+TR12*TR3 CR3 = CC(1,1,K)+TR12*TR2+TR11*TR3 CI5 = TI11*TI5+TI12*TI4 CI4 = TI12*TI5-TI11*TI4 CH(1,K,2) = CR2-CI5 CH(1,K,3) = CR3-CI4 CH(1,K,4) = CR3+CI4 CH(1,K,5) = CR2+CI5 101 CONTINUE IF (IDO .EQ. 1) RETURN IDP2 = IDO+2 DO 103 K=1,L1 DO 102 I=3,IDO,2 IC = IDP2-I TI5 = CC(I,3,K)+CC(IC,2,K) TI2 = CC(I,3,K)-CC(IC,2,K) TI4 = CC(I,5,K)+CC(IC,4,K) TI3 = CC(I,5,K)-CC(IC,4,K) TR5 = CC(I-1,3,K)-CC(IC-1,2,K) TR2 = CC(I-1,3,K)+CC(IC-1,2,K) TR4 = CC(I-1,5,K)-CC(IC-1,4,K) TR3 = CC(I-1,5,K)+CC(IC-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-2)*DR2-WA1(I-1)*DI2 CH(I,K,2) = WA1(I-2)*DI2+WA1(I-1)*DR2 CH(I-1,K,3) = WA2(I-2)*DR3-WA2(I-1)*DI3 CH(I,K,3) = WA2(I-2)*DI3+WA2(I-1)*DR3 CH(I-1,K,4) = WA3(I-2)*DR4-WA3(I-1)*DI4 CH(I,K,4) = WA3(I-2)*DI4+WA3(I-1)*DR4 CH(I-1,K,5) = WA4(I-2)*DR5-WA4(I-1)*DI5 CH(I,K,5) = WA4(I-2)*DI5+WA4(I-1)*DR5 102 CONTINUE 103 CONTINUE RETURN END SUBROUTINE RADBG (IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA) DIMENSION CH(IDO,L1,IP) ,CC(IDO,IP,L1) , 1 C1(IDO,L1,IP) ,C2(IDL1,IP), 2 CH2(IDL1,IP) ,WA(*) DATA TPI/6.28318530717959/ ARG = TPI/FLOAT(IP) DCP = COS(ARG) DSP = SIN(ARG) IDP2 = IDO+2 NBD = (IDO-1)/2 IPP2 = IP+2 IPPH = (IP+1)/2 IF (IDO .LT. L1) GO TO 103 DO 102 K=1,L1 DO 101 I=1,IDO CH(I,K,1) = CC(I,1,K) 101 CONTINUE 102 CONTINUE GO TO 106 103 DO 105 I=1,IDO DO 104 K=1,L1 CH(I,K,1) = CC(I,1,K) 104 CONTINUE 105 CONTINUE 106 DO 108 J=2,IPPH JC = IPP2-J J2 = J+J DO 107 K=1,L1 CH(1,K,J) = CC(IDO,J2-2,K)+CC(IDO,J2-2,K) CH(1,K,JC) = CC(1,J2-1,K)+CC(1,J2-1,K) 107 CONTINUE 108 CONTINUE IF (IDO .EQ. 1) GO TO 116 IF (NBD .LT. L1) GO TO 112 DO 111 J=2,IPPH JC = IPP2-J DO 110 K=1,L1 DO 109 I=3,IDO,2 IC = IDP2-I CH(I-1,K,J) = CC(I-1,2*J-1,K)+CC(IC-1,2*J-2,K) CH(I-1,K,JC) = CC(I-1,2*J-1,K)-CC(IC-1,2*J-2,K) CH(I,K,J) = CC(I,2*J-1,K)-CC(IC,2*J-2,K) CH(I,K,JC) = CC(I,2*J-1,K)+CC(IC,2*J-2,K) 109 CONTINUE 110 CONTINUE 111 CONTINUE GO TO 116 112 DO 115 J=2,IPPH JC = IPP2-J DO 114 I=3,IDO,2 IC = IDP2-I DO 113 K=1,L1 CH(I-1,K,J) = CC(I-1,2*J-1,K)+CC(IC-1,2*J-2,K) CH(I-1,K,JC) = CC(I-1,2*J-1,K)-CC(IC-1,2*J-2,K) CH(I,K,J) = CC(I,2*J-1,K)-CC(IC,2*J-2,K) CH(I,K,JC) = CC(I,2*J-1,K)+CC(IC,2*J-2,K) 113 CONTINUE 114 CONTINUE 115 CONTINUE 116 AR1 = 1. AI1 = 0. DO 120 L=2,IPPH LC = IPP2-L AR1H = DCP*AR1-DSP*AI1 AI1 = DCP*AI1+DSP*AR1 AR1 = AR1H DO 117 IK=1,IDL1 C2(IK,L) = CH2(IK,1)+AR1*CH2(IK,2) C2(IK,LC) = AI1*CH2(IK,IP) 117 CONTINUE DC2 = AR1 DS2 = AI1 AR2 = AR1 AI2 = AI1 DO 119 J=3,IPPH JC = IPP2-J AR2H = DC2*AR2-DS2*AI2 AI2 = DC2*AI2+DS2*AR2 AR2 = AR2H DO 118 IK=1,IDL1 C2(IK,L) = C2(IK,L)+AR2*CH2(IK,J) C2(IK,LC) = C2(IK,LC)+AI2*CH2(IK,JC) 118 CONTINUE 119 CONTINUE 120 CONTINUE DO 122 J=2,IPPH DO 121 IK=1,IDL1 CH2(IK,1) = CH2(IK,1)+CH2(IK,J) 121 CONTINUE 122 CONTINUE DO 124 J=2,IPPH JC = IPP2-J DO 123 K=1,L1 CH(1,K,J) = C1(1,K,J)-C1(1,K,JC) CH(1,K,JC) = C1(1,K,J)+C1(1,K,JC) 123 CONTINUE 124 CONTINUE IF (IDO .EQ. 1) GO TO 132 IF (NBD .LT. L1) GO TO 128 DO 127 J=2,IPPH JC = IPP2-J DO 126 K=1,L1 DO 125 I=3,IDO,2 CH(I-1,K,J) = C1(I-1,K,J)-C1(I,K,JC) CH(I-1,K,JC) = C1(I-1,K,J)+C1(I,K,JC) CH(I,K,J) = C1(I,K,J)+C1(I-1,K,JC) CH(I,K,JC) = C1(I,K,J)-C1(I-1,K,JC) 125 CONTINUE 126 CONTINUE 127 CONTINUE GO TO 132 128 DO 131 J=2,IPPH JC = IPP2-J DO 130 I=3,IDO,2 DO 129 K=1,L1 CH(I-1,K,J) = C1(I-1,K,J)-C1(I,K,JC) CH(I-1,K,JC) = C1(I-1,K,J)+C1(I,K,JC) CH(I,K,J) = C1(I,K,J)+C1(I-1,K,JC) CH(I,K,JC) = C1(I,K,J)-C1(I-1,K,JC) 129 CONTINUE 130 CONTINUE 131 CONTINUE 132 CONTINUE IF (IDO .EQ. 1) RETURN DO 133 IK=1,IDL1 C2(IK,1) = CH2(IK,1) 133 CONTINUE DO 135 J=2,IP DO 134 K=1,L1 C1(1,K,J) = CH(1,K,J) 134 CONTINUE 135 CONTINUE IF (NBD .GT. L1) GO TO 139 IS = -IDO DO 138 J=2,IP IS = IS+IDO IDIJ = IS DO 137 I=3,IDO,2 IDIJ = IDIJ+2 DO 136 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) 136 CONTINUE 137 CONTINUE 138 CONTINUE GO TO 143 139 IS = -IDO DO 142 J=2,IP IS = IS+IDO DO 141 K=1,L1 IDIJ = IS DO 140 I=3,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) 140 CONTINUE 141 CONTINUE 142 CONTINUE 143 RETURN END SUBROUTINE RADF2 (IDO,L1,CC,CH,WA1) DIMENSION CH(IDO,2,L1) ,CC(IDO,L1,2) , 1 WA1(*) DO 101 K=1,L1 CH(1,1,K) = CC(1,K,1)+CC(1,K,2) CH(IDO,2,K) = CC(1,K,1)-CC(1,K,2) 101 CONTINUE IF (IDO-2) 107,105,102 102 IDP2 = IDO+2 DO 104 K=1,L1 DO 103 I=3,IDO,2 IC = IDP2-I TR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2) TI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2) CH(I,1,K) = CC(I,K,1)+TI2 CH(IC,2,K) = TI2-CC(I,K,1) CH(I-1,1,K) = CC(I-1,K,1)+TR2 CH(IC-1,2,K) = CC(I-1,K,1)-TR2 103 CONTINUE 104 CONTINUE IF (MOD(IDO,2) .EQ. 1) RETURN 105 DO 106 K=1,L1 CH(1,2,K) = -CC(IDO,K,2) CH(IDO,1,K) = CC(IDO,K,1) 106 CONTINUE 107 RETURN END SUBROUTINE RADF3 (IDO,L1,CC,CH,WA1,WA2) DIMENSION CH(IDO,3,L1) ,CC(IDO,L1,3) , 1 WA1(*) ,WA2(*) DATA TAUR,TAUI /-.5,.866025403784439/ DO 101 K=1,L1 CR2 = CC(1,K,2)+CC(1,K,3) CH(1,1,K) = CC(1,K,1)+CR2 CH(1,3,K) = TAUI*(CC(1,K,3)-CC(1,K,2)) CH(IDO,2,K) = CC(1,K,1)+TAUR*CR2 101 CONTINUE IF (IDO .EQ. 1) RETURN IDP2 = IDO+2 DO 103 K=1,L1 DO 102 I=3,IDO,2 IC = IDP2-I DR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2) DI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2) DR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3) DI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3) CR2 = DR2+DR3 CI2 = DI2+DI3 CH(I-1,1,K) = CC(I-1,K,1)+CR2 CH(I,1,K) = CC(I,K,1)+CI2 TR2 = CC(I-1,K,1)+TAUR*CR2 TI2 = CC(I,K,1)+TAUR*CI2 TR3 = TAUI*(DI2-DI3) TI3 = TAUI*(DR3-DR2) CH(I-1,3,K) = TR2+TR3 CH(IC-1,2,K) = TR2-TR3 CH(I,3,K) = TI2+TI3 CH(IC,2,K) = TI3-TI2 102 CONTINUE 103 CONTINUE RETURN END SUBROUTINE RADF4 (IDO,L1,CC,CH,WA1,WA2,WA3) DIMENSION CC(IDO,L1,4) ,CH(IDO,4,L1) , 1 WA1(*) ,WA2(*) ,WA3(*) DATA HSQT2 /.7071067811865475/ DO 101 K=1,L1 TR1 = CC(1,K,2)+CC(1,K,4) TR2 = CC(1,K,1)+CC(1,K,3) CH(1,1,K) = TR1+TR2 CH(IDO,4,K) = TR2-TR1 CH(IDO,2,K) = CC(1,K,1)-CC(1,K,3) CH(1,3,K) = CC(1,K,4)-CC(1,K,2) 101 CONTINUE IF (IDO-2) 107,105,102 102 IDP2 = IDO+2 DO 104 K=1,L1 DO 103 I=3,IDO,2 IC = IDP2-I CR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2) CI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2) CR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3) CI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3) CR4 = WA3(I-2)*CC(I-1,K,4)+WA3(I-1)*CC(I,K,4) CI4 = WA3(I-2)*CC(I,K,4)-WA3(I-1)*CC(I-1,K,4) TR1 = CR2+CR4 TR4 = CR4-CR2 TI1 = CI2+CI4 TI4 = CI2-CI4 TI2 = CC(I,K,1)+CI3 TI3 = CC(I,K,1)-CI3 TR2 = CC(I-1,K,1)+CR3 TR3 = CC(I-1,K,1)-CR3 CH(I-1,1,K) = TR1+TR2 CH(IC-1,4,K) = TR2-TR1 CH(I,1,K) = TI1+TI2 CH(IC,4,K) = TI1-TI2 CH(I-1,3,K) = TI4+TR3 CH(IC-1,2,K) = TR3-TI4 CH(I,3,K) = TR4+TI3 CH(IC,2,K) = TR4-TI3 103 CONTINUE 104 CONTINUE IF (MOD(IDO,2) .EQ. 1) RETURN 105 CONTINUE DO 106 K=1,L1 TI1 = -HSQT2*(CC(IDO,K,2)+CC(IDO,K,4)) TR1 = HSQT2*(CC(IDO,K,2)-CC(IDO,K,4)) CH(IDO,1,K) = TR1+CC(IDO,K,1) CH(IDO,3,K) = CC(IDO,K,1)-TR1 CH(1,2,K) = TI1-CC(IDO,K,3) CH(1,4,K) = TI1+CC(IDO,K,3) 106 CONTINUE 107 RETURN END SUBROUTINE RADF5 (IDO,L1,CC,CH,WA1,WA2,WA3,WA4) DIMENSION CC(IDO,L1,5) ,CH(IDO,5,L1) , 1 WA1(*) ,WA2(*) ,WA3(*) ,WA4(*) DATA TR11,TI11,TR12,TI12 /.309016994374947,.951056516295154, 1-.809016994374947,.587785252292473/ DO 101 K=1,L1 CR2 = CC(1,K,5)+CC(1,K,2) CI5 = CC(1,K,5)-CC(1,K,2) CR3 = CC(1,K,4)+CC(1,K,3) CI4 = CC(1,K,4)-CC(1,K,3) CH(1,1,K) = CC(1,K,1)+CR2+CR3 CH(IDO,2,K) = CC(1,K,1)+TR11*CR2+TR12*CR3 CH(1,3,K) = TI11*CI5+TI12*CI4 CH(IDO,4,K) = CC(1,K,1)+TR12*CR2+TR11*CR3 CH(1,5,K) = TI12*CI5-TI11*CI4 101 CONTINUE IF (IDO .EQ. 1) RETURN IDP2 = IDO+2 DO 103 K=1,L1 DO 102 I=3,IDO,2 IC = IDP2-I DR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2) DI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2) DR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3) DI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3) DR4 = WA3(I-2)*CC(I-1,K,4)+WA3(I-1)*CC(I,K,4) DI4 = WA3(I-2)*CC(I,K,4)-WA3(I-1)*CC(I-1,K,4) DR5 = WA4(I-2)*CC(I-1,K,5)+WA4(I-1)*CC(I,K,5) DI5 = WA4(I-2)*CC(I,K,5)-WA4(I-1)*CC(I-1,K,5) CR2 = DR2+DR5 CI5 = DR5-DR2 CR5 = DI2-DI5 CI2 = DI2+DI5 CR3 = DR3+DR4 CI4 = DR4-DR3 CR4 = DI3-DI4 CI3 = DI3+DI4 CH(I-1,1,K) = CC(I-1,K,1)+CR2+CR3 CH(I,1,K) = CC(I,K,1)+CI2+CI3 TR2 = CC(I-1,K,1)+TR11*CR2+TR12*CR3 TI2 = CC(I,K,1)+TR11*CI2+TR12*CI3 TR3 = CC(I-1,K,1)+TR12*CR2+TR11*CR3 TI3 = CC(I,K,1)+TR12*CI2+TR11*CI3 TR5 = TI11*CR5+TI12*CR4 TI5 = TI11*CI5+TI12*CI4 TR4 = TI12*CR5-TI11*CR4 TI4 = TI12*CI5-TI11*CI4 CH(I-1,3,K) = TR2+TR5 CH(IC-1,2,K) = TR2-TR5 CH(I,3,K) = TI2+TI5 CH(IC,2,K) = TI5-TI2 CH(I-1,5,K) = TR3+TR4 CH(IC-1,4,K) = TR3-TR4 CH(I,5,K) = TI3+TI4 CH(IC,4,K) = TI4-TI3 102 CONTINUE 103 CONTINUE RETURN END SUBROUTINE RADFG (IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA) DIMENSION CH(IDO,L1,IP) ,CC(IDO,IP,L1) , 1 C1(IDO,L1,IP) ,C2(IDL1,IP), 2 CH2(IDL1,IP) ,WA(*) DATA TPI/6.28318530717959/ ARG = TPI/FLOAT(IP) DCP = COS(ARG) DSP = SIN(ARG) IPPH = (IP+1)/2 IPP2 = IP+2 IDP2 = IDO+2 NBD = (IDO-1)/2 IF (IDO .EQ. 1) GO TO 119 DO 101 IK=1,IDL1 CH2(IK,1) = C2(IK,1) 101 CONTINUE DO 103 J=2,IP DO 102 K=1,L1 CH(1,K,J) = C1(1,K,J) 102 CONTINUE 103 CONTINUE IF (NBD .GT. L1) GO TO 107 IS = -IDO DO 106 J=2,IP IS = IS+IDO IDIJ = IS DO 105 I=3,IDO,2 IDIJ = IDIJ+2 DO 104 K=1,L1 CH(I-1,K,J) = WA(IDIJ-1)*C1(I-1,K,J)+WA(IDIJ)*C1(I,K,J) CH(I,K,J) = WA(IDIJ-1)*C1(I,K,J)-WA(IDIJ)*C1(I-1,K,J) 104 CONTINUE 105 CONTINUE 106 CONTINUE GO TO 111 107 IS = -IDO DO 110 J=2,IP IS = IS+IDO DO 109 K=1,L1 IDIJ = IS DO 108 I=3,IDO,2 IDIJ = IDIJ+2 CH(I-1,K,J) = WA(IDIJ-1)*C1(I-1,K,J)+WA(IDIJ)*C1(I,K,J) CH(I,K,J) = WA(IDIJ-1)*C1(I,K,J)-WA(IDIJ)*C1(I-1,K,J) 108 CONTINUE 109 CONTINUE 110 CONTINUE 111 IF (NBD .LT. L1) GO TO 115 DO 114 J=2,IPPH JC = IPP2-J DO 113 K=1,L1 DO 112 I=3,IDO,2 C1(I-1,K,J) = CH(I-1,K,J)+CH(I-1,K,JC) C1(I-1,K,JC) = CH(I,K,J)-CH(I,K,JC) C1(I,K,J) = CH(I,K,J)+CH(I,K,JC) C1(I,K,JC) = CH(I-1,K,JC)-CH(I-1,K,J) 112 CONTINUE 113 CONTINUE 114 CONTINUE GO TO 121 115 DO 118 J=2,IPPH JC = IPP2-J DO 117 I=3,IDO,2 DO 116 K=1,L1 C1(I-1,K,J) = CH(I-1,K,J)+CH(I-1,K,JC) C1(I-1,K,JC) = CH(I,K,J)-CH(I,K,JC) C1(I,K,J) = CH(I,K,J)+CH(I,K,JC) C1(I,K,JC) = CH(I-1,K,JC)-CH(I-1,K,J) 116 CONTINUE 117 CONTINUE 118 CONTINUE GO TO 121 119 DO 120 IK=1,IDL1 C2(IK,1) = CH2(IK,1) 120 CONTINUE 121 DO 123 J=2,IPPH JC = IPP2-J DO 122 K=1,L1 C1(1,K,J) = CH(1,K,J)+CH(1,K,JC) C1(1,K,JC) = CH(1,K,JC)-CH(1,K,J) 122 CONTINUE 123 CONTINUE C AR1 = 1. AI1 = 0. DO 127 L=2,IPPH LC = IPP2-L AR1H = DCP*AR1-DSP*AI1 AI1 = DCP*AI1+DSP*AR1 AR1 = AR1H DO 124 IK=1,IDL1 CH2(IK,L) = C2(IK,1)+AR1*C2(IK,2) CH2(IK,LC) = AI1*C2(IK,IP) 124 CONTINUE DC2 = AR1 DS2 = AI1 AR2 = AR1 AI2 = AI1 DO 126 J=3,IPPH JC = IPP2-J AR2H = DC2*AR2-DS2*AI2 AI2 = DC2*AI2+DS2*AR2 AR2 = AR2H DO 125 IK=1,IDL1 CH2(IK,L) = CH2(IK,L)+AR2*C2(IK,J) CH2(IK,LC) = CH2(IK,LC)+AI2*C2(IK,JC) 125 CONTINUE 126 CONTINUE 127 CONTINUE DO 129 J=2,IPPH DO 128 IK=1,IDL1 CH2(IK,1) = CH2(IK,1)+C2(IK,J) 128 CONTINUE 129 CONTINUE C IF (IDO .LT. L1) GO TO 132 DO 131 K=1,L1 DO 130 I=1,IDO CC(I,1,K) = CH(I,K,1) 130 CONTINUE 131 CONTINUE GO TO 135 132 DO 134 I=1,IDO DO 133 K=1,L1 CC(I,1,K) = CH(I,K,1) 133 CONTINUE 134 CONTINUE 135 DO 137 J=2,IPPH JC = IPP2-J J2 = J+J DO 136 K=1,L1 CC(IDO,J2-2,K) = CH(1,K,J) CC(1,J2-1,K) = CH(1,K,JC) 136 CONTINUE 137 CONTINUE IF (IDO .EQ. 1) RETURN IF (NBD .LT. L1) GO TO 141 DO 140 J=2,IPPH JC = IPP2-J J2 = J+J DO 139 K=1,L1 DO 138 I=3,IDO,2 IC = IDP2-I CC(I-1,J2-1,K) = CH(I-1,K,J)+CH(I-1,K,JC) CC(IC-1,J2-2,K) = CH(I-1,K,J)-CH(I-1,K,JC) CC(I,J2-1,K) = CH(I,K,J)+CH(I,K,JC) CC(IC,J2-2,K) = CH(I,K,JC)-CH(I,K,J) 138 CONTINUE 139 CONTINUE 140 CONTINUE RETURN 141 DO 144 J=2,IPPH JC = IPP2-J J2 = J+J DO 143 I=3,IDO,2 IC = IDP2-I DO 142 K=1,L1 CC(I-1,J2-1,K) = CH(I-1,K,J)+CH(I-1,K,JC) CC(IC-1,J2-2,K) = CH(I-1,K,J)-CH(I-1,K,JC) CC(I,J2-1,K) = CH(I,K,J)+CH(I,K,JC) CC(IC,J2-2,K) = CH(I,K,JC)-CH(I,K,J) 142 CONTINUE 143 CONTINUE 144 CONTINUE RETURN END