SUBROUTINE DCFFTF(N,C,WSAVE) C***BEGIN PROLOGUE DCFFTF C***DATE WRITTEN 790601 (YYMMDD) C***REVISION DATE 860115 (YYMMDD) C***CATEGORY NO. J1A2 C***KEYWORDS FOURIER TRANSFORM C***AUTHOR SWARZTRAUBER, P. N., (NCAR) C***PURPOSE Forward transform of a complex, periodic sequence. C***DESCRIPTION C From the book, "Numerical Methods and Software" by C D. Kahaner, C. Moler, S. Nash C Prentice Hall, 1988 C C Subroutine DCFFTF computes the forward complex discrete Fourier C transform (the Fourier analysis). Equivalently, DCFFTF 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 DCFFTF C followed by a call of DCFFTB will multiply the sequence by N. C C The array WSAVE which is used by subroutine DCFFTF must be C initialized by calling subroutine DCFFTI(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 d.p. work array which must be dimensioned at least 4*N+15 C in the program that calls DCFFTF. The WSAVE array must be C initialized by calling subroutine DCFFTI(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 DCFFTF and DCFFTB. 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*K*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 DCFFTF or DCFFTB C C * References * C * * C * 1. P.N. Swarztrauber, Vectorizing the FFTs, in Parallel * C * Computations (G. Rodrigue, ed.), Academic Press, 1982, * C * pp. 51-83. * C * 2. B.L. Buzbee, The SLATEC Common Math Library, in Sources * C * and Development of Mathematical Software (W. Cowell, ed.), * C * Prentice-Hall, 1984, pp. 302-318. * C * * C ********************************************************************* C C***REFERENCES (NONE) C***ROUTINES CALLED DCFTF1 C***END PROLOGUE DCFFTF IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION C(*) ,WSAVE(*) C***FIRST EXECUTABLE STATEMENT DCFFTF IF (N .EQ. 1) RETURN IW1 = N+N+1 IW2 = IW1+N+N CALL DCFTF1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2)) RETURN END SUBROUTINE DCFFTB(N,C,WSAVE) C***BEGIN PROLOGUE DCFFTB C***DATE WRITTEN 790601 (YYMMDD) C***REVISION DATE 860115 (YYMMDD) C***CATEGORY NO. J1A2 C***KEYWORDS FOURIER TRANSFORM C***AUTHOR SWARZTRAUBER, P. N., (NCAR) C***PURPOSE Unnormalized inverse of DCFFTF. C***DESCRIPTION C From the book, "Numerical Methods and Software" by C D. Kahaner, C. Moler, S. Nash C Prentice Hall, 1988 C C Subroutine DCFFTB computes the backward complex discrete Fourier C transform (the Fourier synthesis). Equivalently, DCFFTB 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 DCFFTF followed by a call of DCFFTB will multiply the C sequence by N. C C The array WSAVE which is used by subroutine DCFFTB must be C initialized by calling subroutine DCFFTI(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 d.p. work array which must be dimensioned at least 4*N+15 C in the program that calls DCFFTB. The WSAVE array must be C initialized by calling subroutine DCFFTI(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 DCFFTF and DCFFTB. 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*K*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 DCFFTF or DCFFTB C C * References * C * * C * 1. P.N. Swarztrauber, Vectorizing the FFTs, in Parallel * C * Computations (G. Rodrigue, ed.), Academic Press, 1982, * C * pp. 51-83. * C * 2. B.L. Buzbee, The SLATEC Common Math Library, in Sources * C * and Development of Mathematical Software (W. Cowell, ed.), * C * Prentice-Hall, 1984, pp. 302-318. * C * * C ********************************************************************* C C***REFERENCES (NONE) C***ROUTINES CALLED DCFTB1 C***END PROLOGUE DCFFTB IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION C(*) ,WSAVE(*) C***FIRST EXECUTABLE STATEMENT DCFFTB IF (N .EQ. 1) RETURN IW1 = N+N+1 IW2 = IW1+N+N CALL DCFTB1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2)) RETURN END SUBROUTINE DCFFTI(N,WSAVE) C***BEGIN PROLOGUE DCFFTI C***DATE WRITTEN 790601 (YYMMDD) C***REVISION DATE 860115 (YYMMDD) C***CATEGORY NO. J1A2 C***KEYWORDS FOURIER TRANSFORM C***AUTHOR SWARZTRAUBER, P. N., (NCAR) C***PURPOSE Initialize for DCFFTF and DCFFTB. C***DESCRIPTION C From the book, "Numerical Methods and Software" by C D. Kahaner, C. Moler, S. Nash C Prentice Hall, 1988 C C Subroutine DCFFTI initializes the array WSAVE which is used in C both DCFFTF and DCFFTB. 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 DCFFTF and DCFFTB 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 DCFFTF or DCFFTB. C***REFERENCES (NONE) C***ROUTINES CALLED DCFTI1 C***END PROLOGUE DCFFTI IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION WSAVE(*) C***FIRST EXECUTABLE STATEMENT DCFFTI IF (N .EQ. 1) RETURN IW1 = N+N+1 IW2 = IW1+N+N CALL DCFTI1 (N,WSAVE(IW1),WSAVE(IW2)) RETURN END SUBROUTINE DCFTF1(N,C,CH,WA,IFAC) C***BEGIN PROLOGUE DCFTF1 C***REFER TO DCFFTF C***ROUTINES CALLED DPASSF,DPASF2,DPASF3,DPASF4,DPASF5 C***END PROLOGUE DCFTF1 IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CH(*) ,C(*) ,WA(*) ,IFAC(*) C***FIRST EXECUTABLE STATEMENT DCFTF1 NF = IFAC(2) NA = 0 L1 = 1 IW = 1 DO 116 K1=1,NF IP = IFAC(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 DPASF4 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3)) GO TO 102 101 CALL DPASF4 (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 DPASF2 (IDOT,L1,C,CH,WA(IW)) GO TO 105 104 CALL DPASF2 (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 DPASF3 (IDOT,L1,C,CH,WA(IW),WA(IX2)) GO TO 108 107 CALL DPASF3 (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 DPASF5 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4)) GO TO 111 110 CALL DPASF5 (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 DPASSF (NAC,IDOT,IP,L1,IDL1,C,C,C,CH,CH,WA(IW)) GO TO 114 113 CALL DPASSF (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 SUBROUTINE DCFTI1(N,WA,IFAC) C***BEGIN PROLOGUE DCFTI1 C***REFER TO DCFFTI C***ROUTINES CALLED (NONE) C***END PROLOGUE DCFTI1 IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION WA(*) ,IFAC(*) ,NTRYH(4) DATA NTRYH(1),NTRYH(2),NTRYH(3),NTRYH(4)/3,4,2,5/ C***FIRST EXECUTABLE STATEMENT DCFTI1 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 = 8.0D0*ATAN(1.0D0) ARGH = TPI/DBLE(N) I = 2 L1 = 1 DO 110 K1=1,NF IP = IFAC(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) = 1.0D0 WA(I) = 0.0D0 LD = LD+L1 FI = 0.0D0 ARGLD = DBLE(LD)*ARGH DO 108 II=4,IDOT,2 I = I+2 FI = FI+1.0D0 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 SUBROUTINE DPASF2(IDO,L1,CC,CH,WA1) C***BEGIN PROLOGUE DPASF2 C***REFER TO DCFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE DPASF2 IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) , 1 WA1(*) C***FIRST EXECUTABLE STATEMENT DPASF2 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 IF(IDO/2.LT.L1) GO TO 105 DO 104 K=1,L1 CDIR\$ IVDEP 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 105 DO 107 I=2,IDO,2 CDIR\$ IVDEP DO 106 K=1,L1 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 106 CONTINUE 107 CONTINUE RETURN END SUBROUTINE DPASF3(IDO,L1,CC,CH,WA1,WA2) C***BEGIN PROLOGUE DPASF3 C***REFER TO DCFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE DPASF3 IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) , 1 WA1(*) ,WA2(*) C***FIRST EXECUTABLE STATEMENT DPASF3 TAUR = -.5D0 TAUI = -.5D0*SQRT(3.0D0) 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 IF(IDO/2.LT.L1) GO TO 105 DO 104 K=1,L1 CDIR\$ IVDEP 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 105 DO 107 I=2,IDO,2 CDIR\$ IVDEP DO 106 K=1,L1 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 106 CONTINUE 107 CONTINUE RETURN END SUBROUTINE DPASF4(IDO,L1,CC,CH,WA1,WA2,WA3) C***BEGIN PROLOGUE DPASF4 C***REFER TO DCFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE DPASF4 IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) , 1 WA1(*) ,WA2(*) ,WA3(*) C***FIRST EXECUTABLE STATEMENT DPASF4 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 IF(IDO/2.LT.L1) GO TO 105 DO 104 K=1,L1 CDIR\$ IVDEP 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 105 DO 107 I=2,IDO,2 CDIR\$ IVDEP DO 106 K=1,L1 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 106 CONTINUE 107 CONTINUE RETURN END SUBROUTINE DPASF5(IDO,L1,CC,CH,WA1,WA2,WA3,WA4) C***BEGIN PROLOGUE DPASF5 C***REFER TO DCFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE DPASF5 IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) , 1 WA1(*) ,WA2(*) ,WA3(*) ,WA4(*) C***FIRST EXECUTABLE STATEMENT DPASF5 PI = 4.0D0*ATAN(1.0D0) TR11 = SIN(.1D0*PI) TI11 = -SIN(.4D0*PI) TR12 = -SIN(.3D0*PI) TI12 = -SIN(.2D0*PI) 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 IF(IDO/2.LT.L1) GO TO 105 DO 104 K=1,L1 CDIR\$ IVDEP 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 105 DO 107 I=2,IDO,2 CDIR\$ IVDEP DO 106 K=1,L1 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 106 CONTINUE 107 CONTINUE RETURN END SUBROUTINE DPASSF(NAC,IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA) C***BEGIN PROLOGUE DPASSF C***REFER TO DCFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE DPASSF IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CH(IDO,L1,IP) ,CC(IDO,IP,L1) , 1 C1(IDO,L1,IP) ,WA(*) ,C2(IDL1,IP), 2 CH2(IDL1,IP) C***FIRST EXECUTABLE STATEMENT DPASSF 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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) CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP DO 121 IK=1,IDL1 C2(IK,1) = CH2(IK,1) 121 CONTINUE DO 123 J=2,IP CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 SUBROUTINE DCFTB1(N,C,CH,WA,IFAC) C***BEGIN PROLOGUE DCFTB1 C***REFER TO DCFFTB C***ROUTINES CALLED DPASSB,DPASB2,DPASB3,DPASB4,DPASB5 C***END PROLOGUE DCFTB1 IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CH(*) ,C(*) ,WA(*) ,IFAC(*) C***FIRST EXECUTABLE STATEMENT DCFTB1 NF = IFAC(2) NA = 0 L1 = 1 IW = 1 DO 116 K1=1,NF IP = IFAC(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 DPASB4 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3)) GO TO 102 101 CALL DPASB4 (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 DPASB2 (IDOT,L1,C,CH,WA(IW)) GO TO 105 104 CALL DPASB2 (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 DPASB3 (IDOT,L1,C,CH,WA(IW),WA(IX2)) GO TO 108 107 CALL DPASB3 (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 DPASB5 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4)) GO TO 111 110 CALL DPASB5 (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 DPASSB (NAC,IDOT,IP,L1,IDL1,C,C,C,CH,CH,WA(IW)) GO TO 114 113 CALL DPASSB (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 SUBROUTINE DPASB4(IDO,L1,CC,CH,WA1,WA2,WA3) C***BEGIN PROLOGUE DPASB4 C***REFER TO DCFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE DPASB4 IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) , 1 WA1(*) ,WA2(*) ,WA3(*) C***FIRST EXECUTABLE STATEMENT DPASB4 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 IF(IDO/2.LT.L1) GO TO 105 DO 104 K=1,L1 CDIR\$ IVDEP 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 105 DO 107 I=2,IDO,2 CDIR\$ IVDEP DO 106 K=1,L1 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 106 CONTINUE 107 CONTINUE RETURN END SUBROUTINE DPASB5(IDO,L1,CC,CH,WA1,WA2,WA3,WA4) C***BEGIN PROLOGUE DPASB5 C***REFER TO DCFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE DPASB5 IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) , 1 WA1(*) ,WA2(*) ,WA3(*) ,WA4(*) C***FIRST EXECUTABLE STATEMENT DPASB5 PI = 4.0D0*ATAN(1.0D0) TR11 = SIN(.1D0*PI) TI11 = SIN(.4D0*PI) TR12 = -SIN(.3D0*PI) TI12 = SIN(.2D0*PI) 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 IF(IDO/2.LT.L1) GO TO 105 DO 104 K=1,L1 CDIR\$ IVDEP 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 105 DO 107 I=2,IDO,2 CDIR\$ IVDEP DO 106 K=1,L1 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 106 CONTINUE 107 CONTINUE RETURN END SUBROUTINE DPASSB(NAC,IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA) C***BEGIN PROLOGUE DPASSB C***REFER TO DCFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE DPASSB IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CH(IDO,L1,IP) ,CC(IDO,IP,L1) , 1 C1(IDO,L1,IP) ,WA(*) ,C2(IDL1,IP), 2 CH2(IDL1,IP) C***FIRST EXECUTABLE STATEMENT DPASSB 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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) CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 CDIR\$ IVDEP 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 SUBROUTINE DPASB2(IDO,L1,CC,CH,WA1) C***BEGIN PROLOGUE DPASB2 C***REFER TO DCFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE DPASB2 IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) , 1 WA1(*) C***FIRST EXECUTABLE STATEMENT DPASB2 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 IF(IDO/2.LT.L1) GO TO 105 DO 104 K=1,L1 CDIR\$ IVDEP 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 105 DO 107 I=2,IDO,2 CDIR\$ IVDEP DO 106 K=1,L1 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 106 CONTINUE 107 CONTINUE RETURN END SUBROUTINE DPASB3(IDO,L1,CC,CH,WA1,WA2) C***BEGIN PROLOGUE DPASB3 C***REFER TO DCFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE DPASB3 IMPLICIT DOUBLE PRECISION (A-H,O-Z) DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) , 1 WA1(*) ,WA2(*) C***FIRST EXECUTABLE STATEMENT DPASB3 TAUR = -.5D0 TAUI = .5D0*SQRT(3.0D0) 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 IF(IDO/2.LT.L1) GO TO 105 DO 104 K=1,L1 CDIR\$ IVDEP 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 105 DO 107 I=2,IDO,2 CDIR\$ IVDEP DO 106 K=1,L1 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 106 CONTINUE 107 CONTINUE RETURN END