SUBROUTINE EZFFTF(N,R,AZERO,A,B,WSAVE) C***BEGIN PROLOGUE EZFFTF C***DATE WRITTEN 790601 (YYMMDD) C***REVISION DATE 860115 (YYMMDD) C***CATEGORY NO. J1A1 C***KEYWORDS FOURIER TRANSFORM C***AUTHOR SWARZTRAUBER, P. N., (NCAR) C***PURPOSE A simplified real, periodic, forward transform 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 EZFFTF computes the Fourier coefficients of a real C perodic sequence (Fourier analysis). The transform is defined C below at Output Parameters AZERO, A and B. EZFFTF is a simplified C but slower version of RFFTF. C C Input Parameters C C N the length of the array R to be transformed. The method C is must efficient when N is the product of small primes. C C R a real array of length N which contains the sequence C to be transformed. R is not destroyed. C C C WSAVE a work array which must be dimensioned at least 3*N+15 C in the program that calls EZFFTF. The WSAVE array must be C initialized by calling subroutine EZFFTI(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 EZFFTF and EZFFTB. C C Output Parameters C C AZERO the sum from I=1 to I=N of R(I)/N C C A,B for N even B(N/2)=0. and A(N/2) is the sum from I=1 to C I=N of (-1)**(I-1)*R(I)/N C C for N even define KMAX=N/2-1 C for N odd define KMAX=(N-1)/2 C C then for k=1,...,KMAX C C A(K) equals the sum from I=1 to I=N of C C 2./N*R(I)*COS(K*(I-1)*2*PI/N) C C B(K) equals the sum from I=1 to I=N of C C 2./N*R(I)*SIN(K*(I-1)*2*PI/N) C 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***REFERENCES (NONE) C***ROUTINES CALLED RFFTF C***END PROLOGUE EZFFTF DIMENSION R(*) ,A(*) ,B(*) ,WSAVE(*) C***FIRST EXECUTABLE STATEMENT EZFFTF IF (N-2) 101,102,103 101 AZERO = R(1) RETURN 102 AZERO = .5*(R(1)+R(2)) A(1) = .5*(R(1)-R(2)) RETURN 103 DO 104 I=1,N WSAVE(I) = R(I) 104 CONTINUE CALL RFFTF (N,WSAVE,WSAVE(N+1)) CF = 2./REAL(N) CFM = -CF AZERO = .5*CF*WSAVE(1) NS2 = (N+1)/2 NS2M = NS2-1 DO 105 I=1,NS2M A(I) = CF*WSAVE(2*I) B(I) = CFM*WSAVE(2*I+1) 105 CONTINUE IF (MOD(N,2) .EQ. 0) THEN A(NS2) = .5*CF*WSAVE(N) B(NS2) = 0.0 ENDIF RETURN END SUBROUTINE RFFTF(N,R,WSAVE) C***BEGIN PROLOGUE RFFTF C THIS PROLOGUE HAS BEEN REMOVED FOR REASONS OF SPACE C FOR A COMPLETE COPY OF THIS ROUTINE CONTACT THE AUTHORS C From the book "Numerical Methods and Software" C by D. Kahaner, C. Moler, S. Nash C Prentice Hall 1988 C***END PROLOGUE RFFTF DIMENSION R(*) ,WSAVE(*) C***FIRST EXECUTABLE STATEMENT RFFTF IF (N .EQ. 1) RETURN CALL RFFTF1 (N,R,WSAVE,WSAVE(N+1),WSAVE(2*N+1)) RETURN END SUBROUTINE RFFTF1(N,C,CH,WA,IFAC) C***BEGIN PROLOGUE RFFTF1 C***REFER TO RFFTF C***ROUTINES CALLED RADF2,RADF3,RADF4,RADF5,RADFG C***END PROLOGUE RFFTF1 DIMENSION CH(*) ,C(*) ,WA(*) ,IFAC(*) C***FIRST EXECUTABLE STATEMENT RFFTF1 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 RADF2(IDO,L1,CC,CH,WA1) C***BEGIN PROLOGUE RADF2 C***REFER TO RFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE RADF2 DIMENSION CH(IDO,2,L1) ,CC(IDO,L1,2) , 1 WA1(*) C***FIRST EXECUTABLE STATEMENT RADF2 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 IF((IDO-1)/2.LT.L1) GO TO 108 DO 104 K=1,L1 CDIR$ IVDEP 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 GO TO 111 108 DO 110 I=3,IDO,2 IC = IDP2-I CDIR$ IVDEP DO 109 K=1,L1 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 109 CONTINUE 110 CONTINUE 111 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) C***BEGIN PROLOGUE RADF3 C***REFER TO RFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE RADF3 DIMENSION CH(IDO,3,L1) ,CC(IDO,L1,3) , 1 WA1(*) ,WA2(*) C***FIRST EXECUTABLE STATEMENT RADF3 TAUR = -.5 TAUI = .5*SQRT(3.) 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 IF((IDO-1)/2.LT.L1) GO TO 104 DO 103 K=1,L1 CDIR$ IVDEP 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 104 DO 106 I=3,IDO,2 IC = IDP2-I CDIR$ IVDEP DO 105 K=1,L1 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 105 CONTINUE 106 CONTINUE RETURN END SUBROUTINE RADF4(IDO,L1,CC,CH,WA1,WA2,WA3) C***BEGIN PROLOGUE RADF4 C***REFER TO RFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE RADF4 DIMENSION CC(IDO,L1,4) ,CH(IDO,4,L1) , 1 WA1(*) ,WA2(*) ,WA3(*) C***FIRST EXECUTABLE STATEMENT RADF4 HSQT2 = .5*SQRT(2.) 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 IF((IDO-1)/2.LT.L1) GO TO 111 DO 104 K=1,L1 CDIR$ IVDEP 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 GO TO 110 111 DO 109 I=3,IDO,2 IC = IDP2-I CDIR$ IVDEP DO 108 K=1,L1 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 108 CONTINUE 109 CONTINUE 110 IF (MOD(IDO,2) .EQ. 1) RETURN 105 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) C***BEGIN PROLOGUE RADF5 C***REFER TO RFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE RADF5 DIMENSION CC(IDO,L1,5) ,CH(IDO,5,L1) , 1 WA1(*) ,WA2(*) ,WA3(*) ,WA4(*) C***FIRST EXECUTABLE STATEMENT RADF5 PI = 4.*ATAN(1.) TR11 = SIN(.1*PI) TI11 = SIN(.4*PI) TR12 = -SIN(.3*PI) TI12 = SIN(.2*PI) 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 IF((IDO-1)/2.LT.L1) GO TO 104 DO 103 K=1,L1 CDIR$ IVDEP 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 104 DO 106 I=3,IDO,2 IC = IDP2-I CDIR$ IVDEP DO 105 K=1,L1 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 105 CONTINUE 106 CONTINUE RETURN END SUBROUTINE RADFG(IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA) C***BEGIN PROLOGUE RADFG C***REFER TO RFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE RADFG DIMENSION CH(IDO,L1,IP) ,CC(IDO,IP,L1) , 1 C1(IDO,L1,IP) ,C2(IDL1,IP), 2 CH2(IDL1,IP) ,WA(*) C***FIRST EXECUTABLE STATEMENT RADFG TPI = 8.*ATAN(1.) ARG = TPI/REAL(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 CDIR$ IVDEP 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 CDIR$ IVDEP 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 CDIR$ IVDEP 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