SUBROUTINE CFFT2D(N,F,LDF,W,FORWD) C***BEGIN PROLOGUE CFFT2D C***DATE WRITTEN 870811 (YYMMDD) C***REVISION DATE 870811 (YYMMDD) C***CATEGORY NO. J1B C***KEYWORDS TWO DIMENSIONAL FOURIER TRANSFORM, FFT C***AUTHOR KAHANER, DAVID K., (NBS) C***PURPOSE Two dimensional complex fast Fourier transform. C***DESCRIPTION C From the book, "Numerical Methods and Software" by C D. Kahaner, C. Moler, S. Nash C Prentice Hall, 1988 C Two dimensional fast Fourier transform, forward or backward C of complex N*N matrix F. C C Input: C N: (INTEGER) Number of rows and columns in the matrix F to be C transformed. You must set N > 0, NOT CHECKED. C F: (COMPLEX) Array of N*N complex values to be transformed. C This array is overwritten on output. C LDF: (INTEGER) Leading (first) dimension of the complex array F C in the subroutine that calls CFFT2D. For example, C if you declare F by either C COMPLEX F(0:15,0:20) OR F(16,21) then C set LDF=16. You must have LDF >= N, NOT CHECKED. C W: (COMPLEX) Array for internal use as work storage. C Must be dimensioned by calling program to be C at least 6N+15 REAL words or 3N+8 COMPLEX words. C FORWD: (LOGICAL) Direction of transform. Set to .TRUE. for C forward transform, set to .FALSE. for backward C transform. C C C Output: C F: (COMPLEX) Forward or reverse transformed input matrix. C Output is unscaled, that is, a call to CFFT2D C with FORWD=.TRUE. followed by a call to CFFT2D C with FORWD=.FALSE. returns original data C multiplied by N*N. C C C Remark: C For some applications it is desirable to have the transform scaled so C the center of the N by N frequency square corresponds to zero C frequency. The user can do this replacing the original input data C F(I,J) by F(I,J)*(-1.)**(I+J), I,J =0,...,N-1. C C C***REFERENCES (NONE) C***ROUTINES CALLED CFFTI, CFFTF, CFFTB C***END PROLOGUE CFFT2D COMPLEX F(0:LDF-1,0:*), W(0:*) LOGICAL FORWD C***FIRST EXECUTABLE STATEMENT CFFT2D C Find transform of each row, then of each column C First row transforms CALL CFFTI(N,W(N)) DO 10 I=0,N-1 C Place row in beginning of array W DO 5 J=0,N-1 W(J) = F(I,J) 5 CONTINUE C Compute fft of row IF(FORWD) THEN CALL CFFTF(N,W,W(N)) ELSE CALL CFFTB(N,W,W(N)) ENDIF C Copy back to row of f DO 6 J=0,N-1 F(I,J)=W(J) 6 CONTINUE 10 CONTINUE C Column transforms DO 20 J=0,N-1 C Pass column of F to CFFTF or CFFTB by passing F(0,J). C Similarly CFFTF or CFFTB places results back there. IF(FORWD) THEN CALL CFFTF(N, F(0,J), W(N)) ELSE CALL CFFTB(N, F(0,J), W(N)) ENDIF 20 CONTINUE RETURN END SUBROUTINE CFFTB(N,C,WSAVE) C***BEGIN PROLOGUE CFFTB 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 CFFTF. 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 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 4*N+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*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 CFFTF or CFFTB 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 CFFTB1 C***END PROLOGUE CFFTB DIMENSION C(*) ,WSAVE(*) C***FIRST EXECUTABLE STATEMENT CFFTB IF (N .EQ. 1) RETURN IW1 = N+N+1 IW2 = IW1+N+N CALL CFFTB1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2)) RETURN END SUBROUTINE CFFTB1(N,C,CH,WA,IFAC) C***BEGIN PROLOGUE CFFTB1 C***REFER TO CFFTB C***ROUTINES CALLED PASSB,PASSB2,PASSB3,PASSB4,PASSB5 C***END PROLOGUE CFFTB1 DIMENSION CH(*) ,C(*) ,WA(*) ,IFAC(*) C***FIRST EXECUTABLE STATEMENT CFFTB1 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 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 SUBROUTINE CFFTF(N,C,WSAVE) C***BEGIN PROLOGUE CFFTF 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 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. 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 4*N+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*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 CFFTF or CFFTB 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 CFFTF1 C***END PROLOGUE CFFTF DIMENSION C(*) ,WSAVE(*) C***FIRST EXECUTABLE STATEMENT CFFTF IF (N .EQ. 1) RETURN IW1 = N+N+1 IW2 = IW1+N+N CALL CFFTF1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2)) RETURN END SUBROUTINE CFFTF1(N,C,CH,WA,IFAC) C***BEGIN PROLOGUE CFFTF1 C***REFER TO CFFTF C***ROUTINES CALLED PASSF,PASSF2,PASSF3,PASSF4,PASSF5 C***END PROLOGUE CFFTF1 DIMENSION CH(*) ,C(*) ,WA(*) ,IFAC(*) C***FIRST EXECUTABLE STATEMENT CFFTF1 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 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 SUBROUTINE CFFTI(N,WSAVE) C***BEGIN PROLOGUE CFFTI 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 CFFTF and CFFTB. 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 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 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 CFFTI1 C***END PROLOGUE CFFTI DIMENSION WSAVE(*) C***FIRST EXECUTABLE STATEMENT CFFTI IF (N .EQ. 1) RETURN IW1 = N+N+1 IW2 = IW1+N+N CALL CFFTI1 (N,WSAVE(IW1),WSAVE(IW2)) RETURN END SUBROUTINE CFFTI1(N,WA,IFAC) C***BEGIN PROLOGUE CFFTI1 C***REFER TO CFFTI C***ROUTINES CALLED (NONE) C***END PROLOGUE CFFTI1 DIMENSION WA(*) ,IFAC(*) ,NTRYH(4) DATA NTRYH(1),NTRYH(2),NTRYH(3),NTRYH(4)/3,4,2,5/ C***FIRST EXECUTABLE STATEMENT CFFTI1 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.*ATAN(1.) ARGH = TPI/REAL(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. WA(I) = 0. LD = LD+L1 FI = 0. ARGLD = REAL(LD)*ARGH DO 108 II=4,IDOT,2 I = I+2 FI = FI+1. 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 EZFFT1(N,WA,IFAC) C***BEGIN PROLOGUE EZFFT1 C***REFER TO EZFFTI C***ROUTINES CALLED (NONE) C***END PROLOGUE EZFFT1 DIMENSION WA(*) ,IFAC(*) ,NTRYH(4) DATA NTRYH(1),NTRYH(2),NTRYH(3),NTRYH(4)/4,2,3,5/ C***FIRST EXECUTABLE STATEMENT EZFFT1 TPI = 8.*ATAN(1.) 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 ARGH = TPI/REAL(N) IS = 0 NFM1 = NF-1 L1 = 1 IF (NFM1 .EQ. 0) RETURN DO 111 K1=1,NFM1 IP = IFAC(K1+2) L2 = L1*IP IDO = N/L2 IPM = IP-1 ARG1 = REAL(L1)*ARGH CH1 = 1. SH1 = 0. DCH1 = COS(ARG1) DSH1 = SIN(ARG1) DO 110 J=1,IPM CH1H = DCH1*CH1-DSH1*SH1 SH1 = DCH1*SH1+DSH1*CH1 CH1 = CH1H I = IS+2 WA(I-1) = CH1 WA(I) = SH1 IF (IDO .LT. 5) GO TO 109 DO 108 II=5,IDO,2 I = I+2 WA(I-1) = CH1*WA(I-3)-SH1*WA(I-2) WA(I) = CH1*WA(I-2)+SH1*WA(I-3) 108 CONTINUE 109 IS = IS+IDO 110 CONTINUE L1 = L2 111 CONTINUE RETURN END SUBROUTINE EZFFTB(N,R,AZERO,A,B,WSAVE) C***BEGIN PROLOGUE EZFFTB 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, backward 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 EZFFTB computes a real perodic sequence from its C Fourier coefficients (Fourier synthesis). The transform is C defined below at Output Parameter R. EZFFTB is a simplified C but slower version of RFFTB. C C Input Parameters C C N the length of the output array R. The method is most C efficient when N is the product of small primes. C C AZERO the constant Fourier coefficient C C A,B arrays which contain the remaining Fourier coefficients. C These arrays are not destroyed. C C The length of these arrays depends on whether N is even or C odd. C C If N is even, N/2 locations are required. C If N is odd, (N-1)/2 locations are required C C WSAVE a work array which must be dimensioned at least 3*N+15 C in the program that calls EZFFTB. 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 C Output Parameters C C R if N is even, define KMAX=N/2 C if N is odd, define KMAX=(N-1)/2 C C Then for I=1,...,N C C R(I)=AZERO plus the sum from K=1 to K=KMAX of C C A(K)*COS(K*(I-1)*2*PI/N)+B(K)*SIN(K*(I-1)*2*PI/N) C C ********************* Complex Notation ************************** C C For J=1,...,N C C R(J) equals the sum from K=-KMAX to K=KMAX of C C C(K)*EXP(I*K*(J-1)*2*PI/N) C C where C C C(K) = .5*CMPLX(A(K),-B(K)) for K=1,...,KMAX C C C(-K) = CONJG(C(K)) C C C(0) = AZERO C C and I=SQRT(-1) C C *************** Amplitude - Phase Notation *********************** C C For I=1,...,N C C R(I) equals AZERO plus the sum from K=1 to K=KMAX of C C ALPHA(K)*COS(K*(I-1)*2*PI/N+BETA(K)) C C where C C ALPHA(K) = SQRT(A(K)*A(K)+B(K)*B(K)) C C COS(BETA(K))=A(K)/ALPHA(K) C C SIN(BETA(K))=-B(K)/ALPHA(K) 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 C***REFERENCES (NONE) C***ROUTINES CALLED RFFTB C***END PROLOGUE EZFFTB DIMENSION R(*) ,A(*) ,B(*) ,WSAVE(*) C***FIRST EXECUTABLE STATEMENT EZFFTB IF (N-2) 101,102,103 101 R(1) = AZERO RETURN 102 R(1) = AZERO+A(1) R(2) = AZERO-A(1) RETURN 103 NS2 = (N-1)/2 DO 104 I=1,NS2 R(2*I) = .5*A(I) R(2*I+1) = -.5*B(I) 104 CONTINUE R(1) = AZERO IF (MOD(N,2) .EQ. 0) R(N) = A(NS2+1) CALL RFFTB (N,R,WSAVE(N+1)) RETURN END 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 EZFFTI(N,WSAVE) C***BEGIN PROLOGUE EZFFTI 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 Initialize EZFFTF and EZFFTB C***DESCRIPTION C C Subroutine EZFFTI initializes the array WSAVE which is used in C both EZFFTF and EZFFTB. 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 3*N+15. C The same work array can be used for both EZFFTF and EZFFTB C as long as N remains unchanged. Different WSAVE arrays C are required for different values of N. C 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 EZFFT1 C***END PROLOGUE EZFFTI DIMENSION WSAVE(*) C***FIRST EXECUTABLE STATEMENT EZFFTI IF (N .EQ. 1) RETURN CALL EZFFT1 (N,WSAVE(2*N+1),WSAVE(3*N+1)) RETURN END SUBROUTINE PASSB(NAC,IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA) C***BEGIN PROLOGUE PASSB C***REFER TO CFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE PASSB 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 PASSB 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 PASSB2(IDO,L1,CC,CH,WA1) C***BEGIN PROLOGUE PASSB2 C***REFER TO CFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE PASSB2 DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) , 1 WA1(*) C***FIRST EXECUTABLE STATEMENT PASSB2 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 PASSB3(IDO,L1,CC,CH,WA1,WA2) C***BEGIN PROLOGUE PASSB3 C***REFER TO CFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE PASSB3 DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) , 1 WA1(*) ,WA2(*) C***FIRST EXECUTABLE STATEMENT PASSB3 TAUR = -.5 TAUI = .5*SQRT(3.) 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 PASSB4(IDO,L1,CC,CH,WA1,WA2,WA3) C***BEGIN PROLOGUE PASSB4 C***REFER TO CFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE PASSB4 DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) , 1 WA1(*) ,WA2(*) ,WA3(*) C***FIRST EXECUTABLE STATEMENT PASSB4 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 PASSB5(IDO,L1,CC,CH,WA1,WA2,WA3,WA4) C***BEGIN PROLOGUE PASSB5 C***REFER TO CFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE PASSB5 DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) , 1 WA1(*) ,WA2(*) ,WA3(*) ,WA4(*) C***FIRST EXECUTABLE STATEMENT PASSB5 PI = 4.*ATAN(1.) TR11 = SIN(.1*PI) TI11 = SIN(.4*PI) TR12 = -SIN(.3*PI) TI12 = SIN(.2*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 PASSF(NAC,IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA) C***BEGIN PROLOGUE PASSF C***REFER TO CFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE PASSF 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 PASSF 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 PASSF2(IDO,L1,CC,CH,WA1) C***BEGIN PROLOGUE PASSF2 C***REFER TO CFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE PASSF2 DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) , 1 WA1(*) C***FIRST EXECUTABLE STATEMENT PASSF2 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 PASSF3(IDO,L1,CC,CH,WA1,WA2) C***BEGIN PROLOGUE PASSF3 C***REFER TO CFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE PASSF3 DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) , 1 WA1(*) ,WA2(*) C***FIRST EXECUTABLE STATEMENT PASSF3 TAUR = -.5 TAUI = -.5*SQRT(3.) 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 PASSF4(IDO,L1,CC,CH,WA1,WA2,WA3) C***BEGIN PROLOGUE PASSF4 C***REFER TO CFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE PASSF4 DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) , 1 WA1(*) ,WA2(*) ,WA3(*) C***FIRST EXECUTABLE STATEMENT PASSF4 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 PASSF5(IDO,L1,CC,CH,WA1,WA2,WA3,WA4) C***BEGIN PROLOGUE PASSF5 C***REFER TO CFFTF C***ROUTINES CALLED (NONE) C***END PROLOGUE PASSF5 DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) , 1 WA1(*) ,WA2(*) ,WA3(*) ,WA4(*) C***FIRST EXECUTABLE STATEMENT PASSF5 PI = 4.*ATAN(1.) TR11 = SIN(.1*PI) TI11 = -SIN(.4*PI) TR12 = -SIN(.3*PI) TI12 = -SIN(.2*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 RADB2(IDO,L1,CC,CH,WA1) C***BEGIN PROLOGUE RADB2 C***REFER TO RFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE RADB2 DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) , 1 WA1(*) C***FIRST EXECUTABLE STATEMENT RADB2 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 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 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 GO TO 111 108 DO 110 I=3,IDO,2 IC = IDP2-I CDIR$ IVDEP DO 109 K=1,L1 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 109 CONTINUE 110 CONTINUE 111 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) C***BEGIN PROLOGUE RADB3 C***REFER TO RFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE RADB3 DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) , 1 WA1(*) ,WA2(*) C***FIRST EXECUTABLE STATEMENT RADB3 TAUR = -.5 TAUI = .5*SQRT(3.) 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 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 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 104 DO 106 I=3,IDO,2 IC = IDP2-I CDIR$ IVDEP DO 105 K=1,L1 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 105 CONTINUE 106 CONTINUE RETURN END SUBROUTINE RADB4(IDO,L1,CC,CH,WA1,WA2,WA3) C***BEGIN PROLOGUE RADB4 C***REFER TO RFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE RADB4 DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) , 1 WA1(*) ,WA2(*) ,WA3(*) C***FIRST EXECUTABLE STATEMENT RADB4 SQRT2 = SQRT(2.) 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 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 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 GO TO 111 108 DO 110 I=3,IDO,2 IC = IDP2-I CDIR$ IVDEP DO 109 K=1,L1 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 109 CONTINUE 110 CONTINUE 111 IF (MOD(IDO,2) .EQ. 1) RETURN 105 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) C***BEGIN PROLOGUE RADB5 C***REFER TO RFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE RADB5 DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) , 1 WA1(*) ,WA2(*) ,WA3(*) ,WA4(*) C***FIRST EXECUTABLE STATEMENT RADB5 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 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 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 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 104 DO 106 I=3,IDO,2 IC = IDP2-I CDIR$ IVDEP DO 105 K=1,L1 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 105 CONTINUE 106 CONTINUE RETURN END SUBROUTINE RADBG(IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA) C***BEGIN PROLOGUE RADBG C***REFER TO RFFTB C***ROUTINES CALLED (NONE) C***END PROLOGUE RADBG 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 RADBG TPI = 8.*ATAN(1.) ARG = TPI/REAL(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 CDIR$ IVDEP 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 CDIR$ IVDEP 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 CDIR$ IVDEP 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 CDIR$ IVDEP 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) 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 SUBROUTINE RFFTB(N,R,WSAVE) C***BEGIN PROLOGUE RFFTB 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 Backward transform of a real coefficient array. C***DESCRIPTION C C Subroutine RFFTB computes the real perodic sequence from its C Fourier coefficients (Fourier synthesis). The transform is defined C below at output parameter R. C C Input Parameters C C N the length of the array R to be transformed. The method C is most efficient when N is a product of small primes. C N may change so long as different work arrays are provided. C C R a real array of length N which contains the sequence C to be transformed C C WSAVE a work array which must be dimensioned at least 2*N+15 C in the program that calls RFFTB. The WSAVE array must be C initialized by calling subroutine RFFTI(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 RFFTF and RFFTB. C C C Output Parameters C C R For N even and For I = 1,...,N C C R(I) = R(1)+(-1)**(I-1)*R(N) C C plus the sum from K=2 to K=N/2 of C C 2.*R(2*K-2)*COS((K-1)*(I-1)*2*PI/N) C C -2.*R(2*K-1)*SIN((K-1)*(I-1)*2*PI/N) C C For N odd and For I = 1,...,N C C R(I) = R(1) plus the sum from K=2 to K=(N+1)/2 of C C 2.*R(2*K-2)*COS((K-1)*(I-1)*2*PI/N) C C -2.*R(2*K-1)*SIN((K-1)*(I-1)*2*PI/N) C C ***** Note: C This transform is unnormalized since a call of RFFTF C followed by a call of RFFTB will multiply the input C sequence by N. C C WSAVE contains results which must not be destroyed between C calls of RFFTB or RFFTF. C 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 RFFTB1 C***END PROLOGUE RFFTB DIMENSION R(*) ,WSAVE(*) C***FIRST EXECUTABLE STATEMENT RFFTB IF (N .EQ. 1) RETURN CALL RFFTB1 (N,R,WSAVE,WSAVE(N+1),WSAVE(2*N+1)) RETURN END SUBROUTINE RFFTB1(N,C,CH,WA,IFAC) C***BEGIN PROLOGUE RFFTB1 C***REFER TO RFFTB C***ROUTINES CALLED RADB2,RADB3,RADB4,RADB5,RADBG C***END PROLOGUE RFFTB1 DIMENSION CH(*) ,C(*) ,WA(*) ,IFAC(*) C***FIRST EXECUTABLE STATEMENT RFFTB1 NF = IFAC(2) NA = 0 L1 = 1 IW = 1 DO 116 K1=1,NF IP = IFAC(K1+2) L2 = IP*L1 IDO = N/L2 IDL1 = IDO*L1 IF (IP .NE. 4) GO TO 103 IX2 = IW+IDO IX3 = IX2+IDO IF (NA .NE. 0) GO TO 101 CALL RADB4 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3)) GO TO 102 101 CALL RADB4 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3)) 102 NA = 1-NA GO TO 115 103 IF (IP .NE. 2) GO TO 106 IF (NA .NE. 0) GO TO 104 CALL RADB2 (IDO,L1,C,CH,WA(IW)) GO TO 105 104 CALL RADB2 (IDO,L1,CH,C,WA(IW)) 105 NA = 1-NA GO TO 115 106 IF (IP .NE. 3) GO TO 109 IX2 = IW+IDO IF (NA .NE. 0) GO TO 107 CALL RADB3 (IDO,L1,C,CH,WA(IW),WA(IX2)) GO TO 108 107 CALL RADB3 (IDO,L1,CH,C,WA(IW),WA(IX2)) 108 NA = 1-NA GO TO 115 109 IF (IP .NE. 5) GO TO 112 IX2 = IW+IDO IX3 = IX2+IDO IX4 = IX3+IDO IF (NA .NE. 0) GO TO 110 CALL RADB5 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4)) GO TO 111 110 CALL RADB5 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3),WA(IX4)) 111 NA = 1-NA GO TO 115 112 IF (NA .NE. 0) GO TO 113 CALL RADBG (IDO,IP,L1,IDL1,C,C,C,CH,CH,WA(IW)) GO TO 114 113 CALL RADBG (IDO,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW)) 114 IF (IDO .EQ. 1) NA = 1-NA 115 L1 = L2 IW = IW+(IP-1)*IDO 116 CONTINUE IF (NA .EQ. 0) RETURN DO 117 I=1,N C(I) = CH(I) 117 CONTINUE RETURN END SUBROUTINE RFFTF(N,R,WSAVE) C***BEGIN PROLOGUE RFFTF 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 Forward transform of a real, periodic sequence. C***DESCRIPTION C C Subroutine RFFTF computes the Fourier coefficients of a real C perodic sequence (Fourier analysis). The transform is defined C below at output parameter R. C C Input Parameters C C N the length of the array R to be transformed. The method C is most efficient when N is a product of small primes. C N may change so long as different work arrays are provided C C R a real array of length N which contains the sequence C to be transformed C C WSAVE a work array which must be dimensioned at least 2*N+15 C in the program that calls RFFTF. The WSAVE array must be C initialized by calling subroutine RFFTI(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 RFFTF and RFFTB. C C C Output Parameters C C R R(1) = the sum from I=1 to I=N of R(I) C C If N is even set L = N/2; if N is odd set L = (N+1)/2 C C then for K = 2,...,L C C R(2*K-2) = the sum from I = 1 to I = N of C C R(I)*COS((K-1)*(I-1)*2*PI/N) C C R(2*K-1) = the sum from I = 1 to I = N of C C -R(I)*SIN((K-1)*(I-1)*2*PI/N) C C If N is even C C R(N) = the sum from I = 1 to I = N of C C (-1)**(I-1)*R(I) C C ***** Note: C This transform is unnormalized since a call of RFFTF C followed by a call of RFFTB will multiply the input C sequence by N. C C WSAVE contains results which must not be destroyed between C calls of RFFTF or RFFTB. C 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 RFFTF1 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