2007-01-11 21:25:52 +00:00
|
|
|
SUBROUTINE FOUR2a (DATA,N,NDIM,ISIGN,IFORM)
|
|
|
|
|
|
|
|
|
|
C Cooley-Tukey fast Fourier transform in USASI basic Fortran.
|
|
|
|
|
C multi-dimensional transform, each dimension a power of two,
|
|
|
|
|
C complex or real data.
|
|
|
|
|
|
|
|
|
|
C TRANSFORM(K1,K2,...) = SUM(DATA(J1,J2,...)*EXP(ISIGN*2*PI*SQRT(-1)
|
|
|
|
|
C *((J1-1)*(K1-1)/N(1)+(J2-1)*(K2-1)/N(2)+...))), summed for all
|
|
|
|
|
C J1 and K1 from 1 to N(1), J2 and K2 from 1 TO N(2),
|
|
|
|
|
C etc, for all NDIM subscripts. NDIM must be positive and
|
|
|
|
|
C each N(IDIM) must be a power of two. ISIGN is +1 or -1.
|
|
|
|
|
C Let NTOT = N(1)*N(2)*...*N(NDIM). Then a -1 transform
|
|
|
|
|
C followed by a +1 one (or vice versa) returns NTOT
|
|
|
|
|
C times the original data.
|
|
|
|
|
|
|
|
|
|
C IFORM = 1, 0 or -1, as data is
|
|
|
|
|
C complex, real, or the first half of a complex array. Transform
|
|
|
|
|
C values are returned in array DATA. They are complex, real, or
|
|
|
|
|
C the first half of a complex array, as IFORM = 1, -1 or 0.
|
|
|
|
|
|
|
|
|
|
C The transform of a real array (IFORM = 0) dimensioned N(1) by N(2)
|
|
|
|
|
C by ... will be returned in the same array, now considered to
|
|
|
|
|
C be complex of dimensions N(1)/2+1 by N(2) by .... Note that if
|
|
|
|
|
C IFORM = 0 or -1, N(1) must be even, and enough room must be
|
|
|
|
|
C reserved. The missing values may be obtained by complex conjuga-
|
|
|
|
|
C tion.
|
|
|
|
|
|
|
|
|
|
C The reverse transformation of a half complex array dimensioned
|
|
|
|
|
C N(1)/2+1 by N(2) by ..., is accomplished by setting IFORM
|
|
|
|
|
C to -1. In the N array, N(1) must be the true N(1), not N(1)/2+1.
|
|
|
|
|
C The transform will be real and returned to the input array.
|
|
|
|
|
|
|
|
|
|
C Running time is proportional to NTOT*LOG2(NTOT), rather than
|
|
|
|
|
C the naive NTOT**2. Furthermore, less error is built up.
|
|
|
|
|
|
|
|
|
|
C Written by Norman Brenner of MIT Lincoln Laboratory, January 1969.
|
|
|
|
|
C See IEEE Audio Transactions (June 1967), Special issue on FFT.
|
|
|
|
|
|
|
|
|
|
parameter(NMAX=2048*1024)
|
|
|
|
|
DIMENSION DATA(NMAX), N(1)
|
|
|
|
|
NTOT=1
|
|
|
|
|
DO 10 IDIM=1,NDIM
|
|
|
|
|
10 NTOT=NTOT*N(IDIM)
|
|
|
|
|
IF (IFORM) 70,20,20
|
|
|
|
|
20 NREM=NTOT
|
|
|
|
|
DO 60 IDIM=1,NDIM
|
|
|
|
|
NREM=NREM/N(IDIM)
|
|
|
|
|
NPREV=NTOT/(N(IDIM)*NREM)
|
|
|
|
|
NCURR=N(IDIM)
|
|
|
|
|
IF (IDIM-1+IFORM) 30,30,40
|
|
|
|
|
30 NCURR=NCURR/2
|
|
|
|
|
40 CALL BITRV (DATA,NPREV,NCURR,NREM)
|
|
|
|
|
CALL COOL2 (DATA,NPREV,NCURR,NREM,ISIGN)
|
|
|
|
|
IF (IDIM-1+IFORM) 50,50,60
|
|
|
|
|
50 CALL FIXRL (DATA,N(1),NREM,ISIGN,IFORM)
|
|
|
|
|
NTOT=(NTOT/N(1))*(N(1)/2+1)
|
|
|
|
|
60 CONTINUE
|
|
|
|
|
RETURN
|
|
|
|
|
70 NTOT=(NTOT/N(1))*(N(1)/2+1)
|
|
|
|
|
NREM=1
|
|
|
|
|
DO 100 JDIM=1,NDIM
|
|
|
|
|
IDIM=NDIM+1-JDIM
|
|
|
|
|
NCURR=N(IDIM)
|
|
|
|
|
IF (IDIM-1) 80,80,90
|
|
|
|
|
80 NCURR=NCURR/2
|
|
|
|
|
CALL FIXRL (DATA,N(1),NREM,ISIGN,IFORM)
|
|
|
|
|
NTOT=NTOT/(N(1)/2+1)*N(1)
|
|
|
|
|
90 NPREV=NTOT/(N(IDIM)*NREM)
|
|
|
|
|
CALL BITRV (DATA,NPREV,NCURR,NREM)
|
|
|
|
|
CALL COOL2 (DATA,NPREV,NCURR,NREM,ISIGN)
|
|
|
|
|
100 NREM=NREM*N(IDIM)
|
|
|
|
|
RETURN
|
|
|
|
|
END
|
|
|
|
|
SUBROUTINE BITRV (DATA,NPREV,N,NREM)
|
|
|
|
|
C SHUFFLE THE DATA BY BIT REVERSAL.
|
|
|
|
|
C DIMENSION DATA(NPREV,N,NREM)
|
|
|
|
|
C COMPLEX DATA
|
|
|
|
|
C EXCHANGE DATA(J1,J4REV,J5) WITH DATA(J1,J4,J5) FOR ALL J1 FROM 1
|
|
|
|
|
C TO NPREV, ALL J4 FROM 1 TO N (WHICH MUST BE A POWER OF TWO), AND
|
|
|
|
|
C ALL J5 FROM 1 TO NREM. J4REV-1 IS THE BIT REVERSAL OF J4-1. E.G.
|
|
|
|
|
C SUPPOSE N = 32. THEN FOR J4-1 = 10011, J4REV-1 = 11001, ETC.
|
|
|
|
|
parameter(NMAX=2048*1024)
|
|
|
|
|
DIMENSION DATA(NMAX)
|
|
|
|
|
IP0=2
|
|
|
|
|
IP1=IP0*NPREV
|
|
|
|
|
IP4=IP1*N
|
|
|
|
|
IP5=IP4*NREM
|
|
|
|
|
I4REV=1
|
|
|
|
|
C I4REV = 1+(J4REV-1)*IP1
|
|
|
|
|
DO 60 I4=1,IP4,IP1
|
|
|
|
|
C I4 = 1+(J4-1)*IP1
|
|
|
|
|
IF (I4-I4REV) 10,30,30
|
|
|
|
|
10 I1MAX=I4+IP1-IP0
|
|
|
|
|
DO 20 I1=I4,I1MAX,IP0
|
|
|
|
|
C I1 = 1+(J1-1)*IP0+(J4-1)*IP1
|
|
|
|
|
DO 20 I5=I1,IP5,IP4
|
|
|
|
|
C I5 = 1+(J1-1)*IP0+(J4-1)*IP1+(J5-1)*IP4
|
|
|
|
|
I5REV=I4REV+I5-I4
|
|
|
|
|
C I5REV = 1+(J1-1)*IP0+(J4REV-1)*IP1+(J5-1)*IP4
|
|
|
|
|
TEMPR=DATA(I5)
|
|
|
|
|
TEMPI=DATA(I5+1)
|
|
|
|
|
DATA(I5)=DATA(I5REV)
|
|
|
|
|
DATA(I5+1)=DATA(I5REV+1)
|
|
|
|
|
DATA(I5REV)=TEMPR
|
|
|
|
|
20 DATA(I5REV+1)=TEMPI
|
|
|
|
|
C ADD ONE WITH DOWNWARD CARRY TO THE HIGH ORDER BIT OF J4REV-1.
|
|
|
|
|
30 IP2=IP4/2
|
|
|
|
|
40 IF (I4REV-IP2) 60,60,50
|
|
|
|
|
50 I4REV=I4REV-IP2
|
|
|
|
|
IP2=IP2/2
|
|
|
|
|
IF (IP2-IP1) 60,40,40
|
|
|
|
|
60 I4REV=I4REV+IP2
|
|
|
|
|
RETURN
|
|
|
|
|
END
|
|
|
|
|
SUBROUTINE COOL2 (DATA,NPREV,N,NREM,ISIGN)
|
|
|
|
|
C DISCRETE FOURIER TRANSFORM OF LENGTH N. IN-PLACE COOLEY-TUKEY
|
|
|
|
|
C ALGORITHM, BIT-REVERSED TO NORMAL ORDER, SANDE-TUKEY PHASE SHIFTS.
|
|
|
|
|
C DIMENSION DATA(NPREV,N,NREM)
|
|
|
|
|
C COMPLEX DATA
|
|
|
|
|
C DATA(J1,K4,J5) = SUM(DATA(J1,J4,J5)*EXP(ISIGN*2*PI*I*(J4-1)*
|
|
|
|
|
C (K4-1)/N)), SUMMED OVER J4 = 1 TO N FOR ALL J1 FROM 1 TO NPREV,
|
|
|
|
|
C K4 FROM 1 TO N AND J5 FROM 1 TO NREM. N MUST BE A POWER OF TWO.
|
|
|
|
|
C METHOD--LET IPREV TAKE THE VALUES 1, 2 OR 4, 4 OR 8, ..., N/16,
|
|
|
|
|
C N/4, N. THE CHOICE BETWEEN 2 OR 4, ETC., DEPENDS ON WHETHER N IS
|
|
|
|
|
C A POWER OF FOUR. DEFINE IFACT = 2 OR 4, THE NEXT FACTOR THAT
|
|
|
|
|
C IPREV MUST TAKE, AND IREM = N/(IFACT*IPREV). THEN--
|
|
|
|
|
C DIMENSION DATA(NPREV,IPREV,IFACT,IREM,NREM)
|
|
|
|
|
C COMPLEX DATA
|
|
|
|
|
C DATA(J1,J2,K3,J4,J5) = SUM(DATA(J1,J2,J3,J4,J5)*EXP(ISIGN*2*PI*I*
|
|
|
|
|
C (K3-1)*((J3-1)/IFACT+(J2-1)/(IFACT*IPREV)))), SUMMED OVER J3 = 1
|
|
|
|
|
C TO IFACT FOR ALL J1 FROM 1 TO NPREV, J2 FROM 1 TO IPREV, K3 FROM
|
|
|
|
|
C 1 TO IFACT, J4 FROM 1 TO IREM AND J5 FROM 1 TO NREM. THIS IS
|
|
|
|
|
C A PHASE-SHIFTED DISCRETE FOURIER TRANSFORM OF LENGTH IFACT.
|
|
|
|
|
C FACTORING N BY FOURS SAVES ABOUT TWENTY FIVE PERCENT OVER FACTOR-
|
|
|
|
|
C ING BY TWOS. DATA MUST BE BIT-REVERSED INITIALLY.
|
|
|
|
|
C IT IS NOT NECESSARY TO REWRITE THIS SUBROUTINE INTO COMPLEX
|
|
|
|
|
C NOTATION SO LONG AS THE FORTRAN COMPILER USED STORES REAL AND
|
|
|
|
|
C IMAGINARY PARTS IN ADJACENT STORAGE LOCATIONS. IT MUST ALSO
|
|
|
|
|
C STORE ARRAYS WITH THE FIRST SUBSCRIPT INCREASING FASTEST.
|
|
|
|
|
parameter(NMAX=2048*1024)
|
|
|
|
|
DIMENSION DATA(NMAX)
|
|
|
|
|
|
|
|
|
|
real*8 twopi,wstpr,wstpi,wr,wi,w2r,w2i,w3r,w3i,wtempr
|
|
|
|
|
|
|
|
|
|
TWOPI=6.2831853072*FLOAT(ISIGN)
|
|
|
|
|
IP0=2
|
|
|
|
|
IP1=IP0*NPREV
|
|
|
|
|
IP4=IP1*N
|
|
|
|
|
IP5=IP4*NREM
|
|
|
|
|
IP2=IP1
|
|
|
|
|
C IP2=IP1*IPROD
|
|
|
|
|
NPART=N
|
|
|
|
|
10 IF (NPART-2) 60,30,20
|
|
|
|
|
20 NPART=NPART/4
|
|
|
|
|
GO TO 10
|
|
|
|
|
C DO A FOURIER TRANSFORM OF LENGTH TWO
|
|
|
|
|
30 IF (IP2-IP4) 40,160,160
|
|
|
|
|
40 IP3=IP2*2
|
|
|
|
|
C IP3=IP2*IFACT
|
|
|
|
|
DO 50 I1=1,IP1,IP0
|
|
|
|
|
C I1 = 1+(J1-1)*IP0
|
|
|
|
|
DO 50 I5=I1,IP5,IP3
|
|
|
|
|
C I5 = 1+(J1-1)*IP0+(J4-1)*IP3+(J5-1)*IP4
|
|
|
|
|
I3A=I5
|
|
|
|
|
I3B=I3A+IP2
|
|
|
|
|
C I3 = 1+(J1-1)*IP0+(J2-1)*IP1+(J3-1)*IP2+(J4-1)*IP3+(J5-1)*IP4
|
|
|
|
|
TEMPR=DATA(I3B)
|
|
|
|
|
TEMPI=DATA(I3B+1)
|
|
|
|
|
DATA(I3B)=DATA(I3A)-TEMPR
|
|
|
|
|
DATA(I3B+1)=DATA(I3A+1)-TEMPI
|
|
|
|
|
DATA(I3A)=DATA(I3A)+TEMPR
|
|
|
|
|
50 DATA(I3A+1)=DATA(I3A+1)+TEMPI
|
|
|
|
|
IP2=IP3
|
|
|
|
|
C DO A FOURIER TRANSFORM OF LENGTH FOUR (FROM BIT REVERSED ORDER)
|
|
|
|
|
60 IF (IP2-IP4) 70,160,160
|
|
|
|
|
70 IP3=IP2*4
|
|
|
|
|
C IP3=IP2*IFACT
|
|
|
|
|
C COMPUTE TWOPI THRU WR AND WI IN DOUBLE PRECISION, IF AVAILABLE.
|
|
|
|
|
THETA=TWOPI/FLOAT(IP3/IP1)
|
|
|
|
|
SINTH=SIN(THETA/2)
|
|
|
|
|
WSTPR=-2*SINTH*SINTH
|
|
|
|
|
WSTPI=SIN(THETA)
|
|
|
|
|
WR=1.
|
|
|
|
|
WI=0.
|
|
|
|
|
DO 150 I2=1,IP2,IP1
|
|
|
|
|
C I2 = 1+(J2-1)*IP1
|
|
|
|
|
IF (I2-1) 90,90,80
|
|
|
|
|
80 W2R=WR*WR-WI*WI
|
|
|
|
|
W2I=2*WR*WI
|
|
|
|
|
W3R=W2R*WR-W2I*WI
|
|
|
|
|
W3I=W2R*WI+W2I*WR
|
|
|
|
|
90 I1MAX=I2+IP1-IP0
|
|
|
|
|
DO 140 I1=I2,I1MAX,IP0
|
|
|
|
|
C I1 = 1+(J1-1)*IP0+(J2-1)*IP1
|
|
|
|
|
DO 140 I5=I1,IP5,IP3
|
|
|
|
|
C I5 = 1+(J1-1)*IP0+(J2-1)*IP1+(J4-1)*IP3+(J5-1)*IP4
|
|
|
|
|
I3A=I5
|
|
|
|
|
I3B=I3A+IP2
|
|
|
|
|
I3C=I3B+IP2
|
|
|
|
|
I3D=I3C+IP2
|
|
|
|
|
C I3 = 1+(J1-1)*IP0+(J2-1)*IP1+(J3-1)*IP2+(J4-1)*IP3+(J5-1)*IP4
|
|
|
|
|
IF (I2-1) 110,110,100
|
|
|
|
|
C APPLY THE PHASE SHIFT FACTORS
|
|
|
|
|
100 TEMPR=DATA(I3B)
|
|
|
|
|
DATA(I3B)=W2R*DATA(I3B)-W2I*DATA(I3B+1)
|
|
|
|
|
DATA(I3B+1)=W2R*DATA(I3B+1)+W2I*TEMPR
|
|
|
|
|
TEMPR=DATA(I3C)
|
|
|
|
|
DATA(I3C)=WR*DATA(I3C)-WI*DATA(I3C+1)
|
|
|
|
|
DATA(I3C+1)=WR*DATA(I3C+1)+WI*TEMPR
|
|
|
|
|
TEMPR=DATA(I3D)
|
|
|
|
|
DATA(I3D)=W3R*DATA(I3D)-W3I*DATA(I3D+1)
|
|
|
|
|
DATA(I3D+1)=W3R*DATA(I3D+1)+W3I*TEMPR
|
|
|
|
|
110 T0R=DATA(I3A)+DATA(I3B)
|
|
|
|
|
T0I=DATA(I3A+1)+DATA(I3B+1)
|
|
|
|
|
T1R=DATA(I3A)-DATA(I3B)
|
|
|
|
|
T1I=DATA(I3A+1)-DATA(I3B+1)
|
|
|
|
|
T2R=DATA(I3C)+DATA(I3D)
|
|
|
|
|
T2I=DATA(I3C+1)+DATA(I3D+1)
|
|
|
|
|
T3R=DATA(I3C)-DATA(I3D)
|
|
|
|
|
T3I=DATA(I3C+1)-DATA(I3D+1)
|
|
|
|
|
DATA(I3A)=T0R+T2R
|
|
|
|
|
DATA(I3A+1)=T0I+T2I
|
|
|
|
|
DATA(I3C)=T0R-T2R
|
|
|
|
|
DATA(I3C+1)=T0I-T2I
|
|
|
|
|
IF (ISIGN) 120,120,130
|
|
|
|
|
120 T3R=-T3R
|
|
|
|
|
T3I=-T3I
|
|
|
|
|
130 DATA(I3B)=T1R-T3I
|
|
|
|
|
DATA(I3B+1)=T1I+T3R
|
|
|
|
|
DATA(I3D)=T1R+T3I
|
|
|
|
|
140 DATA(I3D+1)=T1I-T3R
|
|
|
|
|
WTEMPR=WR
|
|
|
|
|
WR=WSTPR*WTEMPR-WSTPI*WI+WTEMPR
|
|
|
|
|
150 WI=WSTPR*WI+WSTPI*WTEMPR+WI
|
|
|
|
|
IP2=IP3
|
|
|
|
|
GO TO 60
|
|
|
|
|
160 RETURN
|
|
|
|
|
END
|
|
|
|
|
SUBROUTINE FIXRL (DATA,N,NREM,ISIGN,IFORM)
|
|
|
|
|
C FOR IFORM = 0, CONVERT THE TRANSFORM OF A DOUBLED-UP REAL ARRAY,
|
|
|
|
|
C CONSIDERED COMPLEX, INTO ITS TRUE TRANSFORM. SUPPLY ONLY THE
|
|
|
|
|
C FIRST HALF OF THE COMPLEX TRANSFORM, AS THE SECOND HALF HAS
|
|
|
|
|
C CONJUGATE SYMMETRY. FOR IFORM = -1, CONVERT THE FIRST HALF
|
|
|
|
|
C OF THE TRUE TRANSFORM INTO THE TRANSFORM OF A DOUBLED-UP REAL
|
|
|
|
|
C ARRAY. N MUST BE EVEN.
|
|
|
|
|
C USING COMPLEX NOTATION AND SUBSCRIPTS STARTING AT ZERO, THE
|
|
|
|
|
C TRANSFORMATION IS--
|
|
|
|
|
C DIMENSION DATA(N,NREM)
|
|
|
|
|
C ZSTP = EXP(ISIGN*2*PI*I/N)
|
|
|
|
|
C DO 10 I2=0,NREM-1
|
|
|
|
|
C DATA(0,I2) = CONJ(DATA(0,I2))*(1+I)
|
|
|
|
|
C DO 10 I1=1,N/4
|
|
|
|
|
C Z = (1+(2*IFORM+1)*I*ZSTP**I1)/2
|
|
|
|
|
C I1CNJ = N/2-I1
|
|
|
|
|
C DIF = DATA(I1,I2)-CONJ(DATA(I1CNJ,I2))
|
|
|
|
|
C TEMP = Z*DIF
|
|
|
|
|
C DATA(I1,I2) = (DATA(I1,I2)-TEMP)*(1-IFORM)
|
|
|
|
|
C 10 DATA(I1CNJ,I2) = (DATA(I1CNJ,I2)+CONJ(TEMP))*(1-IFORM)
|
|
|
|
|
C IF I1=I1CNJ, THE CALCULATION FOR THAT VALUE COLLAPSES INTO
|
|
|
|
|
C A SIMPLE CONJUGATION OF DATA(I1,I2).
|
|
|
|
|
parameter(NMAX=2048*1024)
|
|
|
|
|
DIMENSION DATA(NMAX)
|
|
|
|
|
TWOPI=6.283185307*FLOAT(ISIGN)
|
|
|
|
|
IP0=2
|
|
|
|
|
IP1=IP0*(N/2)
|
|
|
|
|
IP2=IP1*NREM
|
|
|
|
|
IF (IFORM) 10,70,70
|
|
|
|
|
C PACK THE REAL INPUT VALUES (TWO PER COLUMN)
|
|
|
|
|
10 J1=IP1+1
|
|
|
|
|
DATA(2)=DATA(J1)
|
|
|
|
|
IF (NREM-1) 70,70,20
|
|
|
|
|
20 J1=J1+IP0
|
|
|
|
|
I2MIN=IP1+1
|
|
|
|
|
DO 60 I2=I2MIN,IP2,IP1
|
|
|
|
|
DATA(I2)=DATA(J1)
|
|
|
|
|
J1=J1+IP0
|
|
|
|
|
IF (N-2) 50,50,30
|
|
|
|
|
30 I1MIN=I2+IP0
|
|
|
|
|
I1MAX=I2+IP1-IP0
|
|
|
|
|
DO 40 I1=I1MIN,I1MAX,IP0
|
|
|
|
|
DATA(I1)=DATA(J1)
|
|
|
|
|
DATA(I1+1)=DATA(J1+1)
|
|
|
|
|
40 J1=J1+IP0
|
|
|
|
|
50 DATA(I2+1)=DATA(J1)
|
|
|
|
|
60 J1=J1+IP0
|
|
|
|
|
70 DO 80 I2=1,IP2,IP1
|
|
|
|
|
TEMPR=DATA(I2)
|
|
|
|
|
DATA(I2)=DATA(I2)+DATA(I2+1)
|
|
|
|
|
80 DATA(I2+1)=TEMPR-DATA(I2+1)
|
|
|
|
|
IF (N-2) 200,200,90
|
|
|
|
|
90 THETA=TWOPI/FLOAT(N)
|
|
|
|
|
SINTH=SIN(THETA/2.)
|
|
|
|
|
ZSTPR=-2.*SINTH*SINTH
|
|
|
|
|
ZSTPI=SIN(THETA)
|
|
|
|
|
ZR=(1.-ZSTPI)/2.
|
|
|
|
|
ZI=(1.+ZSTPR)/2.
|
|
|
|
|
IF (IFORM) 100,110,110
|
|
|
|
|
100 ZR=1.-ZR
|
|
|
|
|
ZI=-ZI
|
|
|
|
|
110 I1MIN=IP0+1
|
|
|
|
|
I1MAX=IP0*(N/4)+1
|
|
|
|
|
DO 190 I1=I1MIN,I1MAX,IP0
|
|
|
|
|
DO 180 I2=I1,IP2,IP1
|
|
|
|
|
I2CNJ=IP0*(N/2+1)-2*I1+I2
|
|
|
|
|
IF (I2-I2CNJ) 150,120,120
|
|
|
|
|
120 IF (ISIGN*(2*IFORM+1)) 130,140,140
|
|
|
|
|
130 DATA(I2+1)=-DATA(I2+1)
|
|
|
|
|
140 IF (IFORM) 170,180,180
|
|
|
|
|
150 DIFR=DATA(I2)-DATA(I2CNJ)
|
|
|
|
|
DIFI=DATA(I2+1)+DATA(I2CNJ+1)
|
|
|
|
|
TEMPR=DIFR*ZR-DIFI*ZI
|
|
|
|
|
TEMPI=DIFR*ZI+DIFI*ZR
|
|
|
|
|
DATA(I2)=DATA(I2)-TEMPR
|
|
|
|
|
DATA(I2+1)=DATA(I2+1)-TEMPI
|
|
|
|
|
DATA(I2CNJ)=DATA(I2CNJ)+TEMPR
|
|
|
|
|
DATA(I2CNJ+1)=DATA(I2CNJ+1)-TEMPI
|
|
|
|
|
IF (IFORM) 160,180,180
|
|
|
|
|
160 DATA(I2CNJ)=DATA(I2CNJ)+DATA(I2CNJ)
|
|
|
|
|
DATA(I2CNJ+1)=DATA(I2CNJ+1)+DATA(I2CNJ+1)
|
|
|
|
|
170 DATA(I2)=DATA(I2)+DATA(I2)
|
|
|
|
|
DATA(I2+1)=DATA(I2+1)+DATA(I2+1)
|
|
|
|
|
180 CONTINUE
|
|
|
|
|
TEMPR=ZR-.5
|
|
|
|
|
ZR=ZSTPR*TEMPR-ZSTPI*ZI+ZR
|
|
|
|
|
190 ZI=ZSTPR*ZI+ZSTPI*TEMPR+ZI
|
|
|
|
|
C RECURSION SAVES TIME, AT A SLIGHT LOSS IN ACCURACY. IF AVAILABLE,
|
|
|
|
|
C USE DOUBLE PRECISION TO COMPUTE ZR AND ZI.
|
|
|
|
|
200 IF (IFORM) 270,210,210
|
|
|
|
|
C UNPACK THE REAL TRANSFORM VALUES (TWO PER COLUMN)
|
|
|
|
|
210 I2=IP2+1
|
|
|
|
|
I1=I2
|
|
|
|
|
J1=IP0*(N/2+1)*NREM+1
|
|
|
|
|
GO TO 250
|
|
|
|
|
220 DATA(J1)=DATA(I1)
|
|
|
|
|
DATA(J1+1)=DATA(I1+1)
|
|
|
|
|
I1=I1-IP0
|
|
|
|
|
J1=J1-IP0
|
|
|
|
|
230 IF (I2-I1) 220,240,240
|
|
|
|
|
240 DATA(J1)=DATA(I1)
|
|
|
|
|
DATA(J1+1)=0.
|
|
|
|
|
250 I2=I2-IP1
|
|
|
|
|
J1=J1-IP0
|
|
|
|
|
DATA(J1)=DATA(I2+1)
|
|
|
|
|
DATA(J1+1)=0.
|
|
|
|
|
I1=I1-IP0
|
|
|
|
|
J1=J1-IP0
|
|
|
|
|
IF (I2-1) 260,260,230
|
|
|
|
|
260 DATA(2)=0.
|
|
|
|
|
270 RETURN
|
|
|
|
|
END
|
