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|
* fftsubs.F
*
* This software was developed by the Thermal Modeling and Analysis
* Project(TMAP) of the National Oceanographic and Atmospheric
* Administration's (NOAA) Pacific Marine Environmental Lab(PMEL),
* hereafter referred to as NOAA/PMEL/TMAP.
*
* Access and use of this software shall impose the following
* obligations and understandings on the user. The user is granted the
* right, without any fee or cost, to use, copy, modify, alter, enhance
* and distribute this software, and any derivative works thereof, and
* its supporting documentation for any purpose whatsoever, provided
* that this entire notice appears in all copies of the software,
* derivative works and supporting documentation. Further, the user
* agrees to credit NOAA/PMEL/TMAP in any publications that result from
* the use of this software or in any product that includes this
* software. The names TMAP, NOAA and/or PMEL, however, may not be used
* in any advertising or publicity to endorse or promote any products
* or commercial entity unless specific written permission is obtained
* from NOAA/PMEL/TMAP. The user also understands that NOAA/PMEL/TMAP
* is not obligated to provide the user with any support, consulting,
* training or assistance of any kind with regard to the use, operation
* and performance of this software nor to provide the user with any
* updates, revisions, new versions or "bug fixes".
*
* THIS SOFTWARE IS PROVIDED BY NOAA/PMEL/TMAP "AS IS" AND ANY EXPRESS
* OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL NOAA/PMEL/TMAP BE LIABLE FOR ANY SPECIAL,
* INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER
* RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF
* CONTRACT, NEGLIGENCE OR OTHER TORTUOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE ACCESS, USE OR PERFORMANCE OF THIS SOFTWARE.
*
* computation routines for FFT functions
SUBROUTINE four_re (nd, x, a, b, wft)
INTEGER nd, nf, i, j
REAL x(*), wft(*)
REAL a(*), b(*), xn
c uses NCAR FFTPACK code
C Ansley Manke 1/2000 NOAA/PMEL Return A, B real arrays with Fourier coefficients.
C Uses notes by Ned Cokelet 1/2000 on Swartztrauber FFTPACK code.
c Calls: RFFTF
C NF = number of frequencies, half the number of times.
C The code returns frequencies W(i) for i=0 to ND/2, with ND/2 rounded down.
C We do not return a(0) = R1/ND
C We return a(i) and b(i) for i=1,... ND/2
nf = nd/ 2
CALL rfftf (nd, x, wft)
C Normalizing factor of 1./N
c xn = 1.0
xn = 1.0/ REAL(nd)
c Save FFT coefficients in arrays a and b.
j = 0
DO i = 1, nf-1
j = 2* i
a(i) = 2.* xn* x(j)
b(i) = -2.* xn* x(j+1)
ENDDO
C Set a(nf) and b(nf) when nd is even/odd.
IF (nf*2 .eq. nd) THEN ! even ND
a(nf) = xn* x(nd)
b(nf) = 0.
ELSE ! odd ND
a(nf) = 2.* xn* x(nd-1)
b(nf) = -2.* xn* x(nd)
ENDIF
RETURN
END
C SUBROUTINE RFFTF(N,R,WSAVE)
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
SUBROUTINE RFFTF (N,R,WSAVE)
INTEGER N
REAL R(*) ,WSAVE(*)
C
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)
INTEGER N, NF, NA, L2, IW, K1, KH, IP, L1, IDO, IDL1, IX2, IX3
INTEGER I, IX4
REAL CH(*) ,C(*) ,WA(*) ,IFAC(*)
NF = IFAC(2)
NA = 1
L2 = N
IW = N
DO 111 K1=1,NF
KH = NF-K1
IP = IFAC(KH+3)
L1 = L2/IP
IDO = N/L2
IDL1 = IDO*L1
IW = IW-(IP-1)*IDO
NA = 1-NA
IF (IP .NE. 4) GO TO 102
IX2 = IW+IDO
IX3 = IX2+IDO
IF (NA .NE. 0) GO TO 101
CALL RADF4 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3))
GO TO 110
101 CALL RADF4 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3))
GO TO 110
102 IF (IP .NE. 2) GO TO 104
IF (NA .NE. 0) GO TO 103
CALL RADF2 (IDO,L1,C,CH,WA(IW))
GO TO 110
103 CALL RADF2 (IDO,L1,CH,C,WA(IW))
GO TO 110
104 IF (IP .NE. 3) GO TO 106
IX2 = IW+IDO
IF (NA .NE. 0) GO TO 105
CALL RADF3 (IDO,L1,C,CH,WA(IW),WA(IX2))
GO TO 110
105 CALL RADF3 (IDO,L1,CH,C,WA(IW),WA(IX2))
GO TO 110
106 IF (IP .NE. 5) GO TO 108
IX2 = IW+IDO
IX3 = IX2+IDO
IX4 = IX3+IDO
IF (NA .NE. 0) GO TO 107
CALL RADF5 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4))
GO TO 110
107 CALL RADF5 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3),WA(IX4))
GO TO 110
108 IF (IDO .EQ. 1) NA = 1-NA
IF (NA .NE. 0) GO TO 109
CALL RADFG (IDO,IP,L1,IDL1,C,C,C,CH,CH,WA(IW))
NA = 1
GO TO 110
109 CALL RADFG (IDO,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW))
NA = 0
110 L2 = L1
111 CONTINUE
IF (NA .EQ. 1) RETURN
DO 112 I=1,N
C(I) = CH(I)
112 CONTINUE
RETURN
END
C SUBROUTINE RFFTI(N,WSAVE)
C
C SUBROUTINE RFFTI INITIALIZES THE ARRAY WSAVE WHICH IS USED IN
C BOTH RFFTF AND RFFTB. 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 2*N+15.
C THE SAME WORK ARRAY CAN BE USED FOR BOTH RFFTF AND RFFTB
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 RFFTF OR RFFTB.
C
SUBROUTINE RFFTI (N,WSAVE)
INTEGER N
REAL WSAVE(*)
C
IF (N .EQ. 1) RETURN
CALL RFFTI1 (N,WSAVE(N+1),WSAVE(2*N+1))
RETURN
END
SUBROUTINE RFFTI1 (N,WA,IFAC)
INTEGER N, NL, NF, J, NTRY, NR, NQ, IB, I, IS, L1, NFM1, K1
INTEGER IP, LD, IDO, IPM, II, L2
REAL WA(*) ,IFAC(*) ,NTRYH(4)
REAL TPI, ARGH, ARGLD, FI, ARG, DUM
REAL PIMACH
DATA NTRYH(1),NTRYH(2),NTRYH(3),NTRYH(4)/4,2,3,5/
NL = N
NF = 0
J = 0
101 J = J+1
IF (J-4) 102,102,103
102 NTRY = NTRYH(J)
GO TO 104
103 NTRY = NTRY+2
104 NQ = NL/NTRY
NR = NL-NTRY*NQ
IF (NR) 101,105,101
105 NF = NF+1
IFAC(NF+2) = NTRY
NL = NQ
IF (NTRY .NE. 2) GO TO 107
IF (NF .EQ. 1) GO TO 107
DO 106 I=2,NF
IB = NF-I+2
IFAC(IB+2) = IFAC(IB+1)
106 CONTINUE
IFAC(3) = 2
107 IF (NL .NE. 1) GO TO 104
IFAC(1) = N
IFAC(2) = NF
TPI = 2.0*PIMACH(DUM)
ARGH = TPI/FLOAT(N)
IS = 0
NFM1 = NF-1
L1 = 1
IF (NFM1 .EQ. 0) RETURN
DO 110 K1=1,NFM1
IP = IFAC(K1+2)
LD = 0
L2 = L1*IP
IDO = N/L2
IPM = IP-1
DO 109 J=1,IPM
LD = LD+L1
I = IS
ARGLD = FLOAT(LD)*ARGH
FI = 0.
DO 108 II=3,IDO,2
I = I+2
FI = FI+1.
ARG = FI*ARGLD
WA(I-1) = COS(ARG)
WA(I) = SIN(ARG)
108 CONTINUE
IS = IS+IDO
109 CONTINUE
L1 = L2
110 CONTINUE
RETURN
END
REAL FUNCTION PIMACH (DUM)
C PI=3.1415926535897932384626433832795028841971693993751058209749446
C
REAL DUM
PIMACH = 4.*ATAN(1.0)
RETURN
END
SUBROUTINE RADFG (IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA)
INTEGER IDO, IP, L1, IDL1, IPPH, IPP2, IDP2, NBD, IK, J, K, IS
INTEGER IDIJ, I, JC, L, LC, J2, IC
REAL CH(IDO,L1,IP) ,CC(IDO,IP,L1) ,
1 C1(IDO,L1,IP) ,C2(IDL1,IP),
2 CH2(IDL1,IP) ,WA(*)
REAL TPI, DUM, ARG, DCP, DSP, AR1, AI1, AR1H, DC2, DS2, AR2, AI2
REAL AR2H
REAL PIMACH
TPI = 2.0*PIMACH(DUM)
ARG = TPI/FLOAT(IP)
DCP = COS(ARG)
DSP = SIN(ARG)
IPPH = (IP+1)/2
IPP2 = IP+2
IDP2 = IDO+2
NBD = (IDO-1)/2
IF (IDO .EQ. 1) GO TO 119
DO 101 IK=1,IDL1
CH2(IK,1) = C2(IK,1)
101 CONTINUE
DO 103 J=2,IP
DO 102 K=1,L1
CH(1,K,J) = C1(1,K,J)
102 CONTINUE
103 CONTINUE
IF (NBD .GT. L1) GO TO 107
IS = -IDO
DO 106 J=2,IP
IS = IS+IDO
IDIJ = IS
DO 105 I=3,IDO,2
IDIJ = IDIJ+2
DO 104 K=1,L1
CH(I-1,K,J) = WA(IDIJ-1)*C1(I-1,K,J)+WA(IDIJ)*C1(I,K,J)
CH(I,K,J) = WA(IDIJ-1)*C1(I,K,J)-WA(IDIJ)*C1(I-1,K,J)
104 CONTINUE
105 CONTINUE
106 CONTINUE
GO TO 111
107 IS = -IDO
DO 110 J=2,IP
IS = IS+IDO
DO 109 K=1,L1
IDIJ = IS
DO 108 I=3,IDO,2
IDIJ = IDIJ+2
CH(I-1,K,J) = WA(IDIJ-1)*C1(I-1,K,J)+WA(IDIJ)*C1(I,K,J)
CH(I,K,J) = WA(IDIJ-1)*C1(I,K,J)-WA(IDIJ)*C1(I-1,K,J)
108 CONTINUE
109 CONTINUE
110 CONTINUE
111 IF (NBD .LT. L1) GO TO 115
DO 114 J=2,IPPH
JC = IPP2-J
DO 113 K=1,L1
DO 112 I=3,IDO,2
C1(I-1,K,J) = CH(I-1,K,J)+CH(I-1,K,JC)
C1(I-1,K,JC) = CH(I,K,J)-CH(I,K,JC)
C1(I,K,J) = CH(I,K,J)+CH(I,K,JC)
C1(I,K,JC) = CH(I-1,K,JC)-CH(I-1,K,J)
112 CONTINUE
113 CONTINUE
114 CONTINUE
GO TO 121
115 DO 118 J=2,IPPH
JC = IPP2-J
DO 117 I=3,IDO,2
DO 116 K=1,L1
C1(I-1,K,J) = CH(I-1,K,J)+CH(I-1,K,JC)
C1(I-1,K,JC) = CH(I,K,J)-CH(I,K,JC)
C1(I,K,J) = CH(I,K,J)+CH(I,K,JC)
C1(I,K,JC) = CH(I-1,K,JC)-CH(I-1,K,J)
116 CONTINUE
117 CONTINUE
118 CONTINUE
GO TO 121
119 DO 120 IK=1,IDL1
C2(IK,1) = CH2(IK,1)
120 CONTINUE
121 DO 123 J=2,IPPH
JC = IPP2-J
DO 122 K=1,L1
C1(1,K,J) = CH(1,K,J)+CH(1,K,JC)
C1(1,K,JC) = CH(1,K,JC)-CH(1,K,J)
122 CONTINUE
123 CONTINUE
C
AR1 = 1.
AI1 = 0.
DO 127 L=2,IPPH
LC = IPP2-L
AR1H = DCP*AR1-DSP*AI1
AI1 = DCP*AI1+DSP*AR1
AR1 = AR1H
DO 124 IK=1,IDL1
CH2(IK,L) = C2(IK,1)+AR1*C2(IK,2)
CH2(IK,LC) = AI1*C2(IK,IP)
124 CONTINUE
DC2 = AR1
DS2 = AI1
AR2 = AR1
AI2 = AI1
DO 126 J=3,IPPH
JC = IPP2-J
AR2H = DC2*AR2-DS2*AI2
AI2 = DC2*AI2+DS2*AR2
AR2 = AR2H
DO 125 IK=1,IDL1
CH2(IK,L) = CH2(IK,L)+AR2*C2(IK,J)
CH2(IK,LC) = CH2(IK,LC)+AI2*C2(IK,JC)
125 CONTINUE
126 CONTINUE
127 CONTINUE
DO 129 J=2,IPPH
DO 128 IK=1,IDL1
CH2(IK,1) = CH2(IK,1)+C2(IK,J)
128 CONTINUE
129 CONTINUE
C
IF (IDO .LT. L1) GO TO 132
DO 131 K=1,L1
DO 130 I=1,IDO
CC(I,1,K) = CH(I,K,1)
130 CONTINUE
131 CONTINUE
GO TO 135
132 DO 134 I=1,IDO
DO 133 K=1,L1
CC(I,1,K) = CH(I,K,1)
133 CONTINUE
134 CONTINUE
135 DO 137 J=2,IPPH
JC = IPP2-J
J2 = J+J
DO 136 K=1,L1
CC(IDO,J2-2,K) = CH(1,K,J)
CC(1,J2-1,K) = CH(1,K,JC)
136 CONTINUE
137 CONTINUE
IF (IDO .EQ. 1) RETURN
IF (NBD .LT. L1) GO TO 141
DO 140 J=2,IPPH
JC = IPP2-J
J2 = J+J
DO 139 K=1,L1
DO 138 I=3,IDO,2
IC = IDP2-I
CC(I-1,J2-1,K) = CH(I-1,K,J)+CH(I-1,K,JC)
CC(IC-1,J2-2,K) = CH(I-1,K,J)-CH(I-1,K,JC)
CC(I,J2-1,K) = CH(I,K,J)+CH(I,K,JC)
CC(IC,J2-2,K) = CH(I,K,JC)-CH(I,K,J)
138 CONTINUE
139 CONTINUE
140 CONTINUE
RETURN
141 DO 144 J=2,IPPH
JC = IPP2-J
J2 = J+J
DO 143 I=3,IDO,2
IC = IDP2-I
DO 142 K=1,L1
CC(I-1,J2-1,K) = CH(I-1,K,J)+CH(I-1,K,JC)
CC(IC-1,J2-2,K) = CH(I-1,K,J)-CH(I-1,K,JC)
CC(I,J2-1,K) = CH(I,K,J)+CH(I,K,JC)
CC(IC,J2-2,K) = CH(I,K,JC)-CH(I,K,J)
142 CONTINUE
143 CONTINUE
144 CONTINUE
RETURN
END
SUBROUTINE RADF5 (IDO,L1,CC,CH,WA1,WA2,WA3,WA4)
INTEGER IDO, L1, K, IDP2, I, IC
REAL CC(IDO,L1,5) ,CH(IDO,5,L1) ,
1 WA1(*) ,WA2(*) ,WA3(*) ,WA4(*)
REAL CR2, CR3, CR4, CR5, CI2, CI3, CI4, CI5
REAL TR2, TR3, TR4, TR5, TI2, TI3, TI4, TI5
REAL DR2, DR3, DR4, DR5, DI2, DI3, DI4, DI5
REAL TR11, TI11, TR12, TI12
DATA TR11,TI11,TR12,TI12 /.309016994374947,.951056516295154,
1-.809016994374947,.587785252292473/
DO 101 K=1,L1
CR2 = CC(1,K,5)+CC(1,K,2)
CI5 = CC(1,K,5)-CC(1,K,2)
CR3 = CC(1,K,4)+CC(1,K,3)
CI4 = CC(1,K,4)-CC(1,K,3)
CH(1,1,K) = CC(1,K,1)+CR2+CR3
CH(IDO,2,K) = CC(1,K,1)+TR11*CR2+TR12*CR3
CH(1,3,K) = TI11*CI5+TI12*CI4
CH(IDO,4,K) = CC(1,K,1)+TR12*CR2+TR11*CR3
CH(1,5,K) = TI12*CI5-TI11*CI4
101 CONTINUE
IF (IDO .EQ. 1) RETURN
IDP2 = IDO+2
DO 103 K=1,L1
DO 102 I=3,IDO,2
IC = IDP2-I
DR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
DI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
DR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3)
DI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3)
DR4 = WA3(I-2)*CC(I-1,K,4)+WA3(I-1)*CC(I,K,4)
DI4 = WA3(I-2)*CC(I,K,4)-WA3(I-1)*CC(I-1,K,4)
DR5 = WA4(I-2)*CC(I-1,K,5)+WA4(I-1)*CC(I,K,5)
DI5 = WA4(I-2)*CC(I,K,5)-WA4(I-1)*CC(I-1,K,5)
CR2 = DR2+DR5
CI5 = DR5-DR2
CR5 = DI2-DI5
CI2 = DI2+DI5
CR3 = DR3+DR4
CI4 = DR4-DR3
CR4 = DI3-DI4
CI3 = DI3+DI4
CH(I-1,1,K) = CC(I-1,K,1)+CR2+CR3
CH(I,1,K) = CC(I,K,1)+CI2+CI3
TR2 = CC(I-1,K,1)+TR11*CR2+TR12*CR3
TI2 = CC(I,K,1)+TR11*CI2+TR12*CI3
TR3 = CC(I-1,K,1)+TR12*CR2+TR11*CR3
TI3 = CC(I,K,1)+TR12*CI2+TR11*CI3
TR5 = TI11*CR5+TI12*CR4
TI5 = TI11*CI5+TI12*CI4
TR4 = TI12*CR5-TI11*CR4
TI4 = TI12*CI5-TI11*CI4
CH(I-1,3,K) = TR2+TR5
CH(IC-1,2,K) = TR2-TR5
CH(I,3,K) = TI2+TI5
CH(IC,2,K) = TI5-TI2
CH(I-1,5,K) = TR3+TR4
CH(IC-1,4,K) = TR3-TR4
CH(I,5,K) = TI3+TI4
CH(IC,4,K) = TI4-TI3
102 CONTINUE
103 CONTINUE
RETURN
END
SUBROUTINE RADF2 (IDO,L1,CC,CH,WA1)
INTEGER IDO, L1, K, IDP2, I, IC
REAL CH(IDO,2,L1) ,CC(IDO,L1,2) ,
1 WA1(*)
REAL TR2, TI2
DO 101 K=1,L1
CH(1,1,K) = CC(1,K,1)+CC(1,K,2)
CH(IDO,2,K) = CC(1,K,1)-CC(1,K,2)
101 CONTINUE
IF (IDO-2) 107,105,102
102 IDP2 = IDO+2
DO 104 K=1,L1
DO 103 I=3,IDO,2
IC = IDP2-I
TR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
TI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
CH(I,1,K) = CC(I,K,1)+TI2
CH(IC,2,K) = TI2-CC(I,K,1)
CH(I-1,1,K) = CC(I-1,K,1)+TR2
CH(IC-1,2,K) = CC(I-1,K,1)-TR2
103 CONTINUE
104 CONTINUE
IF (MOD(IDO,2) .EQ. 1) RETURN
105 DO 106 K=1,L1
CH(1,2,K) = -CC(IDO,K,2)
CH(IDO,1,K) = CC(IDO,K,1)
106 CONTINUE
107 RETURN
END
SUBROUTINE RADF3 (IDO,L1,CC,CH,WA1,WA2)
INTEGER IDO, L1, I, IC, K, IDP2
REAL CH(IDO,3,L1) ,CC(IDO,L1,3) ,
1 WA1(*) ,WA2(*)
REAL TAUR, TAUI, CR2, DR2, DI2, DR3, DI3, CI2, TR2, TI2, TR3, TI3
DATA TAUR,TAUI /-.5,.866025403784439/
DO 101 K=1,L1
CR2 = CC(1,K,2)+CC(1,K,3)
CH(1,1,K) = CC(1,K,1)+CR2
CH(1,3,K) = TAUI*(CC(1,K,3)-CC(1,K,2))
CH(IDO,2,K) = CC(1,K,1)+TAUR*CR2
101 CONTINUE
IF (IDO .EQ. 1) RETURN
IDP2 = IDO+2
DO 103 K=1,L1
DO 102 I=3,IDO,2
IC = IDP2-I
DR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
DI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
DR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3)
DI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3)
CR2 = DR2+DR3
CI2 = DI2+DI3
CH(I-1,1,K) = CC(I-1,K,1)+CR2
CH(I,1,K) = CC(I,K,1)+CI2
TR2 = CC(I-1,K,1)+TAUR*CR2
TI2 = CC(I,K,1)+TAUR*CI2
TR3 = TAUI*(DI2-DI3)
TI3 = TAUI*(DR3-DR2)
CH(I-1,3,K) = TR2+TR3
CH(IC-1,2,K) = TR2-TR3
CH(I,3,K) = TI2+TI3
CH(IC,2,K) = TI3-TI2
102 CONTINUE
103 CONTINUE
RETURN
END
SUBROUTINE RADF4 (IDO,L1,CC,CH,WA1,WA2,WA3)
INTEGER IDO, L1, K, IDP2, I, IC
REAL CC(IDO,L1,4) ,CH(IDO,4,L1) ,
1 WA1(*) ,WA2(*) ,WA3(*)
REAL HSQT2
REAL CR2, CR3, CR4, CI2, CI3, CI4
REAL TR1, TR2, TR3, TR4, TI1, TI2, TI3, TI4
DATA HSQT2 /.7071067811865475/
DO 101 K=1,L1
TR1 = CC(1,K,2)+CC(1,K,4)
TR2 = CC(1,K,1)+CC(1,K,3)
CH(1,1,K) = TR1+TR2
CH(IDO,4,K) = TR2-TR1
CH(IDO,2,K) = CC(1,K,1)-CC(1,K,3)
CH(1,3,K) = CC(1,K,4)-CC(1,K,2)
101 CONTINUE
IF (IDO-2) 107,105,102
102 IDP2 = IDO+2
DO 104 K=1,L1
DO 103 I=3,IDO,2
IC = IDP2-I
CR2 = WA1(I-2)*CC(I-1,K,2)+WA1(I-1)*CC(I,K,2)
CI2 = WA1(I-2)*CC(I,K,2)-WA1(I-1)*CC(I-1,K,2)
CR3 = WA2(I-2)*CC(I-1,K,3)+WA2(I-1)*CC(I,K,3)
CI3 = WA2(I-2)*CC(I,K,3)-WA2(I-1)*CC(I-1,K,3)
CR4 = WA3(I-2)*CC(I-1,K,4)+WA3(I-1)*CC(I,K,4)
CI4 = WA3(I-2)*CC(I,K,4)-WA3(I-1)*CC(I-1,K,4)
TR1 = CR2+CR4
TR4 = CR4-CR2
TI1 = CI2+CI4
TI4 = CI2-CI4
TI2 = CC(I,K,1)+CI3
TI3 = CC(I,K,1)-CI3
TR2 = CC(I-1,K,1)+CR3
TR3 = CC(I-1,K,1)-CR3
CH(I-1,1,K) = TR1+TR2
CH(IC-1,4,K) = TR2-TR1
CH(I,1,K) = TI1+TI2
CH(IC,4,K) = TI1-TI2
CH(I-1,3,K) = TI4+TR3
CH(IC-1,2,K) = TR3-TI4
CH(I,3,K) = TR4+TI3
CH(IC,2,K) = TR4-TI3
103 CONTINUE
104 CONTINUE
IF (MOD(IDO,2) .EQ. 1) RETURN
105 CONTINUE
DO 106 K=1,L1
TI1 = -HSQT2*(CC(IDO,K,2)+CC(IDO,K,4))
TR1 = HSQT2*(CC(IDO,K,2)-CC(IDO,K,4))
CH(IDO,1,K) = TR1+CC(IDO,K,1)
CH(IDO,3,K) = CC(IDO,K,1)-TR1
CH(1,2,K) = TI1-CC(IDO,K,3)
CH(1,4,K) = TI1+CC(IDO,K,3)
106 CONTINUE
107 RETURN
END
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