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vfft.f
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vfft.f
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! Part of Dflow3d a 3D Navier Stokes solver with variable density for
! simulations of near field dredge plume mixing
! Copyright (C) 2012 Lynyrd de Wit
! This program is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
! This program is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
! You should have received a copy of the GNU General Public License
! along with this program. If not, see <http://www.gnu.org/licenses/>.
function pimach(dummy)
real dummy
pimach = 4.*atan(1.)
end
SUBROUTINE VCOSQB(M,N,X,XT,MDIMX,WSAVE)
C***BEGIN PROLOGUE VCOSQB
C***DATE WRITTEN 860701 (YYMMDD)
C***REVISION DATE 900509 (YYMMDD)
C***CATEGORY NO. J1A3
C***KEYWORDS FAST FOURIER TRANSFORM, COSINE TRANSFORM, ODD WAVE
C NUMBERS, MULTIPLE SEQUENCES
C***AUTHOR BOISVERT, R. F. (NIST)
C***PURPOSE Normalized inverse of VCOSQF.
C***DESCRIPTION
C
C Subroutine VCOSQB computes the backward fast Fourier cosine transform
C of M quarter wave sequences. That is, cosine series representations
C with only odd wave numbers. The transform is defined below at output
C parameter X.
C
C The array WSAVE which is used by subroutine VCOSQB must be
C initialized by calling subroutine VCOSQI(N,WSAVE).
C
C
C Input Parameters
C
C M the number of sequences to be transformed.
C
C N the length of the sequences to be transformed. The method
C is most efficient when N is a product of small primes.
C
C X an array of size at least X(MDIMX,N) which contains the
C the sequences to be transformed. The sequences are stored
C in the ROWS of X. Thus, the Jth sequence is stored in
C X(J,I), I=1,..,N.
C
C XT a work array of size at least XT(MDIMX,N).
C
C MDIMX the first dimension of the array X exactly as it appears in
C the calling program.
C
C WSAVE a work array which must be dimensioned at least 2*N+15
C in the program that calls VCOSQB. The WSAVE array must be
C initialized by calling subroutine VCOSQI(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.
C
C Output Parameters
C
C X For I=1,...,N and J=1,...,M
C
C X(I)= the sum from K=1 to K=N of
C
C 4*X(K)*COS((2*K-1)*(I-1)*PI/(2*N)) /SQRT(4*N)
C
C WSAVE contains initialization calculations which must not
C be destroyed between calls of VCOSQF or VCOSQB.
C
C -----------------------------------------------------------------
C
C NOTE - A call of VCOSQF followed immediately by a call of
C of VCOSQB will return the original sequences X. Thus,
C VCOSQB is the correctly normalized inverse VCOSQF.
C
C -----------------------------------------------------------------
C
C VCOSQB is a straightforward extension of the subprogram COSQB to
C handle M simultaneous sequences. COSQB was originally developed
C by P. N. Swarztrauber of NCAR.
C
C***REFERENCES P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
C Computations, (G. Rodrigue, ed.), Academic Press, 1982,
C pp. 51-83.
C***ROUTINES CALLED (NONE)
C***END PROLOGUE VCOSQB
DIMENSION X(MDIMX,*), XT(MDIMX,*), WSAVE(*)
C***FIRST EXECUTABLE STATEMENT VCOSQB
IF (M .LE. 0) GO TO 900
IF (N .GT. 2) GO TO 300
IF (N .EQ. 2) GO TO 200
GO TO 900
C
C CASE N = 2
C
200 CONTINUE
SCALE = 2.0E0*SQRT(0.50E0)
DO 210 J=1,M
X1 = SCALE*(X(J,1)+X(J,2))
X(J,2) = X(J,1)-X(J,2)
X(J,1) = X1
210 CONTINUE
GO TO 900
C
C CASE N .GT. 2
C
C ... PREPROCESSING
C
300 CONTINUE
NS2 = (N+1)/2
NP2 = N+2
DO 310 I=3,N,2
DO 310 J=1,M
XIM1 = X(J,I-1)+X(J,I)
X(J,I) = X(J,I)-X(J,I-1)
X(J,I-1) = XIM1
310 CONTINUE
DO 320 J=1,M
X(J,1) = X(J,1)+X(J,1)
320 CONTINUE
MODN = MOD(N,2)
IF (MODN .EQ. 0) THEN
DO 330 J=1,M
X(J,N) = X(J,N)+X(J,N)
330 CONTINUE
ENDIF
C
C ... REAL, PERIODIC TRANSFORM
C
CALL VRFFTB (M,N,X,XT,MDIMX,WSAVE(N+1))
C
C ... POSTPROCESSING
C
DO 340 K=2,NS2
KC = NP2-K
DO 340 J=1,M
XT(J,K) = WSAVE(K-1)*X(J,KC)+WSAVE(KC-1)*X(J,K)
XT(J,KC) = WSAVE(K-1)*X(J,K)-WSAVE(KC-1)*X(J,KC)
340 CONTINUE
IF (MODN .EQ. 0) THEN
DO 350 J=1,M
X(J,NS2+1) = WSAVE(NS2)*(X(J,NS2+1)+X(J,NS2+1))
350 CONTINUE
ENDIF
DO 360 K=2,NS2
KC = NP2-K
DO 360 J=1,M
X(J,K) = XT(J,K)+XT(J,KC)
X(J,KC) = XT(J,K)-XT(J,KC)
360 CONTINUE
DO 370 J=1,M
X(J,1) = X(J,1)+X(J,1)
370 CONTINUE
C
C ... NORMALIZATION
C
SCALE = 0.5
DO 380 I=1,N
DO 380 J=1,M
X(J,I) = SCALE*X(J,I)
380 CONTINUE
C
C EXIT
C
900 CONTINUE
RETURN
END
SUBROUTINE VCOSQF(M,N,X,XT,MDIMX,WSAVE)
C***BEGIN PROLOGUE VCOSQF
C***DATE WRITTEN 860701 (YYMMDD)
C***REVISION DATE 900509 (YYMMDD)
C***CATEGORY NO. J1A3
C***KEYWORDS FAST FOURIER TRANSFORM, COSINE TRANSFORM, ODD WAVE
C NUMBERS, MULTIPLE SEQUENCES
C***AUTHOR BOISVERT, R. F. (NIST)
C***PURPOSE Forward cosine transform, odd wave numbers, M sequences.
C***DESCRIPTION
C
C Subroutine VCOSQF computes the forward fast Fourier cosine transform
C of M quarter wave sequences. That is, cosine series representations
C with only odd wave numbers. The transform is defined below at output
C parameter X.
C
C The array WSAVE which is used by subroutine VCOSQF must be
C initialized by calling subroutine VCOSQI(N,WSAVE).
C
C
C Input Parameters
C
C M the number of sequences to be transformed.
C
C N the length of the sequences to be transformed. The method
C is most efficient when N is a product of small primes.
C
C X an array of size at least X(MDIMX,N) which contains the
C the sequences to be transformed. The sequences are stored
C in the ROWS of X. Thus, the Jth sequence is stored in
C X(J,I), I=1,..,N.
C
C XT a work array of size at least XT(MDIMX,N).
C
C MDIMX the first dimension of the array X exactly as it appears in
C the calling program.
C
C WSAVE a work array which must be dimensioned at least 2*N+15
C in the program that calls VCOSQF. The WSAVE array must be
C initialized by calling subroutine VCOSQI(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.
C
C Output Parameters
C
C X For I=1,...,N and J=1,...,M
C
C X(I) = ( X(1) + the sum from K=2 to K=N of
C
C 2*X(K)*COS((2*I-1)*(K-1)*PI/(2*N)) )/SQRT(4*N)
C
C WSAVE contains initialization calculations which must not
C be destroyed between calls of VCOSQF or VCOSQB.
C
C -----------------------------------------------------------------
C
C NOTE - A call of VCOSQF followed immediately by a call of
C of VCOSQB will return the original sequences X. Thus,
C VCOSQB is the correctly normalized inverse VCOSQF.
C
C -----------------------------------------------------------------
C
C VCOSQF is a straightforward extension of the subprogram COSQF to
C handle M simultaneous sequences. COSQF was originally developed
C by P. N. Swarztrauber of NCAR.
C
C***REFERENCES P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
C Computations, (G. Rodrigue, ed.), Academic Press, 1982,
C pp. 51-83.
C***ROUTINES CALLED (NONE)
C***END PROLOGUE VCOSQF
DIMENSION X(MDIMX,*), XT(MDIMX,*), WSAVE(*)
C***FIRST EXECUTABLE STATEMENT VCOSQF
IF (M .LE. 0) GO TO 900
IF (N .GT. 2) GO TO 300
IF (N .LT. 2) GO TO 900
C
C CASE N = 2
C
SQRT2 = SQRT(2.0)
SCALE = 0.50E0/SQRT2
DO 210 J=1,M
TSQX = SQRT2*X(J,2)
X(J,2) = SCALE*(X(J,1)-TSQX)
X(J,1) = SCALE*(X(J,1)+TSQX)
210 CONTINUE
GO TO 900
C
C CASE N .GT. 2
C
300 CONTINUE
C
C ... PREPROCESSING
C
NS2 = (N+1)/2
NP2 = N+2
DO 310 K=2,NS2
KC = NP2-K
DO 310 J=1,M
XT(J,K) = X(J,K)+X(J,KC)
XT(J,KC) = X(J,K)-X(J,KC)
310 CONTINUE
MODN = MOD(N,2)
IF (MODN .EQ. 0) THEN
DO 320 J=1,M
XT(J,NS2+1) = X(J,NS2+1)+X(J,NS2+1)
320 CONTINUE
ENDIF
DO 330 K=2,NS2
KC = NP2-K
DO 330 J=1,M
X(J,K) = WSAVE(K-1)*XT(J,KC)+WSAVE(KC-1)*XT(J,K)
X(J,KC) = WSAVE(K-1)*XT(J,K)-WSAVE(KC-1)*XT(J,KC)
330 CONTINUE
IF (MODN .EQ. 0) THEN
DO 340 J=1,M
X(J,NS2+1) = WSAVE(NS2)*XT(J,NS2+1)
340 CONTINUE
ENDIF
C
C ... REAL, PERIODIC TRANSFORM
C
CALL VRFFTF (M,N,X,XT,MDIMX,WSAVE(N+1))
C
C ... POSTPROCESSING
C
DO 350 I=3,N,2
DO 350 J=1,M
XIM1 = X(J,I-1)-X(J,I)
X(J,I) = X(J,I-1)+X(J,I)
X(J,I-1) = XIM1
350 CONTINUE
C
C ... NORMALIZATION
C
SCALE = 0.5
DO 360 I=1,N
DO 360 J=1,M
X(J,I) = SCALE*X(J,I)
360 CONTINUE
C
C EXIT
C
900 CONTINUE
RETURN
END
SUBROUTINE VCOSQI(N,WSAVE)
C***BEGIN PROLOGUE VCOSQI
C***DATE WRITTEN 860701 (YYMMDD)
C***REVISION DATE 900509 (YYMMDD)
C***CATEGORY NO. J1A3
C***KEYWORDS FAST FOURIER TRANSFORM, COSINE TRANSFORM, ODD WAVE
C NUMBERS, MULTIPLE SEQUENCES
C***AUTHOR BOISVERT, R. F. (NIST)
C***PURPOSE Initialize for VCOSQF and VCOSQB.
C***DESCRIPTION
C
C Subroutine VCOSQI initializes the array WSAVE which is used in
C both VCOSQF and VCOSQB. 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 array to be transformed. The method
C is most efficient when N is a product of small primes.
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 VCOSQF and VCOSQB
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 VCOSQF or VCOSQB.
C
C***REFERENCES P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
C Computations, (G. Rodrigue, ed.), Academic Press, 1982,
C pp. 51-83.
C***ROUTINES CALLED VRFFTI
C***END PROLOGUE VCOSQI
DIMENSION WSAVE(*)
C***FIRST EXECUTABLE STATEMENT VCOSQI
PIH = 0.5*PIMACH(1.0)
DT = PIH/REAL(N)
FK = 0.
DO 101 K=1,N
FK = FK+1.
WSAVE(K) = COS(FK*DT)
101 CONTINUE
CALL VRFFTI (N,WSAVE(N+1))
RETURN
END
SUBROUTINE VCOST(M,N,X,XT,MDIMX,WSAVE)
C***BEGIN PROLOGUE VCOST
C***DATE WRITTEN 860701 (YYMMDD)
C***REVISION DATE 900509 (YYMMDD)
C***CATEGORY NO. J1A3
C***KEYWORDS FAST FOURIER TRANSFORM, COSINE TRANSFORM, MULTIPLE
C SEQUENCES
C***AUTHOR BOISVERT, R. F. (NIST)
C***PURPOSE Cosine transform of one or more real, even sequences.
C***DESCRIPTION
C
C Subroutine VCOST computes the discrete Fourier cosine transform
C of M even sequences X(J,I), J=1,...,M. The transform is defined
C below at output parameter X.
C
C The array WSAVE which is used by subroutine VCOST must be
C initialized by calling subroutine VCOSTI(N,WSAVE).
C
C Input Parameters
C
C M the number of sequences to be transformed.
C
C N the length of the sequence to be transformed. N must be
C greater than 1. The method is most efficient when N-1 is
C is a product of small primes.
C
C X an array of size at least X(MDIMX,N) which contains the
C the sequences to be transformed. The sequences are stored
C in the ROWS of X. Thus, the Jth sequence is stored in
C X(J,I), I=1,..,N.
C
C XT a work array of size at least XT(MDIMX,N-1).
C
C MDIMX the first dimension of the array X exactly as it appears in
C the calling program.
C
C WSAVE a work array which must be dimensioned at least 3*N+15
C in the program that calls VCOST. The WSAVE array must be
C initialized by calling subroutine VCOSTI(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
C Output Parameters
C
C X For I=1,...,N and J=1,...,M
C
C X(J,I) = ( X(J,1)+(-1)**(I-1)*X(J,N)
C
C + the sum from K=2 to K=N-1
C
C 2*X(J,K)*COS((K-1)*(I-1)*PI/(N-1)) )/SQRT(2*(N-1))
C
C WSAVE contains initialization calculations which must not be
C destroyed between calls of VCOST.
C
C -----------------------------------------------------------------
C
C NOTE - A call of VCOST followed immediately by another call
C of VCOST will return the original sequences X. Thus,
C VCOST is the correctly normalized inverse of itself.
C
C -----------------------------------------------------------------
C
C VCOST is a straightforward extension of the subprogram COST to
C handle M simultaneous sequences. The scaling of the sequences
C computed by VCOST is different than that of COST. COST was
C originally developed by P. N. Swarztrauber of NCAR.
C
C***REFERENCES P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
C Computations, (G. Rodrigue, ed.), Academic Press, 1982,
C pp. 51-83.
C***ROUTINES CALLED VRFFTF
C***END PROLOGUE VCOST
DIMENSION X(MDIMX,*), XT(MDIMX,*), WSAVE(*)
C***FIRST EXECUTABLE STATEMENT VCOST
IF (M .LE. 0) GO TO 900
IF (N .LE. 1) GO TO 900
IF (N .GT. 3) GO TO 400
IF (N .EQ. 3) GO TO 300
C
C CASE N = 2
C
SCALE = SQRT(0.50E0)
DO 210 J=1,M
X1H = SCALE*(X(J,1)+X(J,2))
X(J,2) = SCALE*(X(J,1)-X(J,2))
X(J,1) = X1H
210 CONTINUE
GO TO 900
C
C CASE N = 3
C
300 CONTINUE
SCALE = 0.50E0
DO 310 J=1,M
X1P3 = X(J,1)+X(J,3)
TX2 = X(J,2)+X(J,2)
X(J,2) = SCALE*(X(J,1)-X(J,3))
X(J,1) = SCALE*(X1P3+TX2)
X(J,3) = SCALE*(X1P3-TX2)
310 CONTINUE
GO TO 900
C
C CASE N .GT. 3
C
C ... PREPROCESSING
C
400 CONTINUE
NM1 = N-1
NP1 = N+1
NS2 = N/2
DO 410 J=1,M
XT(J,1) = X(J,1)-X(J,N)
X(J,1) = X(J,1)+X(J,N)
410 CONTINUE
DO 420 K=2,NS2
KC = NP1-K
DO 420 J=1,M
T1 = X(J,K)+X(J,KC)
T2 = X(J,K)-X(J,KC)
XT(J,1) = XT(J,1)+WSAVE(KC)*T2
T2 = WSAVE(K)*T2
X(J,K) = T1-T2
X(J,KC) = T1+T2
420 CONTINUE
MODN = MOD(N,2)
IF (MODN .NE. 0) THEN
DO 430 J=1,M
X(J,NS2+1) = X(J,NS2+1)+X(J,NS2+1)
430 CONTINUE
ENDIF
DO 435 J=1,M
X(J,N) = XT(J,1)
435 CONTINUE
C
C ... REAL PERIODIC TRANSFORM
C
CALL VRFFTF (M,NM1,X,XT,MDIMX,WSAVE(NP1))
C
C ... POSTPROCESSING
C
FACTOR = 1.0/SQRT(REAL(NM1))
DO 440 J=1,M
XT(J,1) = X(J,2)
X(J,2) = FACTOR*X(J,N)
440 CONTINUE
DO 450 I=4,N,2
DO 450 J=1,M
XI = X(J,I)
X(J,I) = X(J,I-2)-X(J,I-1)
X(J,I-1) = XT(J,1)
XT(J,1) = XI
450 CONTINUE
IF (MODN .NE. 0) THEN
DO 460 J=1,M
X(J,N) = XT(J,1)
460 CONTINUE
ENDIF
C
C ... NORMALIZATION
C
SCALE = SQRT(0.5)
DO 490 I=1,N
DO 490 J=1,M
X(J,I) = SCALE*X(J,I)
490 CONTINUE
C
C EXIT
C
900 CONTINUE
RETURN
END
SUBROUTINE VCOSTI(N,WSAVE)
C***BEGIN PROLOGUE VCOSTI
C***DATE WRITTEN 860701 (YYMMDD)
C***REVISION DATE 900509 (YYMMDD)
C***CATEGORY NO. J1A3
C***KEYWORDS FAST FOURIER TRANSFORM, COSINE TRANSFORM, MULTIPLE
C SEQUENCES
C***AUTHOR BOISVERT, R. F. (NIST)
C***PURPOSE Initialize for VCOST.
C***DESCRIPTION
C
C Subroutine VCOSTI initializes the array WSAVE which is used in
C subroutine VCOST. 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. The method
C is most efficient when N-1 is a product of small primes.
C
C Output Parameter
C
C WSAVE a work array which must be dimensioned at least 3*N+15.
C Different WSAVE arrays are required for different values
C of N. The contents of WSAVE must not be changed between
C calls of VCOST.
C
C -----------------------------------------------------------------
C
C VCOSTI is a straightforward extension of the subprogram COSTI to
C handle M simultaneous sequences. COSTI was originally developed
C by P. N. Swarztrauber of NCAR.
C
C***REFERENCES P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
C Computations, (G. Rodrigue, ed.), Academic Press, 1982,
C pp. 51-83.
C***ROUTINES CALLED VRFFTI
C***END PROLOGUE VCOSTI
DIMENSION WSAVE(*)
C***FIRST EXECUTABLE STATEMENT VCOSTI
PI = PIMACH(1.0)
IF (N .LE. 3) RETURN
NM1 = N-1
NP1 = N+1
NS2 = N/2
DT = PI/REAL(NM1)
FK = 0.
DO 101 K=2,NS2
FK = FK+1.
WSAVE(K) = 2.*SIN(FK*DT)
101 CONTINUE
FK = 0.
DO 102 K=2,NS2
KC = NP1-K
FK = FK+1.
WSAVE(KC) = 2.*COS(FK*DT)
102 CONTINUE
CALL VRFFTI (NM1,WSAVE(N+1))
RETURN
END
SUBROUTINE VRADB2 (MP,IDO,L1,CC,CH,MDIMC,WA1)
C
C VRFFTPK, VERSION 1, AUGUST 1985
C
DIMENSION CC(MDIMC,IDO,2,L1) ,CH(MDIMC,IDO,L1,2),
1 WA1(IDO)
DO 101 K=1,L1
DO 1001 M=1,MP
CH(M,1,K,1) = CC(M,1,1,K)+CC(M,IDO,2,K)
CH(M,1,K,2) = CC(M,1,1,K)-CC(M,IDO,2,K)
1001 CONTINUE
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
DO 1002 M=1,MP
CH(M,I-1,K,1) = CC(M,I-1,1,K)+CC(M,IC-1,2,K)
CH(M,I,K,1) = CC(M,I,1,K)-CC(M,IC,2,K)
CH(M,I-1,K,2) = WA1(I-2)*(CC(M,I-1,1,K)-CC(M,IC-1,2,K))
1 -WA1(I-1)*(CC(M,I,1,K)+CC(M,IC,2,K))
CH(M,I,K,2) = WA1(I-2)*(CC(M,I,1,K)+CC(M,IC,2,K))+WA1(I-1)
1 *(CC(M,I-1,1,K)-CC(M,IC-1,2,K))
1002 CONTINUE
103 CONTINUE
104 CONTINUE
IF (MOD(IDO,2) .EQ. 1) RETURN
105 DO 106 K=1,L1
DO 1003 M=1,MP
CH(M,IDO,K,1) = CC(M,IDO,1,K)+CC(M,IDO,1,K)
CH(M,IDO,K,2) = -(CC(M,1,2,K)+CC(M,1,2,K))
1003 CONTINUE
106 CONTINUE
107 RETURN
END
SUBROUTINE VRADB3 (MP,IDO,L1,CC,CH,MDIMC,WA1,WA2)
C
C VRFFTPK, VERSION 1, AUGUST 1985
C
DIMENSION CC(MDIMC,IDO,3,L1) ,CH(MDIMC,IDO,L1,3),
1 WA1(IDO) ,WA2(IDO)
ARG=2.*PIMACH(1.0)/3.
TAUR=COS(ARG)
TAUI=SIN(ARG)
DO 101 K=1,L1
DO 1001 M=1,MP
CH(M,1,K,1) = CC(M,1,1,K)+2.*CC(M,IDO,2,K)
CH(M,1,K,2) = CC(M,1,1,K)+(2.*TAUR)*CC(M,IDO,2,K)
1 -(2.*TAUI)*CC(M,1,3,K)
CH(M,1,K,3) = CC(M,1,1,K)+(2.*TAUR)*CC(M,IDO,2,K)
1 +2.*TAUI*CC(M,1,3,K)
1001 CONTINUE
101 CONTINUE
IF (IDO .EQ. 1) RETURN
IDP2 = IDO+2
DO 103 K=1,L1
DO 102 I=3,IDO,2
IC = IDP2-I
DO 1002 M=1,MP
CH(M,I-1,K,1) = CC(M,I-1,1,K)+(CC(M,I-1,3,K)+CC(M,IC-1,2,K))
CH(M,I,K,1) = CC(M,I,1,K)+(CC(M,I,3,K)-CC(M,IC,2,K))
CH(M,I-1,K,2) = WA1(I-2)*
1 ((CC(M,I-1,1,K)+TAUR*(CC(M,I-1,3,K)+CC(M,IC-1,2,K)))-
* (TAUI*(CC(M,I,3,K)+CC(M,IC,2,K))))
2 -WA1(I-1)*
3 ((CC(M,I,1,K)+TAUR*(CC(M,I,3,K)-CC(M,IC,2,K)))+
* (TAUI*(CC(M,I-1,3,K)-CC(M,IC-1,2,K))))
CH(M,I,K,2) = WA1(I-2)*
4 ((CC(M,I,1,K)+TAUR*(CC(M,I,3,K)-CC(M,IC,2,K)))+
8 (TAUI*(CC(M,I-1,3,K)-CC(M,IC-1,2,K))))
5 +WA1(I-1)*
6 ((CC(M,I-1,1,K)+TAUR*(CC(M,I-1,3,K)+CC(M,IC-1,2,K)))-
8 (TAUI*(CC(M,I,3,K)+CC(M,IC,2,K))))
CH(M,I-1,K,3) = WA2(I-2)*
7 ((CC(M,I-1,1,K)+TAUR*(CC(M,I-1,3,K)+CC(M,IC-1,2,K)))+
8 (TAUI*(CC(M,I,3,K)+CC(M,IC,2,K))))
8 -WA2(I-1)*
9 ((CC(M,I,1,K)+TAUR*(CC(M,I,3,K)-CC(M,IC,2,K)))-
8 (TAUI*(CC(M,I-1,3,K)-CC(M,IC-1,2,K))))
CH(M,I,K,3) = WA2(I-2)*
1 ((CC(M,I,1,K)+TAUR*(CC(M,I,3,K)-CC(M,IC,2,K)))-
8 (TAUI*(CC(M,I-1,3,K)-CC(M,IC-1,2,K))))
2 +WA2(I-1)*
3 ((CC(M,I-1,1,K)+TAUR*(CC(M,I-1,3,K)+CC(M,IC-1,2,K)))+
8 (TAUI*(CC(M,I,3,K)+CC(M,IC,2,K))))
1002 CONTINUE
102 CONTINUE
103 CONTINUE
RETURN
END
SUBROUTINE VRADB4 (MP,IDO,L1,CC,CH,MDIMC,WA1,WA2,WA3)
C
C VRFFTPK, VERSION 1, AUGUST 1985
C
DIMENSION CC(MDIMC,IDO,4,L1) ,CH(MDIMC,IDO,L1,4) ,
1 WA1(IDO) ,WA2(IDO) ,WA3(IDO)
SQRT2=SQRT(2.)
DO 101 K=1,L1
DO 1001 M=1,MP
CH(M,1,K,3) = (CC(M,1,1,K)+CC(M,IDO,4,K))
1 -(CC(M,IDO,2,K)+CC(M,IDO,2,K))
CH(M,1,K,1) = (CC(M,1,1,K)+CC(M,IDO,4,K))
1 +(CC(M,IDO,2,K)+CC(M,IDO,2,K))
CH(M,1,K,4) = (CC(M,1,1,K)-CC(M,IDO,4,K))
1 +(CC(M,1,3,K)+CC(M,1,3,K))
CH(M,1,K,2) = (CC(M,1,1,K)-CC(M,IDO,4,K))
1 -(CC(M,1,3,K)+CC(M,1,3,K))
1001 CONTINUE
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
DO 1002 M=1,MP
CH(M,I-1,K,1) = (CC(M,I-1,1,K)+CC(M,IC-1,4,K))
1 +(CC(M,I-1,3,K)+CC(M,IC-1,2,K))
CH(M,I,K,1) = (CC(M,I,1,K)-CC(M,IC,4,K))
1 +(CC(M,I,3,K)-CC(M,IC,2,K))
CH(M,I-1,K,2)=WA1(I-2)*((CC(M,I-1,1,K)-CC(M,IC-1,4,K))
1 -(CC(M,I,3,K)+CC(M,IC,2,K)))-WA1(I-1)
1 *((CC(M,I,1,K)+CC(M,IC,4,K))+(CC(M,I-1,3,K)-CC(M,IC-1,2,K)))
CH(M,I,K,2)=WA1(I-2)*((CC(M,I,1,K)+CC(M,IC,4,K))
1 +(CC(M,I-1,3,K)-CC(M,IC-1,2,K)))+WA1(I-1)
1 *((CC(M,I-1,1,K)-CC(M,IC-1,4,K))-(CC(M,I,3,K)+CC(M,IC,2,K)))
CH(M,I-1,K,3)=WA2(I-2)*((CC(M,I-1,1,K)+CC(M,IC-1,4,K))
1 -(CC(M,I-1,3,K)+CC(M,IC-1,2,K)))-WA2(I-1)
1 *((CC(M,I,1,K)-CC(M,IC,4,K))-(CC(M,I,3,K)-CC(M,IC,2,K)))
CH(M,I,K,3)=WA2(I-2)*((CC(M,I,1,K)-CC(M,IC,4,K))
1 -(CC(M,I,3,K)-CC(M,IC,2,K)))+WA2(I-1)
1 *((CC(M,I-1,1,K)+CC(M,IC-1,4,K))-(CC(M,I-1,3,K)
1 +CC(M,IC-1,2,K)))
CH(M,I-1,K,4)=WA3(I-2)*((CC(M,I-1,1,K)-CC(M,IC-1,4,K))
1 +(CC(M,I,3,K)+CC(M,IC,2,K)))-WA3(I-1)
1 *((CC(M,I,1,K)+CC(M,IC,4,K))-(CC(M,I-1,3,K)-CC(M,IC-1,2,K)))
CH(M,I,K,4)=WA3(I-2)*((CC(M,I,1,K)+CC(M,IC,4,K))
1 -(CC(M,I-1,3,K)-CC(M,IC-1,2,K)))+WA3(I-1)
1 *((CC(M,I-1,1,K)-CC(M,IC-1,4,K))+(CC(M,I,3,K)+CC(M,IC,2,K)))
1002 CONTINUE
103 CONTINUE
104 CONTINUE
IF (MOD(IDO,2) .EQ. 1) RETURN
105 CONTINUE
DO 106 K=1,L1
DO 1003 M=1,MP
CH(M,IDO,K,1) = (CC(M,IDO,1,K)+CC(M,IDO,3,K))
1 +(CC(M,IDO,1,K)+CC(M,IDO,3,K))
CH(M,IDO,K,2) = SQRT2*((CC(M,IDO,1,K)-CC(M,IDO,3,K))
1 -(CC(M,1,2,K)+CC(M,1,4,K)))
CH(M,IDO,K,3) = (CC(M,1,4,K)-CC(M,1,2,K))
1 +(CC(M,1,4,K)-CC(M,1,2,K))
CH(M,IDO,K,4) = -SQRT2*((CC(M,IDO,1,K)-CC(M,IDO,3,K))
1 +(CC(M,1,2,K)+CC(M,1,4,K)))
1003 CONTINUE
106 CONTINUE
107 RETURN
END
SUBROUTINE VRADB5 (MP,IDO,L1,CC,CH,MDIMC,WA1,WA2,WA3,WA4)
C
C VRFFTPK, VERSION 1, AUGUST 1985
C
DIMENSION CC(MDIMC,IDO,5,L1) ,CH(MDIMC,IDO,L1,5),
1 WA1(IDO) ,WA2(IDO) ,WA3(IDO) ,WA4(IDO)
ARG=2.*PIMACH(1.0)/5.
TR11=COS(ARG)
TI11=SIN(ARG)
TR12=COS(2.*ARG)
TI12=SIN(2.*ARG)
DO 101 K=1,L1
DO 1001 M=1,MP
CH(M,1,K,1) = CC(M,1,1,K)+2.*CC(M,IDO,2,K)+2.*CC(M,IDO,4,K)
CH(M,1,K,2) = (CC(M,1,1,K)+TR11*2.*CC(M,IDO,2,K)
1 +TR12*2.*CC(M,IDO,4,K))-(TI11*2.*CC(M,1,3,K)
1 +TI12*2.*CC(M,1,5,K))
CH(M,1,K,3) = (CC(M,1,1,K)+TR12*2.*CC(M,IDO,2,K)
1 +TR11*2.*CC(M,IDO,4,K))-(TI12*2.*CC(M,1,3,K)
1 -TI11*2.*CC(M,1,5,K))
CH(M,1,K,4) = (CC(M,1,1,K)+TR12*2.*CC(M,IDO,2,K)
1 +TR11*2.*CC(M,IDO,4,K))+(TI12*2.*CC(M,1,3,K)
1 -TI11*2.*CC(M,1,5,K))
CH(M,1,K,5) = (CC(M,1,1,K)+TR11*2.*CC(M,IDO,2,K)
1 +TR12*2.*CC(M,IDO,4,K))+(TI11*2.*CC(M,1,3,K)
1 +TI12*2.*CC(M,1,5,K))
1001 CONTINUE
101 CONTINUE
IF (IDO .EQ. 1) RETURN
IDP2 = IDO+2
DO 103 K=1,L1
DO 102 I=3,IDO,2
IC = IDP2-I
DO 1002 M=1,MP
CH(M,I-1,K,1) = CC(M,I-1,1,K)+(CC(M,I-1,3,K)+CC(M,IC-1,2,K))
1 +(CC(M,I-1,5,K)+CC(M,IC-1,4,K))
CH(M,I,K,1) = CC(M,I,1,K)+(CC(M,I,3,K)-CC(M,IC,2,K))
1 +(CC(M,I,5,K)-CC(M,IC,4,K))
CH(M,I-1,K,2) = WA1(I-2)*((CC(M,I-1,1,K)+TR11*
1 (CC(M,I-1,3,K)+CC(M,IC-1,2,K))+TR12
1 *(CC(M,I-1,5,K)+CC(M,IC-1,4,K)))-(TI11*(CC(M,I,3,K)
1 +CC(M,IC,2,K))+TI12*(CC(M,I,5,K)+CC(M,IC,4,K))))
1 -WA1(I-1)*((CC(M,I,1,K)+TR11*(CC(M,I,3,K)-CC(M,IC,2,K))
1 +TR12*(CC(M,I,5,K)-CC(M,IC,4,K)))+(TI11*(CC(M,I-1,3,K)
1 -CC(M,IC-1,2,K))+TI12*(CC(M,I-1,5,K)-CC(M,IC-1,4,K))))
CH(M,I,K,2) = WA1(I-2)*((CC(M,I,1,K)+TR11*(CC(M,I,3,K)
1 -CC(M,IC,2,K))+TR12*(CC(M,I,5,K)-CC(M,IC,4,K)))
1 +(TI11*(CC(M,I-1,3,K)-CC(M,IC-1,2,K))+TI12
1 *(CC(M,I-1,5,K)-CC(M,IC-1,4,K))))+WA1(I-1)
1 *((CC(M,I-1,1,K)+TR11*(CC(M,I-1,3,K)
1 +CC(M,IC-1,2,K))+TR12*(CC(M,I-1,5,K)+CC(M,IC-1,4,K)))
1 -(TI11*(CC(M,I,3,K)+CC(M,IC,2,K))+TI12
1 *(CC(M,I,5,K)+CC(M,IC,4,K))))
CH(M,I-1,K,3) = WA2(I-2)
1 *((CC(M,I-1,1,K)+TR12*(CC(M,I-1,3,K)+CC(M,IC-1,2,K))
1 +TR11*(CC(M,I-1,5,K)+CC(M,IC-1,4,K)))-(TI12*(CC(M,I,3,K)
1 +CC(M,IC,2,K))-TI11*(CC(M,I,5,K)+CC(M,IC,4,K))))
1 -WA2(I-1)
1 *((CC(M,I,1,K)+TR12*(CC(M,I,3,K)-
1 CC(M,IC,2,K))+TR11*(CC(M,I,5,K)-CC(M,IC,4,K)))
1 +(TI12*(CC(M,I-1,3,K)-CC(M,IC-1,2,K))-TI11
1 *(CC(M,I-1,5,K)-CC(M,IC-1,4,K))))
CH(M,I,K,3) = WA2(I-2)
1 *((CC(M,I,1,K)+TR12*(CC(M,I,3,K)-
1 CC(M,IC,2,K))+TR11*(CC(M,I,5,K)-CC(M,IC,4,K)))
1 +(TI12*(CC(M,I-1,3,K)-CC(M,IC-1,2,K))-TI11
1 *(CC(M,I-1,5,K)-CC(M,IC-1,4,K))))
1 +WA2(I-1)
1 *((CC(M,I-1,1,K)+TR12*(CC(M,I-1,3,K)+CC(M,IC-1,2,K))
1 +TR11*(CC(M,I-1,5,K)+CC(M,IC-1,4,K)))-(TI12*(CC(M,I,3,K)
1 +CC(M,IC,2,K))-TI11*(CC(M,I,5,K)+CC(M,IC,4,K))))
CH(M,I-1,K,4) = WA3(I-2)
1 *((CC(M,I-1,1,K)+TR12*(CC(M,I-1,3,K)+CC(M,IC-1,2,K))
1 +TR11*(CC(M,I-1,5,K)+CC(M,IC-1,4,K)))+(TI12*(CC(M,I,3,K)
1 +CC(M,IC,2,K))-TI11*(CC(M,I,5,K)+CC(M,IC,4,K))))
1 -WA3(I-1)
1 *((CC(M,I,1,K)+TR12*(CC(M,I,3,K)-
1 CC(M,IC,2,K))+TR11*(CC(M,I,5,K)-CC(M,IC,4,K)))
1 -(TI12*(CC(M,I-1,3,K)-CC(M,IC-1,2,K))-TI11
1 *(CC(M,I-1,5,K)-CC(M,IC-1,4,K))))
CH(M,I,K,4) = WA3(I-2)
1 *((CC(M,I,1,K)+TR12*(CC(M,I,3,K)-
1 CC(M,IC,2,K))+TR11*(CC(M,I,5,K)-CC(M,IC,4,K)))
1 -(TI12*(CC(M,I-1,3,K)-CC(M,IC-1,2,K))-TI11
1 *(CC(M,I-1,5,K)-CC(M,IC-1,4,K))))
1 +WA3(I-1)
1 *((CC(M,I-1,1,K)+TR12*(CC(M,I-1,3,K)+CC(M,IC-1,2,K))
1 +TR11*(CC(M,I-1,5,K)+CC(M,IC-1,4,K)))+(TI12*(CC(M,I,3,K)
1 +CC(M,IC,2,K))-TI11*(CC(M,I,5,K)+CC(M,IC,4,K))))
CH(M,I-1,K,5) = WA4(I-2)
1 *((CC(M,I-1,1,K)+TR11*(CC(M,I-1,3,K)+CC(M,IC-1,2,K))
1 +TR12*(CC(M,I-1,5,K)+CC(M,IC-1,4,K)))+(TI11*(CC(M,I,3,K)
1 +CC(M,IC,2,K))+TI12*(CC(M,I,5,K)+CC(M,IC,4,K))))
1 -WA4(I-1)
1 *((CC(M,I,1,K)+TR11*(CC(M,I,3,K)-CC(M,IC,2,K))
1 +TR12*(CC(M,I,5,K)-CC(M,IC,4,K)))-(TI11*(CC(M,I-1,3,K)
1 -CC(M,IC-1,2,K))+TI12*(CC(M,I-1,5,K)-CC(M,IC-1,4,K))))
CH(M,I,K,5) = WA4(I-2)
1 *((CC(M,I,1,K)+TR11*(CC(M,I,3,K)-CC(M,IC,2,K))
1 +TR12*(CC(M,I,5,K)-CC(M,IC,4,K)))-(TI11*(CC(M,I-1,3,K)
1 -CC(M,IC-1,2,K))+TI12*(CC(M,I-1,5,K)-CC(M,IC-1,4,K))))
1 +WA4(I-1)
1 *((CC(M,I-1,1,K)+TR11*(CC(M,I-1,3,K)+CC(M,IC-1,2,K))
1 +TR12*(CC(M,I-1,5,K)+CC(M,IC-1,4,K)))+(TI11*(CC(M,I,3,K)
1 +CC(M,IC,2,K))+TI12*(CC(M,I,5,K)+CC(M,IC,4,K))))
1002 CONTINUE
102 CONTINUE
103 CONTINUE
RETURN
END
SUBROUTINE VRADBG (MP,IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,
C
C VRFFTPK, VERSION 1, AUGUST 1985
C
* MDIMC,WA)
DIMENSION CH(MDIMC,IDO,L1,IP) ,CC(MDIMC,IDO,IP,L1) ,
1 C1(MDIMC,IDO,L1,IP) ,C2(MDIMC,IDL1,IP),
2 CH2(MDIMC,IDL1,IP) ,WA(IDO*(IP-1))
!originally WA(IDO), but if I read the code correctly, it should be IDO*(IP-1) large, with WA(IDO) I do get mem-bound errors, L. de Wit 26-8-2024
TPI=2.*PIMACH(1.0)
ARG = TPI/FLOAT(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
DO 1001 M=1,MP
CH(M,I,K,1) = CC(M,I,1,K)
1001 CONTINUE
101 CONTINUE
102 CONTINUE
GO TO 106
103 DO 105 I=1,IDO
DO 104 K=1,L1
DO 1004 M=1,MP
CH(M,I,K,1) = CC(M,I,1,K)
1004 CONTINUE
104 CONTINUE
105 CONTINUE
106 DO 108 J=2,IPPH
JC = IPP2-J
J2 = J+J
DO 107 K=1,L1
DO 1007 M=1,MP
CH(M,1,K,J) = CC(M,IDO,J2-2,K)+CC(M,IDO,J2-2,K)
CH(M,1,K,JC) = CC(M,1,J2-1,K)+CC(M,1,J2-1,K)
1007 CONTINUE
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
DO 109 I=3,IDO,2
IC = IDP2-I
DO 1009 M=1,MP
CH(M,I-1,K,J) = CC(M,I-1,2*J-1,K)+CC(M,IC-1,2*J-2,K)
CH(M,I-1,K,JC) = CC(M,I-1,2*J-1,K)-CC(M,IC-1,2*J-2,K)
CH(M,I,K,J) = CC(M,I,2*J-1,K)-CC(M,IC,2*J-2,K)
CH(M,I,K,JC) = CC(M,I,2*J-1,K)+CC(M,IC,2*J-2,K)
1009 CONTINUE
109 CONTINUE
110 CONTINUE
111 CONTINUE
GO TO 116
112 DO 115 J=2,IPPH
JC = IPP2-J
DO 114 I=3,IDO,2
IC = IDP2-I
DO 113 K=1,L1
DO 1013 M=1,MP
CH(M,I-1,K,J) = CC(M,I-1,2*J-1,K)+CC(M,IC-1,2*J-2,K)
CH(M,I-1,K,JC) = CC(M,I-1,2*J-1,K)-CC(M,IC-1,2*J-2,K)
CH(M,I,K,J) = CC(M,I,2*J-1,K)-CC(M,IC,2*J-2,K)
CH(M,I,K,JC) = CC(M,I,2*J-1,K)+CC(M,IC,2*J-2,K)
1013 CONTINUE
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
DO 1017 M=1,MP
C2(M,IK,L) = CH2(M,IK,1)+AR1*CH2(M,IK,2)
C2(M,IK,LC) = AI1*CH2(M,IK,IP)
1017 CONTINUE
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
DO 1018 M=1,MP
C2(M,IK,L) = C2(M,IK,L)+AR2*CH2(M,IK,J)
C2(M,IK,LC) = C2(M,IK,LC)+AI2*CH2(M,IK,JC)
1018 CONTINUE
118 CONTINUE
119 CONTINUE
120 CONTINUE
DO 122 J=2,IPPH
DO 121 IK=1,IDL1
DO 1021 M=1,MP
CH2(M,IK,1) = CH2(M,IK,1)+CH2(M,IK,J)
1021 CONTINUE
121 CONTINUE
122 CONTINUE
DO 124 J=2,IPPH
JC = IPP2-J
DO 123 K=1,L1
DO 1023 M=1,MP
CH(M,1,K,J) = C1(M,1,K,J)-C1(M,1,K,JC)
CH(M,1,K,JC) = C1(M,1,K,J)+C1(M,1,K,JC)
1023 CONTINUE
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
DO 125 I=3,IDO,2
DO 1025 M=1,MP
CH(M,I-1,K,J) = C1(M,I-1,K,J)-C1(M,I,K,JC)