This document contains the code for a program that performs proper orthogonal decomposition (POD) on velocity field data. It includes sections that: 1) Initialize variables and parameters 2) Read in data files and correct coordinate values 3) Calculate mean velocities, velocity fluctuations, and the correlation matrix 4) Perform eigenvalue decomposition to calculate eigenvalues and eigenvectors 5) Save results like eigenvalues, eigenvectors, and POD modes to files

1. PROGRAM pod
IMPLICIT NONE
INTEGER ::
i,j,Nx,Raw_No,Vx,INFO,a,b,c,k,l,LWORK,n,imod,it,ix,nxdeb,nxfin,nydeb,nyfin,Vxmax,ix1
,ix0,imode,ival,ifile
REAL ::
Xcord,Ycord,u,v,s,waste,sumvel,x,w,pval,pvali,ti,at,array,valuemtx,summ,rms
REAL :: xdec,ydec,height,width,Xhcord,Yhcord,hu,hv,hs
PARAMETER(Nx=2000,Raw_No=5084,Vx=48,LWORK=3*Vx,Vxmax=62)
REAL :: xuv(Raw_No),yuv(Raw_No),velu(Raw_No),velv(Raw_No)
REAL :: sp(Vx),velvec(Nx,Vx),T_velvec(Vx,Nx),meanvel(Nx),vel(Nx,Vx)
REAL :: lambda(Vx),mods(Vx),modsum(Vx),normmodsum(Vx),av(Nx,Vx)
REAL :: atf(Nx,Vx),evec(Vx,Vx),phi(Nx,Vx),prephi(Vx),correl(Vx,Vx)
CHARACTER (LEN=4) :: filenumber
CHARACTER (LEN=100) :: datachar
CHARACTER (LEN=100) :: lone
CHARACTER (LEN=100) :: ltwo
CHARACTER (LEN=100) :: lthree
DOUBLE PRECISION :: WORK(LWORK)
DOUBLE PRECISION :: vp(LWORK)
DOUBLE PRECISION :: Aeg(Vx,Vx)
CHARACTER(*), PARAMETER :: path_data ='/home/sbhattac/Bureau/Fortran_POD/'
CHARACTER(*), PARAMETER :: path_filenumber
='/home/sbhattac/Bureau/Fortran_POD/FileNumber/'
CHARACTER(*), PARAMETER :: path_parameters
='/home/sbhattac/Bureau/Fortran_POD/Parameters/'
CHARACTER(*), PARAMETER :: path_rawdata
='/home/sbhattac/Bureau/Fortran_POD/Raw_Data/'
CHARACTER(*), PARAMETER :: path_correctedfile
='/home/sbhattac/Bureau/Fortran_POD/Corrected_Data/'
CHARACTER(*), PARAMETER :: path_snapshot
='/home/sbhattac/Bureau/Fortran_POD/Snapshot_Files/'
CHARACTER(*), PARAMETER :: path_egvec
='/home/sbhattac/Bureau/Fortran_POD/Egvec_Files/'
CHARACTER(*), PARAMETER :: path_phi
='/home/sbhattac/Bureau/Fortran_POD/Phi_Files/'
CHARACTER(*), PARAMETER :: path_lamda
='/home/sbhattac/Bureau/Fortran_POD/Lamda_Files/'
CHARACTER(*), PARAMETER :: path_eigenvectors
='/home/sbhattac/Bureau/Fortran_POD/Eigenvectors_Files/'
do i=1,Nx
do j=1,Vx
velvec(i,j)=0
vel(i,j)=0
T_velvec(j,i)=0
phi(i,j)=0
atf(i,j)=0
end do
end do
WRITE(*,*)".... CREATION OF 'correct_parameters.ini' ...."
WRITE(*,*) '....Reading Parameters....'
OPEN(22,FILE=path_parameters//'parameters.ini')
OPEN(23,FILE=path_parameters//'correct_parameters.ini')
READ(22,*)datachar
WRITE(23,*)datachar

2. READ(22,*)xdec
WRITE(23,*)xdec+50
READ(22,*)datachar
WRITE(23,*)datachar
READ(22,*)ydec
WRITE(23,*)ydec
READ(22,*)datachar
WRITE(23,*)datachar
READ(22,*)height
WRITE(23,*)height
READ(22,*)datachar
WRITE(23,*)datachar
READ(22,*)width
WRITE(23,*)width
READ(22,*)datachar
WRITE(23,*)datachar
READ(22,*)nxdeb,nxfin
WRITE(23,*)nxdeb,nxfin
READ(22,*)datachar
WRITE(23,*)datachar
READ(22,*)nydeb,nyfin
WRITE(23,*)nydeb,nyfin
CLOSE(22)
xdec = xdec+50.
CLOSE(23)
WRITE(*,*)".... CREATION OF 'correct_parameters.ini' COMPLETE ...."
WRITE(*,*) 'xdec(+50)=',xdec
WRITE(*,*)".... CREATION OF SET OF 'CorrectedFile.ini' ...."
WRITE(*,*) '....Correction of Coordinates....'
OPEN(24,FILE=path_filenumber//'filenumbers.dat')
OPEN(46,FILE=path_data//'Datafile.dat')
DO i=1,Nx
READ(24,*)filenumber
OPEN(25,FILE=path_rawdata//'File'//filenumber//'.dat')
READ(25,*)lone
READ(25,*)ltwo
READ(25,*)lthree

3. DO ival=1,Raw_No
READ(25,*) Xcord,Ycord,u,v,s
xuv(ival)=-1.*Ycord - xdec
yuv(ival)=Xcord - ydec
velu(ival) = -1.*v
velv(ival) = u
IF ( yuv(ival) .GT. 98.0 .AND. yuv(ival) .LT. 99.0 ) THEN
IF ( xuv(ival) .LT. 50.0 .AND. xuv(ival) .GT. -49.0 ) THEN
WRITE(46,*)xuv(ival),velv(ival)
END IF
END IF
END DO
CLOSE(25)
END DO
CLOSE(46)
CLOSE(24)
WRITE(*,*)".... CREATION OF 'Datafile.dat' COMPLETE ...."
OPEN(36,FILE=path_data//'Datafile.dat')
DO ifile=1,Nx
sumvel=0
DO ival=1,Vx
READ(36,*)x,w
sp(ival)=x
vel(ifile,ival)=w
END DO
END DO
DO ival=1,Vx
sumvel=0
DO ifile=1,Nx
sumvel=sumvel+vel(ifile,ival)
END DO
meanvel(ival)=sumvel/Nx
END DO
DO ifile=1,Nx
DO ival=1,Vx
velvec(ifile,ival)=meanvel(ival)-vel(ifile,ival)
END DO
END DO
DO ix0 = 1,Vx
DO ix1 = 1,Vx
correl(ix0,ix1) = 0.
ENDDO
ENDDO
DO it= 1,Nx
DO ix0 = 1,Vx
DO ix1 = 1,Vx
correl(ix0,ix1) =correl(ix0,ix1)+velvec(it,ix0)*velvec(it,ix1)
ENDDO
ENDDO
END DO
DO ix0 = 1,Vx
DO ix1 = 1,Vx
correl(ix1,ix0) = correl(ix1,ix0)/FLOAT(Nx)
ENDDO

4. ENDDO
DO ix0 = 1,Vx
DO ix1 = 1,Vx
Aeg(ix0,ix1)=correl(ix0,ix1)
ENDDO
ENDDO
WRITE(*,*) 'Number of values in matrix_three=',SIZE(Aeg)
CALL dsyev('V','U',Vx,Aeg,Vx,vp,WORK,LWORK,INFO)
IF (INFO.ne.0) then
WRITE (*,*) 'INFO = ',INFO
STOP
END IF
DO k=1,Vx
DO l=1,Vx
evec(k,l)=Aeg(k,Vx+1-l)
END DO
END DO
DO imode=1,Vx
lambda(imode)=vp(Vx+1-imode)
IF (lambda(imode).LT.0.) THEN
WRITE(*,*)'Attention,valeur propre negative'
WRITE(*,*)k
END IF
END DO
!***********************************************************************************
****************************************
WRITE(*,*) '.... CREATTION OF "lamda.dat" ....'
OPEN(41,FILE=path_lamda//'lamda.dat')
OPEN(81,FILE=path_lamda//'loglamda.dat')
DO imode=1,Vx
WRITE(41,*)imode,lambda(imode)
WRITE(81,*)log(float(imode)),log(lambda(imode))
END DO
CLOSE(41)
CLOSE(81)
WRITE(*,*) '.... CREATTION OF "lambda.dat" COMPLETE ....'
!***********************************************************************************
****************************************
WRITE(*,*) '.... CREATTION OF "eigenvectors.dat" ....'
OPEN(42,FILE=path_filenumber//'filenumbers.dat')
DO imode=1,Vx
READ(42,*)filenumber
OPEN(43,FILE=path_eigenvectors//'eigenvectors'//filenumber//'.dat')
DO ival=1,Vx
WRITE(43,121)(sp(ival))/height,evec(ival,imode)
END DO
CLOSE(43)
END DO
CLOSE(42)
WRITE(*,*) '.... CREATTION OF SET OF "eigenvectors.dat" COMPLETE ....'

5. 121 FORMAT (8(e20.6,2X))
!***********************************************************************************
****************************************
WRITE(*,*) '.... CALCULATION OF MODS ....'
!DO imod = 1,Vx
!rms = 0.
!DO it=1,Nx
!av(it,imod)=0.
!DO ix=1,Vx
!av(it,imod) = av(it,imod)+evec(ix,imod)*velvec(it,ix)
!ENDDO
!rms = rms+av(it,imod)**2
!ENDDO
!rms = rms/FLOAT(Nx)
!WRITE(*,*)rms,lambda(imod)
!ENDDO
!OPEN(64,FILE=path_filenumber//'filenumbers.dat')
!DO it=1,Nx
!READ(64,*)filenumber
!OPEN(45,FILE=path_phi//'Phi'//filenumber//'.dat')
!DO imod = 1,Vx
! WRITE(45,122)av(it,imod),(av(it,imod)/SQRT(lambda(imod)))
!END DO
!END DO
!CLOSE(45)
!CLOSE(64)
!122 FORMAT (40(e20.6,2X))
DO ifile=1,Nx
DO ival=1,Vx
at=0
DO imode=1,Vx
ti=velvec(ifile,ival)*evec(ival,imode)
at=at+ti
END DO
atf(ifile,ival)=at
END DO
END DO
DO ival=1,Vx
pval=0
DO ifile=1,Nx
pvali=atf(ifile,ival)
pval=pval+pvali
END DO
prephi(ival)=pval
END DO
DO imode=1,Vx
DO ival=1,Vx
phi(ival,imode)=evec(ival,imode)*prephi(ival)
END DO
END DO
OPEN(64,FILE=path_filenumber//'filenumbers.dat')
DO imode=1,Vx

6. READ(64,*)filenumber
OPEN(45,FILE=path_phi//'Phi'//filenumber//'.dat')
DO ival=1,Vx
WRITE(45,*)sp(ival),phi(ival,imode)
END DO
CLOSE(45)
END DO
CLOSE(64)
WRITE(*,*) '.... CREATTION OF SET OF "Phi.dat" SUCCESSFUL ....'
!***********************************************************************************
****************************************
WRITE(*,*) '.... FORTRAN_POD SUCCESSFUL ....'
END PROGRAM pod