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499 lines
16 KiB
Fortran
499 lines
16 KiB
Fortran
PROGRAM sp2tccpdf
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C***********************************************************************
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C This program computes: *
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C *
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C density of T= T_1+T_2 in a gaussian process i.e. *
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C *
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C wavelengthes for crests <h1 and troughs >h2 *
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C *
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C Sylvie and Igor 7 dec. 1999 *
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C***********************************************************************
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use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb,
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& NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV
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use rind
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IMPLICIT NONE
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double precision, dimension(:,:),allocatable :: BIG
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double precision, dimension(:,:),allocatable :: ansr
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double precision, dimension(: ),allocatable :: ex,CY1,CY2
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double precision, dimension(:,:),allocatable :: xc
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double precision, dimension(: ),allocatable :: fxind,h1,h2
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double precision, dimension(: ),allocatable :: hh1,hh2
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double precision, dimension(: ),allocatable :: R0,R1,R2
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double precision ::CC,U,XddInf,XdInf,XtInf
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double precision, dimension(:,:),allocatable :: a_up,a_lo
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integer , dimension(: ),allocatable :: seed
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integer ,dimension(7) :: indI
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integer :: Ntime,tn,ts,speed,ph,seed1,seed_size,Nx1,Nx2,N0
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integer :: icy,icy2
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double precision :: ds,dT ! lag spacing for covariances
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! DIGITAL:
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! f90 -g2 -C -automatic -o ~/WAT/V4/sp2tthpdf1.exe rind49.f sp2tthpdf1.f
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! SOLARIS:
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!f90 -g -O -w3 -Bdynamic -fixed -o ../sp2tthpdf.exe rind49.f sp2tthpdf1.f
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!print *,'enter sp2thpdf'
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CALL INIT_LEVELS(U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT)
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!print *,'U,Ntime,NIT,speed,SCIS,seed1,Nx,dT'
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!print *,U,Ntime,NIT,speed,SCIS,seed1,Nx,dT
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!Nx1=1
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!Nx2=1
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Nx=Nx1*Nx1
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!print *,'NN',Nx1,Nx2,Nx
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!XSPLT=1.5d0
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if (SCIS.GT.0) then
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allocate(COV(1:Nx))
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call random_seed(SIZE=seed_size)
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allocate(seed(seed_size))
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call random_seed(GET=seed(1:seed_size)) ! get current seed
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seed(1)=seed1 ! change seed
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call random_seed(PUT=seed(1:seed_size))
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deallocate(seed)
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endif
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CALL INITDATA(speed)
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!print *,ntime,speed,u,NIT
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allocate(R0(1:Ntime+1))
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allocate(R1(1:Ntime+1))
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allocate(R2(1:Ntime+1))
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allocate(h1(1:Nx1))
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allocate(h2(1:Nx2))
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CALL INIT_AMPLITUDES(h1,Nx1,h2,Nx2)
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CALL INIT_COVARIANCES(Ntime,R0,R1,R2)
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allocate(hh1(1:Nx))
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allocate(hh2(1:Nx))
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!h transformation
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do icy=1,Nx1
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do icy2=1,Nx2
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hh1((icy-1)*Nx2+icy2)=h1(icy);
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hh2((icy-1)*Nx2+icy2)=h2(icy2);
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enddo
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enddo
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Nj=0
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indI(1)=0
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C ***** The bound 'infinity' is set to 10*sigma *****
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XdInf=10.d0*SQRT(-R2(1))
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XtInf=10.d0*SQRT(R0(1))
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!h1(1)=XtInf
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!h2(1)=XtInf
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! normalizing constant
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CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) )
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allocate(CY1(1:Nx))
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allocate(CY2(1:Nx))
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do icy=1,Nx
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CY1(icy)=exp(-0.5*hh1(icy)*hh1(icy)/100)/(10*sqrt(twopi))
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CY2(icy)=exp(-0.5*hh2(icy)*hh2(icy)/100)/(10*sqrt(twopi))
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enddo
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!print *,CY1
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allocate(ansr(1:Ntime,1:Nx))
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ansr=0.d0
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allocate(fxind(1:Nx))
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fxind=0.d0
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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! Y={X(t2)..,X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)} !!
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! = [Xt Xd Xc] !!
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! !!
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! Nt=tn-2, Nd=3, Nc=2+3 !!
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! !!
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! Xt= contains Nt time points in the indicator function !!
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! Xd= " Nd derivatives !!
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! Xc= " Nc variables to condition on !!
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! (Y1,Y2) dummy variables ind. of all other v. inputing h1,h2 into rindd !!
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! !!
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! There are 6 ( NI=7) regions with constant bariers: !!
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! (indI(1)=0); for i\in (indI(1),indI(2)] u<Y(i)<h1 !!
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! (indI(2)=ts-2); for i\in (indI(2),indI(2)], inf<Y(i)<inf (no restr.) !!
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! (indI(3)=ts-1); for i\in (indI(3),indI(4)], h2 <Y(i)<u !!
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! (indI(4)=Nt) ; for i\in (indI(4),indI(5)], Y(i)<0 (deriv. X'(ts)) !!
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! (indI(5)=Nt+1); for i\in (indI(5),indI(6)], Y(i)>0 (deriv. X'(t1)) !!
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! (indI(6)=Nt+2); for i\in (indI(6),indI(7)], Y(i)>0 (deriv. X'(tn)) !!
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! (indI(7)=Nt+3); NI=7. !!
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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NI=7; Nd=3
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Nc=5; Mb=3
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allocate(a_up(1:Mb,1:(NI-1)))
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allocate(a_lo(1:Mb,1:(NI-1)))
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a_up=0.d0
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a_lo=0.d0
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allocate(BIG(1:(Ntime+Nc+1),1:(Ntime+Nc+1)))
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ALLOCATE(xc(1:Nc,1:Nx))
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allocate(ex(1:(Ntime+Nc+1)))
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!print *,size(ex),Ntime
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ex=0.d0
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!print *,size(ex),ex
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xc(1,1:Nx)=hh1(1:Nx)
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xc(2,1:Nx)=hh2(1:Nx)
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xc(3,1:Nx)=u
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xc(4,1:Nx)=u
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xc(5,1:Nx)=u
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! upp- down- upp-crossings at t1,ts,tn
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a_lo(1,1)=u
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a_up(1,2)=XtInf ! X(ts) is redundant
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a_lo(1,2)=-Xtinf
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a_up(1,3)=u
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a_lo(1,4)=-XdInf
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a_up(1,5)= XdInf
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a_up(1,6)= XdInf
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a_up(2,1)=1.d0
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a_lo(3,3)=1.d0 !signe a voir!!!!!!
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! print *,a_up
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! print *,a_lo
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do tn=N0,Ntime,1
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! do tn=Ntime,Ntime,1
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Ntd=tn+1
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Nt=Ntd-Nd
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Ntdc=Ntd+Nc
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indI(4)=Nt
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indI(5)=Nt+1
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indI(6)=Nt+2
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indI(7)=Ntd
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if (SCIS.gt.0) then
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if (SCIS.EQ.2) then
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Nj=max(Nt,0)
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else
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Nj=min(max(Nt-5, 0),0)
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endif
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endif
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do ts=3,tn-2
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!print *,'ts,tn' ,ts,tn,Ntdc
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CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2)!positive wave period
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indI(2)=ts-2
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indI(3)=ts-1
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CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc),
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& xc,indI,a_lo,a_up)
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ds=dt
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do icy=1,Nx
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! ansr(tn,:)=ansr(tn,:)+fxind*CC*ds./(CY1.*CY2)
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ansr(tn,icy)=ansr(tn,icy)+fxind(icy)*CC*ds/(CY1(icy)*CY2(icy))
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enddo
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enddo ! ts
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print *,'Ready: ',tn,' of ',Ntime
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enddo !tn
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!print *,'ansr',ansr
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300 open (unit=11, file='dens.out', STATUS='unknown')
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!print *, ansr
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do ts=1,Ntime
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do ph=1,Nx
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!write(11,*) ansr(ts,ph),hh1(ph),hh2(ph)
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write(11,111) ansr(ts,ph)
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enddo
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enddo
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111 FORMAT(2x,F12.8)
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close(11)
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900 deallocate(big)
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deallocate(fxind)
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deallocate(ansr)
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deallocate(xc)
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deallocate(ex)
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deallocate(R0)
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deallocate(R1)
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deallocate(R2)
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if (allocated(COV) ) then
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deallocate(COV)
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endif
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deallocate(h1)
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deallocate(h2)
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deallocate(hh1)
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deallocate(hh2)
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deallocate(a_up)
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deallocate(a_lo)
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stop
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!return
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CONTAINS
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SUBROUTINE INIT_LEVELS
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& (U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT)
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IMPLICIT NONE
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integer, intent(out):: Ntime,N0,NIT,speed,Nx1,Nx2,SCIS,seed1
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double precision ,intent(out) :: U,dT
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OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
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READ (14,*) U
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READ (14,*) Ntime
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READ (14,*) N0
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READ (14,*) NIT
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READ (14,*) speed
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READ (14,*) SCIS
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READ (14,*) seed1
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READ (14,*) Nx1,Nx2
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READ (14,*) dT
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if (Ntime.lt.5) then
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print *,'The number of wavelength points is too small, stop'
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stop
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end if
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CLOSE(UNIT=14)
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RETURN
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END SUBROUTINE INIT_LEVELS
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C******************************************************
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SUBROUTINE INIT_AMPLITUDES(h1,Nx1,h2,Nx2)
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IMPLICIT NONE
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double precision, dimension(:), intent(out) :: h1,h2
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integer, intent(in) :: Nx1,Nx2
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integer :: ix
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OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
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C
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C Reading in amplitudes
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C
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do ix=1,Nx1
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READ (4,*) H1(ix)
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enddo
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do ix=1,Nx2
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READ (4,*) H2(ix)
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enddo
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CLOSE(UNIT=4)
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RETURN
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END SUBROUTINE INIT_AMPLITUDES
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C**************************************************
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C***********************************************************************
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C***********************************************************************
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SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2)
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IMPLICIT NONE
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double precision, dimension(:),intent(out) :: R0,R1,R2
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integer,intent(in) :: Ntime
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integer :: i
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open (unit=1, file='Cd0.in',STATUS='unknown')
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open (unit=2, file='Cd1.in',STATUS='unknown')
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open (unit=3, file='Cd2.in',STATUS='unknown')
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do i=1,Ntime
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read(1,*) R0(i)
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read(2,*) R1(i)
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read(3,*) R2(i)
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enddo
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close(1)
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close(2)
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close(3)
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return
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END SUBROUTINE INIT_COVARIANCES
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C***********************************************************************
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C***********************************************************************
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C**********************************************************************
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SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2)
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IMPLICIT NONE
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double precision, dimension(:,:),intent(inout) :: BIG
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double precision, dimension(:),intent(in) :: R0,R1,R2
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integer ,intent(in) :: tn,ts
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integer :: i,j,Ntd1,N !=Ntdc
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double precision :: tmp
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! the order of the variables in the covariance matrix
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! are organized as follows:
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!
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! ||X(t2)..X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)||
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! = [Xt Xd Xc]
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! where
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!
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! Xt= time points in the indicator function
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! Xd= derivatives
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! Xc=variables to condition on
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! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s),
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! then Cov(X'(t),X(s))=dr(t,s)/dt. Now for stationary X(t) we have
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! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result).
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!
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! Consequently Cov(X'(t),X(s)) = -r'(s-t) = -sign(s-t)*r'(|s-t|)
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! Cov(X'(t),X'(s)) = -r''(s-t) = -r''(|s-t|)
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! Cov(X''(t),X'(s)) = r'''(s-t) = sign(s-t)*r'''(|s-t|)
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! Cov(X''(t),X(s)) = r''(s-t) = r''(|s-t|)
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! Cov(X''(t),X''(s)) = r''''(s-t) = r''''(|s-t|)
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Ntd1=tn+1
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N=Ntd1+Nc
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do i=1,tn-2
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!cov(Xt)
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do j=i,tn-2
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BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1))
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enddo
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!cov(Xt,Xc)
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BIG(i ,Ntd1+1) = 0.d0 !cov(X(ti+1),Y1)
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BIG(i ,Ntd1+2) = 0.d0 !cov(X(ti+1),Y2)
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BIG(i ,Ntd1+4) = R0(i+1) !cov(X(ti+1),X(t1))
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BIG(tn-1-i ,Ntd1+5) = R0(i+1) !cov(X(t.. ),X(tn))
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!Cov(Xt,Xd)=cov(X(ti+1),x(tj)
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BIG(i,Ntd1-1) =-R1(i+1) !cov(X(ti+1),X'(t1))
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BIG(tn-1-i,Ntd1)= R1(i+1) !cov(X(ti+1),X'(tn))
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enddo
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!cov(Xd)
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BIG(Ntd1 ,Ntd1 ) = -R2(1)
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BIG(Ntd1-1,Ntd1 ) = -R2(tn) !cov(X'(t1),X'(tn))
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BIG(Ntd1-1,Ntd1-1) = -R2(1)
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BIG(Ntd1-2,Ntd1-1) = -R2(ts) !cov(X'(ts),X'(t1))
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BIG(Ntd1-2,Ntd1-2) = -R2(1)
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BIG(Ntd1-2,Ntd1 ) = -R2(tn+1-ts) !cov(X'(ts),X'(tn))
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!cov(Xc)
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BIG(Ntd1+1,Ntd1+1) = 100.d0 ! cov(Y1 Y1)
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BIG(Ntd1+1,Ntd1+2) = 0.d0 ! cov(Y1 Y2)
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BIG(Ntd1+1,Ntd1+3) = 0.d0 ! cov(Y1 X(ts))
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BIG(Ntd1+1,Ntd1+4) = 0.d0 ! cov(Y1 X(t1))
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BIG(Ntd1+1,Ntd1+5) = 0.d0 ! cov(Y1 X(tn))
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BIG(Ntd1+2,Ntd1+2) = 100.d0 ! cov(Y2 Y2)
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BIG(Ntd1+2,Ntd1+3) = 0.d0 ! cov(Y2 X(ts))
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BIG(Ntd1+2,Ntd1+4) = 0.d0 ! cov(Y2 X(t1))
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BIG(Ntd1+2,Ntd1+5) = 0.d0 ! cov(Y2 X(tn))
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BIG(Ntd1+3,Ntd1+3) = R0(1) ! cov(X(ts),X (ts)
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BIG(Ntd1+3,Ntd1+4) = R0(ts) ! cov(X(ts),X (t1))
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BIG(Ntd1+3,Ntd1+5) = R0(tn+1-ts) ! cov(X(ts),X (tn))
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BIG(Ntd1+4,Ntd1+4) = R0(1) ! cov(X(t1),X (t1))
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BIG(Ntd1+4,Ntd1+5) = R0(tn) ! cov(X(t1),X (tn))
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BIG(Ntd1+5,Ntd1+5) = R0(1) ! cov(X(tn),X (tn))
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!cov(Xd,Xc)
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BIG(Ntd1 ,Ntd1+1) = 0.d0 !cov(X'(tn),Y1)
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BIG(Ntd1 ,Ntd1+2) = 0.d0 !cov(X'(tn),Y2)
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BIG(Ntd1-1 ,Ntd1+1) = 0.d0 !cov(X'(t1),Y1)
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BIG(Ntd1-1 ,Ntd1+2) = 0.d0 !cov(X'(t1),Y2)
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BIG(Ntd1-2 ,Ntd1+1) = 0.d0 !cov(X'(ts),Y1)
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BIG(Ntd1-2 ,Ntd1+2) = 0.d0 !cov(X'(ts),Y2)
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BIG(Ntd1 ,Ntd1+4) = R1(tn) !cov(X'(tn),X(t1))
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BIG(Ntd1 ,Ntd1+5) = 0.d0 !cov(X'(tn),X(tn))
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BIG(Ntd1-1,Ntd1+4) = 0.d0 !cov(X'(t1),X(t1))
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BIG(Ntd1-1,Ntd1+5) =-R1(tn) !cov(X'(t1),X(tn))
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BIG(Ntd1 ,Ntd1+3) = R1(tn+1-ts) !cov(X'(tn),X (ts))
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BIG(Ntd1-1,Ntd1+3) =-R1(ts) !cov(X'(t1),X (ts))
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BIG(Ntd1-2,Ntd1+3) = 0.d0 !cov(X'(ts),X (ts)
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BIG(Ntd1-2,Ntd1+4) = R1(ts) !cov(X'(ts),X (t1))
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BIG(Ntd1-2,Ntd1+5) = -R1(tn+1-ts) !cov(X'(ts),X (tn))
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do i=1,tn-2
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j=abs(i+1-ts)
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!cov(Xt,Xc)
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BIG(i,Ntd1+3) = R0(j+1) !cov(X(ti+1),X(ts))
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!Cov(Xt,Xd)
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if ((i+1-ts).lt.0) then
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BIG(i,Ntd1-2) = R1(j+1)
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else !cov(X(ti+1),X'(ts))
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BIG(i,Ntd1-2) = -R1(j+1)
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endif
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enddo
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! make lower triangular part equal to upper
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do j=1,N-1
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do i=j+1,N
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tmp =BIG(j,i)
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BIG(i,j)=tmp
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enddo
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enddo
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C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
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C 10 format(6F8.4)
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RETURN
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END SUBROUTINE COV_INPUT
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SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2)
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IMPLICIT NONE
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double precision, dimension(:,:), intent(out) :: BIG
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double precision, dimension(:), intent(in) :: R0,R1,R2
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integer :: pt,i,j
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! the order of the variables in the covariance matrix
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! are organized as follows;
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! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc]
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!
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! where Xd is the derivatives
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!
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! Xt= time points in the indicator function
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! Xd= derivatives
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! Xc=variables to condition on
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!cov(Xc)
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BIG(pt+2,pt+2) = R0(1)
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BIG(pt+1,pt+1) = R0(1)
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BIG(pt+1,pt+2) = R0(pt)
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!cov(Xd)
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BIG(pt,pt) = -R2(1)
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BIG(pt-1,pt-1) = -R2(1)
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BIG(pt-1,pt) = -R2(pt)
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!cov(Xd,Xc)
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BIG(pt,pt+2) = 0.d0
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BIG(pt,pt+1) = R1(pt)
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BIG(pt-1,pt+2) = -R1(pt)
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BIG(pt-1,pt+1) = 0.d0
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|
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if (pt.GT.2) then
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!cov(Xt)
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do i=1,pt-2
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do j=i,pt-2
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BIG(i,j) = R0(j-i+1)
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enddo
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enddo
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!cov(Xt,Xc)
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do i=1,pt-2
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BIG(i,pt+1) = R0(i+1)
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BIG(pt-1-i,pt+2) = R0(i+1)
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enddo
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!Cov(Xt,Xd)=cov(X(ti+1),x(tj))
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do i=1,pt-2
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BIG(i,pt-1) = -R1(i+1)
|
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BIG(pt-1-i,pt)= R1(i+1)
|
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enddo
|
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endif
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|
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! make lower triangular part equal to upper
|
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do j=1,pt+1
|
|
do i=j+1,pt+2
|
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BIG(i,j)=BIG(j,i)
|
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enddo
|
|
enddo
|
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C write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
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C 10 format(6F8.4)
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RETURN
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END SUBROUTINE COV_INPUT2
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END PROGRAM sp2tccpdf
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