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357 lines
11 KiB
Fortran
357 lines
11 KiB
Fortran
PROGRAM sp2mM1
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C***********************************************************************************
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C Computes upper lower bounds for density of maximum and the following minimum *
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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 :: ansrup
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double precision, dimension(:,:),allocatable :: ansrlo
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double precision, dimension(: ),allocatable :: ex,h
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double precision, dimension(:,:),allocatable :: xc
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double precision, dimension(:,:),allocatable :: fxind
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double precision, dimension(: ),allocatable :: R0,R1,R2,R3,R4
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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 :: Nstart,Ntime,tn,ts,speed,seed1,seed_size
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integer :: status,i,j,ij,Nx1
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double precision :: ds,dT ! lag spacing for covariances
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! f90 sp2AmM1.f rind52.f
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CALL INIT_LEVELS(Ntime,Nstart,NIT,speed,Nx1,dT)
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Nx=Nx1*(Nx1-1)/2
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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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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(R3(1:Ntime+1))
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allocate(R4(1:Ntime+1))
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allocate(h(1:Nx1))
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CALL INIT_AMPLITUDES(h,Nx1)
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CALL INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4)
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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! Y= X'(t2)...X'(tn-1)||X''(t1) X''(tn)||X(t1) X(tn) X'(t1) X'(tn) !!
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! = [ Xt Xd Xc ] !!
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! !!
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! Nt=tn-2, Nd=2, Nc=4 !!
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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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! !!
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! There are 3 ( NI=4) regions with constant bariers: !!
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! (indI(1)=0); for i\in (indI(1),indI(2)] Y(i)<0. !!
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! (indI(2)=Nt) ; for i\in (indI(2)+1,indI(3)], Y(i)<0 (deriv. X''(t1)) !!
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! (indI(3)=Nt+1); for i\in (indI(3)+1,indI(4)], Y(i)>0 (deriv. X''(tn)) !!
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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NI=4; Nd=2
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Nc=4; Mb=1
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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(R4(1))
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XtInf=10.d0*SQRT(-R2(1))
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! normalizing constant
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CC=TWOPI*SQRT(-R2(1)/R4(1))
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allocate(BIG(1:Ntime+Nc,1:Ntime+Nc),stat=status)
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if (status.ne.0) then
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print *,'can not allocate BIG'
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end if
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allocate(ex(1:Ntime+Nc),stat=status)
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if (status.ne.0) then
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print *,'can not allocate ex'
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end if
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allocate(ansrup(1:Nx1,1:Nx1))
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ansrup=0.d0
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allocate(ansrlo(1:Nx1,1:Nx1))
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ansrlo=0.d0
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allocate(fxind(1:Nx,1:2))
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fxind=0.d0 !this is not needed
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allocate(xc(1:Nc,1:Nx))
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allocate(a_up(Mb,NI-1))
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allocate(a_lo(Mb,NI-1))
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a_up=0.d0
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a_lo=0.d0
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ij=0
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do i=2,Nx1
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do j=1,i-1
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ij=ij+1
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xc(1,ij)=h(i)
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xc(2,ij)=h(j)
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enddo
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enddo
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xc(3,1:Nx)=0.d0
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xc(4,1:Nx)=0.d0
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a_lo(1,1)=-Xtinf
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a_lo(1,2)=-XdInf
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a_up(1,3)=+XdInf
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Nstart=MAX(2,Nstart)
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if (SCIS.GT.0) then
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open (unit=11, file='COV.out', STATUS='unknown')
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write(11,*) 0.d0
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endif
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do Ntd=Nstart,Ntime
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Ntdc=Ntd+Nc
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ex=0.d0
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BIG=0.d0
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CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,R0,R1,R2,R3,R4) ! positive wave period
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Nt=Ntd-Nd;
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indI(2)=Nt;
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indI(3)=Nt+1;
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indI(4)=Ntd;
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CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up)
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ij=0
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do i=2,Nx1
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do j=1,i-1
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ij=ij+1
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ansrup(i,j)=ansrup(i,j)+fxind(ij,1)*CC*dt
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ansrlo(i,j)=ansrlo(i,j)+fxind(ij,2)*CC*dt
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enddo
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enddo
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if (SCIS.GT.0) then
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write(11,*) COV(1) ! save coefficient of variation
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endif
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print *,'Ready: ',Ntd,' of ',Ntime
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enddo
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goto 300
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300 open (unit=11, file='dens.out', STATUS='unknown')
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do i=1,Nx1
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do j=1,Nx1
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write(11,*) ansrup(i,j),ansrlo(i,j)
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enddo
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enddo
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close(11)
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900 continue
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deallocate(BIG)
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deallocate(ex)
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deallocate(fxind)
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deallocate(ansrup)
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deallocate(ansrlo)
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deallocate(xc)
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deallocate(R0)
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deallocate(R1)
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deallocate(R2)
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deallocate(R3)
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deallocate(R4)
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deallocate(h)
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if (allocated(COV) ) then
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deallocate(COV)
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endif
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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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& (Ntime,Nstart,NIT,speed,Nx,dT)
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IMPLICIT NONE
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integer, intent(out):: Ntime,Nstart,NIT,speed,Nx
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double precision ,intent(out) :: dT
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OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
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READ (14,*) Ntime
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READ (14,*) Nstart
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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,*) Nx
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READ (14,*) dT
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if (Ntime.lt.2) 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(h,Nx)
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IMPLICIT NONE
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double precision, dimension(:), intent(out) :: h
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integer, intent(in) :: Nx
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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,Nx
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READ (4,*) H(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,R3,R4)
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IMPLICIT NONE
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double precision, dimension(:),intent(out) :: R0,R1,R2
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double precision, dimension(:),intent(out) :: R3,R4
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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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open (unit=4, file='Cd3.in',STATUS='unknown')
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open (unit=5, file='Cd4.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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read(4,*) R3(i)
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read(5,*) R4(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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close(3)
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close(5)
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return
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END SUBROUTINE INIT_COVARIANCES
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C**********************************************************************
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SUBROUTINE COV_INPUT(BIG,tn,R0,R1,R2,R3,R4)
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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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double precision, dimension(:),intent(in) :: R3,R4
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integer ,intent(in) :: tn
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integer :: i,j,N
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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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! X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X(t1),X(tn),X'(t1),X'(tn)
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! = [ Xt | Xd | Xc ]
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!
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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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N=tn+4
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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) = -R2(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 ,tn+1) = R1(i+1) !cov(X'(ti+1),X(t1))
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BIG(tn-1-i ,tn+2) = -R1(i+1) !cov(X'(ti+1),X(tn))
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BIG(i ,tn+3) = -R2(i+1) !cov(X'(ti+1),X'(t1))
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BIG(tn-1-i ,tn+4) = -R2(i+1) !cov(X'(ti+1),X'(tn))
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!Cov(Xt,Xd)
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BIG(i,tn-1) = R3(i+1) !cov(X'(ti+1),X''(t1))
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BIG(tn-1-i,tn) =-R3(i+1) !cov(X'(ti+1),X''(tn))
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enddo
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!cov(Xd)
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BIG(tn-1 ,tn-1 ) = R4(1)
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BIG(tn-1,tn ) = R4(tn) !cov(X''(t1),X''(tn))
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BIG(tn ,tn ) = R4(1)
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!cov(Xc)
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BIG(tn+1,tn+1) = R0(1) ! cov(X(t1),X(t1))
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BIG(tn+1,tn+2) = R0(tn) ! cov(X(t1),X(tn))
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BIG(tn+1,tn+3) = 0.d0 ! cov(X(t1),X'(t1))
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BIG(tn+1,tn+4) = R1(tn) ! cov(X(t1),X'(tn))
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BIG(tn+2,tn+2) = R0(1) ! cov(X(tn),X(tn))
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BIG(tn+2,tn+3) =-R1(tn) ! cov(X(tn),X'(t1))
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BIG(tn+2,tn+4) = 0.d0 ! cov(X(tn),X'(tn))
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BIG(tn+3,tn+3) =-R2(1) ! cov(X'(t1),X'(t1))
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BIG(tn+3,tn+4) =-R2(tn) ! cov(X'(t1),X'(tn))
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BIG(tn+4,tn+4) =-R2(1) ! cov(X'(tn),X'(tn))
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!Xc=X(t1),X(tn),X'(t1),X'(tn)
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!Xd=X''(t1),X''(tn)
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!cov(Xd,Xc)
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BIG(tn-1 ,tn+1) = R2(1) !cov(X''(t1),X(t1))
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BIG(tn-1 ,tn+2) = R2(tn) !cov(X''(t1),X(tn))
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BIG(tn-1 ,tn+3) = 0.d0 !cov(X''(t1),X'(t1))
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BIG(tn-1 ,tn+4) = R3(tn) !cov(X''(t1),X'(tn))
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BIG(tn ,tn+1) = R2(tn) !cov(X''(tn),X(t1))
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BIG(tn ,tn+2) = R2(1) !cov(X''(tn),X(tn))
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BIG(tn ,tn+3) =-R3(tn) !cov(X''(tn),X'(t1))
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BIG(tn ,tn+4) = 0.d0 !cov(X''(tn),X'(tn))
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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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RETURN
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END SUBROUTINE COV_INPUT
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END PROGRAM sp2mM1
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