PROGRAM sp2mM1 C*********************************************************************************** C Computes upper lower bounds for density of maximum and the following minimum * C*********************************************************************************** use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV use rind IMPLICIT NONE double precision, dimension(:,:),allocatable :: BIG double precision, dimension(:,:),allocatable :: ansrup double precision, dimension(:,:),allocatable :: ansrlo double precision, dimension(: ),allocatable :: ex,h double precision, dimension(:,:),allocatable :: xc double precision, dimension(:,:),allocatable :: fxind double precision, dimension(: ),allocatable :: R0,R1,R2,R3,R4 double precision ::CC,U,XddInf,XdInf,XtInf double precision, dimension(:,:),allocatable :: a_up,a_lo integer , dimension(: ),allocatable :: seed integer ,dimension(7) :: indI integer :: Nstart,Ntime,tn,ts,speed,seed1,seed_size integer :: status,i,j,ij,Nx1 double precision :: ds,dT ! lag spacing for covariances ! f90 sp2AmM1.f rind52.f CALL INIT_LEVELS(Ntime,Nstart,NIT,speed,Nx1,dT) Nx=Nx1*(Nx1-1)/2 if (SCIS.GT.0) then allocate(COV(1:Nx)) call random_seed(SIZE=seed_size) allocate(seed(seed_size)) call random_seed(GET=seed(1:seed_size)) ! get current seed seed(1)=seed1 ! change seed call random_seed(PUT=seed(1:seed_size)) deallocate(seed) endif CALL INITDATA(speed) allocate(R0(1:Ntime+1)) allocate(R1(1:Ntime+1)) allocate(R2(1:Ntime+1)) allocate(R3(1:Ntime+1)) allocate(R4(1:Ntime+1)) allocate(h(1:Nx1)) CALL INIT_AMPLITUDES(h,Nx1) CALL INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Y= X'(t2)...X'(tn-1)||X''(t1) X''(tn)||X(t1) X(tn) X'(t1) X'(tn) !! ! = [ Xt Xd Xc ] !! ! !! ! Nt=tn-2, Nd=2, Nc=4 !! ! !! ! Xt= contains Nt time points in the indicator function !! ! Xd= " Nd derivatives !! ! Xc= " Nc variables to condition on !! ! !! ! There are 3 ( NI=4) regions with constant bariers: !! ! (indI(1)=0); for i\in (indI(1),indI(2)] Y(i)<0. !! ! (indI(2)=Nt) ; for i\in (indI(2)+1,indI(3)], Y(i)<0 (deriv. X''(t1)) !! ! (indI(3)=Nt+1); for i\in (indI(3)+1,indI(4)], Y(i)>0 (deriv. X''(tn)) !! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! NI=4; Nd=2 Nc=4; Mb=1 Nj=0 indI(1)=0 C ***** The bound 'infinity' is set to 10*sigma ***** XdInf=10.d0*SQRT(R4(1)) XtInf=10.d0*SQRT(-R2(1)) ! normalizing constant CC=TWOPI*SQRT(-R2(1)/R4(1)) allocate(BIG(1:Ntime+Nc,1:Ntime+Nc),stat=status) if (status.ne.0) then print *,'can not allocate BIG' end if allocate(ex(1:Ntime+Nc),stat=status) if (status.ne.0) then print *,'can not allocate ex' end if allocate(ansrup(1:Nx1,1:Nx1)) ansrup=0.d0 allocate(ansrlo(1:Nx1,1:Nx1)) ansrlo=0.d0 allocate(fxind(1:Nx,1:2)) fxind=0.d0 !this is not needed allocate(xc(1:Nc,1:Nx)) allocate(a_up(Mb,NI-1)) allocate(a_lo(Mb,NI-1)) a_up=0.d0 a_lo=0.d0 ij=0 do i=2,Nx1 do j=1,i-1 ij=ij+1 xc(1,ij)=h(i) xc(2,ij)=h(j) enddo enddo xc(3,1:Nx)=0.d0 xc(4,1:Nx)=0.d0 a_lo(1,1)=-Xtinf a_lo(1,2)=-XdInf a_up(1,3)=+XdInf Nstart=MAX(2,Nstart) if (SCIS.GT.0) then open (unit=11, file='COV.out', STATUS='unknown') write(11,*) 0.d0 endif do Ntd=Nstart,Ntime Ntdc=Ntd+Nc ex=0.d0 BIG=0.d0 CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,R0,R1,R2,R3,R4) ! positive wave period Nt=Ntd-Nd; indI(2)=Nt; indI(3)=Nt+1; indI(4)=Ntd; CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) ij=0 do i=2,Nx1 do j=1,i-1 ij=ij+1 ansrup(i,j)=ansrup(i,j)+fxind(ij,1)*CC*dt ansrlo(i,j)=ansrlo(i,j)+fxind(ij,2)*CC*dt enddo enddo if (SCIS.GT.0) then write(11,*) COV(1) ! save coefficient of variation endif print *,'Ready: ',Ntd,' of ',Ntime enddo goto 300 300 open (unit=11, file='dens.out', STATUS='unknown') do i=1,Nx1 do j=1,Nx1 write(11,*) ansrup(i,j),ansrlo(i,j) enddo enddo close(11) 900 continue deallocate(BIG) deallocate(ex) deallocate(fxind) deallocate(ansrup) deallocate(ansrlo) deallocate(xc) deallocate(R0) deallocate(R1) deallocate(R2) deallocate(R3) deallocate(R4) deallocate(h) if (allocated(COV) ) then deallocate(COV) endif stop !return CONTAINS SUBROUTINE INIT_LEVELS & (Ntime,Nstart,NIT,speed,Nx,dT) IMPLICIT NONE integer, intent(out):: Ntime,Nstart,NIT,speed,Nx double precision ,intent(out) :: dT OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') READ (14,*) Ntime READ (14,*) Nstart READ (14,*) NIT READ (14,*) speed READ (14,*) SCIS READ (14,*) seed1 READ (14,*) Nx READ (14,*) dT if (Ntime.lt.2) then print *,'The number of wavelength points is too small, stop' stop end if CLOSE(UNIT=14) RETURN END SUBROUTINE INIT_LEVELS C****************************************************** SUBROUTINE INIT_AMPLITUDES(h,Nx) IMPLICIT NONE double precision, dimension(:), intent(out) :: h integer, intent(in) :: Nx integer :: ix OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') C C Reading in amplitudes C do ix=1,Nx READ (4,*) H(ix) enddo CLOSE(UNIT=4) RETURN END SUBROUTINE INIT_AMPLITUDES C************************************************** C*********************************************************************** C*********************************************************************** SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4) IMPLICIT NONE double precision, dimension(:),intent(out) :: R0,R1,R2 double precision, dimension(:),intent(out) :: R3,R4 integer,intent(in) :: Ntime integer :: i open (unit=1, file='Cd0.in',STATUS='unknown') open (unit=2, file='Cd1.in',STATUS='unknown') open (unit=3, file='Cd2.in',STATUS='unknown') open (unit=4, file='Cd3.in',STATUS='unknown') open (unit=5, file='Cd4.in',STATUS='unknown') do i=1,Ntime read(1,*) R0(i) read(2,*) R1(i) read(3,*) R2(i) read(4,*) R3(i) read(5,*) R4(i) enddo close(1) close(2) close(3) close(3) close(5) return END SUBROUTINE INIT_COVARIANCES C********************************************************************** SUBROUTINE COV_INPUT(BIG,tn,R0,R1,R2,R3,R4) IMPLICIT NONE double precision, dimension(:,:),intent(inout) :: BIG double precision, dimension(:),intent(in) :: R0,R1,R2 double precision, dimension(:),intent(in) :: R3,R4 integer ,intent(in) :: tn integer :: i,j,N double precision :: tmp ! the order of the variables in the covariance matrix ! are organized as follows: ! X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X(t1),X(tn),X'(t1),X'(tn) ! = [ Xt | Xd | Xc ] ! ! where ! ! Xt= time points in the indicator function ! Xd= derivatives ! Xc=variables to condition on ! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s), ! then Cov(X'(t),X(s))=dr(t,s)/dt. Now for stationary X(t) we have ! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result). ! ! Consequently Cov(X'(t),X(s)) = -r'(s-t) = -sign(s-t)*r'(|s-t|) ! Cov(X'(t),X'(s)) = -r''(s-t) = -r''(|s-t|) ! Cov(X''(t),X'(s)) = r'''(s-t) = sign(s-t)*r'''(|s-t|) ! Cov(X''(t),X(s)) = r''(s-t) = r''(|s-t|) ! Cov(X''(t),X''(s)) = r''''(s-t) = r''''(|s-t|) N=tn+4 do i=1,tn-2 !cov(Xt) do j=i,tn-2 BIG(i,j) = -R2(j-i+1) ! cov(X'(ti+1),X'(tj+1)) enddo !cov(Xt,Xc) BIG(i ,tn+1) = R1(i+1) !cov(X'(ti+1),X(t1)) BIG(tn-1-i ,tn+2) = -R1(i+1) !cov(X'(ti+1),X(tn)) BIG(i ,tn+3) = -R2(i+1) !cov(X'(ti+1),X'(t1)) BIG(tn-1-i ,tn+4) = -R2(i+1) !cov(X'(ti+1),X'(tn)) !Cov(Xt,Xd) BIG(i,tn-1) = R3(i+1) !cov(X'(ti+1),X''(t1)) BIG(tn-1-i,tn) =-R3(i+1) !cov(X'(ti+1),X''(tn)) enddo !cov(Xd) BIG(tn-1 ,tn-1 ) = R4(1) BIG(tn-1,tn ) = R4(tn) !cov(X''(t1),X''(tn)) BIG(tn ,tn ) = R4(1) !cov(Xc) BIG(tn+1,tn+1) = R0(1) ! cov(X(t1),X(t1)) BIG(tn+1,tn+2) = R0(tn) ! cov(X(t1),X(tn)) BIG(tn+1,tn+3) = 0.d0 ! cov(X(t1),X'(t1)) BIG(tn+1,tn+4) = R1(tn) ! cov(X(t1),X'(tn)) BIG(tn+2,tn+2) = R0(1) ! cov(X(tn),X(tn)) BIG(tn+2,tn+3) =-R1(tn) ! cov(X(tn),X'(t1)) BIG(tn+2,tn+4) = 0.d0 ! cov(X(tn),X'(tn)) BIG(tn+3,tn+3) =-R2(1) ! cov(X'(t1),X'(t1)) BIG(tn+3,tn+4) =-R2(tn) ! cov(X'(t1),X'(tn)) BIG(tn+4,tn+4) =-R2(1) ! cov(X'(tn),X'(tn)) !Xc=X(t1),X(tn),X'(t1),X'(tn) !Xd=X''(t1),X''(tn) !cov(Xd,Xc) BIG(tn-1 ,tn+1) = R2(1) !cov(X''(t1),X(t1)) BIG(tn-1 ,tn+2) = R2(tn) !cov(X''(t1),X(tn)) BIG(tn-1 ,tn+3) = 0.d0 !cov(X''(t1),X'(t1)) BIG(tn-1 ,tn+4) = R3(tn) !cov(X''(t1),X'(tn)) BIG(tn ,tn+1) = R2(tn) !cov(X''(tn),X(t1)) BIG(tn ,tn+2) = R2(1) !cov(X''(tn),X(tn)) BIG(tn ,tn+3) =-R3(tn) !cov(X''(tn),X'(t1)) BIG(tn ,tn+4) = 0.d0 !cov(X''(tn),X'(tn)) ! make lower triangular part equal to upper do j=1,N-1 do i=j+1,N tmp =BIG(j,i) BIG(i,j)=tmp enddo enddo RETURN END SUBROUTINE COV_INPUT END PROGRAM sp2mM1