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!----------------------------------------------------------------------
!----------------------------------------------------------------------
! man : Stable manifold of the origen in the Lorenz model
!----------------------------------------------------------------------
!----------------------------------------------------------------------
SUBROUTINE FUNC(NDIM,U,ICP,PAR,IJAC,F,DFDU,DFDP)
! ---------- ----
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM, ICP(*), IJAC
DOUBLE PRECISION, INTENT(IN) :: U(NDIM), PAR(*)
DOUBLE PRECISION, INTENT(OUT) :: F(NDIM)
DOUBLE PRECISION, INTENT(INOUT) :: DFDU(NDIM,NDIM), DFDP(NDIM,*)
DOUBLE PRECISION Period
Period=PAR(11)
F(1)= Period * (PAR(3) * (U(2)- U(1)))
F(2)= Period * (PAR(1)*U(1) - U(2) - U(1)*U(3))
F(3)= Period * (U(1)*U(2) - PAR(2)*U(3))
END SUBROUTINE FUNC
!----------------------------------------------------------------------
SUBROUTINE STPNT(NDIM,U,PAR,T)
! ---------- -----
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM
DOUBLE PRECISION, INTENT(INOUT) :: U(NDIM),PAR(*)
DOUBLE PRECISION, INTENT(IN) :: T
DOUBLE PRECISION rad,h,Period,RLength,pi,theta,cs,sn,V1(3),V2(3)
PAR(1)=28.
PAR(2)=8.d0/3.d0
PAR(3)=10.
rad=5.0
h=0.1
Period=1e-5
RLength=0.
PAR(4)=rad
PAR(5)=h
CALL EIGV(NDIM,PAR,V1,V2)
! Set initial approximate solution (for small Period)
pi=4*ATAN(1.d0)
theta=2*pi*h
cs=COS(theta)
sn=SIN(theta)
U(1)= rad * ( cs*V1(1) + sn*V2(1) )
U(2)= rad * ( cs*V1(2) + sn*V2(2) )
U(3)= rad * ( cs*V1(3) + sn*V2(3) )
PAR(6) = U(1)
PAR(7) = U(2)
PAR(8) = U(3)
PAR(9) = SQRT(U(1)**2 + U(2)**2 + U(3)**2)
PAR(11)=Period
PAR(12)=RLength
END SUBROUTINE STPNT
!----------------------------------------------------------------------
SUBROUTINE BCND(NDIM,PAR,ICP,NBC,U0,U1,FB,IJAC,DBC)
! ---------- ----
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM, ICP(*), NBC, IJAC
DOUBLE PRECISION, INTENT(IN) :: PAR(*), U0(NDIM), U1(NDIM)
DOUBLE PRECISION, INTENT(OUT) :: FB(NBC)
DOUBLE PRECISION, INTENT(INOUT) :: DBC(NBC,*)
DOUBLE PRECISION V1(3),V2(3),pi,rad,h,theta,cs,sn
CALL EIGV(NDIM,PAR,V1,V2)
pi=4*ATAN(1.d0)
rad=PAR(4)
h=PAR(5)
theta=2*pi*h
cs=COS(theta)
sn=SIN(theta)
! At time=0
FB(1)= U0(1) - rad * ( cs*V1(1) + sn*V2(1) )
FB(2)= U0(2) - rad * ( cs*V1(2) + sn*V2(2) )
FB(3)= U0(3) - rad * ( cs*V1(3) + sn*V2(3) )
! At time=1
FB(4)= U1(1) - PAR(6)
FB(5)= U1(2) - PAR(7)
FB(6)= U1(3) - PAR(8)
FB(7)= SQRT(U1(1)**2 + U1(2)**2 + U1(3)**2) - PAR(9)
END SUBROUTINE BCND
!----------------------------------------------------------------------
SUBROUTINE EIGV(NDIM,PAR,V1,V2)
! ---------- ----
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM
DOUBLE PRECISION, INTENT(IN) :: PAR(*)
DOUBLE PRECISION, INTENT(OUT) :: V1(NDIM),V2(NDIM)
LOGICAL, SAVE :: ifirst = .TRUE.
DOUBLE PRECISION e,ss
! Stable eigenvalue/vector 1
V1(1)= 0.
V1(2)= 0.
V1(3)= 1./2.66667
! Stable eigenvalue/vector 2
e=-(11+SQRT(1201.d0))/2
V2(1)=1+e
V2(2)=PAR(1)
V2(3)= 0.
ss=SQRT(V2(1)**2+V2(2)**2)
V2(1)=V2(1)/(ss*22.8277)
V2(2)=V2(2)/(ss*22.8277)
IF(ifirst)THEN
WRITE(10,*)V2(1),V2(2)
ifirst=.FALSE.
ENDIF
END SUBROUTINE EIGV
!----------------------------------------------------------------------
SUBROUTINE ICND(NDIM,PAR,ICP,NINT,U,UOLD,UDOT,UPOLD,FI,IJAC,DINT)
! ---------- ----
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM, ICP(*), NINT, IJAC
DOUBLE PRECISION, INTENT(IN) :: PAR(*)
DOUBLE PRECISION, INTENT(IN) :: U(NDIM), UOLD(NDIM), UDOT(NDIM), UPOLD(NDIM)
DOUBLE PRECISION, INTENT(OUT) :: FI(NINT)
DOUBLE PRECISION, INTENT(INOUT) :: DINT(NINT,*)
DOUBLE PRECISION FF(3),DFDU(1),DFDP(1)
CALL FUNC(NDIM,U,ICP,PAR,0,FF,DFDU,DFDP)
FI(1)=SQRT(FF(1)**2 + FF(2)**2 + FF(3)**2 ) - PAR(12)
END SUBROUTINE ICND
SUBROUTINE PVLS
END SUBROUTINE PVLS
SUBROUTINE FOPT
END SUBROUTINE FOPT
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