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!----------------------------------------------------------------------
!----------------------------------------------------------------------
! aut.f90 : Model AUTO-equations file
!----------------------------------------------------------------------
!----------------------------------------------------------------------
SUBROUTINE FUNC(NDIM,U,ICP,PAR,IJAC,F,DFDU,DFDP)
! ---------- ----
!
! Evaluates the algebraic equations or ODE right hand side
!
! Input arguments :
! NDIM : Dimension of the algebraic or ODE system
! U : State variables
! ICP : Array indicating the free parameter(s)
! PAR : Equation parameters
!
! Values to be returned :
! F : Equation or ODE right hand side values
!
! Normally unused Jacobian arguments : IJAC, DFDU, DFDP (see manual)
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM, IJAC, ICP(*)
DOUBLE PRECISION, INTENT(IN) :: U(NDIM), PAR(*)
DOUBLE PRECISION, INTENT(OUT) :: F(NDIM)
DOUBLE PRECISION, INTENT(INOUT) :: DFDU(NDIM,NDIM),DFDP(NDIM,*)
F(1)= ....
F(2)= ....
END SUBROUTINE FUNC
!----------------------------------------------------------------------
!----------------------------------------------------------------------
SUBROUTINE STPNT(NDIM,U,PAR)
! ---------- -----
!
! Input arguments :
! NDIM : Dimension of the algebraic or ODE system
!
! Values to be returned :
! U : A starting solution vector
! PAR : The corresponding equation-parameter values
!
! Note : For time- or space-dependent solutions this subroutine has
! arguments (NDIM,U,PAR,T), where the scalar input parameter T
! contains the varying time or space variable value.
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM
DOUBLE PRECISION, INTENT(INOUT) :: U(NDIM),PAR(*)
DOUBLE PRECISION, INTENT(IN) :: T
! Initialize the equation parameters
PAR(1)= ....
PAR(2)= ....
! Initialize the solution
U(1)= ....
U(2)= ....
END SUBROUTINE STPNT
!----------------------------------------------------------------------
!----------------------------------------------------------------------
SUBROUTINE BCND(NDIM,PAR,ICP,NBC,U0,U1,FB,IJAC,DBC)
! ---------- ----
!
! Boundary Conditions
!
! Input arguments :
! NDIM : Dimension of the ODE system
! PAR : Equation parameters
! ICP : Array indicating the free parameter(s)
! NBC : Number of boundary conditions
! U0 : State variable values at the left boundary
! U1 : State variable values at the right boundary
!
! Values to be returned :
! FB : The values of the boundary condition functions
!
! Normally unused Jacobian arguments : IJAC, DBC (see manual)
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,*)
!XXX FB(1)=
!XXX FB(2)=
END SUBROUTINE BCND
!----------------------------------------------------------------------
!----------------------------------------------------------------------
SUBROUTINE ICND(NDIM,PAR,ICP,NINT,U,UOLD,UDOT,UPOLD,FI,IJAC,DINT)
! ---------- ----
!
! Integral Conditions
!
! Input arguments :
! NDIM : Dimension of the ODE system
! PAR : Equation parameters
! ICP : Array indicating the free parameter(s)
! NINT : Number of integral conditions
! U : Value of the vector function U at `time' t
!
! The following input arguments, which are normally not needed,
! correspond to the preceding point on the solution branch
! UOLD : The state vector at 'time' t
! UDOT : Derivative of UOLD with respect to arclength
! UPOLD : Derivative of UOLD with respect to `time'
!
! Normally unused Jacobian arguments : IJAC, DINT
!
! Values to be returned :
! FI : The value of the vector integrand
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,*)
!XXX FI(1)=
END SUBROUTINE ICND
!----------------------------------------------------------------------
!----------------------------------------------------------------------
SUBROUTINE FOPT(NDIM,U,ICP,PAR,IJAC,FS,DFDU,DFDP)
! ---------- ----
!
! Defines the objective function for algebraic optimization problems
!
! Supplied variables :
! NDIM : Dimension of the state equation
! U : The state vector
! ICP : Indices of the control parameters
! PAR : The vector of control parameters
!
! Values to be returned :
! FS : The value of the objective function
!
! Normally unused Jacobian argument : IJAC, DFDP
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM, ICP(*), IJAC
DOUBLE PRECISION, INTENT(IN) :: U(NDIM), PAR(*)
DOUBLE PRECISION, INTENT(OUT) :: FS
DOUBLE PRECISION, INTENT(INOUT) :: DFDU(NDIM),DFDP(*)
!XXX FS=
END SUBROUTINE FOPT
!----------------------------------------------------------------------
!----------------------------------------------------------------------
SUBROUTINE PVLS(NDIM,U,PAR)
! ---------- ----
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM
DOUBLE PRECISION, INTENT(IN) :: U(NDIM)
DOUBLE PRECISION, INTENT(INOUT) :: PAR(*)
!----------------------------------------------------------------------
! NOTE :
! Parameters set in this subroutine should be considered as ``solution
! measures'' and be used for output purposes only.
!
! They should never be used as `true'' continuation parameters.
!
! They may, however, be added as ``over-specified parameters'' in the
! parameter list associated with the AUTO-Constant NICP, in order to
! print their values on the screen and in the ``p.xxx file.
!
! They may also appear in the list associated with AUTO-Constant NUZR.
!
!----------------------------------------------------------------------
! For algebraic problems the argument U is, as usual, the state vector.
! For differential equations the argument U represents the approximate
! solution on the entire interval [0,1]. In this case its values must
! be accessed indirectly by calls to GETP, as illustrated below.
!----------------------------------------------------------------------
!
! Set PAR(2) equal to the L2-norm of U(1)
!XX PAR(2)=GETP('NRM',1,U)
!
! Set PAR(3) equal to the minimum of U(2)
!XX PAR(3)=GETP('MIN',2,U)
!
! Set PAR(4) equal to the value of U(2) at the left boundary.
!XX PAR(4)=GETP('BV0',2,U)
!
! Set PAR(5) equal to the pseudo-arclength step size used.
!XX PAR(5)=GETP('STP',1,U)
!
!----------------------------------------------------------------------
! The first argument of GETP may be one of the following:
! 'NRM' (L2-norm), 'MAX' (maximum),
! 'INT' (integral), 'BV0 (left boundary value),
! 'MIN' (minimum), 'BV1' (right boundary value).
!
! Also available are
! 'STP' (Pseudo-arclength step size used).
! 'FLD' (`Fold function', which vanishes at folds).
! 'BIF' (`Bifurcation function', which vanishes at singular points).
! 'HBF' (`Hopf function'; which vanishes at Hopf points).
! 'SPB' ( Function which vanishes at secondary periodic bifurcations).
!----------------------------------------------------------------------
END SUBROUTINE PVLS
!----------------------------------------------------------------------
!----------------------------------------------------------------------
|
