rosex.f90

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!> @file rosex.f90
!! @ingroup FORT1THREAD_EXAMPLES
!!
!! 
!! Extended Rosenbrock function.
!! 
!!
!! For more information about the individual callbacks, please have a look at the source code.
 
!> Main program. A simple setup and call of CONOPT
!!
Program rosex
 
   Use proginfo
   Use coidef
   IMPLICIT NONE
!
!  Declare the user callback routines as Integer, External:
!
   Integer, External :: ros_readmatrix ! Mandatory Matrix definition routine defined below
   Integer, External :: ros_fdeval     ! Function and Derivative evaluation routine
                                       ! needed a nonlinear model.
   Integer, External :: std_status     ! Standard callback for displaying solution status
   Integer, External :: std_solution   ! Standard callback for displaying solution values
   Integer, External :: std_message    ! Standard callback for managing messages
   Integer, External :: std_errmsg     ! Standard callback for managing error messages
#if defined(itl)
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Ros_ReadMatrix
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Ros_FDEval
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Std_Status
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Std_Solution
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Std_Message
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Std_ErrMsg
#endif
!
!  Control vector
!
   INTEGER :: numcallback
   INTEGER, Dimension(:), Pointer :: cntvect
   INTEGER :: coi_error
!
!  The model is an unconstrained problem in which the objective is the
!  sum of N identical copies of the Rosenbrock function placed after
!  each other:
!
!  min sum(i, (1-x(2*i-1))**2+100*(x(2*i)-x(2*i-1)**2)**2)
!
!  The number of Rosenborck functions
!
   Integer :: nr
   Integer :: miter_ini
   real*8 :: memused, memini
!
!  Create and initialize a Control Vector
!
   call startup
 
   numcallback = coidef_size()
   Allocate( cntvect(numcallback) )
   coi_error = coidef_inifort( cntvect )
!
!  Tell CONOPT about the size of the model by populating the Control Vector:
!
   nr = 100
   coi_error = max( coi_error, coidef_numvar( cntvect, 2*nr ) ) ! # variables
   coi_error = max( coi_error, coidef_numcon( cntvect, 1 ) )    ! # constraints
   coi_error = max( coi_error, coidef_numnz( cntvect, 2*nr ) ) ! # nonzeros in the Jacobian
   coi_error = max( coi_error, coidef_numnlnz( cntvect, 2*nr ) ) ! # of which are nonlinear
   coi_error = max( coi_error, coidef_optdir( cntvect, -1 ) )   ! Minimize
   coi_error = max( coi_error, coidef_objcon( cntvect, 1 ) )    ! Objective is constraint 1
   coi_error = max( coi_error, coidef_optfile( cntvect, 'rosex.opt'  ) )
!
!  Tell CONOPT about the callback routines:
!
   coi_error = max( coi_error, coidef_readmatrix( cntvect, ros_readmatrix ) )
   coi_error = max( coi_error, coidef_fdeval( cntvect, ros_fdeval     ) )
   coi_error = max( coi_error, coidef_status( cntvect, std_status     ) )
   coi_error = max( coi_error, coidef_solution( cntvect, std_solution   ) )
   coi_error = max( coi_error, coidef_message( cntvect, std_message    ) )
   coi_error = max( coi_error, coidef_errmsg( cntvect, std_errmsg     ) )
 
#if defined(LICENSE_INT_1) && defined(LICENSE_INT_2) && defined(LICENSE_INT_3) && defined(LICENSE_TEXT)
   coi_error = max( coi_error, coidef_license( cntvect, license_int_1, license_int_2, license_int_3, license_text) )
#endif
 
   If ( coi_error .ne. 0 ) THEN
      write(*,*)
      write(*,*) '**** Fatal Error while loading CONOPT Callback routines.'
      write(*,*)
      call flog( "Skipping Solve due to setup errors", 1 )
   ENDIF
!
!  Start CONOPT:
!
   coi_error = coi_solve( cntvect )
   If ( coi_error /= 0 ) then
      call flog( "Solve 1: Errors encountered during solution", 1 )
   elseif ( stacalls == 0 .or. solcalls == 0 ) then
      call flog( "Solve 1: Status or Solution routine was not called", 1 )
   elseif ( sstat /= 1 .or. mstat /= 2 ) then
      call flog( "Solve 1: Solver and Model Status was not as expected (1,2)", 1 )
   elseif ( abs( obj-0.0d0 ) > 0.000001d0 ) then
      call flog( "Solve 1: Incorrect objective returned", 1 )
   endif
 
!
!  Ask for the amount of memory used and the number of iterations
!
   memini = coiget_maxheapused( cntvect )
   miter_ini = miter
   write(*,*) 'Solve 1 used',memini,' MBytes of memory and',miter_ini,' iterations.'
   write(10,*) 'Solve 1 used',memini,' MBytes of memory and',miter_ini,' iterations.'
!
!  Solve a model with a little less memory.  We expect to run out of memory or use more iterations
!  We may run with less memory by turning some 2nd order info off, but the solve should be slower. (Not true!!)
!
   coi_error = max( coi_error, coidef_maxheap( cntvect, memini-8.d2/1024.d0**2  ) ) ! take 800 reals less
   coi_error = coi_solve( cntvect )
   memused = coiget_maxheapused( cntvect )
   write(*,*) 'Solve 2 used',memused,' MBytes of memory and',miter,' iterations. Return code=',coi_error
   write(10,*) 'Solve 2 used',memused,' MBytes of memory and',miter,' iterations. Return code=',coi_error
!   if ( Miter <= Miter_Ini .and. (COI_Error < 113 .or. COI_Error > 114) ) then
!      call flog( "Solve 2: Error return was not slower or 113 or 114 (insufficient memory)", 1 )
!   Endif
!
!  Solve a model with NR increased by one using the same amount of memory.
!  We expect to run out of memory or use more iterations
!
   coi_error = 0 ! Reset before next experiment
   coi_error = max( coi_error, coidef_maxheap( cntvect, memini ) ) ! take the memory from last call
   nr = nr + 1 ! Increase the number of functions and redefine the quantities that change:
   coi_error = max( coi_error, coidef_numvar( cntvect, 2*nr ) ) ! # variables
   coi_error = max( coi_error, coidef_numnz( cntvect, 2*nr ) ) ! # nonzeros in the Jacobian
   coi_error = max( coi_error, coidef_numnlnz( cntvect, 2*nr ) ) ! # of which are nonlinear
   coi_error = coi_solve( cntvect )
   memused = coiget_maxheapused( cntvect )
   write(*,*) 'Solve 3 used',memused,' MBytes of memory and',miter,' iterations. Return code=',coi_error
   write(10,*) 'Solve 3 used',memused,' MBytes of memory and',miter,' iterations. Return code=',coi_error
!   if ( Miter <= Miter_Ini .and. (COI_Error < 113 .or. COI_Error > 114) ) then
!      call flog( "Solve 3: Error return was not slower or 113 or 114 (insufficient memory)", 1 )
!   Endif
!
!  Solve the previous model with a very large amount of memory.
!  We expect to run correctly.
!
   coi_error = 0 ! Reset before next experiment
   coi_error = max( coi_error, coidef_maxheap( cntvect, 1.0d20 ) ) ! Allow a lot of memory
   coi_error = coi_solve( cntvect )
   memused = coiget_maxheapused( cntvect )
   write(*,*) 'Solve 4 used',memused,' MBytes of memory. Return code=',coi_error
   write(10,*) 'Solve 4 used',memused,' MBytes of memory. Return code=',coi_error
   If ( coi_error /= 0 ) then
      call flog( "Solve 4: Errors encountered during solution", 1 )
   elseif ( stacalls == 0 .or. solcalls == 0 ) then
      call flog( "Solve 4: Status or Solution routine was not called", 1 )
   elseif ( sstat /= 1 .or. mstat /= 2 ) then
      call flog( "Solve 4: Solver and Model Status was not as expected (1,2)", 1 )
   elseif ( abs( obj-0.0d0 ) > 0.000001d0 ) then
      call flog( "Solve 4: Incorrect objective returned", 1 )
   endif
   write(*,*)
   write(*,*) 'End of Extended Rosenbrock Function example. Return code=',coi_error
 
   if ( coi_free(cntvect) /= 0 ) call flog( "Error while freeing control vector",1)
 
   call flog( "Successful Solve", 0 )
 
End Program rosex
!
! ============================================================================
!  Define information about the model:
!
 
!>  Define information about the model
!!
!! @include{doc} readMatrix_params.dox
Integer Function ros_readmatrix( lower, curr, upper, vsta, type, rhs, esta,      &
                                 colsta, rowno, value, nlflag, n, m, nz,  &
                                 usrmem )
#if defined(itl)
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Ros_ReadMatrix
#endif
      IMPLICIT NONE
   integer, intent (in)                      :: n      ! number of variables
   integer, intent (in)                      :: m      ! number of constraints
   integer, intent (in)                      :: nz     ! number of nonzeros
   real*8,  intent (in out), dimension(n)    :: lower  ! vector of lower bounds
   real*8,  intent (in out), dimension(n)    :: curr   ! vector of initial values
   real*8,  intent (in out), dimension(n)    :: upper  ! vector of upper bounds
   integer, intent (in out), dimension(n)    :: vsta   ! vector of initial variable status
                                                       ! (not defined here)
   integer, intent (out),    dimension(m)    :: type   ! vector of equation types
   integer, intent (in out), dimension(m)    :: esta   ! vector of initial equation status
                                                       ! (not defined here)
   real*8,  intent (in out), dimension(m)    :: rhs    ! vector of right hand sides
   integer, intent (in out), dimension(n+1)  :: colsta ! vector with start of column indices
   integer, intent (out),    dimension(nz)   :: rowno  ! vector of row numbers
   integer, intent (in out), dimension(nz)   :: nlflag ! vector of nonlinearity flags
   real*8,  intent (in out), dimension(nz)   :: value  ! vector of matrix values
   real*8   usrmem(*)                                  ! optional user memory
 
   Integer :: nr
   Integer :: i
 
   nr = n / 2
!
!  Information about Variables:
!  Default: Lower = -Inf, Curr = 0, and Upper = +inf.
!  Default: the status information in Vsta is not used.
!
   DO i = 1, nr
      curr(2*i-1) = -1.d0
      curr(2*i  ) = +1.d0
   enddo
!
!  Information about Constraints:
!  Default: Rhs = 0
!  Default: the status information in Esta and the function
!           value in FV are not used.
!  Default: Type: There is no default.
!           0 = Equality,
!           1 = Greater than or equal,
!           2 = Less than or equal,
!           3 = Non binding.
!
!  Constraint 1 (Objective)
!  Rhs = 0.0 and type Non binding
!
   type(1) = 3
!
!  Information about the Jacobian. We have to define Rowno, Value,
!  Nlflag and Colsta.
!
!  Colsta = Start of column indices (No Defaults):
!  Rowno  = Row indices
!  Value  = Value of derivative (by default only linear
!                                derivatives are used)
!  Nlflag = 0 for linear and 1 for nonlinear derivative
!           (not needed for completely linear models)
!
!  Indices
!       x(1)  x(2)  x(3)  x(4)
!  1:    1     2     3     4    etc
!
!  Nonlinearity Structure: L = 0 are linear and NL = 1 are nonlinear
!       x(1)  x(2)  x(3)  x(4)
!  1:    NL    NL    NL    NL  etc
!
!  Value (Linear only)
!
   DO i = 1, nr*2+1
      colsta(i) = i
   enddo
   DO i = 1, nr*2
      rowno(i)  = 1
      nlflag(i) = 1
   enddo
 
   ros_readmatrix = 0 ! Return value means OK
 
end Function ros_readmatrix
!
!==========================================================================
!  Compute nonlinear terms and non-constant Jacobian elements
!
 
!>  Compute nonlinear terms and non-constant Jacobian elements
!!
!! @include{doc} fdeval_params.dox
Integer Function ros_fdeval( x, g, jac, rowno, jcnm, mode, ignerr, errcnt, &
                             n, nz, thread, usrmem )
#if defined(itl)
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Ros_FDEval
#endif
      IMPLICIT NONE
   integer, intent (in)                      :: n      ! number of variables
   integer, intent (in)                      :: rowno  ! number of the row to be evaluated
   integer, intent (in)                      :: nz     ! number of nonzeros in this row
   real*8,  intent (in),     dimension(n)    :: x      ! vector of current solution values
   real*8,  intent (in out)                  :: g      ! constraint value
   real*8,  intent (in out), dimension(n)    :: jac    ! vector of derivatives for current constraint
   integer, intent (in),     dimension(nz)   :: jcnm   ! list of variables that appear nonlinearly
                                                       ! in this row. Ffor information only.
   integer, intent (in)                      :: mode   ! evaluation mode: 1 = function value
                                                       ! 2 = derivatives, 3 = both
   integer, intent (in)                      :: ignerr ! if 1 then errors can be ignored as long
                                                       ! as errcnt is incremented
   integer, intent (in out)                  :: errcnt ! error counter to be incremented in case
                                                       ! of function evaluation errors.
   integer, intent (in)                      :: thread
   real*8   usrmem(*)                                  ! optional user memory
 
   Integer :: nr
   Integer :: i
 
   nr = n / 2
!
!  Row 1: the objective function is nonlinear
!
   if ( rowno .eq. 1 ) then
!
!  Mode = 1 or 3. Function value:
!
      if ( mode .eq. 1 .or. mode .eq. 3 ) then
         g = 0.d0
         do i = 1, nr
            g = g + (x(2*i-1)-1.d0)**2 + 1.d2*(x(2*i)-x(2*i-1)**2)**2
         enddo
      endif
!
!  Mode = 2 or 3: Derivative values:
!
      if ( mode .eq. 2 .or. mode .eq. 3 ) then
         do i = 1, nr
            jac(2*i-1) = 2.d0*(x(2*i-1)-1.d0) - 4.d2*(x(2*i)-x(2*i-1)**2)*x(2*i-1)
            jac(2*i  ) = 2.d2*(x(2*i)-x(2*i-1)**2)
         enddo
      endif
   endif
   ros_fdeval = 0
 
end Function ros_fdeval