square4.f90

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!> @file square4.f90
!! @ingroup FORT1THREAD_EXAMPLES
!!
!! A square model where we pretend that the last two constraints are completely
!! nonlinear except for the last term.
!! 
!! \f{eqnarray*}{
!! &x1 + x2      = 10 \\
!! &x1 - x2      =  0 \\
!! &x1 + x2 + x3 =  9
!! \f}
!! 
!! In a second case we add a lower bound on x3 of 0 so the model becomes
!! infeasible.
!! The model is similar to square2, but the slack variable in equation 3
!! has been made explicit as a structural variable
!! 
!!
!! 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 square
 
   Use proginfo
   Use coidef
   Use casedata_num
   implicit None
!
!  Declare the user callback routines as Integer, External:
!
   Integer, External :: sq_readmatrix  ! Mandatory Matrix definition routine defined below
   Integer, External :: sq_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 :: Sq_ReadMatrix
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Sq_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
 
   Integer :: i
   Logical :: error
 
   real*8, dimension(3) :: xsol1 = (/ 5.d0, 5.d0, -1.d0 /)
   real*8, dimension(3) :: usol1 = (/ 10.d0, 0.d0, 9.d0 /)
 
   call startup
!
!  Create and initialize a Control Vector
!
   numcallback = coidef_size()
   Allocate( cntvect(numcallback) )
   coi_error = coidef_inifort( cntvect )
!
!  Tell CONOPT about the size of the model by populating the Control Vector:
!
   coi_error = max( coi_error, coidef_numvar( cntvect, 3 ) )  ! 3 variables
   coi_error = max( coi_error, coidef_numcon( cntvect, 3 ) )  ! 3 constraints
   coi_error = max( coi_error, coidef_numnz( cntvect, 7 ) )  ! 6 nonzeros in the Jacobian
   coi_error = max( coi_error, coidef_numnlnz( cntvect, 4 ) )  ! 4 of which are nonlinear
   coi_error = max( coi_error, coidef_square( cntvect, 1 ) )  ! 1 means Square system
   coi_error = max( coi_error, coidef_optfile( cntvect, 'square4.opt' ) )
!
!  Tell CONOPT about the callback routines:
!
   coi_error = max( coi_error, coidef_readmatrix( cntvect, sq_readmatrix ) )
   coi_error = max( coi_error, coidef_fdeval( cntvect, sq_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
!
!  Allocate space for the solution and status vectors.
!
   do_allocate = .true.
!
!  Start CONOPT:
!
   casenum = 1
   coi_error = coi_solve( cntvect )
 
   write(*,*)
   write(*,*) 'End of Square4 - case 1 example. Return code=',coi_error
 
   If ( coi_error /= 0 ) then
      call flog( "Case 1: Errors encountered during solution", 1 )
   elseif ( stacalls == 0 .or. solcalls == 0 ) then
      call flog( "Case 1: Status or Solution routine was not called", 1 )
   elseif ( sstat /= 1 .or. mstat < 15 .or. mstat > 16 ) then
      call flog( "Case 1: Solver or Model status not as expected (1,15) or (1,16)", 1 )
   elseif ( obj /= 0.d0 ) Then
      call flog( "Case 1: Objective for square model was not as expected 0.0", 1 )
   else
!
!  Check the primal and dual solution itself
!
      error = .false.
      do i = 1, 3
         if ( abs(xprim(i)-xsol1(i)) > 1.d-7 ) error = .true.
         if ( abs(xdual(i)) > 1.d-7 ) error = .true.
         if ( abs(udual(i)) > 1.d-7 ) error = .true.
         if ( abs(uprim(i)- usol1(i)) > 1.e-7 ) error = .true.
      enddo
      if ( error ) call flog( "Case 1: Numerical solution was not as expected.", 1 )
!
!  Check the status information
!
      do i = 1, 3
         if ( xbasc(i) /= 2 ) error = .true.  ! Basic
         if ( xstat(i) /= 0 ) error = .true.  ! Normal
!         if ( Ubasc(i) /= 0 ) error = .true.  ! Lower
         if ( ustat(i) /= 0 ) error = .true.  ! Normal
      enddo
      if ( error ) call flog( "Case 1: Status information was not as expected.", 1 )
   endif
!
!  Start CONOPT with second case where the right hand side in equation 3 is 11:
!
   casenum = 2
   coi_error = coi_solve( cntvect )
 
   write(*,*)
   write(*,*) 'End of Square4 example case 2. Return code=',coi_error
 
   If ( coi_error /= 0 ) then
      call flog( "Case 2: Errors encountered during solution", 1 )
   elseif ( stacalls == 0 .or. solcalls == 0 ) then
      call flog( "Case 2: Status or Solution routine was not called", 1 )
   elseif ( sstat /= 1 .or. mstat < 4 .or. mstat > 5 ) then
      call flog( "Case 2: Solver or Model status not as expected (1,4) or (1,5)", 1 )
   elseif ( obj /= 0.d0 ) Then
      call flog( "Case 2: Objective for square model was not as expected 0.0", 1 )
   else
!
!  Check the primal and dual solution itself
!
      error = .false.
      do i = 1, 3
         if ( abs(xdual(i)) > 1.d-7 ) error = .true.
         if ( abs(udual(i)) > 1.d-7 ) error = .true.
      enddo
      if ( error ) call flog( "Case 2: Numerical solution was not as expected.", 1 )
!
!  Check the status information
!
      do i = 1, 3
         if ( xbasc(i) /= 2 ) error = .true.  ! Basic
         if ( xstat(i) /= 0 ) error = .true.  ! Normal
!         if ( Ubasc(i) /= 0 ) error = .true.  ! Lower
      enddo
      if ( ustat(1) /= 2 .and. ustat(3) /= 2 ) error = .true. ! One of them must be infeasible
!      if ( Ubasc(3) /= 1 ) error = .true.  ! Upper
      if ( error ) call flog( "Case 2: Status information was not as expected.", 1 )
   endif
 
   if ( coi_free(cntvect) /= 0 ) call flog( "Error while freeing control vector",1)
 
   call flog( "Successful Solve", 0 )
 
End Program square
!
! ============================================================================
!  Define information about the model:
!
 
!>  Define information about the model
!!
!! @include{doc} readMatrix_params.dox
Integer Function sq_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 :: Sq_ReadMatrix
#endif
   Use casedata_num
   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
!
!  Information about Variables:
!  Default: Lower = -Inf, Curr = 0, and Upper = +inf.
!  Default: the status information in Vsta is not used.
!
!  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.
   if ( casenum == 2 ) then
      lower(3) = 0.d0
   endif
!
!  Constraint 1
!  Rhs = 10 and type Equal
!
   rhs(1)  = 10.d0
   type(1) = 0
!
!  Constraint 2
!  Rhs = 0 and type Equality
!
   type(2) = 0
!
!  Constraint 3
!  Rhs = 9 and type Equality
!
   rhs(3)  = 9.d0
   type(3) = 0
!
!  Information about the Jacobian. We use the standard method with
!  Rowno, Value, Nlflag and Colsta and we do not use Colno.
!
!  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)
!  1:    1     4
!  2:    2     5
!  3:    3     6      7
!
   colsta(1) =  1
   colsta(2) =  4
   colsta(3) =  7
   colsta(4) =  8
   rowno(1)  =  1
   rowno(2)  =  2
   rowno(3)  =  3
   rowno(4)  =  1
   rowno(5)  =  2
   rowno(6)  =  3
   rowno(7)  =  3
!
!  Nonlinearity Structure: L = 0 are linear and NL = 1 are nonlinear
!       x(1)  x(2)  x(3)
!  1:    L     L
!  2:    NL    NL
!  3:    NL    NL    L
!
   nlflag(1) =  0
   nlflag(2) =  1
   nlflag(3) =  1
   nlflag(4) =  0
   nlflag(5) =  1
   nlflag(6) =  1
   nlflag(7) =  0
!
!  Value (Linear only)
!       x(1)  x(2)  x(3)  x(4)
!  1:    1     1
!  2:    NL    NL
!  3:    NL    NL
!
   value(1)  = 1.d0
   value(4)  = 1.d0
   value(7)  = 1.d0
 
  sq_readmatrix = 0 ! Return value means OK
 
end Function sq_readmatrix
!
!==========================================================================
!  Compute nonlinear terms and non-constant Jacobian elements
!
 
!>  Compute nonlinear terms and non-constant Jacobian elements
!!
!! @include{doc} fdeval_params.dox
Integer Function sq_fdeval( x, g, jac, rowno, jcnm, mode, ignerr, errcnt, &
                            n, nz, thread, usrmem )
#if defined(itl)
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Sq_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
!
!  Row 1: Is declared as linear and should not be called.
!
   if ( rowno .eq. 1 ) then
      sq_fdeval = 1
      return
!
!  Row 2: x1 + x2 assumed to be nonlinear
!
   elseif ( rowno .eq. 2 ) then
!
!  Mode = 1 or 3: Function value
!
      if ( mode .eq. 1 .or. mode .eq. 3 ) then
         g = x(1) - x(2)
      endif
!
!  Mode = 2 or 3: Derivatives
!
      if ( mode .eq. 2 .or. mode .eq. 3 ) then
         jac(1) =  1.d0
         jac(2) = -1.d0
      endif
   elseif ( rowno .eq. 3 ) then
!
!  Mode = 1 or 3: Function value
!
      if ( mode .eq. 1 .or. mode .eq. 3 ) then
         g = x(1) + x(2)
      endif
!
!  Mode = 2 or 3: Derivatives
!
      if ( mode .eq. 2 .or. mode .eq. 3 ) then
         jac(1) =  1.d0
         jac(2) =  1.d0
      endif
   endif
   sq_fdeval = 0
 
end Function sq_fdeval