pinsquare.f90

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!> @file pinsquare.f90
!! @ingroup FORT1THREAD_EXAMPLES
!!
!! 
!! This is a CONOPT implementation of the Pindyck model from the
!! GAMS model library. The original model is revised so the P
!! variables are fixed. This gives rise to a square system of
!! equations and the Square option is tested.
!! 
!! The model also uses the standard TriOrd routine to show the
!! pre-triangular part of the model.
!! The model can be made infeasible in the pretriangular part
!! by changing a bound (indicated by a comment at lower(78)).
!! 
!!
!! 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 pinsquare
   Use proginfo
   Use coidef
   Use data_t
   Implicit none
!
!  Declare the user callback routines as Integer, External:
!
   Integer, External :: pin_readmatrix ! Mandatory Matrix definition routine defined below
   Integer, External :: pin_fdeval     ! Function and Derivative evaluation routine
                                       ! needed a nonlinear model.
   Integer, External :: std_status     ! Standard callback for displaying solution status
   Integer, External :: pin_solution   ! Specialized callback for displaying solution values
   Integer, External :: std_message    ! Standard callback for managing messages
   Integer, External :: std_errmsg     ! Standard callback for managing error messages
   Integer, External :: std_triord     ! Standard callback for triangular order
#if defined(itl)
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Pin_ReadMatrix
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Pin_FDEval
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Std_Status
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Pin_Solution
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Std_Message
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Std_ErrMsg
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Std_TriOrd
#endif
!
!  Control vector
!
   INTEGER :: numcallback
   INTEGER, Dimension(:), Pointer :: cntvect
   INTEGER :: coi_error
!
!  Create and initialize a Control Vector
!
   call startup
   numcallback = coidef_size()
   Allocate( cntvect(numcallback) )
   coi_error = coidef_inifort( cntvect )
!
!  Define the number of time periods, T.
!
   t = 16
!
!  Tell CONOPT about the size of the model by populating the Control Vector:
!
!  Number of variables (excl. slacks): 7 per period
!
   coi_error = max( coi_error, coidef_numvar( cntvect, 7 * t ) )
!
!  Number of equations: 1 objective + 6 per period
!
   coi_error = max( coi_error, coidef_numcon( cntvect, 1 + 6 * t ) )
!
!  Number of nonzeros in the Jacobian. See the counting in ReadMatrix below:
!  For each period there is 1 in the objective, 16 for unlagged
!  variables and 4 for lagged variables.
!
   coi_error = max( coi_error, coidef_numnz( cntvect, 17 * t + 4 * (t-1) ) )
!
!  Number of nonlinear nonzeros. 5 unlagged for each period.
!
   coi_error = max( coi_error, coidef_numnlnz( cntvect, 5 * t ) )
!
!  Direction: +1 = maximization.
!
   coi_error = max( coi_error, coidef_optdir( cntvect, 1 ) )
!
!  Objective: Constraint no 1
!
   coi_error = max( coi_error, coidef_objcon( cntvect, 1 ) )
!
!  Square system ( the objective above is not really needed or used )
!
   coi_error = max( coi_error, coidef_square( cntvect, 1 ) )
!
!  Options file = test.opt
!
   coi_error = max( coi_error, coidef_optfile( cntvect, 'test.opt'  ) )
!
!  Tell CONOPT about the callback routines:
!
   coi_error = max( coi_error, coidef_readmatrix( cntvect, pin_readmatrix ) )
   coi_error = max( coi_error, coidef_fdeval( cntvect, pin_fdeval     ) )
   coi_error = max( coi_error, coidef_status( cntvect, std_status     ) )
   coi_error = max( coi_error, coidef_solution( cntvect, pin_solution   ) )
   coi_error = max( coi_error, coidef_message( cntvect, std_message    ) )
   coi_error = max( coi_error, coidef_errmsg( cntvect, std_errmsg     ) )
   coi_error = max( coi_error, coidef_triord( cntvect, std_triord     ) )
 
#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 )
 
   write(*,*)
   write(*,*) 'End of Pinsquare Model. Return code=',coi_error
 
   If ( coi_error /= 0 ) then
      call flog( "Errors encountered during solution", 1 )
   elseif ( stacalls == 0 .or. solcalls == 0 ) then
      call flog( "Status or Solution routine was not called", 1 )
   elseif ( mstat /= 16 .or. sstat /= 1 ) then
      call flog( "The model or solver status was not (16,1) as expected", 1 )
   endif
 
   if ( coi_free(cntvect) /= 0 ) call flog( "Error while freeing control vector",1)
 
   call flog( "Successful Solve", 0 )
 
end Program pinsquare
!
! =====================================================================
!  Define information about the model structure
!
 
!>  Define information about the model
!!
!! @include{doc} readMatrix_params.dox
Integer Function pin_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 :: Pin_ReadMatrix
#endif
   Use data_t
   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 :: it, is, i, icol, iz
!
!  Define the information for the columns.
!
!  We should not supply status information, vsta.
!
!  We order the variables as follows:
!  td, cs, s, d, r, p, and rev. All variables for period 1 appears
!  first followed by all variables for period 2 etc.
!
!  td, cs, s, and d have lower bounds of 0, r and p have lower
!  bounds of 1, and rev has no lower bound.
!  All have infinite upper bounds (default).
!  The initial value of td is 18, s is 7, cs is 7*t, d is td-s,
!  p is 14, and r is r(t-1)-d. No initial value for rev.
!
   do it = 1, t
      is = 7*(it-1)
      lower(is+1) = 0.d0
      lower(is+2) = 0.d0
      lower(is+3) = 0.d0
      lower(is+4) = 0.d0
      lower(is+5) = 1.d0
      lower(is+6) = 1.d0
      curr(is+1)  = 18.d0
      curr(is+2)  = 7.d0*it
      curr(is+3)  = 7.d0
      curr(is+4)  = curr(is+1) - curr(is+3)
      if ( it .gt. 1 ) then
         curr(is+5) = curr(is+5-7) - curr(is+4)
      else
         curr(is+5) = 500.d0 - curr(is+4)
      endif
      curr(is+6)  = 14.d0
!
!  Now fix P at the initial value
!
      lower(is+6) = curr(is+6)
      upper(is+6) = curr(is+6)
   enddo
!
!  To make the model infeasible, add a lower bound on variable 78
!  above the recursive value of  14.245
!
!   lower(78) = 15
!
!  Define the information for the rows
!
!  We order the constraints as follows: The objective is first,
!  followed by tddef, sdef, csdef, ddef, rdef, and revdef for
!  the first period, the same for the second period, etc.
!
!  The objective is a nonbinding constraint:
!
   type(1) = 3
!
!  All others are equalities:
!
   do i = 2, m
      type(i) = 0
   enddo
!
!  Right hand sides: In all periods except the first, only tddef
!  has a nonzero right hand side of 1+2.3*1.015**(t-1).
!  In the initial period there are contributions from lagged
!  variables in the constraints that have lagged variables.
!
   do it = 1, t
      is = 1 + 6*(it-1)
      rhs(is+1) = 1.d0+2.3d0*1.015d0**(it-1)
   enddo
!
!  tddef: + 0.87*td(0)
!
   rhs(2) = rhs(2) + 0.87d0*18.d0
!
!  sdef: +0.75*s(0)
!
   rhs(3) =  0.75d0*6.5d0
!
!  csdef: +1*cs(0)
!
   rhs(4) =  0.d0
!
!  rdef: +1*r(0)
!
   rhs(6) = 500.d0
!
!  Define the structure and content of the Jacobian:
!  To help define the Jacobian pattern and values it can be useful to
!  make a picture of the Jacobian. We describe the variables for one
!  period and the constraints they are part of:
!
!              td   cs   s    d    r    p    rev
!  Obj                                      (1+r)**(1-t)
! Period t:
!  tddef       1.0                      0.13
!  sdef             NL   1.0            NL
!  csdef            1.0 -1.0
!  ddef       -1.0       1.0  1.0
!  rdef                       1.0  1.0
!  revdef                     NL   NL   NL   1.0
! Period t+1:
!  tddef      -0.87
!  sdef                 -0.75
!  csdef           -1.0
!  ddef
!  rdef                           -1.0
!  revdef
!
!  The Jacobian has to be sorted column-wise so we will just define
!  the elements column by column according to the table above:
!
   iz   = 1
   icol = 1
   do it = 1, t
!
!  is points to the position before the first equation for the period
!
      is = 1 + 6*(it-1)
!
!  Column td:
!
      colsta(icol) = iz
      icol       = icol + 1
      rowno(iz)  = is+1
      value(iz)  = +1.d0
      nlflag(iz) = 0
      iz         = iz + 1
      rowno(iz)  = is+4
      value(iz)  = -1.d0
      nlflag(iz) = 0
      iz         = iz + 1
      if ( it .lt. t ) then
         rowno(iz)  = is+7
         value(iz)  = -0.87d0
         nlflag(iz) = 0
         iz         = iz + 1
      endif
!
!  Column cs
!
      colsta(icol) = iz
      icol       = icol + 1
      rowno(iz)  = is+2
      nlflag(iz) = 1
      iz         = iz + 1
      rowno(iz)  = is+3
      value(iz)  = +1.d0
      nlflag(iz) = 0
      iz         = iz + 1
      if ( it .lt. t ) then
         rowno(iz)  = is+9
         value(iz)  = -1.d0
         nlflag(iz) = 0
         iz         = iz + 1
      endif
!
!  Column s
!
      colsta(icol) = iz
      icol       = icol + 1
      rowno(iz)  = is+2
      value(iz)  = +1.d0
      nlflag(iz) = 0
      iz         = iz + 1
      rowno(iz)  = is+3
      value(iz)  = -1.d0
      nlflag(iz) = 0
      iz         = iz + 1
      rowno(iz)  = is+4
      value(iz)  = +1.d0
      nlflag(iz) = 0
      iz         = iz + 1
      if ( it .lt. t ) then
         rowno(iz)  = is+8
         value(iz)  = -0.75d0
         nlflag(iz) = 0
         iz         = iz + 1
      endif
!
!  Column d:
!
      colsta(icol) = iz
      icol       = icol + 1
      rowno(iz)  = is+4
      value(iz)  = +1.d0
      nlflag(iz) = 0
      iz         = iz + 1
      rowno(iz)  = is+5
      value(iz)  = +1.d0
      nlflag(iz) = 0
      iz         = iz + 1
      rowno(iz)  = is+6
      nlflag(iz) = 1
      iz         = iz + 1
!
!  Column r:
!
      colsta(icol) = iz
      icol       = icol + 1
      rowno(iz)  = is+5
      value(iz)  = +1.d0
      nlflag(iz) = 0
      iz         = iz + 1
      rowno(iz)  = is+6
      nlflag(iz) = 1
      iz         = iz + 1
      if ( it .lt. t ) then
         rowno(iz)  = is+11
         value(iz)  = -1.d0
         nlflag(iz) = 0
         iz         = iz + 1
      endif
!
!  Column p:
!
      colsta(icol) = iz
      icol       = icol + 1
      rowno(iz)  = is+1
      value(iz)  = +0.13d0
      nlflag(iz) = 0
      iz         = iz + 1
      rowno(iz)  = is+2
      nlflag(iz) = 1
      iz         = iz + 1
      rowno(iz)  = is+6
      nlflag(iz) = 1
      iz         = iz + 1
!
!  Column rev:
!
      colsta(icol) = iz
      icol       = icol + 1
      rowno(iz)  = +1
      value(iz)  = 1.05d0**(1-it)
      nlflag(iz) = 0
      iz         = iz + 1
      rowno(iz)  = is+6
      value(iz)  = 1.d0
      nlflag(iz) = 0
      iz         = iz + 1
   enddo
   colsta(icol) = iz
 
   pin_readmatrix = 0
 
end Function pin_readmatrix
!
! =====================================================================
!  Compute nonlinear terms and non-constant Jacobian elements
!
 
!>  Compute nonlinear terms and non-constant Jacobian elements
!!
!! @include{doc} fdeval_params.dox
Integer Function pin_fdeval( x, g, jac, rowno, jcnm, mode, ignerr, errcnt, &
                             n, nz, thread, usrmem )
#if defined(itl)
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Pin_FDEval
#endif
   Use data_t
   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 it, is
   real*8  h1, h2
!
!  Compute the number of the period
!
   pin_fdeval = 0
   it = (rowno+4) / 6
   is = 7*(it-1)
   if ( rowno == (it-1)*6+3 ) then
!
!  sdef equation. Nonlinear term = -(1.1+0.1*p)*1.02**(-cs/7)
!
      h1 = (1.1d0+0.1d0*x(is+6))
      h2 = 1.02d0**(-x(is+2)/7.d0)
      if ( mode == 1 .or. mode == 3 ) then
         g = -h1*h2
      endif
      if ( mode == 2 .or. mode == 3 ) then
         jac(is+2) = h1*h2*log(1.02d0)/7.d0
         jac(is+6) = -h2*0.1d0
      endif
   elseif ( rowno == (it-1)*6+7 ) then
!
!  revdef equation. Nonlinear term = -d*(p-250/r)
!
      if ( mode == 1 .or. mode == 3 ) then
         g = -x(is+4)*(x(is+6)-250.d0/x(is+5))
      endif
      if ( mode == 2 .or. mode == 3 ) then
         jac(is+4) = -(x(is+6)-250.d0/x(is+5))
         jac(is+5) = -x(is+4)*250d0/x(is+5)**2
         jac(is+6) = -x(is+4)
      endif
   else
!
!  Error - this equation is not nonlinear
!
      write(*,*)
      write(*,*) 'Error. FDEval called with rowno=',rowno
      write(*,*)
      pin_fdeval = 1
   endif
 
end Function pin_fdeval
 
Integer Function pin_solution( XVAL, XMAR, XBAS, XSTA, YVAL, YMAR, YBAS, YSTA, N, M, USRMEM )
#if defined(itl)
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Pin_Solution
#endif
!
!  Specialized solution callback routine with names for variables and constraints
!
   Use proginfo
   Use data_t
   IMPLICIT NONE
   INTEGER, Intent(IN)                  :: n, m
   INTEGER, Intent(IN),    Dimension(N) :: xbas, xsta
   INTEGER, Intent(IN),    Dimension(M) :: ybas, ysta
   real*8,  Intent(IN),    Dimension(N) :: xval, xmar
   real*8,  Intent(IN),    Dimension(M) :: yval, ymar
   real*8,  Intent(IN OUT)              :: usrmem(*)
   character*6, parameter, dimension(7) :: vname = (/'td    ','cs    ','s     ','d     ','r     ','p     ','rev   '/)
   character*6, parameter, dimension(6) :: ename = (/'tddef ','sdef  ','csdef ','ddef  ','rdef  ','revdef'/)
 
   INTEGER :: i, it, i1
   CHARACTER*5, Parameter, Dimension(4) :: stat = (/ 'Lower','Upper','Basic','Super' /)
 
   WRITE(10,"(/' Variable   Solution value    Reduced cost    B-stat'/)")
   i = 0
   do it = 1, t
      DO i1 = 1, 7
         i = i + 1
         WRITE(10,"(1X,A6,i2,1p,E20.6,E16.6,4X,A5 )") vname(i1), it, xval(i), xmar(i), stat(1+xbas(i))
      ENDDO
   enddo
 
   WRITE(10,"(/' Constrnt   Activity level    Marginal cost   B-stat'/)")
   i = 1
   WRITE(10,"(1x,'Objective',1P,E19.6,E16.6,4X,A5 )") yval(i), ymar(i), stat(1+ybas(i))
   do it = 1, t
      do i1 = 1, 6
         i = i + 1
         WRITE(10,"(1x,A6,i2,1P,E20.6,E16.6,4X,A5 )") ename(i1),it, yval(i), ymar(i), stat(1+ybas(i))
      enddo
   ENDDO
 
   solcalls = solcalls + 1
   pin_solution = 0
 
END Function pin_solution