leastl1.f90

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!> @file leastl1.f90
!! @ingroup FORT1THREAD_EXAMPLES
!!
!! 
!! We solve the following nonlinear linear L1 estimation model:
!! 
!! @verbatim
!! min sum(i, resp(i)+resm(i) )
!! 
!! sum(j, a(i,j)*x(j) + b(i,j)*x(j)**2 ) + resp(i) - resm(i) = obs(i)
!! @endverbatim
!! 
!! where a, b, and obs are known data, x are the parameter to be estimated,
!! and resp and resm are positive variables measuring positive and
!! negative deviations to be minimized.
!! 
!!
!! For more information about the individual callbacks, please have a look at the source code.
 
 
REAL FUNCTION rndx( )
!
!  Defines a pseudo random number between 0 and 1
!
   IMPLICIT NONE
 
   Integer, save :: seed = 12359
 
   seed = mod(seed*1027+25,1048576)
   rndx = float(seed)/float(1048576)
 
END FUNCTION rndx
 
subroutine defdata
!
!  Define values for A, B, and Obs
!
   Use lsq_70
   IMPLICIT NONE
 
   Integer :: i, j
   real*8, Parameter ::  xtarg = -1.0
   real*8, Parameter ::  noise = 1.0
   Real, External :: Rndx
   real*8 :: o
 
   do i = 1, nobs
      o = 0.d0
      do j = 1, dimx
         a(i,j) = rndx()
         b(i,j) = rndx()
         o = o + a(i,j) * xtarg + b(i,j) * xtarg**2
      enddo
      obs(i) = o + noise * rndx()
   enddo
 
end subroutine defdata
!
!  Main program.
!
!> Main program. A simple setup and call of CONOPT
!!
Program leastl1
 
   Use proginfo
   Use coidef
   Use lsq_70
   implicit None
!
!  Declare the user callback routines as Integer, External:
!
   Integer, External :: lsq_readmatrix ! Mandatory Matrix definition routine defined below
   Integer, External :: lsq_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 :: Lsq_ReadMatrix
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Lsq_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
 
   call startup
!
!  Define data
!
   Call defdata
!
!  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, 2*nobs + dimx ) )
   coi_error = max( coi_error, coidef_numcon( cntvect, nobs + 1 ) )
   coi_error = max( coi_error, coidef_numnz( cntvect, nobs * (dimx+4) ) )
   coi_error = max( coi_error, coidef_numnlnz( cntvect, nobs * dimx ) )
   coi_error = max( coi_error, coidef_optdir( cntvect, -1 ) ) ! Minimize
   coi_error = max( coi_error, coidef_objcon( cntvect, nobs + 1 ) )  ! Objective is last constraint
   coi_error = max( coi_error, coidef_optfile( cntvect, 'leastl1.opt'  ) )
!
!  Tell CONOPT about the callback routines:
!
   coi_error = max( coi_error, coidef_readmatrix( cntvect, lsq_readmatrix ) )
   coi_error = max( coi_error, coidef_fdeval( cntvect, lsq_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     ) )
   coi_error = max( coi_error, coidef_debugfv( cntvect, 0 ) )  ! Debug Fdeval on or off
 
#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
!
!  Save the solution so we can check the duals:
!
   do_allocate = .true.
!
!  Start CONOPT:
!
   coi_error = coi_solve( cntvect )
 
   write(*,*)
   write(*,*) 'End of Least Square example 1. 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 ( .not. ( sstat == 1 .and. mstat == 2 ) ) then
      call flog( "Solver or Model status was not as expected (1,2)", 1 )
!   elseif ( abs( OBJ - 19.44434311d0 ) > 1.d-7 ) then
!      call flog( "Incorrect objective returned", 1 )
   Else
      Call checkdual( 'LeastL1', minimize )
   endif
 
   if ( coi_free(cntvect) /= 0 ) call flog( "Error while freeing control vector",1)
 
   call flog( "Successful Solve", 0 )
 
End Program leastl1
!
! ============================================================================
!  Define information about the model:
!
 
!>  Define information about the model
!!
!! @include{doc} readMatrix_params.dox
Integer Function lsq_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 :: Lsq_ReadMatrix
#endif
   Use lsq_70
   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 :: i, j, k
!
!  Information about Variables:
!  Default: Lower = -Inf, Curr = 0, and Upper = +inf.
!  Default: the status information in Vsta is not used.
!  X : New initial = 0.8
!  Resp: New lower = 0.0
!  Resm: New lower = 0.0
!
   do i = 1, dimx
      curr(i) = -0.8d0
   enddo
   do j = 1, 2*nobs
      lower(dimx+j) = 0.0d0
   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.
!
!  Constraints 1 to Nobs:
!  Rhs = Obs(i) and type Equality
!
   do i = 1, nobs
      rhs(i)  = obs(i)
      type(i) = 0
   enddo
!
!  Constraint Nobs + 1 (Objective)
!  Rhs = 0 and type Non binding
!
   type(nobs+1) = 3
!
!  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(i)  resp(j) resm(j)
!  j:    NL   L=1      L=-1
!  obj:       L=1      L=1
!
   k = 1
   do i = 1, dimx       ! x(i) variables
      colsta(i) =  k
      do j = 1, nobs
         rowno(k)  = j
         nlflag(k) = 1
         k         = k + 1
      enddo
   enddo
   do j = 1, nobs       ! resp(j) variables
      colsta(dimx+j) = k
      rowno(k)  = j
      nlflag(k) = 0
      value(k)  = 1.d0
      k         = k + 1
      rowno(k)  = nobs+1
      nlflag(k) = 0
      value(k)  = 1.d0
      k         = k + 1
   enddo
   do j = 1, nobs       ! resm(j) variables
      colsta(dimx+nobs+j) = k
      rowno(k)  = j
      nlflag(k) = 0
      value(k)  = -1.d0
      k         = k + 1
      rowno(k)  = nobs+1
      nlflag(k) = 0
      value(k)  = 1.d0
      k         = k + 1
   enddo
   colsta(dimx+2*nobs+1) = k
 
   lsq_readmatrix = 0 ! Return value means OK
 
end Function lsq_readmatrix
!
!==========================================================================
!  Compute nonlinear terms and non-constant Jacobian elements
!
 
!>  Compute nonlinear terms and non-constant Jacobian elements
!!
!! @include{doc} fdeval_params.dox
Integer Function lsq_fdeval( x, g, jac, rowno, jcnm, mode, ignerr, errcnt, &
                             n, nz, thread, usrmem )
#if defined(itl)
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Lsq_FDEval
#endif
   use lsq_70
   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 :: j
   real*8  :: s
!
!  Row Nobs+1: the objective function is linear
!
   if ( rowno .eq. nobs+1 ) then
      lsq_fdeval = 1; Return ! This is an error
!
!  Row 1 to Nobs: The observation definitions:
!
   else
!
!  Mode = 1 or 3: Function value - x-part only
!
      if ( mode .eq. 1 .or. mode .eq. 3 ) then
         s = 0.d0
         do j = 1, dimx
            s = s + a(rowno,j)*x(j) + b(rowno,j)*x(j)**2
         enddo
         g = s
      endif
!
!  Mode = 2 or 3: Derivatives
!
      if ( mode .eq. 2 .or. mode .eq. 3 ) then
         do j = 1, dimx
            jac(j) = a(rowno,j) + 2.d0*b(rowno,j)*x(j)
         enddo
      endif
   endif
   lsq_fdeval = 0
 
end Function lsq_fdeval