leastsq10.f90

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!> @file leastsq10.f90
!! @ingroup FORT1THREAD_EXAMPLES
!!
!!
!! This model is similar to leastsq5, but this time we define 2nd order
!! directional information in the form of both an `2DDirIni` routine
!! where the bulk of the work is done and a `2DDir` routine that just
!! copies the information.
!!
!! We solve the following nonlinear least squares model:
!!
!! \f[
!! \min \sum_i res_{i}^2 \\
!!
!! \sum_j ( a_{ij}x_j + b_{ij}x_j^2 ) + res_i = obs_i
!! \f]
!!
!! where \f$a\f$, \f$b\f$, and \f$obs\f$ are known data, and \f$res\f$ and \f$x\f$ are the
!! variables of the model.
!!
!!
!! For more information about the individual callbacks, please have a look at the source code.
 
#if defined(_WIN32) && !defined(_WIN64)
#define dec_directives_win32
#endif
 
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_700
   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 leastsquare
 
   Use proginfo
   Use conopt
   Use lsq_700
   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 :: lsq_2ddirini   ! Initialization routine for Directional 2nd derivatives
   Integer, External :: lsq_2ddir      ! Directional 2nd derivative routine
   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
#ifdef dec_directives_win32
!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 :: Lsq_2DDirIni
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Lsq_2DDir
!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, Dimension(:), Pointer :: cntvect
   INTEGER :: coi_error
 
   call startup
!
!  Define data
!
   Call defdata
!
!  Create and initialize a Control Vector
!
   coi_error = coi_create( cntvect )
!
!  Tell CONOPT about the size of the model by populating the Control Vector:
!
   coi_error = max( coi_error, coidef_numvar( cntvect, nobs + dimx ) )
   coi_error = max( coi_error, coidef_numcon( cntvect, nobs + 1 ) )
   coi_error = max( coi_error, coidef_numnz( cntvect, nobs * (dimx+2) ) )
   coi_error = max( coi_error, coidef_numnlnz( cntvect, nobs * (dimx+1) ) )
   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, 'leastsq10.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_2ddirini( cntvect, lsq_2ddirini   ) )
   coi_error = max( coi_error, coidef_2ddir( cntvect, lsq_2ddir      ) )
   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(CONOPT_LICENSE_INT_1) && defined(CONOPT_LICENSE_INT_2) && defined(CONOPT_LICENSE_INT_3) && defined(CONOPT_LICENSE_TEXT)
   coi_error = max( coi_error, coidef_license( cntvect, conopt_license_int_1, conopt_license_int_2, conopt_license_int_3, conopt_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 Least Square example 10. 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 ( sstat /= 1 .or. mstat /= 2 ) then
      call flog( "Solver and Model Status was not as expected (1,2)", 1 )
   elseif ( abs( obj - 19.44434311d0 ) > 1.d-7 ) then
      call flog( "Incorrect objective returned", 1 )
   endif
 
   if ( coi_free(cntvect) /= 0 ) call flog( "Error while freeing control vector",1)
 
   call flog( "Successful Solve", 0 )
!
!  Free solution memory
!
   call finalize
 
End Program leastsquare
!
! ============================================================================
!  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 )
#ifdef dec_directives_win32
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Lsq_ReadMatrix
#endif
   Use lsq_700
   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.
!
   do i = 1, dimx
      curr(i) = -0.8d0
   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. CONOPT expects a columnwise
!  representation in 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(i)  res(j)
!  j:    NL   L=1
!  obj:       NL
!  3:
!
   k = 1
   do j = 1, dimx
      colsta(j) =  k
      do i = 1, nobs
         rowno(k)  = i
         nlflag(k) = 1
         k         = k + 1
      enddo
   enddo
   do i = 1, nobs
      colsta(dimx+i) = k
      rowno(k)  = i
      nlflag(k) = 0
      value(k)  = 1.d0
      k         = k + 1
      rowno(k)  = nobs+1
      nlflag(k) = 1
      k         = k + 1
   enddo
   colsta(dimx+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 Recursive function lsq_fdeval( x, g, jac, rowno, jcnm, mode, ignerr, errcnt, &
                                       n, nz, thread, usrmem )
#ifdef dec_directives_win32
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Lsq_FDEval
#endif
   use lsq_700
   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 :: i,j
   real*8  :: s
!
!  Row 1: the objective function is nonlinear
!
   if ( rowno .eq. nobs+1 ) then
!
!  Mode = 1 or 3. Function value: G = sum(i, res(i)**2)
!
      if ( mode .eq. 1 .or. mode .eq. 3 ) then
         s    = 0.d0
         do i = 1, nobs
            s = s + x(dimx+i)**2
         enddo
         g    = s
      endif
!
!  Mode = 2 or 3: Derivative values:
!
      if ( mode .eq. 2 .or. mode .eq. 3 ) then
         do i = 1, nobs
            jac(dimx+i) = 2*x(dimx+i)
         enddo
      endif
!
!  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
 
 
!>  Computes the second derivative of a constraint in a direction
!!
!! @include{doc} 2DDir_params.dox
Integer Function lsq_2ddir( X, DX, D2G, ROWNO, JCNM, NODRV, N, NJ, THREAD, USRMEM )
#ifdef dec_directives_win32
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Lsq_2DDir
#endif
   Use lsq_700
   implicit none
   INTEGER, Intent(IN)                       :: rowno, n, nj, thread
   INTEGER, Intent(IN OUT)                   :: nodrv
   INTEGER, Dimension(NJ), Intent(IN)        :: jcnm
   real*8,  Dimension(N),  Intent(IN)        :: x
   real*8,  Dimension(N),  Intent(IN)        :: dx
   real*8,  Dimension(N),  Intent(OUT)       :: d2g
   real*8,  Intent(IN OUT)                   :: usrmem(*)
   integer :: i, j
 
   if ( rowno .eq. nobs+1 ) then
!
!  Objective row: sum(i, res(i)**2 )
!
      do j = 1, dimx
         d2g(j) = 0.d0
      enddo
      do i = 1, nobs
         d2g(dimx+i) = 2.d0*dx(dimx+i)
      enddo
   else
!
!  Constraint row with b(i,j)*x(j)**2 as only nonlinear term
!
      do j = 1, dimx
         d2g(j) = c(rowno,j) ! Extract the value computed in 2DDirIni below
      enddo
      do i = 1, nobs
         d2g(dimx+i) = 0.d0
      enddo
   endif
 
   lsq_2ddir = 0
 
End Function lsq_2ddir
 
 
!>  Computes the second derivative of a constraint in a direction
!!
!! @include{doc} 2DDir_params.dox
 
!>  Initialises the second derivative in a direction evaluation. Called each time the point or the direction changes
!!
!! @include{doc} 2DDirIni_params.dox
Integer Function lsq_2ddirini( X, DX, RowList, ListSize, NumThread, NewPT, NODRV, NumVar, USRMEM )
#ifdef dec_directives_win32
!DEC$ ATTRIBUTES STDCALL, REFERENCE, NOMIXED_STR_LEN_ARG :: Lsq_2DDirIni
#endif
   Use lsq_700
   implicit none
   INTEGER, Intent(IN)                       :: listsize, numthread, newpt, numvar
   Integer, Intent(IN OUT)                   :: nodrv
   real*8,  Dimension(NumVar),  Intent(IN)   :: x
   real*8,  Dimension(NumVar),  Intent(IN)   :: dx
   Integer, Dimension(ListSize),Intent(IN)   :: rowlist
   real*8,  Intent(IN OUT)                   :: usrmem(*)
 
   integer :: i, j
 
!
!  Constraint row i has b(i,j)*x(j)**2 as only nonlinear term and the
!  directional derivative is 2*b(i,j)*dx(j). The value is saved here and
!  used in the subsequent calls to Lsq_2DDir
!
   write(10,*) 'Inside 2DDirIni: NewPt=',newpt
   Do i = 1, nobs
      do j = 1, dimx
         c(i,j) = 2.d0*b(i,j)*dx(j)
      enddo
   enddo
 
   lsq_2ddirini = 0
 
End Function lsq_2ddirini