Chimie Théorique » Opt'n Path

 subroutine hupdate_all(n, ds, dgrad, Hess)

  use Path_module, only :  HUpdate,Hinv

  use Io_module, only : IoOut

  IMPLICIT NONE

  INTEGER, PARAMETER :: KINT=KIND(1)

  INTEGER, PARAMETER :: KREAL=KIND(1.0D0)

  INTEGER(KINT), INTENT(IN) :: n

  real(KREAL), INTENT(IN) :: ds(n), dgrad(n)

  REAL(KREAL),INTENT(INOUT) :: Hess(n:n)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!

! This subroutine is a driver for the update of the Hessian 

! in the Quasi-Newton optimization step.

! We propose mostly update of the inverse Hessian.

!

! input:

!  - n: number of coordinates

!  - ds: GeomOld-Geom (expressed in the optimization coord.)

!  - dgrad: GradOld-Grad  (expressed in the optimization coord.)

!

!  input/output:

!  - Hess: old Hessian in input, replaced by updated Hessian on output

!

!!!!!!!!!!!!!!!!

!

! For now, we propose :

! - For update of inverse Hessian:

!      - BFGS (Broyden, Fletcher, Goldfarb, and Shanno)

!      - DFP (Davidson - Fletcher - Powell )

!      - MS (Murtagh-Sargent)

!

! - For update of hessian:

!      - Bofill (combination of Murtagh-Sargent and Powell-symmetric-Broyden

!      - MS (Murtagh-Sargent)

!      - BFGS

!      - DFP

!----------------------------------------------------

! We use the fact that some formula are the dual of other

! that is, one can convert the formula for update of the Hessian 

! into the update of the inverse Hessian by replacing the Hessian

! (denoted by B in the Fletcher book and in the Nocedal&Wrigth book)

! by the inverse hessian (denoted by H), and replacing ds by dgrad in the

! formula.

! See for example:

! 1) Numerical Optimization, Springer 2nd Ed., 2006

! by Jorge Nocedal & Stephen J. Wright

! 2) ractical Methods of Optimization, John Wiley & Sons, second ed., 1987.

! by R. Fletcher

!

!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  interface

     function valid(string) result (isValid)

       logical                  :: isValid

       character(*), intent(in) :: string

     end function valid

  end interface

  ! ======================================================================

  LOGICAL :: Debug

  ! ======================================================================

  debug = valid ('HESS') .OR. Valid('HUPDATE')

  if (debug) WRITE(*,*) "================================= Entering Hupdate_all ==============="

  SELECT CASE (Hinv)

     CASE (.TRUE.)

        SELECT CASE (HUpdate)

           CASE ("BFGS")

              Call Hinvup_BFGS(n,ds,dgrad,hess)

           CASE ("MS")

! we use the fact that MS is self-dual 

              Call Hupdate_MS(n,dgrad,ds,hess)

           CASE ("DFP")

              Call Hinvup_DFP(n,ds,dgrad,hess)

           CASE DEFAULT

              WRITE(*,*) Trim(HUpdate) // " not known: using BFGS"

              Call Hinvup_BFGS(n,ds,dgrad,hess)

         END SELECT

     CASE (.FALSE.)

        SELECT CASE (HUpdate)

           CASE ("BOFILL")

              Call Hupdate_Bofill(n,ds,dgrad,hess)

           CASE ("MS")

              Call Hupdate_MS(n,ds,dgrad,hess)

           CASE ("DFP")

! we use the fact that DFP is the dual of BFGS

              Call Hinvup_BFGS(n,dgrad,ds,hess)

           CASE ("BFGS")

! we use the fact that DFP is the dual of BFGS

              Call Hinvup_DFP(n,dgrad,ds,hess)

           CASE DEFAULT

              WRITE(*,*) Trim(HUpdate) // " not known: using Bofill"

              Call Hupdate_Bofill(n,ds,dgrad,hess)

           END SELECT

    END SELECT

  if (debug) WRITE(*,*) "================================= Exiting Hupdate_all ==============="

end subroutine hupdate_all