uobyqa Subroutine

public subroutine uobyqa(n, x, rhobeg, rhoend, iprint, maxfun, calfun)

This subroutine seeks the least value of a function of many variables, by a trust region method that forms quadratic models by interpolation.

Arguments

Type IntentOptional Attributes Name
integer, intent(in) :: n

the number of variables and must be at least two
real(kind=wp), intent(inout), dimension(*) :: x

Initial values of the variables must be set in X(1),X(2),...,X(N). They will be changed to the values that give the least calculated F.
real(kind=wp), intent(in) :: rhobeg

RHOBEG and RHOEND must be set to the initial and final values of a trust region radius, so both must be positive with RHOEND<=RHOBEG. Typically RHOBEG should be about one tenth of the greatest expected change to a variable, and RHOEND should indicate the accuracy that is required in the final values of the variables.
real(kind=wp), intent(in) :: rhoend

RHOBEG and RHOEND must be set to the initial and final values of a trust region radius, so both must be positive with RHOEND<=RHOBEG. Typically RHOBEG should be about one tenth of the greatest expected change to a variable, and RHOEND should indicate the accuracy that is required in the final values of the variables.
integer, intent(in) :: iprint

The value of IPRINT should be set to 0, 1, 2 or 3, which controls the amount of printing. Specifically, there is no output if IPRINT=0 and there is output only at the return if IPRINT=1. Otherwise, each new value of RHO is printed, with the best vector of variables so far and the corresponding value of the objective function. Further, each new value of F with its variables are output if IPRINT=3.
integer, intent(in) :: maxfun

upper bound on the number of calls of CALFUN.
procedure(func) :: calfun

It must set F to the value of the objective function for the variables X(1),X(2),...,X(N).

Calls

proc~~uobyqa~~CallsGraph proc~uobyqa uobyqa proc~uobyqb uobyqb proc~uobyqa->proc~uobyqb proc~lagmax lagmax proc~uobyqb->proc~lagmax proc~trstep~2 trstep proc~uobyqb->proc~trstep~2

Called by

proc~~uobyqa~~CalledByGraph proc~uobyqa uobyqa proc~uobyqa_test uobyqa_test proc~uobyqa_test->proc~uobyqa

Source Code

    subroutine uobyqa (n, x, rhobeg, rhoend, iprint, maxfun, calfun)

        implicit none

        integer,intent(in)    :: n               !! the number of variables and must be at least two
        real(wp),intent(inout),dimension(*) :: x !! Initial values of the variables must be set in X(1),X(2),...,X(N). They
                                                 !! will be changed to the values that give the least calculated F.
        real(wp),intent(in)   :: rhobeg          !! RHOBEG and RHOEND must be set to the initial and final values of a trust
                                                 !! region radius, so both must be positive with RHOEND<=RHOBEG. Typically
                                                 !! RHOBEG should be about one tenth of the greatest expected change to a
                                                 !! variable, and RHOEND should indicate the accuracy that is required in
                                                 !! the final values of the variables.
        real(wp),intent(in)   :: rhoend          !! RHOBEG and RHOEND must be set to the initial and final values of a trust
                                                 !! region radius, so both must be positive with RHOEND<=RHOBEG. Typically
                                                 !! RHOBEG should be about one tenth of the greatest expected change to a
                                                 !! variable, and RHOEND should indicate the accuracy that is required in
                                                 !! the final values of the variables.
        integer,intent(in)    :: iprint          !! The value of IPRINT should be set to 0, 1, 2 or 3, which controls the
                                                 !! amount of printing. Specifically, there is no output if IPRINT=0 and
                                                 !! there is output only at the return if IPRINT=1. Otherwise, each new
                                                 !! value of RHO is printed, with the best vector of variables so far and
                                                 !! the corresponding value of the objective function. Further, each new
                                                 !! value of F with its variables are output if IPRINT=3.
        integer,intent(in)   :: maxfun           !! upper bound on the number of calls of CALFUN.
        procedure (func)     :: calfun           !! It must set F to the value of the objective
                                                 !! function for the variables X(1),X(2),...,X(N).

        real(wp),dimension(:),allocatable :: w
        integer :: npt,ixb,ixo,ixn,ixp,ipq,ipl,ih,ig,id,ivl,iw

        ! Partition the working space array, so that different parts of it can be
        ! treated separately by the subroutine that performs the main calculation.

        npt = (n*n+3*n+2) / 2
        ixb = 1
        ixo = ixb + n
        ixn = ixo + n
        ixp = ixn + n
        ipq = ixp + n * npt
        ipl = ipq + npt - 1
        ih = ipl + (npt-1) * npt
        ig = ih + n * n
        id = ig + n
        ivl = ih
        iw = id + n

        ! The array W will be used for working space
        allocate(w((N**4+8*N**3+23*N**2+42*N+max(2*N**2+4,18*N))/4))

        call uobyqb (n, x, rhobeg, rhoend, iprint, maxfun, npt, w(ixb), w(ixo), w(ixn), &
                     w(ixp), w(ipq), w(ipl), w(ih), w(ig), w(id), w(ivl), w(iw), calfun)

        deallocate(w)

    end subroutine uobyqa