hybrd1 Subroutine

public subroutine hybrd1(fcn, n, x, fvec, tol, info)

the purpose of hybrd1 is to find a zero of a system of n nonlinear functions in n variables by a modification of the powell hybrid method. this is done by using the more general nonlinear equation solver hybrd. the user must provide a subroutine which calculates the functions. the jacobian is then calculated by a forward-difference approximation.

Arguments

Type IntentOptional Attributes Name
procedure(fcn_hybrd) :: fcn

user-supplied subroutine which calculates the functions
integer, intent(in) :: n

a positive integer input variable set to the number of functions and variables.
real(kind=wp), intent(inout), dimension(n) :: x

an array of length n. on input x must contain an initial estimate of the solution vector. on output x contains the final estimate of the solution vector.
real(kind=wp), intent(out), dimension(n) :: fvec

an output array of length n which contains the functions evaluated at the output x.
real(kind=wp), intent(in) :: tol

a nonnegative input variable. termination occurs when the algorithm estimates that the relative error between x and the solution is at most tol.
integer, intent(out) :: info

an integer output variable. if the user has terminated execution, info is set to the (negative) value of iflag. see description of fcn. otherwise, info is set as follows: info = 0 improper input parameters. info = 1 algorithm estimates that the relative error between x and the solution is at most tol. info = 2 number of calls to fcn has reached or exceeded 200*(n+1). info = 3 tol is too small. no further improvement in the approximate solution x is possible. info = 4 iteration is not making good progress.

Calls

proc~~hybrd1~~CallsGraph proc~hybrd1 minpack_module::hybrd1 proc~hybrd minpack_module::hybrd proc~hybrd1->proc~hybrd proc~dogleg minpack_module::dogleg proc~hybrd->proc~dogleg proc~dpmpar minpack_module::dpmpar proc~hybrd->proc~dpmpar proc~enorm minpack_module::enorm proc~hybrd->proc~enorm proc~fdjac1 minpack_module::fdjac1 proc~hybrd->proc~fdjac1 proc~qform minpack_module::qform proc~hybrd->proc~qform proc~qrfac minpack_module::qrfac proc~hybrd->proc~qrfac proc~r1mpyq minpack_module::r1mpyq proc~hybrd->proc~r1mpyq proc~r1updt minpack_module::r1updt proc~hybrd->proc~r1updt proc~dogleg->proc~dpmpar proc~dogleg->proc~enorm proc~fdjac1->proc~dpmpar proc~qrfac->proc~dpmpar proc~qrfac->proc~enorm proc~r1updt->proc~dpmpar

Called by

proc~~hybrd1~~CalledByGraph proc~hybrd1 minpack_module::hybrd1 proc~halo_to_rv_diffcorr halo_orbit_module::halo_to_rv_diffcorr proc~halo_to_rv_diffcorr->proc~hybrd1

Source Code

    subroutine hybrd1(fcn,n,x,fvec,tol,info)

    implicit none

    procedure(fcn_hybrd)                :: fcn      !! user-supplied subroutine which calculates the functions
    integer,intent(in)                  :: n        !! a positive integer input variable set to the number
                                                    !! of functions and variables.
    integer,intent(out)                 :: info     !! an integer output variable. if the user has
                                                    !! terminated execution, info is set to the (negative)
                                                    !! value of `iflag`. see description of `fcn`. otherwise,
                                                    !! `info` is set as follows:
                                                    !!  ***info = 0*** improper input parameters.
                                                    !!  ***info = 1*** algorithm estimates that the relative error
                                                    !!  between `x` and the solution is at most `tol`.
                                                    !!  ***info = 2*** number of calls to `fcn` has reached or exceeded
                                                    !!  `200*(n+1)`.
                                                    !!  ***info = 3*** `tol` is too small. no further improvement in
                                                    !!  the approximate solution `x` is possible.
                                                    !!  ***info = 4*** iteration is not making good progress.
    real(wp),intent(in)                 :: tol      !! a nonnegative input variable. termination occurs
                                                    !! when the algorithm estimates that the relative error
                                                    !! between `x` and the solution is at most `tol`.
    real(wp),dimension(n),intent(inout) :: x        !! an array of length `n`. on input `x` must contain
                                                    !! an initial estimate of the solution vector. on output `x`
                                                    !! contains the final estimate of the solution vector.
    real(wp),dimension(n),intent(out)   :: fvec     !! an output array of length `n` which contains
                                                    !! the functions evaluated at the output `x`.

    integer :: lwa                           !! length of `wa` work array
    real(wp),dimension(:),allocatable :: wa  !! work array
    integer :: index , j , lr , maxfev , ml , mode , mu , nfev , nprint
    real(wp) :: epsfcn , xtol
    real(wp),dimension(n) :: diag

    real(wp),parameter :: factor = 100.0_wp

    info = 0

    ! check the input parameters for errors.
    if ( n>0 .and. tol>=zero ) then

        !set up inputs:
        lwa     = (n*(3*n+13))/2    ! the work array was formerly an input
        allocate(wa(lwa))           !
        wa      = 0.0_wp            !
        maxfev  = 200*(n+1)
        xtol    = tol
        ml      = n - 1
        mu      = n - 1
        epsfcn  = zero
        mode    = 2
        diag    = one
        nprint  = 0
        lr      = (n*(n+1))/2
        index   = 6*n + lr

        ! call hybrd:
        call hybrd(fcn,n,x,fvec,xtol,maxfev,ml,mu,epsfcn,diag,mode,&
                   factor,nprint,info,nfev,wa(index+1),n,wa(6*n+1),lr,&
                   wa(n+1),wa(2*n+1),wa(3*n+1),wa(4*n+1),wa(5*n+1))
        if ( info==5 ) info = 4

        deallocate(wa)

    endif

    end subroutine hybrd1