brentq_solver Derived Type

type, public, extends(root_solver) :: brentq_solver

brentq root solver


Inherits

type~~brentq_solver~~InheritsGraph type~brentq_solver brentq_solver type~root_solver root_solver type~brentq_solver->type~root_solver

Type-Bound Procedures

procedure, public :: initialize => initialize_root_solver

initialize the class [must be called first]

  • private subroutine initialize_root_solver(me, f, ftol, rtol, atol, maxiter)

    Initialize the root_solver class.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(root_solver), intent(out) :: me
    procedure(func) :: f

    user function f(x) to find the root of
    real(kind=wp), intent(in), optional :: ftol

    absolute tolerance for f=0
    real(kind=wp), intent(in), optional :: rtol

    relative tol for x
    real(kind=wp), intent(in), optional :: atol

    absolute tol for x
    integer, intent(in), optional :: maxiter

    maximum number of iterations

procedure, public :: solve

main routine for finding the root

  • private subroutine solve(me, ax, bx, xzero, fzero, iflag, fax, fbx, bisect_on_failure)

    Main wrapper routine for all the methods.

    Arguments

    Type IntentOptional Attributes Name
    class(root_solver), intent(inout) :: me
    real(kind=wp), intent(in) :: ax

    left endpoint of initial interval
    real(kind=wp), intent(in) :: bx

    right endpoint of initial interval
    real(kind=wp), intent(out) :: xzero

    abscissa approximating a zero of f in the interval ax,bx
    real(kind=wp), intent(out) :: fzero

    value of f at the root (f(xzero))
    integer, intent(out) :: iflag

    status flag (-1=error, 0=root found, -4=ax must be /= bx)
    real(kind=wp), intent(in), optional :: fax

    if f(ax) is already known, it can be input here
    real(kind=wp), intent(in), optional :: fbx

    if f(bx) is already known, it can be input here
    logical, intent(in), optional :: bisect_on_failure

    if true, then if the specified method fails, it will be retried using the bisection method. (default is False). Note that this can use up to maxiter additional function evaluations.

procedure, public :: find_root => brentq

  • private subroutine brentq(me, ax, bx, fax, fbx, xzero, fzero, iflag)

    Classic Brent's method to find a zero of the function f on the sign changing interval [ax, bx], but with a different formula for the extrapolation step.

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    Arguments

    Type IntentOptional Attributes Name
    class(brentq_solver), intent(inout) :: me
    real(kind=wp), intent(in) :: ax

    left endpoint of initial interval
    real(kind=wp), intent(in) :: bx

    right endpoint of initial interval
    real(kind=wp), intent(in) :: fax

    f(ax)
    real(kind=wp), intent(in) :: fbx

    f(ax)
    real(kind=wp), intent(out) :: xzero

    abscissa approximating a zero of f in the interval ax,bx
    real(kind=wp), intent(out) :: fzero

    value of f at the root (f(xzero))
    integer, intent(out) :: iflag

    status flag (0=root found, -2=max iterations reached)

Source Code

    type,extends(root_solver),public :: brentq_solver
    !! brentq root solver
    private
    contains
    private
    procedure,public :: find_root => brentq
    end type brentq_solver