nonlin_solve::brent_solver Type Reference

Defines a solver based upon Brent's method for solving an equation of one variable without using derivatives. More...

Inheritance diagram for nonlin_solve::brent_solver:

Public Member Functions
procedure, public	solve brent_solve
	Solves the equation.
Public Member Functions inherited from nonlin_core::equation_solver_1var
procedure, public	get_max_fcn_evals es1_get_max_eval
	Gets the maximum number of function evaluations allowed during a single solve.
procedure, public	set_max_fcn_evals es1_set_max_eval
	Sets the maximum number of function evaluations allowed during a single solve.
procedure, public	get_fcn_tolerance es1_get_fcn_tol
	Gets the convergence on function value tolerance.
procedure, public	set_fcn_tolerance es1_set_fcn_tol
	Sets the convergence on function value tolerance.
procedure, public	get_var_tolerance es1_get_var_tol
	Gets the convergence on change in variable tolerance.
procedure, public	set_var_tolerance es1_set_var_tol
	Sets the convergence on change in variable tolerance.
procedure, public	get_print_status es1_get_print_status
	Gets a logical value determining if iteration status should be printed.
procedure, public	set_print_status es1_set_print_status
	Sets a logical value determining if iteration status should be printed.
procedure, public	get_diff_tolerance es1_get_diff_tol
	Gets the convergence on slope of the function (derivative) tolerance.
procedure, public	set_diff_tolerance es1_set_diff_tol
	Sets the convergence on slope of the function (derivative) tolerance.

Additional Inherited Members
Public Attributes inherited from nonlin_core::equation_solver_1var
real(real64)	m_fcntol = 1.0d-8
	The convergence criteria on function value.
real(real64)	m_xtol = 1.0d-12
	The convergence criteria on change in variable value.
real(real64)	m_difftol = 1.0d-12
	The convergence criteria on the slope of the function (derivative)
logical	m_printstatus = .false.
	Set to true to print iteration status; else, false.

Detailed Description

Defines a solver based upon Brent's method for solving an equation of one variable without using derivatives.

Definition at line 398 of file nonlin_solve.f90.

Member Function/Subroutine Documentation

solve()

procedure, public nonlin_solve::brent_solver::solve

virtual

Solves the equation.

Syntax

subroutine solve(class(brent_solver) this, class(fcn1var_helper) fcn, real(real64) x, type(value_pair) lim, optional real(real64) f, optional type(iteration_behavior) ib, optional class(errors) err)

Parameters

[in,out]	this	The brent_solver object.
[in]	fcn	The fcn1var_helper object containing the equation to solve.
[in,out]	x	A parameter used to return the solution. Notice, any input value will be ignored as this routine relies upon the search limits in lim to provide a starting point.
[in]	lim	A value_pair object defining the search limits.
[out]	f	An optional parameter used to return the function residual as computed at x.
[out]	ib	An optional output, that if provided, allows the caller to obtain iteration performance statistics.
[out]	err	An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows. NL_INVALID_OPERATION_ERROR: Occurs if no equations have been defined. NL_INVALID_INPUT_ERROR: Occurs if the number of equations is different than the number of variables. NL_CONVERGENCE_ERROR: Occurs if the algorithm cannot converge within the allowed number of iterations.

Example

The following code provides an example of how to solve an equation of one variable using Brent's method.

program main
    use nonlin_core, only : fcn1var, fcn1var_helper, value_pair
    use nonlin_solve, only : brent_solver
 
    type(fcn1var_helper) :: obj
    procedure(fcn1var), pointer :: fcn
    type(brent_solver) :: solver
    real(real64) :: x, f
    type(value_pair) :: limits
 
    ! Define the solution limits
    limits%x1 = 1.5d0
    limits%x2 = 5.0d0
 
    ! Define the function
    fcn => fcn1
    call obj%set_fcn(fcn)
 
    ! Solve the equation
    call solver%solve(obj, x, limits, f)
 
    ! Print the output and the residual:
    print '(AF5.3)', "The solution: ", x
    print '(AE9.3)', "The residual: ", f
contains
    ! f(x) = sin(x) / x, SOLUTION: x = n * pi for n = 1, 2, 3, ...
    function fcn1(x) result(f)
        real(real64), intent(in) :: x
        real(real64) :: f
        f = sin(x) / x
    end function
end program

The above program returns the following results.

The solution: 3.142
The residual: -.751E-11

See Also

• Wikipedia
• Numerical Recipes
• R.P. Brent, "Algorithms for Minimization without Derivatives," Dover Publications, January 2002. ISBN 0-486-41998-3. Further information available here.

Implements nonlin_core::equation_solver_1var.

Definition at line 479 of file nonlin_solve.f90.

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The documentation for this type was generated from the following file:

• D:/Code/nonlin/src/nonlin_solve.f90