nonlin_solve::newton_1var_solver Type Reference

Defines a solver based upon Newtons's method for solving an equation of one variable. The algorithm uses a bisection method in conjunction with Newton's method in order to keep bounds upon the Newton iterations. More...

Inheritance diagram for nonlin_solve::newton_1var_solver:

Public Member Functions
procedure, public	solve newt1var_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 Newtons's method for solving an equation of one variable. The algorithm uses a bisection method in conjunction with Newton's method in order to keep bounds upon the Newton iterations.

Definition at line 502 of file nonlin_solve.f90.

Member Function/Subroutine Documentation

solve()

procedure, public nonlin_solve::newton_1var_solver::solve

virtual

Solves the equation.

Syntax

subroutine solve(class(newton_1var_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

program example
    use iso_fortran_env
    use nonlin_core
    use nonlin_solve
    implicit none
 
    ! Local variables
    type(fcn1var_helper) :: obj
    procedure(fcn1var), pointer :: fcn
    type(newton_1var_solver) :: solver
    real(real64) :: x, f
    type(value_pair) :: limits
    type(iteration_behavior) :: tracking
 
    ! Define the search limits
    limits%x1 = 1.5d0
    limits%x2 = 5.0d0
 
    ! Establish the function
    fcn => fcn1
    call obj%set_fcn(fcn)
 
    ! Solve the equation
    call solver%solve(obj, x, limits, f, ib = tracking)
 
    ! Print the output and the residual
    print '(AF7.5)', "The solution: ", x
    print '(AE10.3)', "The residual: ", f
    print '(AI0)', "Iterations: ", tracking%iter_count
    print '(AI0)', "Function Evaluations: ", tracking%fcn_count
    print '(AI0)', "Derivative Evaluations: ", tracking%jacobian_count
    print '(AL1)', "Converge on Function Value: ", tracking%converge_on_fcn
    print '(AL1)', "Converge on Change in Variable: ", tracking%converge_on_chng
    print '(AL1)', "Converge on Derivative: ", tracking%converge_on_zero_diff
 
contains
    ! The function:
    ! 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 produces the following output.

The solution: 3.14159
The residual:  0.314E-11
Iterations: 3
Function Evaluations: 7
Derivative Evaluations: 4
Converge on Function Value: T
Converge on Change in Variable: F
Converge on Derivative: F

Implements nonlin_core::equation_solver_1var.

Definition at line 591 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