nonlin_solve::newton_solver Type Reference

Defines a Newton solver. More...

Inheritance diagram for nonlin_solve::newton_solver:

Public Member Functions
procedure, public	solve ns_solve
	Applies Newton's method in conjunction with a backtracking type line search to solve N equations of N unknowns.
Public Member Functions inherited from nonlin_solve::line_search_solver
procedure, public	get_line_search lss_get_line_search
	Gets the line search module.
procedure, public	set_line_search lss_set_line_search
	Sets the line search module.
procedure, public	set_default_line_search lss_set_default
	Establishes a default line_search object for the line search module.
procedure, public	is_line_search_defined lss_is_line_search_defined
	Tests to see if a line search module is defined.
procedure, public	get_use_line_search lss_get_use_search
	Gets a value determining if a line-search should be employed.
procedure, public	set_use_line_search lss_set_use_search
	Sets a value determining if a line-search should be employed.
Public Member Functions inherited from nonlin_core::equation_solver
procedure, public	get_max_fcn_evals es_get_max_eval
	Gets the maximum number of function evaluations allowed during a single solve.
procedure, public	set_max_fcn_evals es_set_max_eval
	Sets the maximum number of function evaluations allowed during a single solve.
procedure, public	get_fcn_tolerance es_get_fcn_tol
	Gets the convergence on function value tolerance.
procedure, public	set_fcn_tolerance es_set_fcn_tol
	Sets the convergence on function value tolerance.
procedure, public	get_var_tolerance es_get_var_tol
	Gets the convergence on change in variable tolerance.
procedure, public	set_var_tolerance es_set_var_tol
	Sets the convergence on change in variable tolerance.
procedure, public	get_gradient_tolerance es_get_grad_tol
	Gets the convergence on slope of the gradient vector tolerance.
procedure, public	set_gradient_tolerance es_set_grad_tol
	Sets the convergence on slope of the gradient vector tolerance.
procedure, public	get_print_status es_get_print_status
	Gets a logical value determining if iteration status should be printed.
procedure, public	set_print_status es_set_print_status
	Sets a logical value determining if iteration status should be printed.

Additional Inherited Members
Public Attributes inherited from nonlin_solve::line_search_solver
logical	m_uselinesearch = .true.
	Set to true if a line search should be used regardless of the status of m_lineSearch.
Public Attributes inherited from nonlin_core::equation_solver
real(real64)	m_fcntol = 1.0d-8
	The convergence criteria on function values.
real(real64)	m_xtol = 1.0d-12
	The convergence criteria on change in variable values.
real(real64)	m_gtol = 1.0d-12
	The convergence criteria for the slope of the gradient vector.
logical	m_printstatus = .false.
	Set to true to print iteration status; else, false.

Detailed Description

Defines a Newton solver.

Definition at line 287 of file nonlin_solve.f90.

Member Function/Subroutine Documentation

solve()

procedure, public nonlin_solve::newton_solver::solve

virtual

Applies Newton's method in conjunction with a backtracking type line search to solve N equations of N unknowns.

Syntax

subroutine solve(class(newton_solver) this, class(vecfcn_helper) fcn, real(real64) x(:), real(real64) fvec(:), optional type(iteration_behavior) ib, optional class(errors) err)

Parameters

[in,out]	this	The equation_solver-based object.
[in]	fcn	The vecfcn_helper object containing the equations to solve.
[in,out]	x	On input, an N-element array containing an initial estimate to the solution. On output, the updated solution estimate. N is the number of variables.
[out]	fvec	An N-element array that, on output, will contain the values of each equation as evaluated at the variable values given in 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_ARRAY_SIZE_ERROR: Occurs if any of the input arrays are not sized correctly. NL_DIVERGENT_BEHAVIOR_ERROR: Occurs if the direction vector is pointing in an apparent uphill direction. NL_CONVERGENCE_ERROR: Occurs if the line search cannot converge within the allowed number of iterations. NL_OUT_OF_MEMORY_ERROR: Occurs if there is insufficient memory available. NL_SPURIOUS_CONVERGENCE_ERROR: Occurs as a warning if the slope of the gradient vector becomes sufficiently close to zero.

Example

The following code provides an example of how to solve a system of N equations of N unknonwns using Newton's method.

program main
    use nonlin_core, only : vecfcn, vecfcn_helper
    use nonlin_solve, only : newton_solver
 
    type(vecfcn_helper) :: obj
    procedure(vecfcn), pointer :: fcn
    type(newton_solver) :: solver
    real(real64) :: x(2), f(2)
 
    ! Set the initial conditions to [1, 1]
    x = 1.0d0
 
    ! Define the function
    fcn => fcn1
    call obj%set_fcn(fcn, 2, 2)
 
    ! Solve the system of equations.  The solution overwrites X
    call solver%solve(obj, x, f)
 
    ! Print the output and the residual:
    print '(AF5.3AF5.3A)', "The solution: (", x(1), ", ", x(2), ")"
    print '(AE8.3AE8.3A)', "The residual: (", f(1), ", ", f(2), ")"
contains
    ! System of Equations:
    !
    ! x**2 + y**2 = 34
    ! x**2 - 2 * y**2 = 7
    !
    ! Solution:
    ! x = +/-5
    ! y = +/-3
    subroutine fcn1(x, f)
        real(real64), intent(in), dimension(:) :: x
        real(real64), intent(out), dimension(:) :: f
        f(1) = x(1)**2 + x(2)**2 - 34.0d0
        f(2) = x(1)**2 - 2.0d0 * x(2)**2 - 7.0d0
    end subroutine
end program

The above program returns the following results.

The solution: (5.000, 3.000)
The residual: (.000E+00, .000E+00)

See Also

• Wikipedia

Implements nonlin_core::equation_solver.

Definition at line 378 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