nonlin_core::equation_solver_1var Type Reference

A base class for various solvers of equations of one variable. More...

Inheritance diagram for nonlin_core::equation_solver_1var:

Public Member Functions
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(nonlin_solver_1var), deferred, pass, public	solve nonlin_solver_1var
	Solves the equation.
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.

Public Attributes
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.

Private Attributes
integer(int32)	m_maxeval = 100
	The maximum number of function evaluations allowed per solve.

Detailed Description

A base class for various solvers of equations of one variable.

Example

The following example illustrates the solution of an equation of one variable by means of Brent's method.

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(brent_solver) :: solver
    real(real64) :: x, f
    type(value_pair) :: limits
 
    ! 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)
 
    ! Print the output and the residual
    print '(AF7.5)', "The solution: ", x
    print '(AE10.3)', "The residual: ", f
 
contains
    ! The function:
    ! f(x) = sin(x) / x, solution: x = x * 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: 3.15159
The residual: -0.751E-11

Definition at line 1512 of file nonlin_core.f90.

Member Function/Subroutine Documentation

get_diff_tolerance()

procedure, public nonlin_core::equation_solver_1var::get_diff_tolerance

Gets the convergence on slope of the function (derivative) tolerance.

Syntax

pure real(real64) function get_diff_tolerance(class(equation_solver_1var) this)

Parameters

[in]

this

The equation_solver object.

Returns

The tolerance value.

Definition at line 1625 of file nonlin_core.f90.

get_fcn_tolerance()

procedure, public nonlin_core::equation_solver_1var::get_fcn_tolerance

Gets the convergence on function value tolerance.

Syntax

pure real(real64) function get_fcn_tolerance(class(equation_solver_1var) this)

Parameters

[in]

this

The equation_solver_1var object.

Returns

The tolerance value.

Definition at line 1556 of file nonlin_core.f90.

get_max_fcn_evals()

procedure, public nonlin_core::equation_solver_1var::get_max_fcn_evals

Gets the maximum number of function evaluations allowed during a single solve.

Syntax

pure integer(int32) function get_max_fcn_evals(class(equation_solver_1var) this)

Parameters

[in]

this

The equation_solver_1var object.

Returns

The maximum number of function evaluations.

Definition at line 1535 of file nonlin_core.f90.

get_print_status()

procedure, public nonlin_core::equation_solver_1var::get_print_status

Gets a logical value determining if iteration status should be printed.

Syntax

pure logical function get_print_status(class(equation_solver_1var) this)

Parameters

[in]

this

The equation_solver_1var object.

Returns

True if the iteration status should be printed; else, false.

Definition at line 1597 of file nonlin_core.f90.

get_var_tolerance()

procedure, public nonlin_core::equation_solver_1var::get_var_tolerance

Gets the convergence on change in variable tolerance.

Syntax

pure real(real64) function get_var_tolerance(class(equation_solver_1var) this)

Parameters

[in]

this

The equation_solver_1var object.

Returns

The tolerance value.

Definition at line 1576 of file nonlin_core.f90.

set_diff_tolerance()

procedure, public nonlin_core::equation_solver_1var::set_diff_tolerance

Sets the convergence on slope of the function (derivative) tolerance.

Syntax

subroutine set_diff_tolerance(class(equation_solver_1var) this, real(real64) x)

Parameters

[in,out]	this	The equation_solver object.
[in]	x	The tolerance value.

Example

See the equation_solver type for an example on how to establish the gradient vector slope tolerance.

Definition at line 1640 of file nonlin_core.f90.

set_fcn_tolerance()

procedure, public nonlin_core::equation_solver_1var::set_fcn_tolerance

Sets the convergence on function value tolerance.

Syntax

subroutine set_fcn_tolerance(class(equation_solver_1var) this, real(real64) x)

Parameters

[in,out]	this	The equation_solver_1var object.
[in]	x	The tolerance value.

Definition at line 1566 of file nonlin_core.f90.

set_max_fcn_evals()

procedure, public nonlin_core::equation_solver_1var::set_max_fcn_evals

Sets the maximum number of function evaluations allowed during a single solve.

Syntax

subroutine set_max_fcn_evals(class(equation_solver_1var) this, integer(int32) n)

Parameters

[in,out]	this	The equation_solver_1var object.
[in]	n	The maximum number of function evaluations.

Definition at line 1546 of file nonlin_core.f90.

set_print_status()

procedure, public nonlin_core::equation_solver_1var::set_print_status

Sets a logical value determining if iteration status should be printed.

Syntax

subroutine set_print_status(class(equation_solver_1var) this, logical x)

Parameters

[in,out]	this	The equation_solver_1var object.
[in]	x	True if the iteration status should be printed; else, false.

Definition at line 1608 of file nonlin_core.f90.

set_var_tolerance()

procedure, public nonlin_core::equation_solver_1var::set_var_tolerance

Sets the convergence on change in variable tolerance.

Syntax

subroutine set_var_tolerance(class(equation_solver_1var) this, real(real64) x)

Parameters

[in,out]	this	The equation_solver_1var object.
[in]	x	The tolerance value.

Definition at line 1586 of file nonlin_core.f90.

solve()

procedure(nonlin_solver_1var), deferred, pass, public nonlin_core::equation_solver_1var::solve

pure virtual

Solves the equation.

Example

See the equation_solver_1var type for an example on how to solve a system of equations.

Implemented in nonlin_solve::brent_solver, and nonlin_solve::newton_1var_solver.

Definition at line 1614 of file nonlin_core.f90.

Member Data Documentation

m_difftol

real(real64) nonlin_core::equation_solver_1var::m_difftol = 1.0d-12

The convergence criteria on the slope of the function (derivative)

Definition at line 1521 of file nonlin_core.f90.

m_fcntol

real(real64) nonlin_core::equation_solver_1var::m_fcntol = 1.0d-8

The convergence criteria on function value.

Definition at line 1517 of file nonlin_core.f90.

m_maxeval

integer(int32) nonlin_core::equation_solver_1var::m_maxeval = 100

private

The maximum number of function evaluations allowed per solve.

Definition at line 1515 of file nonlin_core.f90.

m_printstatus

logical nonlin_core::equation_solver_1var::m_printstatus = .false.

Set to true to print iteration status; else, false.

Definition at line 1523 of file nonlin_core.f90.

m_xtol

real(real64) nonlin_core::equation_solver_1var::m_xtol = 1.0d-12

The convergence criteria on change in variable value.

Definition at line 1519 of file nonlin_core.f90.

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

• D:/Code/nonlin/src/nonlin_core.f90