nonlin_core::equation_optimizer Type Reference

A base class for optimization of an equation of multiple variables. More...

Inheritance diagram for nonlin_core::equation_optimizer:

Public Member Functions
procedure, public	get_max_fcn_evals oe_get_max_eval
	Gets the maximum number of function evaluations allowed.
procedure, public	set_max_fcn_evals oe_set_max_eval
	Sets the maximum number of function evaluations allowed.
procedure, public	get_tolerance oe_get_tol
	Gets the tolerance on convergence.
procedure, public	set_tolerance oe_set_tol
	Sets the tolerance on convergence.
procedure, public	get_print_status oe_get_print_status
	Gets a logical value determining if iteration status should be printed.
procedure, public	set_print_status oe_set_print_status
	Sets a logical value determining if iteration status should be printed.
procedure(nonlin_optimize_fcn), deferred, pass, public	solve nonlin_optimize_fcn
	Optimizes the equation.

Public Attributes
real(real64)	m_tol = 1.0d-12
	The error tolerance used to determine convergence.
logical	m_printstatus = .false.
	Set to true to print iteration status; else, false.

Private Attributes
integer(int32)	m_maxeval = 500
	The maximum number of function evaluations allowed.

Detailed Description

A base class for optimization of an equation of multiple variables.

Example

The following example illustrates how to find the minimum of a function of multipler variables by means of the BFGS method.

program example
    use iso_fortran_env
    use nonlin_core
    use nonlin_optimize
    implicit none
 
    ! Local Variables
    type(bfgs) :: solver
    type(fcnnvar_helper) :: obj
    procedure(fcnnvar), pointer :: fcn
    procedure(gradientfcn), pointer :: grad
    real(real64) :: x(2), f
 
    ! Tell the solver where to find the function
    fcn => beale
    grad => bealegrad
    call obj%set_fcn(fcn, 2)
    call obj%set_gradient_fcn(grad)
 
    ! Define an initial guess
    x = 1.0d0
 
    ! Compute the solution
    call solver%solve(obj, x, f)
 
    ! Display the output
    print '(AF7.5AF7.5A)', "Minimum: (", x(1), ", ", x(2), ")"
    print '(AE9.3)', "Function Value: ", f
contains
    ! The Beale function:
    ! f(x) = (1.5 - x + xy)**2 + (2.25 - x + xy**2)**2 + (2.625 - x + xy**3)**2
    ! The minimum is at x = 3, y = 0.5, and f(3, 0.5) = 0
    function beale(x) result(f)
        real(real64), intent(in), dimension(:) :: x
        real(real64) :: f
        f = (1.5d0 - x(1) + x(1) * x(2))**2 + &
            (2.25d0 - x(1) + x(1) * x(2)**2)**2 + &
            (2.625d0 - x(1) + x(1) * x(2)**3)**2
    end function
 
    ! The gradient
    subroutine bealegrad(x, g)
        real(real64), intent(in), dimension(:) :: x
        real(real64), intent(out), dimension(:) :: g
 
        g(1) = 2.0d0 * (x(2)**3 - 1.0d0) * (x(1) * x(2)**3 - x(1) + 2.625d0) + &
            2.0d0 * (x(2)**2 - 1.0d0) * (x(1) * x(2)**2 - x(1) + 2.25d0) + &
            2.0d0 * (x(2) - 1.0d0) * (x(1) * x(2) - x(1) + 1.5d0)
 
        g(2) = 6.0d0 * x(1) * x(2)**2 * (x(1) * x(2)**3 - x(1) + 2.625d0) + &
            4.0d0 * x(1) * x(2) * (x(1) * x(2)**2 - x(1) + 2.25d0) + &
            2.0d0 * x(1) * (x(1) * x(2) - x(1) + 1.5d0)
    end subroutine
end program

The above program produces the following output.

Minimum: (3.00000, 0.50000)
Function Value: 0.999E-28

Definition at line 1767 of file nonlin_core.f90.

Member Function/Subroutine Documentation

get_max_fcn_evals()

procedure, public nonlin_core::equation_optimizer::get_max_fcn_evals

Gets the maximum number of function evaluations allowed.

Syntax

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

Parameters

[in]

this

The equation_optimizer object.

Returns

The maximum number of function evaluations.

Definition at line 1785 of file nonlin_core.f90.

get_print_status()

procedure, public nonlin_core::equation_optimizer::get_print_status

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

Syntax

pure logical get_print_status(class(equation_optimizer) this)

Parameters

[in]

this

The equation_optimizer object.

Returns

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

Definition at line 1826 of file nonlin_core.f90.

get_tolerance()

procedure, public nonlin_core::equation_optimizer::get_tolerance

Gets the tolerance on convergence.

Syntax

pure real(real64) function get_tolerance(class(equation_optimizer) this)

Parameters

[in]

this

The equation_optimizer object.

Returns

The convergence tolerance.

Definition at line 1805 of file nonlin_core.f90.

set_max_fcn_evals()

procedure, public nonlin_core::equation_optimizer::set_max_fcn_evals

Sets the maximum number of function evaluations allowed.

Syntax

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

Parameters

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

Definition at line 1795 of file nonlin_core.f90.

set_print_status()

procedure, public nonlin_core::equation_optimizer::set_print_status

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

Syntax

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

Parameters

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

Definition at line 1837 of file nonlin_core.f90.

set_tolerance()

procedure, public nonlin_core::equation_optimizer::set_tolerance

Sets the tolerance on convergence.

Syntax

subroutine set_tolerance(class(equation_optimizer) this, real(real64) x)

Parameters

[in,out]	this	The equation_optimizer object.
[in]	x	The convergence tolerance.

Definition at line 1815 of file nonlin_core.f90.

solve()

procedure(nonlin_optimize_fcn), deferred, pass, public nonlin_core::equation_optimizer::solve

pure virtual

Optimizes the equation.

Example

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

Implemented in nonlin_optimize::bfgs, and nonlin_optimize::nelder_mead.

Definition at line 1843 of file nonlin_core.f90.

Member Data Documentation

m_maxeval

integer(int32) nonlin_core::equation_optimizer::m_maxeval = 500

private

The maximum number of function evaluations allowed.

Definition at line 1770 of file nonlin_core.f90.

m_printstatus

logical nonlin_core::equation_optimizer::m_printstatus = .false.

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

Definition at line 1774 of file nonlin_core.f90.

m_tol

real(real64) nonlin_core::equation_optimizer::m_tol = 1.0d-12

The error tolerance used to determine convergence.

Definition at line 1772 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