nonlin_core::fcn1var_helper Type Reference

Defines a type capable of encapsulating an equation of one variable of the form: f(x) = 0. More...

Public Member Functions
procedure, public	fcn f1h_fcn
	Executes the routine containing the function to evaluate.
procedure, public	is_fcn_defined f1h_is_fcn_defined
	Tests if the pointer to the function containing the equation to solve has been assigned.
procedure, public	set_fcn f1h_set_fcn
	Establishes a pointer to the routine containing the equations to solve.
procedure, public	is_derivative_defined f1h_is_diff_defined
	Tests if the pointer to the function containing the derivative of the function to solve is defined.
procedure, public	diff f1h_diff_fcn
	Computes the derivative of the function. If a routine for computing the derivative is not defined, the derivative is estimated via finite differences.
procedure, public	set_diff f1h_set_diff

Static Public Attributes
procedure(fcn1var), pointer, nopass	m_diff => null()
	A pointer to a function capable of computing the derivative of m_fcn.

Static Private Attributes
procedure(fcn1var), pointer, nopass	m_fcn => null()
	A pointer to the target fcn1var routine.

Detailed Description

Defines a type capable of encapsulating an equation of one variable of the form: f(x) = 0.

Example

The following example illustrates the use of this type to solve an equation using 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: 3.14159
The residual: -0.751E-11

Definition at line 682 of file nonlin_core.f90.

Member Function/Subroutine Documentation

diff()

procedure, public nonlin_core::fcn1var_helper::diff

Computes the derivative of the function. If a routine for computing the derivative is not defined, the derivative is estimated via finite differences.

Syntax

real(real64) function derivative(class(fcn1var_helper) this, real(real64) x, optional real(real64) f)

Parameters

[in]	this	The fcn1var_helper object.
[in]	x	The value of the independent variable at which the derivative is to be computed.
[in]	f	An optional input specifying the function value at x. If supplied, and the derivative is being estimated numerically, the function will not be evaluated at x.

Definition at line 796 of file nonlin_core.f90.

fcn()

procedure, public nonlin_core::fcn1var_helper::fcn

Executes the routine containing the function to evaluate.

Syntax

real(real64) function fcn(class(fcn1var_helper) this, real(real64) x)

Parameters

[in]	this	The fcn1var_helper object.
[in]	x	The value of the independent variable at which the function should be evaluated.

Returns

The value of the function at x.

Definition at line 700 of file nonlin_core.f90.

is_derivative_defined()

procedure, public nonlin_core::fcn1var_helper::is_derivative_defined

Tests if the pointer to the function containing the derivative of the function to solve is defined.

Syntax

logical function is_derivative_defined(class(fcn1var_helper) this)

Parameters

[in]

this

The fcn1var_helper object.

Returns

Returns true if the pointer has been assigned; else, false.

Definition at line 782 of file nonlin_core.f90.

is_fcn_defined()

procedure, public nonlin_core::fcn1var_helper::is_fcn_defined

Tests if the pointer to the function containing the equation to solve has been assigned.

Syntax

logical function is_fcn_defined(class(fcn1var_helper) this)

Parameters

[in]

this

The fcn1var_helper object.

Returns

Returns true if the pointer has been assigned; else, false.

Definition at line 711 of file nonlin_core.f90.

set_diff()

procedure, public nonlin_core::fcn1var_helper::set_diff

Definition at line 806 of file nonlin_core.f90.

set_fcn()

procedure, public nonlin_core::fcn1var_helper::set_fcn

Establishes a pointer to the routine containing the equations to solve.

Syntax

subroutine set_fcn(class(fcn1var_helper) this, procedure(fcn1var) pointer fcn)

Parameters

[in,out]	this	The fcn1var_helper object.
[in]	fcn	The function pointer.

Example

The following example illustrates how to use this routine to inform the solver of the function to solve. This particular example utilizes Brent's method to compute the solution.

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: 3.14159
The residual: -0.751E-11

Definition at line 771 of file nonlin_core.f90.

Member Data Documentation

m_diff

procedure(fcn1var), pointer, nopass nonlin_core::fcn1var_helper::m_diff => null()

static

A pointer to a function capable of computing the derivative of m_fcn.

Definition at line 687 of file nonlin_core.f90.

m_fcn

procedure(fcn1var), pointer, nopass nonlin_core::fcn1var_helper::m_fcn => null()

staticprivate

A pointer to the target fcn1var routine.

Definition at line 685 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