A base class for various solvers of nonlinear systems of equations. More...

Inheritance diagram for nonlin_core::equation_solver:

Public Member Functions
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.

procedure(nonlin_solver), deferred, pass, public	solve nonlin_solver
	Solves the system of equations.

Public Attributes
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.

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 nonlinear systems of equations.

Example: The following example illustrates the use of the newton_solver type, which includes this type in its inheritance chain, to solve a system of equations. Several options are utilized in the example to illustrate much of the solver functionallity. Notice, many of these options are not necessary to compute the solution; however, they do provide means of control over the solver. For a more minimalistic example see the vecfcn_helper type.
program example

use iso_fortran_env

use nonlin_core

use nonlin_solve

implicit none

! Local Variables

type(vecfcn_helper) :: obj

procedure(vecfcn), pointer :: fcn

type(newton_solver) :: solver

real(real64) :: x(2), f(2)

type(iteration_behavior) :: tracking

! Assign a pointer to the subroutine containing the equations to solve

fcn => fcns

call obj%set_fcn(fcn, 2, 2) ! There are 2 equations with 2 unknowns

! Set up solver parameters

call solver%set_max_fcn_evals(1000) ! Specify the maximum number of function evaluations before iteration termination

call solver%set_fcn_tolerance(1.0d-10)

call solver%set_var_tolerance(1.0d-10)

call solver%set_gradient_tolerance(1.0d-10)

! Tell the solver to print out a status update at each iteration - the default behavior does not print updates

call solver%set_print_status(.true.)

! Define an initial guess

x = 1.0d0 ! Equivalent to x = [1.0d0, 1.0d0]

! Solve the system of equations, but include solver statistics tracking

call solver%solve(obj, x, f, tracking)

! Display the output

print *, ""

print '(AF7.5AF7.5A)', "Solution: (", x(1), ", ", x(2), ")"

print '(AE9.3AE9.3A)', "Residual: (", f(1), ", ", f(2), ")"

print '(AI0)', "Iteration Count: ", tracking%iter_count

print '(AI0)', "Function Evaluations: ", tracking%fcn_count

print '(AI0)', "Jacobian 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 Zero Slope Gradient Vector: ", tracking%converge_on_zero_diff

contains

! Define the routine containing the equations to solve. The equations are:

! x**2 + y**2 = 34

! x**2 - 2 * y**2 = 7

subroutine fcns(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

nonlin_core
nonlin_core
Definition nonlin_core.f90:167

nonlin_solve
nonlin_solve
Definition nonlin_solve.f90:8

The above program produces the following output.
Iteration: 1

Function Evaluations: 3

Jacobian Evaluations: 1

Change in Variable: 0.545E+00

Residual: 0.272E+02

Iteration: 2

Function Evaluations: 5

Jacobian Evaluations: 2

Change in Variable: 0.504E+00

Residual: 0.743E+01

Iteration: 3

Function Evaluations: 6

Jacobian Evaluations: 3

Change in Variable: 0.132E+00

Residual: 0.522E+00

Iteration: 4

Function Evaluations: 7

Jacobian Evaluations: 4

Change in Variable: 0.882E-02

Residual: 0.199E-02

Iteration: 5

Function Evaluations: 8

Jacobian Evaluations: 5

Change in Variable: 0.389E-04

Residual: 0.302E-07

Solution: (5.00000, 3.00000)

Residual: (0.000E+00, 0.000E+00)

Iteration Count: 6

Function Evaluations: 9

Jacobian Evaluations: 6

Converge on Function Value: T

Converge on Change in Variable: F

Converge on Zero Slope Gradient Vector: F

Definition at line 1260 of file nonlin_core.f90.

Member Function/Subroutine Documentation

◆ get_fcn_tolerance()

procedure, public nonlin_core::equation_solver::get_fcn_tolerance

Gets the convergence on function value tolerance.

Syntax: pure real(real64) get_fcn_tolerance(class(equation_solver) this)

Parameters

[in] this The equation_solver object.

Returns: The tolerance value.

Definition at line 1308 of file nonlin_core.f90.

◆ get_gradient_tolerance()

procedure, public nonlin_core::equation_solver::get_gradient_tolerance

Gets the convergence on slope of the gradient vector tolerance.

Syntax: pure real(real64) function get_gradient_tolerance(class(equation_solver))

Parameters

[in] this The equation_solver object.

Returns: The tolerance value.

Definition at line 1357 of file nonlin_core.f90.

◆ get_max_fcn_evals()

procedure, public nonlin_core::equation_solver::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) this)

Parameters

[in] this The equation_solver object.

Returns: The maximum number of function evaluations.

Definition at line 1283 of file nonlin_core.f90.

◆ get_print_status()

procedure, public nonlin_core::equation_solver::get_print_status

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

Syntax: pure logical get_print_status(class(equation_solver) this)

Parameters

[in] this The equation_solver object.

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

Definition at line 1383 of file nonlin_core.f90.

◆ get_var_tolerance()

procedure, public nonlin_core::equation_solver::get_var_tolerance

Gets the convergence on change in variable tolerance.

Syntax: pure real(real64) function get_var_tolerance(class(equation_solver) this)

Parameters

[in] this The equation_solver object.

Returns: The tolerance value.

Definition at line 1332 of file nonlin_core.f90.

◆ set_fcn_tolerance()

procedure, public nonlin_core::equation_solver::set_fcn_tolerance

Sets the convergence on function value tolerance.

Syntax: subroutine set_fcn_tolerance(class(equation_solver) 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 function value tolerance.

Definition at line 1322 of file nonlin_core.f90.

◆ set_gradient_tolerance()

procedure, public nonlin_core::equation_solver::set_gradient_tolerance

Sets the convergence on slope of the gradient vector tolerance.

Syntax: subroutine set_gradient_tolerance(class(equation_solver) 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 1372 of file nonlin_core.f90.

◆ set_max_fcn_evals()

procedure, public nonlin_core::equation_solver::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) this, integer(int32) n)

Parameters

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

Example: See the equation_solver type for an example on how to establish the limit on number of function evaluations.

Definition at line 1298 of file nonlin_core.f90.

◆ set_print_status()

procedure, public nonlin_core::equation_solver::set_print_status

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

Syntax: subroutine set_print_status(class(equation_solver) this, logical x)

Parameters

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

Example: See the equation_solver type for an example on how to enable iteration update printing.

Definition at line 1398 of file nonlin_core.f90.

◆ set_var_tolerance()

procedure, public nonlin_core::equation_solver::set_var_tolerance

Sets the convergence on change in variable tolerance.

Syntax: subroutine set_var_tolerance(class(equation_solver) 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 change in variable tolerance.

Definition at line 1346 of file nonlin_core.f90.

◆ solve()

procedure(nonlin_solver), deferred, pass, public nonlin_core::equation_solver::solve

pure virtual

Solves the system of equations.

Example: See the equation_solver type for an example on how to solve a system of equations.

Implemented in nonlin_solve::newton_solver, and nonlin_solve::quasi_newton_solver.

Definition at line 1404 of file nonlin_core.f90.

Member Data Documentation

◆ m_fcntol

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

The convergence criteria on function values.

Definition at line 1265 of file nonlin_core.f90.

◆ m_gtol

real(real64) nonlin_core::equation_solver::m_gtol = 1.0d-12

The convergence criteria for the slope of the gradient vector.

Definition at line 1269 of file nonlin_core.f90.

◆ m_maxeval

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

private

The maximum number of function evaluations allowed per solve.

Definition at line 1263 of file nonlin_core.f90.

◆ m_printstatus

logical nonlin_core::equation_solver::m_printstatus = .false.

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

Definition at line 1271 of file nonlin_core.f90.

◆ m_xtol

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

The convergence criteria on change in variable values.

Definition at line 1267 of file nonlin_core.f90.

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

D:/Code/nonlin/src/nonlin_core.f90

Public Member Functions

Public Attributes

Private Attributes

Detailed Description

Member Function/Subroutine Documentation

◆ get_fcn_tolerance()

◆ get_gradient_tolerance()

◆ get_max_fcn_evals()

◆ get_print_status()

◆ get_var_tolerance()

◆ set_fcn_tolerance()

◆ set_gradient_tolerance()

◆ set_max_fcn_evals()

◆ set_print_status()

◆ set_var_tolerance()

◆ solve()

Member Data Documentation

◆ m_fcntol

◆ m_gtol

◆ m_maxeval

◆ m_printstatus

◆ m_xtol