line_search – NONLIN

type, public :: line_search

Defines a type capable of performing an inexact, backtracking line search to find a point as far along the specified direction vector that is usable for unconstrained minimization problems.

Type-Bound Procedures

get_distance_factor get_max_fcn_evals get_scaling_factor ls_search_mimo ls_search_miso search set_distance_factor set_max_fcn_evals set_scaling_factor

Type-Bound Procedures

procedure, public :: get_distance_factor => ls_get_dist

private pure function ls_get_dist(this) result(x)

Gets a distance factor defining the minimum distance along the search direction vector is practical.

Arguments

Type	Intent	Optional	Attributes		Name
class(line_search),	intent(in)			::	this	The line_search object.

Return Value real(kind=real64)

The distance factor. A value of 1 indicates the full length of the vector.

procedure, public :: get_max_fcn_evals => ls_get_max_eval

private pure function ls_get_max_eval(this) result(n)

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

Arguments

Type	Intent	Optional	Attributes		Name
class(line_search),	intent(in)			::	this	The line_search object.

Return Value integer(kind=int32)

The maximum number of function evaluations.

procedure, public :: get_scaling_factor => ls_get_scale

private pure function ls_get_scale(this) result(x)

Gets the scaling of the product of the gradient and direction vectors $\alpha$ such that $f(\vec{x} + \lambda \vec{p}) \le f(\vec{x}) + \lambda \alpha \vec{p}^{T} \vec{g}$ , where $\vec{p}$ is the search direction vector, $\vec{g}$ is the gradient vector, and $\lambda$ is the scaling factor.

Arguments

Type	Intent	Optional	Attributes		Name
class(line_search),	intent(in)			::	this	The line_search object.

Return Value real(kind=real64)

The scaling factor.

procedure, public, :: ls_search_mimo

private subroutine ls_search_mimo(this, fcn, xold, grad, dir, x, fvec, fold, fx, ib, err)

Utilizes an inexact, backtracking line search to find a point as far along the specified direction vector that is usable for unconstrained minimization problems.

Arguments

Type	Intent	Optional	Attributes		Name
class(line_search),	intent(in)			::	this	The line_search object.
class(vecfcn_helper),	intent(in)			::	fcn	A vecfcn_helper object containing the system of equations.
real(kind=real64),	intent(in),		dimension(:)	::	xold	An N-element array defining the initial point, where N is the number of variables.
real(kind=real64),	intent(in),		dimension(:)	::	grad	An N-element array defining the gradient of fcn evaluated at xold.
real(kind=real64),	intent(in),		dimension(:)	::	dir	An N-element array defining the search direction.
real(kind=real64),	intent(out),		dimension(:)	::	x	An N-element array where the updated solution point will be written.
real(kind=real64),	intent(out),		dimension(:)	::	fvec	An M-element array containing the M equation values evaluated at x, where M is the number of equations.
real(kind=real64),	intent(in),	optional		::	fold	An optional input that provides the value resulting from: $\frac{1}{2} \vec{f_{old}} \cdot \vec{f_{old}}$ . If not provided, fcn is evalauted at xold, and the aforementioned relationship is computed.
real(kind=real64),	intent(out),	optional		::	fx	The result of the operation: $\frac{1}{2} \vec{f} \cdot \vec{f}$ .
type(iteration_behavior),		optional		::	ib	An optional output, that if provided, allows the caller to obtain iteration performance statistics.
class(errors),	intent(inout),	optional,	target	::	err	An error handling object.

procedure, public, :: ls_search_miso

private subroutine ls_search_miso(this, fcn, xold, grad, dir, x, fold, fx, ib, err)

Utilizes an inexact, backtracking line search to find a point as far along the specified direction vector that is usable for unconstrained minimization problems.

Arguments

Type	Intent	Optional	Attributes		Name
class(line_search),	intent(in)			::	this	The line_search object.
class(fcnnvar_helper),	intent(in)			::	fcn	A fcnnvar_helper object containing the system of equations.
real(kind=real64),	intent(in),		dimension(:)	::	xold	An N-element array defining the initial point, where N is the number of variables.
real(kind=real64),	intent(in),		dimension(:)	::	grad	An N-element array defining the gradient of fcn evaluated at xold.
real(kind=real64),	intent(in),		dimension(:)	::	dir	An N-element array defining the search direction.
real(kind=real64),	intent(out),		dimension(:)	::	x	An N-element array where the updated solution point will be written.
real(kind=real64),	intent(in),	optional		::	fold	An optional input that provides the function value at xold. If not provided, fcn is evalauted at xold.
real(kind=real64),	intent(out),	optional		::	fx	The value of the function as evaluated at x.
type(iteration_behavior),		optional		::	ib	An optional output, that if provided, allows the caller to obtain iteration performance statistics.
class(errors),	intent(inout),	optional,	target	::	err	An error handling object.

generic, public :: search => ls_search_mimo, ls_search_miso

private subroutine ls_search_mimo(this, fcn, xold, grad, dir, x, fvec, fold, fx, ib, err)

Utilizes an inexact, backtracking line search to find a point as far along the specified direction vector that is usable for unconstrained minimization problems.

Arguments

Type	Intent	Optional	Attributes		Name
class(line_search),	intent(in)			::	this	The line_search object.
class(vecfcn_helper),	intent(in)			::	fcn	A vecfcn_helper object containing the system of equations.
real(kind=real64),	intent(in),		dimension(:)	::	xold	An N-element array defining the initial point, where N is the number of variables.
real(kind=real64),	intent(in),		dimension(:)	::	grad	An N-element array defining the gradient of fcn evaluated at xold.
real(kind=real64),	intent(in),		dimension(:)	::	dir	An N-element array defining the search direction.
real(kind=real64),	intent(out),		dimension(:)	::	x	An N-element array where the updated solution point will be written.
real(kind=real64),	intent(out),		dimension(:)	::	fvec	An M-element array containing the M equation values evaluated at x, where M is the number of equations.
real(kind=real64),	intent(in),	optional		::	fold	An optional input that provides the value resulting from: $\frac{1}{2} \vec{f_{old}} \cdot \vec{f_{old}}$ . If not provided, fcn is evalauted at xold, and the aforementioned relationship is computed.
real(kind=real64),	intent(out),	optional		::	fx	The result of the operation: $\frac{1}{2} \vec{f} \cdot \vec{f}$ .
type(iteration_behavior),		optional		::	ib	An optional output, that if provided, allows the caller to obtain iteration performance statistics.
class(errors),	intent(inout),	optional,	target	::	err	An error handling object.

private subroutine ls_search_miso(this, fcn, xold, grad, dir, x, fold, fx, ib, err)

Utilizes an inexact, backtracking line search to find a point as far along the specified direction vector that is usable for unconstrained minimization problems.

Arguments

Type	Intent	Optional	Attributes		Name
class(line_search),	intent(in)			::	this	The line_search object.
class(fcnnvar_helper),	intent(in)			::	fcn	A fcnnvar_helper object containing the system of equations.
real(kind=real64),	intent(in),		dimension(:)	::	xold	An N-element array defining the initial point, where N is the number of variables.
real(kind=real64),	intent(in),		dimension(:)	::	grad	An N-element array defining the gradient of fcn evaluated at xold.
real(kind=real64),	intent(in),		dimension(:)	::	dir	An N-element array defining the search direction.
real(kind=real64),	intent(out),		dimension(:)	::	x	An N-element array where the updated solution point will be written.
real(kind=real64),	intent(in),	optional		::	fold	An optional input that provides the function value at xold. If not provided, fcn is evalauted at xold.
real(kind=real64),	intent(out),	optional		::	fx	The value of the function as evaluated at x.
type(iteration_behavior),		optional		::	ib	An optional output, that if provided, allows the caller to obtain iteration performance statistics.
class(errors),	intent(inout),	optional,	target	::	err	An error handling object.

procedure, public :: set_distance_factor => ls_set_dist

private subroutine ls_set_dist(this, x)

Sets a distance factor defining the minimum distance along the search direction vector is practical.

Arguments

Type	Intent	Optional	Attributes		Name
class(line_search),	intent(inout)			::	this	The line_search object.
real(kind=real64),	intent(in)			::	x	The distance factor. A value of 1 indicates the full length of the vector. Notice, this value is restricted to lie in the set [0.1, 1.0).

procedure, public :: set_max_fcn_evals => ls_set_max_eval

private subroutine ls_set_max_eval(this, x)

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

Arguments

Type	Intent	Optional	Attributes		Name
class(line_search),	intent(inout)			::	this	The line_search object.
integer(kind=int32),	intent(in)			::	x	The maximum number of function evaluations.

procedure, public :: set_scaling_factor => ls_set_scale

private subroutine ls_set_scale(this, x)

Sets the scaling of the product of the gradient and direction vectors $\alpha$ such that $f(\vec{x} + \lambda \vec{p}) \le f(\vec{x}) + \lambda \alpha \vec{p}^{T} \vec{g}$ , where $\vec{p}$ is the search direction vector, $\vec{g}$ is the gradient vector, and $\lambda$ is the scaling factor.

Arguments

Type	Intent	Optional	Attributes		Name
class(line_search),	intent(inout)			::	this	The line_search object.
real(kind=real64),	intent(in)			::	x	The scaling factor.

line_search Derived Type

Contents

Type-Bound Procedures

type, public :: line_search

Contents

Type-Bound Procedures

Type-Bound Procedures

procedure, public :: get_distance_factor => ls_get_dist

private pure function ls_get_dist(this) result(x)

Arguments

Return Value real(kind=real64)

procedure, public :: get_max_fcn_evals => ls_get_max_eval

private pure function ls_get_max_eval(this) result(n)

Arguments

Return Value integer(kind=int32)

procedure, public :: get_scaling_factor => ls_get_scale

private pure function ls_get_scale(this) result(x)

Arguments

Return Value real(kind=real64)

procedure, public, :: ls_search_mimo

private subroutine ls_search_mimo(this, fcn, xold, grad, dir, x, fvec, fold, fx, ib, err)

Arguments

procedure, public, :: ls_search_miso

private subroutine ls_search_miso(this, fcn, xold, grad, dir, x, fold, fx, ib, err)

Arguments

generic, public :: search => ls_search_mimo, ls_search_miso

private subroutine ls_search_mimo(this, fcn, xold, grad, dir, x, fvec, fold, fx, ib, err)

Arguments

private subroutine ls_search_miso(this, fcn, xold, grad, dir, x, fold, fx, ib, err)

Arguments

procedure, public :: set_distance_factor => ls_set_dist

private subroutine ls_set_dist(this, x)

Arguments

procedure, public :: set_max_fcn_evals => ls_set_max_eval

private subroutine ls_set_max_eval(this, x)

Arguments

procedure, public :: set_scaling_factor => ls_set_scale

private subroutine ls_set_scale(this, x)

Arguments