Module NEWTON

Some simple Newton solvers

Uses

- MODgvec_Globals
Help

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Used by

Help

Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Interfaces

public interface NewtonMin1D

public interface NewtonMin1D()

Arguments
None

public interface NewtonRoot1D

public interface NewtonRoot1D()

Arguments
None

public interface NewtonRoot1D_FdF

public interface NewtonRoot1D_FdF()

Arguments
None

public interface NewtonMin2D

public interface NewtonMin2D()

Arguments
None

public interface NewtonRoot2D

public interface NewtonRoot2D()

Arguments
None

public interface t_newton_Root1D_wrap_Min1D

public function newton_Root1D_wrap_Min1D_new(parent) result(sf)

constructor for the Min1D type wrapped for Root1D

Arguments

Type	Intent	Optional	Attributes		Name
class(c_newton_Min1D),	intent(in)			::	parent

Return Value type(t_newton_Root1D_wrap_Min1D)

Abstract Interfaces

abstract interface

public function i_newton_Min1D(sf, x) result(y1x1)

Arguments

Type	Intent	Optional	Attributes		Name
class(c_newton_Min1D),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	x

Return Value real(kind=wp)

abstract interface

public function i_newton_Root1D(sf, x) result(y1x1)

Arguments

Type	Intent	Optional	Attributes		Name
class(c_newton_Root1D),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	x

Return Value real(kind=wp)

abstract interface

public function i_newton_Root1D_FdF(sf, x) result(y2x1)

Arguments

Type	Intent	Optional	Attributes		Name
class(c_newton_Root1D_FdF),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	x

Return Value real(kind=wp), (2)

abstract interface

public function i_newton_Min2D_FR(sf, x) result(y1x2)

Arguments

Type	Intent	Optional	Attributes		Name
class(c_newton_Min2D),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	x(2)

Return Value real(kind=wp)

abstract interface

public function i_newton_Min2D_dFR(sf, x) result(y2x2)

Arguments

Type	Intent	Optional	Attributes		Name
class(c_newton_Min2D),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	x(2)

Return Value real(kind=wp), (2)

abstract interface

public function i_newton_Min2D_ddFR(sf, x) result(y22x2)

Arguments

Type	Intent	Optional	Attributes		Name
class(c_newton_Min2D),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	x(2)

Return Value real(kind=wp), (2,2)

abstract interface

public function i_newton_Root2D_FR(sf, x) result(y2x2)

Arguments

Type	Intent	Optional	Attributes		Name
class(c_newton_Root2D),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	x(2)

Return Value real(kind=wp), (2)

abstract interface

public function i_newton_Root2D_dFR(sf, x) result(y22x2)

Arguments

Type	Intent	Optional	Attributes		Name
class(c_newton_Root2D),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	x(2)

Return Value real(kind=wp), (2,2)

Derived Types

type, public, ABSTRACT :: c_newton_Min1D

Type-Bound Procedures

procedure(i_newton_Min1D), public, deferred :: FR
procedure(i_newton_Min1D), public, deferred :: dFR
procedure(i_newton_Min1D), public, deferred :: ddFR

type, public, ABSTRACT :: c_newton_Root1D

Type-Bound Procedures

procedure(i_newton_Root1D), public, deferred :: FR
procedure(i_newton_Root1D), public, deferred :: dFR

type, public, extends(c_newton_Root1D) :: t_newton_Root1D_wrap_Min1D

This functional wraps a functional passed to Min1D for use with Root1D (returns the derivative: FR -> dFR, dFR -> ddFR)

Components

Type	Visibility	Attributes		Name		Initial
class(c_newton_Min1D),	public,	ALLOCATABLE	::	parent

Constructor

public function newton_Root1D_wrap_Min1D_new (parent)	constructor for the Min1D type wrapped for Root1D

Type-Bound Procedures

procedure, public :: FR => newton_Root1D_wrap_Min1D_FR
procedure, public :: dFR => newton_Root1D_wrap_Min1D_dFR

type, public, ABSTRACT :: c_newton_Root1D_FdF

Type-Bound Procedures

procedure(i_newton_Root1D_FdF), public, deferred :: FRdFR

type, public, ABSTRACT :: c_newton_Min2D

Type-Bound Procedures

procedure(i_newton_Min2D_FR), public, deferred :: FR
procedure(i_newton_Min2D_dFR), public, deferred :: dFR
procedure(i_newton_Min2D_ddFR), public, deferred :: ddFR

type, public, ABSTRACT :: c_newton_Root2D

Type-Bound Procedures

procedure(i_newton_Root2D_FR), public, deferred :: FR
procedure(i_newton_Root2D_dFR), public, deferred :: dFR

Functions

public function NewtonMin1D(tol, a, b, maxstep, x, fobj) result(fmin)

Newton's iterative algorithm to find the minimimum of function f(x) in the interval [a,b], using df(x)=0 and the derivative

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	tol	abort tolerance
real(kind=wp),	intent(in)	::	a	search interval
real(kind=wp),	intent(in)	::	b	search interval
real(kind=wp),	intent(in)	::	maxstep	max\|dx\| allowed
real(kind=wp),	intent(inout)	::	x	initial guess on input, result on output
class(c_newton_Min1D),	intent(in)	::	fobj	functional to minimize with f(x), d/dx f(x), d^2/dx^2 f(x)

Return Value real(kind=wp)

on output =f(x)

public function newton_Root1D_wrap_Min1D_new(parent) result(sf)

constructor for the Min1D type wrapped for Root1D

Arguments

Type	Intent	Optional	Attributes		Name
class(c_newton_Min1D),	intent(in)			::	parent

Return Value type(t_newton_Root1D_wrap_Min1D)

public function newton_Root1D_wrap_Min1D_FR(sf, x) result(y1x1)

f(x) function of the Min1D type wrapped for Root1D

Arguments

Type	Intent	Optional	Attributes		Name
class(t_newton_Root1D_wrap_Min1D),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	x

Return Value real(kind=wp)

public function newton_Root1D_wrap_Min1D_dFR(sf, x) result(y1x1)

d/dx f(x) function of the Min1D type wrapped for Root1D

Arguments

Type	Intent	Optional	Attributes		Name
class(t_newton_Root1D_wrap_Min1D),	intent(in)			::	sf
real(kind=wp),	intent(in)			::	x

Return Value real(kind=wp)

public function NewtonRoot1D(tol, a, b, maxstep, xin, F0, fobj) result(xout)

Newton's iterative algorithm to find the root of function FR(x(:)) in the interval [a(:),b(:)], using d/dx(:)F(x)=0 and the derivative

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	tol	abort tolerance
real(kind=wp),	intent(in)	::	a	search interval
real(kind=wp),	intent(in)	::	b	search interval
real(kind=wp),	intent(in)	::	maxstep	max\|dx\| allowed
real(kind=wp),	intent(in)	::	xin	initial guess
real(kind=wp),	intent(in)	::	F0	function to find root is FR(x)-F0
class(c_newton_Root1D)		::	fobj

Return Value real(kind=wp)

on output =f(x)

public function NewtonRoot1D_FdF(tol, a, b, maxstep, xin, F0, fobj) result(xout)

Newton's iterative algorithm to find the root of function FR(x(:)) in the interval [a(:),b(:)], using d/dx(:)F(x)=0 and the derivative

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	tol	abort tolerance
real(kind=wp),	intent(in)	::	a	search interval
real(kind=wp),	intent(in)	::	b	search interval
real(kind=wp),	intent(in)	::	maxstep	max\|dx\| allowed
real(kind=wp),	intent(in)	::	xin	initial guess on input
real(kind=wp),	intent(in)	::	F0	function to find root is FR(x)-F0
class(c_newton_Root1D_FdF)		::	fobj	function to find root f(x) & derivative d/dx f(x) as FRdFR method

Return Value real(kind=wp)

output x for f(x)=0

public function NewtonMin2D(tol, a, b, x, fobj) result(fmin)

Newton's iterative algorithm to find the minimimum of function f(x,y) in the interval x(i)[a(i),b(i)], using grad(f(x)=0 and the derivative

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	tol	abort tolerance
real(kind=wp),	intent(in)	::	a(2)	search interval (2D)
real(kind=wp),	intent(in)	::	b(2)	search interval (2D)
real(kind=wp),	intent(inout)	::	x(2)	initial guess on input, result on output
class(c_newton_Min2D)		::	fobj	functional f(x,y) to minimize with f, f', f''

Return Value real(kind=wp)

on output =f(x,y)

public function NewtonRoot2D(tol, a, b, maxstep, xin, fobj) result(xout)

Newton's iterative algorithm to find the root of function [f1(x1,x2),f2(x1,x2)]=[0,0] in the interval a(i)<=x(i)<=b(i), using the Jacobian dfi/dxj, i=1,2, j=1,2, such that fi(x1,x2)=fi(x1_0,x2_0)+ [dfi/dx1,dfi/dx2].[dx1,dx2] in each step, we find dx1,dx2 st -[[dfi/dxj]] dxj =fi(x1_0,x2_0)

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	tol	abort tolerance
real(kind=wp),	intent(in)	::	a(2)	search interval (2D)
real(kind=wp),	intent(in)	::	b(2)	search interval (2D)
real(kind=wp),	intent(in)	::	maxstep(2)	max\|dx\| allowed
real(kind=wp),	intent(in)	::	xin(2)	initial guess
class(c_newton_Root2D)		::	fobj	function to find root f1(x1,x2)=0,f2(x1,x2)=0 and derivatives d fi(x1,x2)/dxj

Return Value real(kind=wp), (2)

x1,x2 that have f1(x1,x2)=0 and f2(x1,x2)=0

MODgvec_Newton Module

Contents

Interfaces

Abstract Interfaces

Derived Types

Functions

Module NEWTON

Uses

Used by

Interfaces

public interface NewtonMin1D

public interface NewtonMin1D()

Arguments

public interface NewtonRoot1D

public interface NewtonRoot1D()

Arguments

public interface NewtonRoot1D_FdF

public interface NewtonRoot1D_FdF()

Arguments

public interface NewtonMin2D

public interface NewtonMin2D()

Arguments

public interface NewtonRoot2D

public interface NewtonRoot2D()

Arguments

public interface t_newton_Root1D_wrap_Min1D

public function newton_Root1D_wrap_Min1D_new(parent) result(sf)

Arguments

Return Value type(t_newton_Root1D_wrap_Min1D)

Abstract Interfaces

abstract interface

public function i_newton_Min1D(sf, x) result(y1x1)

Arguments

Return Value real(kind=wp)

abstract interface

public function i_newton_Root1D(sf, x) result(y1x1)

Arguments

Return Value real(kind=wp)

abstract interface

public function i_newton_Root1D_FdF(sf, x) result(y2x1)

Arguments

Return Value real(kind=wp), (2)

abstract interface

public function i_newton_Min2D_FR(sf, x) result(y1x2)

Arguments

Return Value real(kind=wp)

abstract interface

public function i_newton_Min2D_dFR(sf, x) result(y2x2)

Arguments

Return Value real(kind=wp), (2)

abstract interface

public function i_newton_Min2D_ddFR(sf, x) result(y22x2)

Arguments

Return Value real(kind=wp), (2,2)

abstract interface

public function i_newton_Root2D_FR(sf, x) result(y2x2)

Arguments

Return Value real(kind=wp), (2)

abstract interface

public function i_newton_Root2D_dFR(sf, x) result(y22x2)

Arguments

Return Value real(kind=wp), (2,2)

Derived Types

type, public, ABSTRACT :: c_newton_Min1D

Type-Bound Procedures

type, public, ABSTRACT :: c_newton_Root1D

Type-Bound Procedures

type, public, extends(c_newton_Root1D) :: t_newton_Root1D_wrap_Min1D

Components

Constructor

Type-Bound Procedures

type, public, ABSTRACT :: c_newton_Root1D_FdF

Type-Bound Procedures

type, public, ABSTRACT :: c_newton_Min2D

Type-Bound Procedures

type, public, ABSTRACT :: c_newton_Root2D

Type-Bound Procedures

Functions

public function NewtonMin1D(tol, a, b, maxstep, x, fobj) result(fmin)

Arguments