Solves a non-linear system of the form A(X)=Y. More...

#include <newton.hh>

Inheritance diagram for concepts::Newton< F >:

Public Types
typedef Cmplxtype< F >::type	c_type
	Real type of data type. More...

typedef Realtype< F >::type	r_type
	Real type of data type. More...

Public Member Functions
virtual void	apply_ ()
	Intrinsic application method without argument. More...

virtual void	apply_ (const Vector< typename F::d_type > &fncY, Vector< typename F::d_type > &fncX)

virtual const uint	dimX () const
	Returns the size of the image space of the operator (number of rows of the corresponding matrix) More...

virtual const uint	dimY () const
	Returns the size of the source space of the operator (number of columns of the corresponding matrix) More...

virtual void	hide_messages ()

	Newton (std::function< Vector< typename F::d_type >(Vector< typename F::d_type >)> A, Real dx, uint dimY, uint dimX, Real tol=1e-8, Real iterMax=1000)
	Constructor. More...

	Newton (std::function< Vector< typename F::d_type >(Vector< typename F::d_type >)> A, std::function< F(Vector< typename F::d_type >)> JacA, uint dimY, uint dimX, Real tol=1e-8, Real iterMax=50)
	Constructor. More...

void	operator() ()
	Application method without second argument. Used for parallel solvers. More...

virtual void	operator() (const Function< c_type > &fncY, Function< c_type > &fncX)
	Application operator for complex function `fncY`. More...

virtual void	operator() (const Function< r_type > &fncY, Function< F > &fncX)
	Application operator for real function `fncY`. More...

void	operator() (const Matrix< c_type > &mX, Matrix< c_type > &mY)
	Application method to complex matrices. Calls apply_() More...

void	operator() (const Matrix< r_type > &mX, Matrix< F > &mY)
	Application method to real matrices. Calls function apply() More...

virtual void	operator() (const Vector< c_type > &fncY, Vector< c_type > &fncX)
	Application operator for complex function `fncY`. More...

virtual void	operator() (const Vector< r_type > &fncY, Vector< F > &fncX)
	Application operator for real vector `fncY`. More...

virtual void	show_messages ()

virtual	~Newton ()

Public Attributes
F::d_type	type

Protected Member Functions
virtual void	apply_ (const Vector< F > &fncY, Vector< F > &fncX)=0
	Intrinsic application method, i.e. More...

virtual std::ostream &	info (std::ostream &os) const

virtual void	setLinearSolver_ (F *Jacobian)
	Set linear solver. More...

Protected Attributes
std::function< Vector< typename F::d_type >Vector< typename F::d_type >)> &	A_
	Function that evaluates the matrix A applied to vector X. More...

bool	definedJacA_
	Flag that states if the Jacobian matrix has been set. More...

uint	dimX_
	Size of the unknown. More...

uint	dimY_
	Size of the data. More...

Real	dx_
	Step for the computation of the pseudo-Jacobian. More...

uint	iterMax_
	Maximum number of iterations. More...

std::function< F(Vector< typename F::d_type >)> *	JacA_
	Function that evaluates the Jacobian of matrix A applied to vector X. More...

std::unique_ptr< concepts::Operator< typename F::d_type > >	linearSolver_
	Internal linear solver. More...

Real	tol_
	Tolerance for the functional. More...

bool	verbose_
	Internal flag for verbosity. More...

Detailed Description

template<class F>
class concepts::Newton< F >

Solves a non-linear system of the form A(X)=Y.

Definition at line 35 of file newton.hh.

Member Typedef Documentation

◆ c_type

typedef Cmplxtype<F>::type concepts::VecOperator< F >::c_type

inherited

Real type of data type.

Definition at line 120 of file compositions.hh.

◆ r_type

typedef Realtype<F>::type concepts::VecOperator< F >::r_type

inherited

Real type of data type.

Definition at line 118 of file compositions.hh.

Constructor & Destructor Documentation

◆ Newton() [1/2]

template<class F >

concepts::Newton< F >::Newton	(	std::function< Vector< typename F::d_type >(Vector< typename F::d_type >)>	A,
		Real	dx,
		uint	dimY,
		uint	dimX,
		Real	tol = `1e-8`,
		Real	iterMax = `1000`
	)

inline

Constructor.

Parameters

A	non-linear operator that has to be solved
dimY	size of the data
dimX	size of the unknown
dx	step for the algorithm
tol	(optional) tolerance that will be used for the algorithm
iterMax	(optional) maximum number of iterations before the algorithm decides failure

Definition at line 51 of file newton.hh.

◆ Newton() [2/2]

template<class F >

concepts::Newton< F >::Newton	(	std::function< Vector< typename F::d_type >(Vector< typename F::d_type >)>	A,
		std::function< F(Vector< typename F::d_type >)>	JacA,
		uint	dimY,
		uint	dimX,
		Real	tol = `1e-8`,
		Real	iterMax = `50`
	)

inline

Constructor.

Parameters

A	non-linear operator that has to be solved
JacA	Jacobian of the non-linear operator A
dimY	size of the data
dimX	size of the unknown
dx	step for the algorithm
tol	(optional) tolerance that will be used for the algorithm
iterMax	(optional) maximum number of iterations before the algorithm decides failure

Definition at line 67 of file newton.hh.

◆ ~Newton()

template<class F >

virtual concepts::Newton< F >::~Newton ( )

inlinevirtual

Definition at line 75 of file newton.hh.

Member Function Documentation

◆ apply_() [1/3]

template<class F >

virtual void concepts::Newton< F >::apply_ ( )

virtual

Intrinsic application method without argument.

Implements concepts::VecOperator< F::d_type >.

◆ apply_() [2/3]

virtual void concepts::VecOperator< F >::apply_	(	const Vector< F > &	fncY,
		Vector< F > &	fncX
	)

protectedpure virtualinherited

Intrinsic application method, i.e.

real Operator and real Vector or complex Operator and real Vector.

◆ apply_() [3/3]

template<class F >

virtual void concepts::Newton< F >::apply_	(	const Vector< typename F::d_type > &	fncY,
		Vector< typename F::d_type > &	fncX
	)

virtual

◆ dimX()

template<class F >

virtual const uint concepts::Operator< F >::dimX ( ) const

inlinevirtualinherited

Returns the size of the image space of the operator (number of rows of the corresponding matrix)

Definition at line 93 of file compositions.hh.

◆ dimY()

template<class F >

virtual const uint concepts::Operator< F >::dimY ( ) const

inlinevirtualinherited

Returns the size of the source space of the operator (number of columns of the corresponding matrix)

Definition at line 98 of file compositions.hh.

◆ hide_messages()

template<class F >

virtual void concepts::Newton< F >::hide_messages ( )

virtual

◆ info()

virtual std::ostream& concepts::VecOperator< F >::info ( std::ostream & os ) const

protectedvirtualinherited

Reimplemented from concepts::Operator< F >.

◆ operator()() [1/7]

void concepts::VecOperator< F >::operator()

virtualinherited

Application method without second argument. Used for parallel solvers.

Reimplemented from concepts::Operator< F >.

◆ operator()() [2/7]

virtual void concepts::VecOperator< F >::operator()	(	const Function< c_type > &	fncY,
		Function< c_type > &	fncX
	)

virtualinherited

Application operator for complex function fncY.

Computes fncX = A(fncY) where A is this operator. fncX becomes complex.

In derived classes its enough to implement the operator() for complex Operator's. If a real counterpart is not implemented, the function fncY is splitted into real and imaginary part and the application operator for real functions is called for each. Then the result is combined.

If in a derived class the operator() for complex Operator's is not implemented, a exception is thrown from here.

Reimplemented from concepts::Operator< F >.

◆ operator()() [3/7]

virtual void concepts::VecOperator< F >::operator()	(	const Function< r_type > &	fncY,
		Function< F > &	fncX
	)

virtualinherited

Application operator for real function fncY.

Computes fncX = A(fncY) where A is this operator.

fncX becomes the type of the operator, for real data it becomes real, for complex data it becomes complex.

In derived classes its enough to implement the operator() for real Operator's. If a complex counterpart is not implemented, the function fncY is transformed to a complex function and then the application operator for complex functions is called.

If in a derived class the operator() for real Operator's is not implemented, a exception is thrown from here.

Reimplemented from concepts::Operator< F >.

◆ operator()() [4/7]

void concepts::VecOperator< F >::operator()	(	const Matrix< c_type > &	mX,
		Matrix< c_type > &	mY
	)

inherited

Application method to complex matrices. Calls apply_()

◆ operator()() [5/7]

void concepts::VecOperator< F >::operator()	(	const Matrix< r_type > &	mX,
		Matrix< F > &	mY
	)

inherited

Application method to real matrices. Calls function apply()

◆ operator()() [6/7]

virtual void concepts::VecOperator< F >::operator()	(	const Vector< c_type > &	fncY,
		Vector< c_type > &	fncX
	)

virtualinherited

Application operator for complex function fncY.

Computes fncX = A(fncY) where A is this operator. fncX becomes complex.

In derived classes its enough to implement the operator() for complex Operator's. If a real counterpart is not implemented, the vector fncY is splitted into real and imaginary part and the application operator for real vectors is called for each. Then the result is combined

If in a derived class the operator() for complex Operator's i not implemented, a exception is thrown from here.

◆ operator()() [7/7]

virtual void concepts::VecOperator< F >::operator()	(	const Vector< r_type > &	fncY,
		Vector< F > &	fncX
	)

virtualinherited

Application operator for real vector fncY.

Computes fncX = A(fncY) where A is this operator.

Type of fncX becomes that of the operator, for real data it becomes real, for complex data it becomes complex.

In derived classes its enough to implement the operator() for real Operator's. If a complex counterpart is not implemented, the vector fncY is transformed to a complex vector and then the application for complex vectors is called.

If in a derived class the operator() for real Operator's is not implemented, a exception is thrown from here.

◆ setLinearSolver_()

◆ type

template<class F >

F::d_type concepts::Newton< F >::type

Definition at line 39 of file newton.hh.

◆ verbose_

template<class F >

bool concepts::Newton< F >::verbose_

protected

Internal flag for verbosity.

Definition at line 118 of file newton.hh.

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

operator/newton.hh

concepts::Newton< F > Class Template Referenceabstract

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

template<class F> class concepts::Newton< F >

Member Typedef Documentation

◆ c_type

◆ r_type

Constructor & Destructor Documentation

◆ Newton() [1/2]

◆ Newton() [2/2]

◆ ~Newton()

Member Function Documentation

◆ apply_() [1/3]

◆ apply_() [2/3]

◆ apply_() [3/3]

◆ dimX()

◆ dimY()

◆ hide_messages()

◆ info()

◆ operator()() [1/7]

◆ operator()() [2/7]

◆ operator()() [3/7]

◆ operator()() [4/7]

◆ operator()() [5/7]

◆ operator()() [6/7]

◆ operator()() [7/7]

◆ setLinearSolver_()

◆ show_messages()

Member Data Documentation

◆ A_

◆ definedJacA_

◆ dimX_

◆ dimY_

◆ dx_

◆ iterMax_

◆ JacA_

◆ linearSolver_

◆ tol_

◆ type

◆ verbose_

template<class F>
class concepts::Newton< F >