Define the harmonic equation by inheriting the Equation base class. More...

Inheritance diagram for CppNoddy::Example::Harmonic_equation< _Type, _Xtype >:

Public Member Functions
	Harmonic_equation ()
	The harmonic equation is a 2nd order ODE. More...

void	residual_fn (const DenseVector< _Type > &z, DenseVector< _Type > &g) const
	The Berman equation. More...

void	matrix0 (const DenseVector< _Type > &x, DenseMatrix< _Type > &m) const
	Define the matrix in terms of the current state vector. More...

	Harmonic_equation ()
	The eqn is a 3rd order complex nonlinear ODE because the eigenvalue is an unknown. More...

void	residual_fn (const DenseVector< D_complex > &z, DenseVector< D_complex > &g) const
	Define the harmonic eqn. More...

void	matrix0 (const DenseVector< D_complex > &z, DenseMatrix< D_complex > &m) const
	matrix to multiply the BVP coordinate More...

	Harmonic_equation ()
	The harmonic equation is 2nd order. More...

void	residual_fn (const DenseVector< double > &z, DenseVector< double > &f) const
	We implement the equation as 2 first-order ODEs. More...

Public Member Functions inherited from CppNoddy::Equation_1matrix< _Type, _Xtype >
	Equation_1matrix (const unsigned &order)
	Constructor for equation class. More...

virtual	~Equation_1matrix ()
	An empty destructor, virtual since we have virtual methods. More...

void	update (const DenseVector< _Type > &state)
	Update the Equation object for the current set of state variables. More...

const DenseMatrix< _Type > &	matrix0 () const
	Return a handle to the matrix. More...

virtual void	get_jacobian_of_matrix0_mult_vector (const DenseVector< _Type > &state, const DenseVector< _Type > &vec, DenseMatrix< _Type > &h) const
	Return the product of the Jacobian-of-the-matrix and a vector 'vec' when the equation has a given 'state'. More...

Public Member Functions inherited from CppNoddy::Residual_with_coords< _Type, _Xtype >
	Residual_with_coords (const unsigned &order, const unsigned &ncoords)
	Constructor for a 'square' residual object that is, N residuals for N unknowns. More...

	Residual_with_coords (const unsigned &order, const unsigned &nvars, const unsigned &ncoords)
	Constructor for a 'non-square' residual object that is, there are less residual constraints than unknowns. More...

virtual	~Residual_with_coords ()
	An empty destructor. More...

_Xtype &	coord (const unsigned &i)
	General handle access to the coordinates. More...

const _Xtype &	coord (const unsigned &i) const
	General handle access to the coordinates. More...

Public Member Functions inherited from CppNoddy::Residual< _Type >
	Residual (const unsigned &order)
	Constructor for a 'square' residual object that is, N residuals for N unknowns. More...

	Residual (const unsigned &order, const unsigned &nvars)
	Constructor for a 'non-square' residual object that is, there are less residual constraints than unknowns. More...

virtual	~Residual ()
	An empty destructor, virtual since we have virtual methods. More...

void	update (const DenseVector< _Type > &state)
	Update the Residual object for the current set of state variables. More...

const DenseVector< _Type > &	residual () const
	Return a handle to the residuals corresponding to the last update state. More...

const DenseMatrix< _Type > &	jacobian () const
	Retrun a handle to the Jacobian of the residual corresponding to the last update state. More...

_Type &	delta ()

const _Type &	delta () const

unsigned	get_order () const
	Get the order of the residual vector. More...

unsigned	get_number_of_vars () const
	Get the number of variables that this residual condition is defined for. More...

virtual void	residual_fn (const DenseVector< _Type > &state, DenseVector< _Type > &f) const
	A blank virtual residual function method. More...

Public Member Functions inherited from CppNoddy::Equation_1matrix< D_complex >
	Equation_1matrix (const unsigned &order)
	Constructor for equation class. More...

virtual	~Equation_1matrix ()
	An empty destructor, virtual since we have virtual methods. More...

void	update (const DenseVector< D_complex > &state)
	Update the Equation object for the current set of state variables. More...

const DenseMatrix< D_complex > &	matrix0 () const
	Return a handle to the matrix. More...

virtual void	get_jacobian_of_matrix0_mult_vector (const DenseVector< D_complex > &state, const DenseVector< D_complex > &vec, DenseMatrix< D_complex > &h) const
	Return the product of the Jacobian-of-the-matrix and a vector 'vec' when the equation has a given 'state'. More...

Public Member Functions inherited from CppNoddy::Residual_with_coords< _Type, _Xtype >
	Residual_with_coords (const unsigned &order, const unsigned &ncoords)
	Constructor for a 'square' residual object that is, N residuals for N unknowns. More...

	Residual_with_coords (const unsigned &order, const unsigned &nvars, const unsigned &ncoords)
	Constructor for a 'non-square' residual object that is, there are less residual constraints than unknowns. More...

virtual	~Residual_with_coords ()
	An empty destructor. More...

_Xtype &	coord (const unsigned &i)
	General handle access to the coordinates. More...

const _Xtype &	coord (const unsigned &i) const
	General handle access to the coordinates. More...

Public Member Functions inherited from CppNoddy::Equation< double >
	Equation (const unsigned &order)
	Constructor for equation class. More...

virtual	~Equation ()
	An empty destructor, virtual since we have virtual methods. More...

Public Attributes
double	lambda
	A parameter. More...

Additional Inherited Members
virtual void	matrix0 (const DenseVector< _Type > &x, DenseMatrix< _Type > &m) const
	Define the matrix in terms of the current state vector. More...

Protected Member Functions inherited from CppNoddy::Residual< _Type >
virtual void	jacobian (const DenseVector< _Type > &state, DenseMatrix< _Type > &jac) const
	Because the residual evaluation at the current state is assumed to have already been done by the 'update' method, this routine is protected. More...

virtual void	matrix0 (const DenseVector< D_complex > &x, DenseMatrix< D_complex > &m) const
	Define the matrix in terms of the current state vector. More...

Protected Attributes inherited from CppNoddy::Residual_with_coords< _Type, _Xtype >
std::vector< _Xtype >	coords
	The coordinates stored for this residual. More...

Protected Attributes inherited from CppNoddy::Residual< _Type >
DenseMatrix< _Type >	JAC_AT_LAST_STATE
	Jacobian for the last state vector. More...

DenseVector< _Type >	FN_AT_LAST_STATE
	Residual for the last state vector. More...

DenseVector< _Type >	LAST_STATE
	The last state vector. More...

_Type	DELTA
	A default step for FD computation of the Jacobian. More...

unsigned	ORDER_OF_SYSTEM
	The order of the system of equations. More...

unsigned	NUMBER_OF_VARS
	The number of elements in the state vector. More...

Protected Attributes inherited from CppNoddy::Residual_with_coords< _Type, _Xtype >
std::vector< _Xtype >	coords
	The coordinates stored for this residual. More...

Detailed Description

template<typename _Type, typename _Xtype>
class CppNoddy::Example::Harmonic_equation< _Type, _Xtype >

Define the harmonic equation by inheriting the Equation base class.

Define the harmonic equation by inheriting Equation base class.

Definition at line 25 of file BVPHarmonic.cpp.

Constructor & Destructor Documentation

◆ Harmonic_equation() [1/3]

template<typename _Type , typename _Xtype >

CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::Harmonic_equation ( )

inline

The harmonic equation is a 2nd order ODE.

Definition at line 30 of file BVPHarmonic.cpp.

30: Equation_1matrix<_Type, _Xtype>( 2 ) {}

CppNoddy::Equation_1matrix

An equation object base class used in the IBVP classes (and others).

Definition: Equation_1matrix.h:18

◆ Harmonic_equation() [2/3]

template<typename _Type , typename _Xtype >

CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::Harmonic_equation ( )

inline

The eqn is a 3rd order complex nonlinear ODE because the eigenvalue is an unknown.

Definition at line 38 of file EVPHarmonicLocal.cpp.

38: Equation_1matrix<D_complex> ( 3 ) {}

◆ Harmonic_equation() [3/3]

template<typename _Type , typename _Xtype >

CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::Harmonic_equation ( )

inline

The harmonic equation is 2nd order.

Definition at line 21 of file IVPHarmonic.cpp.

                          : Equation<double> ( 2 )
      {
      }

Member Function Documentation

◆ matrix0() [1/2]

template<typename _Type , typename _Xtype >

void CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::matrix0	(	const DenseVector< _Type > &	x,
		DenseMatrix< _Type > &	m
	)		const

inlinevirtual

Define the matrix in terms of the current state vector.

Parameters

x	The current state vector.
m	The matrix.

Reimplemented from CppNoddy::Equation_1matrix< _Type, _Xtype >.

Definition at line 39 of file BVPHarmonic.cpp.

      {
        Utils_Fill::fill_identity(m);
      }

◆ matrix0() [2/2]

template<typename _Type , typename _Xtype >

void CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::matrix0	(	const DenseVector< D_complex > &	z,
		DenseMatrix< D_complex > &	m
	)		const

inlinevirtual

matrix to multiply the BVP coordinate

Reimplemented from CppNoddy::Equation_1matrix< D_complex >.

Definition at line 51 of file EVPHarmonicLocal.cpp.

      {
        Utils_Fill::fill_identity(m);
      }

References Utils_Fill::fill_identity(), and m.

◆ residual_fn() [1/3]

template<typename _Type , typename _Xtype >

void CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::residual_fn	(	const DenseVector< _Type > &	z,
		DenseVector< _Type > &	g
	)		const

inlinevirtual

The Berman equation.

Reimplemented from CppNoddy::Residual< _Type >.

Definition at line 33 of file BVPHarmonic.cpp.

      {
        g[ f ] = z[ fd ];
        g[ fd ] = - z[ f ];
      }

References f, fd, CppNoddy::Example::g(), and CppNoddy::Example::z().

◆ residual_fn() [2/3]

template<typename _Type , typename _Xtype >

void CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::residual_fn	(	const DenseVector< D_complex > &	z,
		DenseVector< D_complex > &	g
	)		const

inline

Define the harmonic eqn.

Definition at line 41 of file EVPHarmonicLocal.cpp.

      {
        g[ f ] = z[ fd ];
        g[ fd ] = - z[ lambda ] * z[ f ];
        // inclusion of eigenvalue everywhere maintains the bandedness,
        // albeit at an obvious cost.
        g[ lambda ] = 0.0;
      }

References f, fd, CppNoddy::Example::g(), CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::lambda, and CppNoddy::Example::z().

◆ residual_fn() [3/3]

template<typename _Type , typename _Xtype >

void CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::residual_fn	(	const DenseVector< double > &	z,
		DenseVector< double > &	f
	)		const

inline

We implement the equation as 2 first-order ODEs.

Definition at line 26 of file IVPHarmonic.cpp.

      {
        f[ 0 ] = z[ 1 ];
        f[ 1 ] = - lambda * z[ 0 ];
      }

References f, CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::lambda, and CppNoddy::Example::z().

Member Data Documentation

◆ lambda

template<typename _Type , typename _Xtype >

double CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::lambda

A parameter.

Definition at line 33 of file IVPHarmonic.cpp.

Referenced by main(), and CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::residual_fn().

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

Tests/BVP/BVPHarmonic.cpp
Tests/IVP/IVPHarmonic.cpp
Tests/EVP/EVPHarmonicLocal.cpp

Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Harmonic_equation() [1/3]

◆ Harmonic_equation() [2/3]

◆ Harmonic_equation() [3/3]

Member Function Documentation

◆ matrix0() [1/2]

◆ matrix0() [2/2]

◆ residual_fn() [1/3]

◆ residual_fn() [2/3]

◆ residual_fn() [3/3]

Member Data Documentation

◆ lambda